<%BANNER%>

Side-Implanted Piezoresistive Shear Stress Sensor for Turbulent Boundary Layer Measurement

Permanent Link: http://ufdc.ufl.edu/UFE0017550/00001

Material Information

Title: Side-Implanted Piezoresistive Shear Stress Sensor for Turbulent Boundary Layer Measurement
Physical Description: 1 online resource (180 p.)
Language: english
Creator: Li, Yawei
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: drie, friction, implanted, mems, micromachining, optimization, piezoresistive, rie, sensor, shear, side, skin, stress
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this dissertation, I discuss the device modeling, design optimization, fabrication, packaging and characterization of a micromachined floating element piezoresistive shear stress sensor for the time-resolved, direct measurement of fluctuating wall shear stress in a turbulent flow. This device impacts a broad range of applications from fundamental scientific research to industrial flow control and biomedical applications. The sensor structure integrates side-implanted, diffused resistors into the silicon tethers for piezoresistive detection. Temperature compensation is enabled by integrating a fixed, dummy Wheatstone bridge adjacent to the active shear-stress sensor. A theoretical nonlinear mechanical model is combined with a piezoresistive sensing model to determine the electromechanical sensitivity. Lumped element modeling (LEM) is used to estimate the resonant frequency. Finite element modeling is employed to verify the quasi-static and dynamic models. Two dominant electrical noise sources in the piezoresistive shear stress sensor, 1/f noise and thermal noise, and amplifier noise were considered to determine the noise floor. These models were then leveraged to obtain optimal sensor designs for several sets of specifications. The cost function, minimum detectable shear stress (MDS) formulated in terms of sensitivity and noise floor, is minimized subject to nonlinear constraints of geometry, linearity, bandwidth, power, resistance, and manufacturing limitations. The optimization results indicate a predicted optimal device performance with a MDS of O(0.1 mPa) and a dynamic range greater than 75 dB. A sensitivity analysis indicates that the device performance is most responsive to variations in tether width. The sensors are fabricated using an 8-mask, bulk micromachining process on a silicon wafer. An n-well layer is formed to control the space-charge layer thickness of reverse-biased p/n junction-isolated piezoresistors. The sensor geometry is realized using reactive ion etch (RIE) and deep reactive ion etch (DRIE). Hydrogen annealing is employed to smooth the sidewall scalloping caused by DRIE. The piezoresistors are achieved by side-wall boron implantation. The structure is finally released from the backside using the combination of DRIE and RIE. Electrical characterization indicates linear junction-isolated resistors, and a negligible leakage current ( < 0.12 uA) for the junction-isolated diffused piezoresistors up to a reverse bias voltage of -10 V. Using a known acoustically-excited wall shear stress for calibration, the sensor exhibited a sensitivity of 4.24 uV/Pa , a noise floor of 11.4 mPa/root Hz at 1 kHz, a linear response up to the maximum testing range of 2 Pa, and a flat dynamic response up to the testing limit of 6.7 kHz. These results, coupled with a wind-tunnel suitable package, result in a suitable transducer for turbulence measurements in low-speed flows, a first for piezoresistive MEMS-based direct shear stress sensors.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yawei Li.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Sheplak, Mark.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0017550:00001

Permanent Link: http://ufdc.ufl.edu/UFE0017550/00001

Material Information

Title: Side-Implanted Piezoresistive Shear Stress Sensor for Turbulent Boundary Layer Measurement
Physical Description: 1 online resource (180 p.)
Language: english
Creator: Li, Yawei
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: drie, friction, implanted, mems, micromachining, optimization, piezoresistive, rie, sensor, shear, side, skin, stress
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this dissertation, I discuss the device modeling, design optimization, fabrication, packaging and characterization of a micromachined floating element piezoresistive shear stress sensor for the time-resolved, direct measurement of fluctuating wall shear stress in a turbulent flow. This device impacts a broad range of applications from fundamental scientific research to industrial flow control and biomedical applications. The sensor structure integrates side-implanted, diffused resistors into the silicon tethers for piezoresistive detection. Temperature compensation is enabled by integrating a fixed, dummy Wheatstone bridge adjacent to the active shear-stress sensor. A theoretical nonlinear mechanical model is combined with a piezoresistive sensing model to determine the electromechanical sensitivity. Lumped element modeling (LEM) is used to estimate the resonant frequency. Finite element modeling is employed to verify the quasi-static and dynamic models. Two dominant electrical noise sources in the piezoresistive shear stress sensor, 1/f noise and thermal noise, and amplifier noise were considered to determine the noise floor. These models were then leveraged to obtain optimal sensor designs for several sets of specifications. The cost function, minimum detectable shear stress (MDS) formulated in terms of sensitivity and noise floor, is minimized subject to nonlinear constraints of geometry, linearity, bandwidth, power, resistance, and manufacturing limitations. The optimization results indicate a predicted optimal device performance with a MDS of O(0.1 mPa) and a dynamic range greater than 75 dB. A sensitivity analysis indicates that the device performance is most responsive to variations in tether width. The sensors are fabricated using an 8-mask, bulk micromachining process on a silicon wafer. An n-well layer is formed to control the space-charge layer thickness of reverse-biased p/n junction-isolated piezoresistors. The sensor geometry is realized using reactive ion etch (RIE) and deep reactive ion etch (DRIE). Hydrogen annealing is employed to smooth the sidewall scalloping caused by DRIE. The piezoresistors are achieved by side-wall boron implantation. The structure is finally released from the backside using the combination of DRIE and RIE. Electrical characterization indicates linear junction-isolated resistors, and a negligible leakage current ( < 0.12 uA) for the junction-isolated diffused piezoresistors up to a reverse bias voltage of -10 V. Using a known acoustically-excited wall shear stress for calibration, the sensor exhibited a sensitivity of 4.24 uV/Pa , a noise floor of 11.4 mPa/root Hz at 1 kHz, a linear response up to the maximum testing range of 2 Pa, and a flat dynamic response up to the testing limit of 6.7 kHz. These results, coupled with a wind-tunnel suitable package, result in a suitable transducer for turbulence measurements in low-speed flows, a first for piezoresistive MEMS-based direct shear stress sensors.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yawei Li.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Sheplak, Mark.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0017550:00001


This item has the following downloads:


Full Text
xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20101208_AAAAIN INGEST_TIME 2010-12-08T12:08:15Z PACKAGE UFE0017550_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 45328 DFID F20101208_AAAUOX ORIGIN DEPOSITOR PATH li_y_Page_054.pro GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
134fb4a1aba0b22f58481a039600aad5
SHA-1
307de28b33ab5003897a0caea410bea9b23a4881
97185 F20101208_AAAUQA li_y_Page_065.jp2
8ed0b4c8ff020f343771b79c7e601d2c
82a6b531f34c3964729cf08b17df1bd72677cd73
22393 F20101208_AAAUPL li_y_Page_018.QC.jpg
50882b326dcad30cdce4cece55f270f3
28ed831af1fa110006744d9fd2ee4bf2350ac426
12757 F20101208_AAAUOY li_y_Page_170.QC.jpg
37fe14f32d27b0e4bc78a64d4e1e9d7c
032a0f0d71ec63eaeed75918d7f7bb1fab7ab78c
2091 F20101208_AAAUQB li_y_Page_066.txt
792ff444d2ed9d6fd7f1fc8149d73b6e
8f19535355b5861305288593f7f6f4c395afc2a6
1053954 F20101208_AAAUPM li_y_Page_015.tif
e0959c5f201a37dee79e7966a8778e51
a489caf7b0910a8bc8a373d24f61e05b3e6f4c28
8773 F20101208_AAAUOZ li_y_Page_158.QC.jpg
263aa41cbc94e8acdddaa509b08d7706
e9ba84c7b11064128c172e808b327c9aca9316ba
33724 F20101208_AAAUQC li_y_Page_030.QC.jpg
2857e27bade87979fb1142bd2cf2b3f4
6ccafef30e83d601b824b99c9289e3cd6904c66b
2083 F20101208_AAAUPN li_y_Page_038.txt
0aa3dfb5e6f105a6ea4056cd3f849313
c6e6fa930c48d56437fad7564a9f785441932a7e
29079 F20101208_AAAUQD li_y_Page_171.jpg
0020d6c82cb78a7e82b186212581d4b1
244705a7636069ec013e84b25bb97a7920600542
98263 F20101208_AAAUPO li_y_Page_053.jp2
a5ddc21b08078253df60e96528c4f507
43121ac9aa1c2e38b05df3ac8aa9b3df02f6c6c2
24992 F20101208_AAAUQE li_y_Page_145.QC.jpg
5ce3cb86bf8c6d31c5c17597813d5fb4
28ec88382674dd55bd6674ab84fe9288e4b2f8a1
17961 F20101208_AAAUPP li_y_Page_148.QC.jpg
c3117614df9b382dd2dccaaba7361aa8
c4a82b4200470fcd98adf145c5bda6889cd4e461
8113 F20101208_AAAUQF li_y_Page_129.QC.jpg
6150b4899b5a3dd0171cf1fa364af2b4
2d8973551ab7368218df3a23988b3ed263ccd139
7980 F20101208_AAAUPQ li_y_Page_023thm.jpg
9d7c87cc4a5b39225f2a06f147230031
63d6deaf69c5c325c4375315855f8cd52009c8ec
5482 F20101208_AAAUQG li_y_Page_028.pro
c7714d21274b259166323296b7f5da08
7ae8d4c02593506c5122b1020601b1ce7fbb7a58
31576 F20101208_AAAUPR li_y_Page_023.QC.jpg
b59afe2d4346b84631a97c60377b1029
bc28c962ec38b540f1d9bf141cd77aea4be0fb16
5904 F20101208_AAAUQH li_y_Page_162thm.jpg
77a4531fc346110108d5b1e6e5beff80
140fae78d81cab9efe885df35eb7b8a2bcac9795
14611 F20101208_AAAUPS li_y_Page_130.QC.jpg
00163b7a4aa75d7ac3e2c97ea895a864
0d1626981cd4385e89704abf42b08157481e3f1b
102648 F20101208_AAAUQI li_y_Page_004.jpg
3284d7504138060738d3054833e14784
b984265abf42f1335c365724eb884802638abb46
139346 F20101208_AAAUPT li_y_Page_174.jpg
02d4171fe24f5974f64fec14dcd0c836
1d6c63aef44e986df9903d08ce2b9eb3027f15e5
1299 F20101208_AAAUPU li_y_Page_013.txt
ac8ef75ed23d545ff4b18f96a6019743
b166d4e6b35c4be7e9ab52a86a6da553602010fd
43839 F20101208_AAAUQJ li_y_Page_051.jpg
a719e91a30757a9465a31636e7976b9c
fd142b3480f2d876136615c18d680c0387a86709
71258 F20101208_AAAUPV li_y_Page_168.jpg
bb5a6fddfa9b27acf486f6f2a79dde8a
feeba6690c519c2634441d31bd8566df89eca2e9
64312 F20101208_AAAUQK li_y_Page_175.pro
8b3432a457f052a4adda56c1634a14a7
6099182c215f127c0e5211d05419d8ecb9b8d61f
25523 F20101208_AAAUPW li_y_Page_001.jp2
46acad110068b58be8e7d8f9e5c79580
ac9879130b79ec6eda3bb944de75523e012dd249
7104 F20101208_AAAURA li_y_Page_096thm.jpg
287703bbc3feccaab975a15476eae74e
d33d0b79177dc71d12bb2dbacb9a4ca1a1c301b9
24939 F20101208_AAAUQL li_y_Page_150.pro
d78ec5ee7294ad6573451c12a18855f7
335cfacd867f9b60575546f0a7954d0cc48213ac
1836 F20101208_AAAUPX li_y_Page_053.txt
ac6f2b13ad6b12cc8eb449291f6f7124
48f73ad3382573fd3905dc25adcb7de595fa8ae7
5937 F20101208_AAAUQM li_y_Page_157thm.jpg
26d8116733acdd770454d4f23f93fd66
150d71e10111f31e19a833c51c1175b02895c197
46769 F20101208_AAAUPY li_y_Page_155.jp2
68d8ecccb16da0170771bb419f97f166
3a1ec260dfabe9053549eeca67f47a9c9e10cb2d
8258 F20101208_AAAURB li_y_Page_030thm.jpg
7b146b4356d6330026fd15b33991ca9b
c981ea2c910fbde1fd81647ae386635a2d08c919
9010 F20101208_AAAUQN li_y_Page_123thm.jpg
850b363bd11a0d67224c469fa99a3028
41212270ed3251672e6edad11f6c1bfddb4afc3f
32272 F20101208_AAAUPZ li_y_Page_031.QC.jpg
e6e86ef855e38cf50f600461727e99c4
3f3a0b3f77d9430c59196c96189699650ead5414
56827 F20101208_AAAURC li_y_Page_044.pro
5e04b04e7aed35b84a571e50435b9804
55ae1eea192184e31ba0e24f66c1acfbd089628f
10394 F20101208_AAAUQO li_y_Page_171.QC.jpg
b4595b4e1b3cef2c095a1e4f8b58b9c1
fcd19accd0ab8b00a54fa7eff14c7fc6ea0a16af
33677 F20101208_AAAURD li_y_Page_163.pro
dc6be1b9e497443f62b68e6bc1644b5d
1f515b1db99331daf3fe3f64ac142f7f50d51531
27442 F20101208_AAAUQP li_y_Page_146.pro
ad5bb9736823606a27acf8a8deddaab6
be096aaaa77cd2493ef1b8478c974dc385e7acbe
F20101208_AAAURE li_y_Page_039.tif
62e2824b5fcfbf7a739a9e715e04c34f
55cdaca4e0ad3bf7d4899e9e0462b66bdf19d08a
87491 F20101208_AAAUQQ li_y_Page_057.jp2
b31671b8bf102d9661948543232b899d
4ead144bb20b48bfce7c9bfd7bdbfff7eb3cc1c2
F20101208_AAAURF li_y_Page_041.tif
6b356ceb0b20768f1f0d71a8dd7eb5ff
2194722d24d5d8ded0017170b62380a72e7b47b7
20232 F20101208_AAAUQR li_y_Page_154.QC.jpg
78ef90c4e21bd675f3348e8969e09ee6
57e039e43667ee4db57405b82702685730e9c9a3
F20101208_AAAURG li_y_Page_074.tif
5147affee7eb39c303b910fb526f7015
5a5fa8bd7978ada1e8b4bb790c6cfad37609727c
4719 F20101208_AAAUQS li_y_Page_159thm.jpg
a3c225311316fcdfc5e4f636cfe2397f
82bd6cfea7650a7a253c7ca545d2950e8b607eba
82703 F20101208_AAAURH li_y_Page_166.jp2
510f47e44935a6e01eaeb4f11badcc70
db4cf0924b24d8ced5d712cd375299c9da0a2c39
1969 F20101208_AAAUQT li_y_Page_032.txt
9dd28b67b71bc7492bcd853f0de434eb
d4405050f8d7000c3fd97728e09cd43ff1884534
1964 F20101208_AAAURI li_y_Page_036.txt
6cb972fefe43d7813d89924f2a199e89
a8555acec0605093d8545693940faf75bee0d059
8092 F20101208_AAAUQU li_y_Page_135.QC.jpg
11a1b095b06ab0bba013df657ed9d595
e200c225f33cff03fb307e0364e6db7ee33fe262
44828 F20101208_AAAURJ li_y_Page_115.jpg
8c19ec9f81c0f035bcd1d917375da1c4
7216690db91f13794f822cb898ea1cf5dac568ff
25271604 F20101208_AAAUQV li_y_Page_081.tif
980c278bcebfa7791e96a371f9bda548
8e539db5afbbe15e5c951b706c117f88b2fe16b7
F20101208_AAAUQW li_y_Page_106.tif
6a18331b2e0084a374817c6bfbdedf87
bf821abd498b388c168148a5139261ed591ccfa7
4982 F20101208_AAAURK li_y_Page_047thm.jpg
106b704a08e51ba44fc3918c20e1d352
83b29ac5ceb172bcadba4d268a23269bdf9d4860
41905 F20101208_AAAUQX li_y_Page_036.pro
bcc4bb1ac13585fae6d284235841759d
56515846dcc1a2b17c46d9da83945a509176b14d
19544 F20101208_AAAUSA li_y_Page_179.QC.jpg
9b02b1b54d3ebc95b84c96dcd975d9a8
3f8427cb9e0651ec608cdb395b7f7499fb7d9641
80080 F20101208_AAAURL li_y_Page_019.jp2
373cdeadbb4f2d1019d8324525696318
5e982b5338f284fc32fddf280272cf3464522f31
2075 F20101208_AAAUQY li_y_Page_094.txt
4779fa2f9ae878448195ab9c77cb0739
c27f8e7e5d665f1441f2d0330b3760478d55a8a3
11401 F20101208_AAAUSB li_y_Page_133.pro
8e5c74883aa418c27b7aa127bece25df
0296cf915946cd6e913daf554a6751c0e8e8b6c3
697 F20101208_AAAURM li_y_Page_131.txt
e1abc37a15fd411f69b5661376b2196e
a1bdcf46890313f56d8c4438e971083ea545e982
F20101208_AAAUQZ li_y_Page_174.tif
7025c76a86616eb0ea2fc13d13d9ff85
16dec36c016e2991ee6d5f730c0fa2e2b6508caf
F20101208_AAAUSC li_y_Page_088.tif
3c2f52258a4d97ccfe4b50c9c51f8408
f7e89b1abc2c17972647d25822e1f38a5f9bae99
43556 F20101208_AAAURN li_y_Page_100.pro
408199d62f8d0e30432c6f371bfb365c
1362768f29702a7bafd6ef63c70a340809ca1d95
16631 F20101208_AAAUSD li_y_Page_086.QC.jpg
c3ae79f9adc73c407ffabcca254fe937
508f33fe7b4c4f2f24ff17d0fbbc25f2e31f35c9
28136 F20101208_AAAURO li_y_Page_158.jp2
8c1c035d28bc11a6cf84a99c06359684
a889fb7aed937c24ab2364cfc72836222d63b4e5
40214 F20101208_AAAUSE li_y_Page_012.QC.jpg
c2442173f48a4612f41b61734d2bb864
6e817ae7ce3a78dd5e4442050c3be8acbc4e6750
1989 F20101208_AAAURP li_y_Page_022.txt
0ab43b0607341d1d716f0d02bfe15751
c2cdd476d0ad371b4accec3b237756c0ae58034d
8233 F20101208_AAAUSF li_y_Page_021thm.jpg
7d907f09f5c5864bb3876e26696bb3de
ca54e712a1c6a4cadc248dee7315a0bfe004860f
110606 F20101208_AAAURQ li_y_Page_118.jp2
25120070a4f89e594079462461fa1fe5
98cb8b2afb88fcf1748f532c2e9f4fbac725676c
6009 F20101208_AAAUSG li_y_Page_134thm.jpg
9e73965d90f999e1d25765679c96ac4a
6f5902c1d833f241e5c66e56848da748e673be0d
F20101208_AAAURR li_y_Page_080.tif
bfb6028e1bd22d9be1ae6c5810368416
a8eee881841fb9f189813d4caaa6ffac62f8dcd8
17932 F20101208_AAAUSH li_y_Page_150.QC.jpg
6bbdd2d5992a01a27e915f7d6c7d8b76
2c671c9c1a39ed8195e71609d60b775ae9dad896
91402 F20101208_AAAURS li_y_Page_036.jp2
b1fa46ff13102ecbea6f8a02e2d70759
c736040656d0b89fd54237605f2e4080687586bf
102355 F20101208_AAAUSI li_y_Page_023.jp2
79532ceae78007bcae0a5e4dc1c92c3f
a43abb62de85eb3b3aae409dcb3a6e05fdac6001
50063 F20101208_AAAURT li_y_Page_061.pro
693a42dc5986a9b31a43d81e2ce28950
125c8e87565e7e69fee77044c503cb23ed2547c1
F20101208_AAAUSJ li_y_Page_168.tif
1d0468a3ee15f20b55878e9b33b947ef
34984a9e5e7c0876284a0940dca9c194d5cb5810
143699 F20101208_AAAURU li_y_Page_011.jpg
08990c69ddcedb82138385fd870614d9
3547fb40f9d91b92607da29f934c7e1aacc642b2
F20101208_AAAUSK li_y_Page_164.tif
3d9b0a5d84a36df61e4d809c72b6cc5f
2d8eeab32f7007cdcfcebe61fcdb8113015971cb
F20101208_AAAURV li_y_Page_087.tif
3767f40a5608ccec5a5628cf5e2dc104
42794faff8aa78a749e954fa51a8022e9274656f
F20101208_AAAURW li_y_Page_017.tif
8f33cfc8636304951571a2cca3c3e9de
4c9d30cf5cce6a6d9665523fecd6eeea11737aa1
F20101208_AAAUTA li_y_Page_145.tif
a47b7c27b97a8ab437954e365fd8865a
4b9c5487938af836f154e02ad2729dc9c4fc509a
1295 F20101208_AAAUSL li_y_Page_148.txt
dda4b1e09b0c000c5af9b921ef349196
575c5961f9b5bc6373ac76c14984e74cf73e8869
9180 F20101208_AAAURX li_y_Page_051.pro
7b190521ab9be48b4387e43b59d234ee
47e544cc18245599b3b780b9365a146a04f1fc25
15471 F20101208_AAAUTB li_y_Page_155.pro
7647d037d6fcd4285613f559b0ee979f
5a458c2ec84aa7e79a08dada0365198acfd065d7
33435 F20101208_AAAUSM li_y_Page_016.QC.jpg
aa89dec4409e13f14780b396128faf1c
675df859029026b208489717f4475cd78f4365bc
31065 F20101208_AAAURY li_y_Page_143.QC.jpg
c3f743ac6e1c8cf7a85703d3b2313b3a
e11c8e0a522c1257934cd4464d4a5d07b8545395
52959 F20101208_AAAUTC li_y_Page_126.pro
3b64fe668504271b24573c885899cd77
aaad2247efd397c2c32d4d11d585284cdc4ddc87
50608 F20101208_AAAUSN li_y_Page_138.pro
9a43a15066f12e71cdb4e3d957e2a697
d88905605c5392be565530f968b94bf214ded150
18794 F20101208_AAAURZ li_y_Page_013.QC.jpg
36f0c2b24d8a36a46ce150595d1406a4
5b818c5299cd12c89f542243f04be45f7b302204
4608 F20101208_AAAUTD li_y_Page_144thm.jpg
6ed9416ff586d7e9ff057b5601b615e4
c9e3ba5527614ebab7d960d567b294ea8b0619fe
F20101208_AAAUSO li_y_Page_043.tif
5a282bab1e47ee38f1bea359f7d61ae9
00fd50f37df28eb005087cd7b6d7dd9a534df190
114362 F20101208_AAAUTE li_y_Page_142.jp2
9a4391e6d0914f271854159af5f76789
a458c2978bdb15c8f8dee430ca27184c7d1e4b93
9062 F20101208_AAAUSP li_y_Page_073thm.jpg
4b1caf3435989f4c7d57a9dbfe895f0f
5eae76f99f088ee9295f0ea0a7f118ddc6ddecb2
547880 F20101208_AAAUTF li_y_Page_086.jp2
7d1b8b602c576712066137f6d6c6b5c3
8d9f345e0c580fe4ab6bc143a6681a7d8e98d8ae
30021 F20101208_AAAUSQ li_y_Page_100.QC.jpg
843765a64e428ce7ab92d5b9e3a8c051
7415c8ac0ee24a217e00e7cd356e67e05a9d6324
92708 F20101208_AAAUTG li_y_Page_120.jpg
1d6d66e9e2519b71a314ad9dde61be3e
90ef13373f3c1169bf5df2523e8d5fdfa95f4df4
1930 F20101208_AAAUSR li_y_Page_107.txt
ec763e1ed28d7ed51af6ea04843d8cb3
818eab087b63539ab94752be93caf7204857b2bf
42980 F20101208_AAAUTH li_y_Page_015.pro
57d069f509ad5789e60f068c48be5e84
053dd13dba8f0d1ff230e37623d069dd1ef755aa
1866 F20101208_AAAUSS li_y_Page_062.txt
570dffc8c39c0f849449a21f129b6305
1005e7f2d13d419487268443859e8a5d185baae6
473 F20101208_AAAUTI li_y_Page_051.txt
48f74a51cd0c34d67c991bf625c34180
52cee4b999c4ee1163b29fa9a3c576eff8b81798
62958 F20101208_AAAUST li_y_Page_157.jpg
5945000477a3743825ff2739a8b59f0f
46d42cdb4b451e17b02c7f96dc676ce056593af6
53620 F20101208_AAAUTJ li_y_Page_039.pro
f28ef355d1374dab82bf91ace1840445
540e2f5d73454f0fd024e134b556d00e6b90d49c
24413 F20101208_AAAUSU li_y_Page_157.pro
4eb66a93bffe8354eedc4f974cb41897
b90ed48b60314a655d7d4ffef85988951f6748e1
108893 F20101208_AAAUTK li_y_Page_043.jpg
993eaf09ae8e86ea1069c00a8c8bfd45
ac0f34c0ecfaaeb654ae91f60528c24d7f57ea47
F20101208_AAAUSV li_y_Page_138.tif
29794af1cf93515a13c6f703ffb108f3
b73a897c05c21be4edeef94f8126d28611016702
8414 F20101208_AAAUTL li_y_Page_118thm.jpg
b8d88e80ab8812a4533d391d9b7b1efb
7650d08737e5df00669279f8476e0c088925aa2d
F20101208_AAAUSW li_y_Page_074.txt
92bf9a83afa2562a7eb1d8554149cfff
dc784dd5469f0b21ae357f416116d5436743d019
68075 F20101208_AAAUSX li_y_Page_162.jpg
eb4dadd78d2df1ff042a6877618c8ce7
4d4e096b518fd13642717aeb3f0bacc0cee8880f
35380 F20101208_AAAUUA li_y_Page_118.QC.jpg
19b30be6a81de0e27ad5ea73cc94b132
e2e5d40f98112df7ab1b57f3a132cdff924e59b1
5950 F20101208_AAAUTM li_y_Page_079thm.jpg
19ad36467b711ad475359d0819255f2d
e79a5bb7978d3b960c1cccf9c81b52a1a1fb9dae
F20101208_AAAUSY li_y_Page_121.tif
5d1cf57d8f89dee1328e9d09feee469d
4e272872d02c46a4de8e3b6fb8aa802a2835a534
44541 F20101208_AAAUUB li_y_Page_078.pro
a7eb362f3b5fb95f569eec9f2f6611de
871c8771d9b4b8cf210007351ab49fa26aa20577
48292 F20101208_AAATQL li_y_Page_029.pro
071e8f808dc5643e64a43671216c36f8
cbe41a26bf65aa0224a71ecc78d8a6321cab0940
83957 F20101208_AAAUTN li_y_Page_063.jp2
a18719ce7e5edf7002c6614028c89c1e
c3daa1cb6c9f6bbf227791187ad44cb89bf13a71
274 F20101208_AAAUSZ li_y_Page_144.txt
2907e9be4be6a2dd1542285bb1e12c8c
caf953e24f882dede2a3ef041d432438a845923c
68151 F20101208_AAATRA li_y_Page_174.pro
24595f775c20a323e92f2d3fa47aa79c
8c6e153da8fded4fbd4d9007c591a2efaa4797a9
310 F20101208_AAAUUC li_y_Page_101.txt
042e240f7672afa8a36e2a6ba57f7ca8
2e664d9086a8c4f9ff8787d020ab1d224bc6ed97
22655 F20101208_AAATQM li_y_Page_117.QC.jpg
28a733a022d4e76d913ec9b1bd76edbc
d0fb63fb93cf50e4b409e4f3b5069f1918e8f4d5
326061 F20101208_AAAUTO li_y_Page_046.jp2
320c30fc0c936166db72fec5b8185ba4
5c938fcdfb946091b22eda15a1d3577f44c01594
6898 F20101208_AAATRB li_y_Page_083thm.jpg
aa6b6894ddb7b7d8ac3663b723cb0bda
9531c663ea7bde9c22bc2861f866106fc24e3bbe
30028 F20101208_AAAUUD li_y_Page_078.QC.jpg
c37f710fabcd2381073aaf1cc16c18b8
8d1b81d230ada2b1bbb0c83a5d0779faf1b47e45
28561 F20101208_AAATQN li_y_Page_096.QC.jpg
e286ae9203ec8388bbd10dd824201dfe
7f9dbdaf7ed66757bc27fdeac5157ea003265668
6325 F20101208_AAAUTP li_y_Page_007thm.jpg
ed717dd315e39df6b093df644b88350f
3c26d6763d9a0115323e214f1af42eec19772bc5
44221 F20101208_AAATRC li_y_Page_059.pro
b2986252e3c98bfbc2faa211f4037208
8d568074f21e809d54303d49a36f9dcc1c0311f2
F20101208_AAAUUE li_y_Page_142.tif
459680345dec1a1471cf7278af2999c5
299db4ae885e6327c90b06b67b755d9bdd7ed35c
88016 F20101208_AAAUTQ li_y_Page_008.jpg
fcb9f694238e0fb8b97aa6b34d0bc452
082eb70502e6843b61c3cacbb554b0e7288a20ef
35148 F20101208_AAATRD li_y_Page_035.pro
67f0f67239faec53ec192b0e9d092965
616ae6840233efa1b5271303409cb6474c047298
1671 F20101208_AAAUUF li_y_Page_149.txt
78de7052c1c59fb4911d9d10b938f26b
2ba4df8597ca1f8ecf6e9e32fc7267fb8e60d8ad
1816 F20101208_AAATQO li_y_Page_078.txt
30260e3cd66860a7499bc810f7410b6c
0432055336b11b431abbec31f5380fe9d1ec13b2
F20101208_AAAVAA li_y_Page_020.tif
c4bdd28b9b873759021fac3baf99e8c6
d4014cde9bd84b0bb5b3130ca1dcf35185ee8298
30075 F20101208_AAAUTR li_y_Page_149.pro
6b5263401093e6e5f671681e0103a043
60664a7544ed44b9563a4f2ce5e14d6597b06a11
248 F20101208_AAATRE li_y_Page_114.txt
36d68a7696aa1dcf8120888e133655d2
4d22e6107c0e3f9c74d3ce669946f217fa26bb3c
5730 F20101208_AAAUUG li_y_Page_020thm.jpg
c9bafafaf79fca14e8b9c5c6b2ee47f0
a2b4bccf809bc43fdc4b29d12a1b546b50801e5d
53381 F20101208_AAATQP li_y_Page_042.pro
4ff2ae476a3313ef5c06a74b4dc0639a
11afc35ddbd991566769494870c3a97bdc097744
F20101208_AAAVAB li_y_Page_025.tif
a2cefff4de430405cf20bc63b7b7bf8f
09977a46fbc38cf6db6779c8ac24f92a6ab3ff7f
F20101208_AAAUTS li_y_Page_154.tif
34ed506a5ce176b34b9b5ada593e27c1
4c75e88d461dfbf0e218a7fb99b31ac6e85d0de9
68024 F20101208_AAATRF li_y_Page_012.pro
f8276697d4a71b492823b85834e73133
7339cab352d0bb54b6e8a76bc7383c479725b772
F20101208_AAAUUH li_y_Page_023.tif
c546cdfabca077a3348224e5f5dad08b
d651a2b7d2bf294c607640c434f4abe187271d5b
34723 F20101208_AAATQQ li_y_Page_092.QC.jpg
59db7b227cd941033eec84813dc2a3bc
dab1f8b8a69ddaff58a6e368716b26c8b62e86bf
F20101208_AAAVAC li_y_Page_026.tif
b858a29127526e73f05cf4f489e84eb2
816b3373871a1ba5b7b523c0f85827105c45af5d
106709 F20101208_AAAUTT li_y_Page_017.jpg
8f5144a0d9061f2bfb2ed433c5402a5e
4b361bd67afd82f38f57d9eb02acd4903b77d468
37399 F20101208_AAATRG li_y_Page_071.pro
f923a292c04ef58b523eedd09af4eb79
59582864047970c00e57b3145d45fe8569ed5276
7785 F20101208_AAAUUI li_y_Page_097thm.jpg
4e3a4e440c990e925876df92395ee497
77c0e8b2f977786618c2920e215a0589a8090687
837 F20101208_AAATQR li_y_Page_083.txt
4fca817e64e1b1aa00d77ac221ec1d8e
e6cbd757ad54af364529882c229112c88d20bff8
F20101208_AAAVAD li_y_Page_027.tif
b5a0a478aeec49da2fa71347e1bb54f3
71e550f29d69a140e75cf9e70bb50804e36d83be
13454 F20101208_AAAUTU li_y_Page_180.QC.jpg
220e6054de5cc9bb9069c3d985f7b9c4
17dae0ec329058ba470aceac6990febad18cd686
867424 F20101208_AAATRH li_y_Page_112.jp2
1270a012956ad33aff5af39cee1c10bb
a4c44b3c90f6d2edc683ff0fbbfab8f050254953
12371 F20101208_AAAUUJ li_y_Page_081.pro
e84669b0cfd6ae23ce870a09d637c1c4
4b5fca1f14f188e31fd6cdeceed622b63338851f
3087 F20101208_AAATQS li_y_Page_171thm.jpg
d9fd0f2264039209dfe3206e9a50db16
feab6a4ad8e3d016bcde798f1cf76b90705bfcf0
F20101208_AAAVAE li_y_Page_028.tif
f9deaf704db2b367a597a8a365c1c9c8
210d1d3ca3e1491c2181c1b1f3af5c25249c166f
122379 F20101208_AAAUTV li_y_Page_173.jp2
1ab81708061c02cdaa4744f391697623
852bd63fb98a55ebcd0cee2380e88dd5eb3a8783
510894 F20101208_AAATRI li_y_Page_132.jp2
adf54352116aed11dca8faeb77be161f
2624a1e4d7003729673d46cb261457a7996ef373
42000 F20101208_AAAUUK li_y_Page_096.pro
4721e10bcf222255b6522209227f36c8
1fd49ccbd008d8043610615082532d27ea210ecd
30336 F20101208_AAATQT li_y_Page_127.jpg
bc313ecf13baf3ac3113aaf1074e2bdc
c5df3ddc4668d558bc1301d3d245670e9d153c3f
F20101208_AAAVAF li_y_Page_031.tif
9c0a12d6b85a9c0b616b23ee37fa4f3d
9e52ee2fad60e7598f69c668fd0bc221d76bc1b5
60012 F20101208_AAAUTW li_y_Page_177.pro
49ff35ec40be17831ae2fb543d9ccd27
c8795e25d6b7e381252437aeb7b1965ecb0bb582
2120 F20101208_AAATRJ li_y_Page_118.txt
90de3974591cb1554f9bff027c602dd6
525a32032e91d39b7f89e66f8cd522f25c3352e0
260833 F20101208_AAAUUL li_y_Page_136.jp2
e0836c44999e44724d25c168e28a2ca0
0001b85b4318fd3944a36ba84dc55824294a1669
F20101208_AAATQU li_y_Page_165.tif
21e56801cac413374f1f17093eb38f1f
78f3264cc174a785d7a56bc12516fb2c3f2e48ef
F20101208_AAAVAG li_y_Page_034.tif
31685aff16a44b2dde543906c0464feb
d3642d69a65ba57d46ea54d661902dc0cc7d2d53
70891 F20101208_AAAUVA li_y_Page_035.jpg
af979cde1f12aebdbc3413fc05e118ae
830cb3bdb3297cec99f5d4ba0a4e3e2ba5067e96
F20101208_AAAUTX li_y_Page_103.tif
f81322c26220daf5ed44baa48dc3131e
f2ea08c440530f7a099bca0b1464baf2c4cf4046
2138 F20101208_AAATRK li_y_Page_125.txt
3932531fb445f8da40945ceb6d00def9
1219ce739d71c7b7a5f5f6453c32a2cb6601577f
263232 F20101208_AAAUUM UFE0017550_00001.xml FULL
8dcf3b4050cb3d5750fb39353c0cd75f
f1670348b821a765f3127ec101a26eb10a9ae82d
34350 F20101208_AAATQV li_y_Page_066.QC.jpg
4f7b76ed77f48288de998c3671f7d47d
1a31f166c1250c34514e49a25ddf11486af0c11b
F20101208_AAAVAH li_y_Page_035.tif
c7e1b8d2fb756046d7104b3cb93766c5
2eb3ea7ae99018d68684e0acf08fc9cda3f4ce92
69176 F20101208_AAAUVB li_y_Page_037.jpg
63089a74a38c70a0fd49742e8729ebf8
93f1813b635c1ad9bf72d0e5ed3b3bc5725b1aca
103602 F20101208_AAAUTY li_y_Page_122.jpg
751016a8d1cee613f0aa7f459d262920
ef1fb9ea981496bee417612e6d5270f8a57755b1
1857 F20101208_AAATQW li_y_Page_143.txt
25dcf8af1263b28c1973c16a703e23a3
2f727693b0ae55e96432a35076649b5a76e355b7
F20101208_AAAVAI li_y_Page_036.tif
fd6aecbf78c385f9ba3459ccf3d54532
a59fdb86c89fb7f37ea68940892b0202d5545aea
108724 F20101208_AAAUVC li_y_Page_039.jpg
8d2339fe3baf192c71c6ee7d5738b695
931918c6e0762e825446d76d9c21d60649fafeb9
7667 F20101208_AAATSA li_y_Page_159.pro
100517d5f1eebcbc1e1e8b01cdafe89c
cab9a83f1c482970399879c0861daf4f539a916c
4586 F20101208_AAATRL li_y_Page_025thm.jpg
3dbcf7dab62faa4813d450656ae0262f
017a8153cd61ed51b6d4c642df55ccece0ae0f5a
49081 F20101208_AAATQX li_y_Page_089.jpg
42d6f1a99d7938ae7bfd6fc083125448
a9f5a5eabe41cf04f238211f540db274d90c62ef
53501 F20101208_AAAUTZ li_y_Page_148.jpg
fa081d08784a1d8cda6fbd004d2b150a
136fe034e278f81574ab85680c6321a3a947298b
F20101208_AAAVAJ li_y_Page_040.tif
15a3449f014282dafbbec32df63e787d
c99956f343f04282736ca4005ce148a4ce303a9e
112754 F20101208_AAAUVD li_y_Page_044.jpg
8d22c67c7bb19e477e34d340b912e83b
48ac560607ffda2719a6c99f8c1c703079068d62
391 F20101208_AAATSB li_y_Page_136.txt
8579c0fcf98a50aa5c37a68c6a331bd2
e733829c0edb14ec31433b021fe7adaae06c54fe
36632 F20101208_AAATRM li_y_Page_044.QC.jpg
9b4664e1d4a0ce70a6bbcfac0e49a20c
4f5a9f47f0b90309bc2ccde52937fc6b5cbde367
63871 F20101208_AAATQY li_y_Page_146.jp2
c292243698007b701b58b66315623df6
86a3ad9f6234ba71b6706655244eb5e247363640
F20101208_AAAVAK li_y_Page_047.tif
263ac1373bc4537314f80852bf855435
a11f1e160145708d9e838ce2e51d89972e24a4ce
50769 F20101208_AAAUVE li_y_Page_050.jpg
fa6ebb484827b4a2b07a7f81fbf40844
098401ea017d192b1c9767be9f5a8b03bcba5a2e
45571 F20101208_AAATSC li_y_Page_120.pro
3e81fa59c28f6a3fdffc1f24604963a3
9228f594fea188eeadc304045fb7f56271cc8342
F20101208_AAATRN li_y_Page_065.tif
8dac91a232132d09c33b8b3860a7273e
4009419082e77542a9e271968ecaecce291d9d01
26652 F20101208_AAAUUP li_y_Page_001.jpg
b58085d64c29f3aa46b5a019ef38c060
ac678b8015f2978f22f9a5c57277296839a4f264
985499 F20101208_AAATQZ li_y_Page_117.jp2
b926a06e79318412f35ad0b050beabea
54595bab2c50371e847c8dabf11fb8db6785eb3d
F20101208_AAAVAL li_y_Page_048.tif
ed3d0dabc0d2e61ddaae1bf99fc42f93
846fbcfeb6a0465bdf35dccfca97f989978663ed
41447 F20101208_AAAUVF li_y_Page_052.jpg
9c0acff9e13dea03ec88fd1238b6942a
08f1877651fd3aa93cdbd842b1225d71e7718834
2155 F20101208_AAATSD li_y_Page_095.txt
67b54c0691f817044fe5b971ca446f19
4293eb3a099148dc1725d2738560cf57ef85c338
382 F20101208_AAATRO li_y_Page_084.txt
6a1be56e546a03b32ef5a7efbd1d3ed0
0b36612d73fc9ff1cc9db79918a47cb6905f8827
74990 F20101208_AAAUUQ li_y_Page_005.jpg
45dd154a43f24bae1c47a9a555fcb2a5
de51d1fba5a77b9274f5aa89f663bbfbf3efe0ab
F20101208_AAAVBA li_y_Page_083.tif
40b39a8567bf5b4facda61ac8b147dbc
bc50322577c8fb79155a37735e0d7096accecb3f
F20101208_AAAVAM li_y_Page_050.tif
89520898bbedab550082431d01b11cd6
44ae178f845ecfd5d69921caee5117be612750b1
82853 F20101208_AAAUVG li_y_Page_055.jpg
585836f79bba25f1c3ce114d66bc3764
1555e9a1b464374681d139f665b085a9d26d75d7
125053 F20101208_AAAUUR li_y_Page_007.jpg
c1de6e5067de10f4fe6e3007f3fd6e54
389c0de20ad2d24544f83067d24a23f600d1563a
39636 F20101208_AAATSE li_y_Page_130.jpg
2174e90e0adb697c997af4afa86d05ce
80b6cba3b8e782820c87f888975123d378fe9aea
27034 F20101208_AAATRP li_y_Page_140.QC.jpg
dd0f4f0a30896d3392165dfc28c9d48e
f98afd63dd052354f8cab3e52c92c1d1b16d1cc3
F20101208_AAAVBB li_y_Page_086.tif
8e082b61e68f75c8129d5b58b10e830b
aee07d175e9c01885c61eb20bdea8c2aec6b62e8
F20101208_AAAVAN li_y_Page_052.tif
6f6cb3feb8e6983afd4b426a7aeb5efc
fdfe3d34f1ae21a43288993f87b4a23b12d4332f
88118 F20101208_AAAUVH li_y_Page_059.jpg
0d792ec572389651b54c1b68d2615123
e69ab102d03b412f512c1ae40a73232fdb9ab7ca
66378 F20101208_AAAUUS li_y_Page_013.jpg
5109c303a669b35e1097a2b4547f5be5
70c2fdeb69b98b39f63a80d1bb963fc3492e4508
101924 F20101208_AAATSF li_y_Page_139.jpg
7f6fb48540fd9bcb89ddcd9e5c18dced
4591505ecb1d9d25110ad6188edd88b8fa50c7e9
49582 F20101208_AAATRQ li_y_Page_124.pro
48aa37cfa2f3401add41dbee0ffae549
42136ebdfb902f32b17bb86d4f3f5940697c1b11
F20101208_AAAVBC li_y_Page_093.tif
9d89ca6aaa2a810f6cc3573e212f6bee
01db4283ebe07f0a03b6e2c23981351b5a9a6d2d
F20101208_AAAVAO li_y_Page_053.tif
2225c31b0c8a24c6b8b1e64318c6bc4d
ac19a105ce7a582c7b3e7c04516a86ce552f0a4d
82131 F20101208_AAAUVI li_y_Page_060.jpg
394be7bf3ace39d88507fc5f8e674fc8
58f28074a9bbc3bda893def1018d9201e9cbc6aa
96921 F20101208_AAAUUT li_y_Page_022.jpg
ffd158b2cc7ea7bfda7a29433a2d57dd
48e1405c9c0543e7600568e7579892f84a5dadee
6323 F20101208_AAATSG li_y_Page_045thm.jpg
a46320307d789df413efc97e4830929d
9b01d703046ef07236845b83f2b478df63d22b1c
79434 F20101208_AAATRR li_y_Page_161.jpg
15bf1b648b3c342d5ed82cb550bf5206
ad36156f49bc7710301997a23abc7f7bbe26549c
F20101208_AAAVBD li_y_Page_094.tif
1f5c31f7e9a1104a337a13fb386e610b
764cc81014def1e6fca6e52868f9c34b3904df10
F20101208_AAAVAP li_y_Page_054.tif
e5ae901110f8800e97c46bdfaa67c6dd
edec1f0ea96a541835a01581d2aa6693b0224b76
105606 F20101208_AAAUVJ li_y_Page_066.jpg
40abcfd5999688393c0a02dcec077934
51a16600c5d6953e3b6c516f1dd65d1d510f52f9
95040 F20101208_AAAUUU li_y_Page_023.jpg
9055c78a39c23f7e31eced5470324f55
ce85ed05a1d7e4dc1eee9fb3321706ad296b2973
36398 F20101208_AAATSH li_y_Page_178.QC.jpg
12cf9219dfad581f8121f13baa76523b
09fcc5d257a564ba91aee7d3f843e75ff131206b
24821 F20101208_AAATRS li_y_Page_167.QC.jpg
aaec934337dcc86d15a613b6eea248d1
d40cab268ecdebb5b7ec15e9e0a316141ae863ec
F20101208_AAAVBE li_y_Page_095.tif
46c9c38e650b5a0eedf5c139cb4a8ffe
2662c5860a8e5f91edf3c723ba3fafb22ecad49c
F20101208_AAAVAQ li_y_Page_055.tif
727e54159b32e9a40d658b5a0cd14a7e
4f49ec2fec0157dbf446e3f9369f69a2f5327023
70798 F20101208_AAAUVK li_y_Page_068.jpg
fe164f933b163a447368c414a7eaa5cc
3d69af670d70360a5e25d992dd947e88bc856882
57100 F20101208_AAAUUV li_y_Page_025.jpg
d24be0ba0d0f4f56f1859f188f338f83
e2ab7a858ce25d2fb1d2ef3b8feb7a7336db89f9
36424 F20101208_AAATSI li_y_Page_110.QC.jpg
f1e14dffb27ec08222cc952849a3501b
b57d7d16ab1ac1d154e3a33ee6f23f0027c11385
108154 F20101208_AAATRT li_y_Page_139.jp2
5433097f7e6ee50a9b7ef3685ca8459b
650de612faebb93dca6c3960cbf2fc7de9f37b18
F20101208_AAAVBF li_y_Page_100.tif
f1c02028fb4466efe55d3d7c5aca4fa8
985a02a20919aa1e4ed2db2530b2b4100deb7dad
F20101208_AAAVAR li_y_Page_056.tif
71299851a2abf3eff08f0b6088b5a549
6b39518acba098fd176ea5adf79cba0d936e80d1
79422 F20101208_AAAUVL li_y_Page_071.jpg
7fbb9ff9604807135b2aefa51b5f0182
d5c3d68668f568a9d46351def705dfd140618522
52085 F20101208_AAAUUW li_y_Page_026.jpg
bd2a8714b517c83b1d5bd8f6c9317fe6
1707da18693fcb6a4938a39d7fcb2a41dac24b71
106245 F20101208_AAATSJ li_y_Page_108.jpg
91ddbf9ee33f6e2fdde8a2ff2c53ef11
8539efb2d67050f8f6a809d0fa824d48666d0063
371 F20101208_AAATRU li_y_Page_158.txt
aec8e0262790e14f43d5da98d684f302
d7a1abcbfa211b19a8111d2623d405df6e9edd70
F20101208_AAAVBG li_y_Page_101.tif
8df1e5d91600d7a67d738b0f831993a3
8bac3d100102ef7cf67eac8589886c78f9631c61
F20101208_AAAVAS li_y_Page_057.tif
6218ccd3b8578cac545101112ec514e2
184b849cdef42db813bd9de05a1165e788a2b022
70547 F20101208_AAAUWA li_y_Page_099.jpg
125dd05f402343999477d8f1cdf2c9da
1f6725ff4ea458b08b5701caddd1acd8bbba509b
98777 F20101208_AAAUVM li_y_Page_076.jpg
c85a3c54a4c3a655e94c6d1f5f5b8505
39c78f9823c626fcbc51198c3bd7216e48712aa8
34392 F20101208_AAAUUX li_y_Page_027.jpg
2395bd4940d78e7f9b2fed5a214e0b07
69d45e971a6f91321ff797424b5143304eeb0446
1051970 F20101208_AAATSK li_y_Page_013.jp2
dacdf55c3f59b67f6b072bc182e7d3dc
09cd38a56f4c66eea8584a7be3b4b00e413376d9
F20101208_AAATRV li_y_Page_144.pro
7e02e2e0fb54d3f9aeecbcc6e51c9972
f2295bb2693f70513a261129c1fffd97e534f473
F20101208_AAAVBH li_y_Page_105.tif
e594916343693d064a62ca348cc5120d
18430435bff99d30a045634981a2b0fabb81c55a
F20101208_AAAVAT li_y_Page_061.tif
58283c5fa481413a2bd76e05910ca1b0
65067fa3da4ce6b78612fc2aac6dcea50e4baed6
17801 F20101208_AAAUWB li_y_Page_101.jpg
852e2da6567f362e20e37058fff78553
b103673e1344511f45db9895f283662a4669cf8e
70345 F20101208_AAAUVN li_y_Page_079.jpg
ef2e69c62792af9a47498a77b6b6c013
cf7c5062b2731002da7b7fef3f82759140917a96
101008 F20101208_AAAUUY li_y_Page_031.jpg
4c207e76824890b34a73b97fd3e20235
6835f502527e3a1fbc4c8d4137e398142ad25456
2641 F20101208_AAATSL li_y_Page_127thm.jpg
22b909d93ca5e8e8be87f2ef476562e3
a3a83c8731df048d87a90b16961a8612d507f6a4
3640 F20101208_AAATRW li_y_Page_027thm.jpg
fd60eeaeb86aa67d523db0a1b558c934
4e33b394774931333d25a18556530e041842869e
F20101208_AAAVBI li_y_Page_108.tif
5cbc77da4d60b3f1298b859fd91d4c87
c3bdae293bbcb6b7df9d5908e62545db2759af55
F20101208_AAAVAU li_y_Page_062.tif
aa760c376d5743c45451c7e232218241
af3e15cc459223f1fe0eebc9798fead69d0d85f5
54373 F20101208_AAAUWC li_y_Page_103.jpg
f0f9459f9afff881dee84abb4f602d9b
0b2e62779538ee4b221e55f1ddc7d9533097d899
86227 F20101208_AAAUUZ li_y_Page_033.jpg
08f4776db82a26fa1ba613716d6e1377
f372e210693fd9a598512bf04599748cbf515c79
F20101208_AAATRX li_y_Page_059.tif
0c1137345d1af5e4844b7a2c5d03a2dc
c98a5cbc676a1be1e92fccc467ad7d73aeba84ea
7809 F20101208_AAATTA li_y_Page_031thm.jpg
38fd1cd35a193935b88727824ceaacc8
a85a320250d545e4078703aea5ea63c83adcf83b
F20101208_AAAVBJ li_y_Page_109.tif
22b5973a0d22d0a660edae3b1b27f617
cbb88ce48316c1908e1e0f3894a3285aa7793a38
F20101208_AAAVAV li_y_Page_068.tif
cb468d48322c3c53236fa9ca7e9909b7
9e990beac79bc732b0b821ab6f58b7b8aa59e012
107170 F20101208_AAAUWD li_y_Page_105.jpg
cbdda981ec795f1de42382c329e229bd
8f79904713e5c42c9546eef4be3e91e0ac4f496c
21098 F20101208_AAAUVO li_y_Page_080.jpg
5069545e9ab2e1688ad18e4bc959bce1
bcdf52a7e16d6c6a2de4cba3df931d4d9f1557bd
9049 F20101208_AAATSM li_y_Page_110thm.jpg
c8891971f0bb65dbaa4a0753e56bfc68
db0d6c93dae7c076859840a97a845334f44bbfe2
F20101208_AAATRY li_y_Page_127.tif
cfa06ca83852341be3a0ffa95aa88c83
8140c73f4cb4a98e437149ffa54b860794154547
82384 F20101208_AAATTB li_y_Page_034.jpg
410d5958098a1436fbb987985c0e1ff9
fae9ee0b922cc9733c396d158ca58d555fe66833
F20101208_AAAVBK li_y_Page_110.tif
dc49bbcc839a5f8e82fffa365113a208
556ccc9af4ce3d4b32bc3f06cb8ab2ac4e86be63
F20101208_AAAVAW li_y_Page_075.tif
66d9037099ab2e9aa9a9330c98b27268
94648705490be8a17a2519e520c210fd6012e1e1
101257 F20101208_AAAUWE li_y_Page_107.jpg
7c864a83d4a5c7d8def8be5e818a6698
e71b15b2a087b3a941db40f9af35bab610389011
47073 F20101208_AAAUVP li_y_Page_082.jpg
af6eeac01f02b7d35ea7a055b620ce72
7812848ccf11e91f7a0cb801b3eab85663a0134b
16875 F20101208_AAATSN li_y_Page_082.QC.jpg
308da1cfb95f2b2ff384c67a35fff795
d88e1b669b564700b87bb2d945f6910ecb06538a
32270 F20101208_AAATRZ li_y_Page_141.QC.jpg
a7f94067c90108933454c03c7eb45da8
0842a557c673f80adba56de4346bd45029f404cc
F20101208_AAATTC li_y_Page_033.tif
0b36fd3333c615f4a52ada60f0c28cbb
b994defa4adef2a1b58c49b540cf552cda487eb4
F20101208_AAAVBL li_y_Page_111.tif
9fbe6cd288060533e13e6dff175e0fea
f204e032ab45f8cbf919a2bf97e62ae5de387d12
F20101208_AAAVAX li_y_Page_077.tif
f28547e379a695ae0247d87e6c6fb94a
a0947e54993255c1772ae90ce7fbd9aed44f280b
85343 F20101208_AAAUWF li_y_Page_112.jpg
94f9dfc1b14cb7bc2c9e0f413d3f5ee1
435eee0a677c0d44b5ae65c150d0dd1bd19ba8bb
48832 F20101208_AAAUVQ li_y_Page_085.jpg
c7a094781c3baafedb5e51a59afa5176
960f690e2733b4f6e2a907321d4b27f8b27af14f
45993 F20101208_AAATSO li_y_Page_093.pro
8ebeb6308fd58ba217924525a462977a
2e37b2ab08d9e98dde1665d3d3cccbcbe138ea1e
9649 F20101208_AAATTD li_y_Page_172.QC.jpg
fcb1a31b22d5a7ac768baeeac25d855d
b880250378a09f4b0eeb8e4c5fd8ae1e9adfd969
F20101208_AAAVCA li_y_Page_146.tif
939509710443e86dbe6847cdd604b08d
2272664c01ad33b577d7eaa05a474178a456a877
F20101208_AAAVBM li_y_Page_112.tif
d51d0f5a866118e1fd99165dc64b42d7
a2b11e421b7705e7906031198929a1a5f7bcff17
36877 F20101208_AAAUWG li_y_Page_113.jpg
a2fa8b1e8c47632997c639e59b0381f1
e6f283f2dd0e80c33eec3d298caf4cf85c978875
53332 F20101208_AAAUVR li_y_Page_086.jpg
062e2ea17f204e797ba357906893a4c5
6d6933674317d24888a290551876006077871746
112008 F20101208_AAATSP li_y_Page_017.jp2
2246af3eb042d657a9381d90627c7ba0
6c1d929d6a1ab74261a2714f6ac014aba4a988c6
6701 F20101208_AAATTE li_y_Page_037thm.jpg
548e18e6a3fe1c9d3361e8b545eedffe
7b23a02288461d9a086d142c8fa1c211e308f057
F20101208_AAAVCB li_y_Page_147.tif
e967065e06772b16e0b8c849d3d19e9e
77b4812620cb3f869b47a8ce7c3a00066ac2282f
F20101208_AAAVBN li_y_Page_115.tif
ae353d78d67ef44f399dae772bfc7323
c89034c98bff8739198054ab61545a3fc8694bf8
F20101208_AAAVAY li_y_Page_079.tif
356790ed79060c103b1ccf6c6d8603fd
08a7faf99604da5dbda825b862ff283b909d620f
79581 F20101208_AAAUWH li_y_Page_116.jpg
36acd7796ebb39c29b10387d597978ff
af1b5fd43471624feca7f271d11e96fb6146e23b
45469 F20101208_AAAUVS li_y_Page_087.jpg
0e9d0e7e78265ff31aa8bf42c644b23d
25158fe96d4c9d3715aa30b2e11dad9d9389fb6d
101885 F20101208_AAATSQ li_y_Page_061.jpg
864727a9adf1ede1d3cfaa44b3cef65e
405c23e7f1972a50a5c5610b20fd361316bec689
491813 F20101208_AAATTF li_y_Page_084.jp2
d306627c5bcb3674089e4d6ad54ed0e1
b20417448213c2646e39159d4e92328f27160fcf
F20101208_AAAVCC li_y_Page_148.tif
0fc237b0bb5d647068689b39fe87f6da
88769b92f99ae435f0812e953c5bca3f7dbc14eb
F20101208_AAAVBO li_y_Page_116.tif
8d6bb61694dc4f6e0ad54f35c5819886
e6c888f4dc3d48aa51b119ad08cbfb3d6cf079ce
F20101208_AAAVAZ li_y_Page_082.tif
2c2cb2a632d63b65533dea6fd467e339
b708ea4a2edf46f32b0412c033074726c8319e9d
103907 F20101208_AAAUWI li_y_Page_118.jpg
3ca2430b2ae8fd45d4ecfba77b81e6b1
63606facd838a7ddf0370949a74617dae7283a67
54938 F20101208_AAAUVT li_y_Page_090.jpg
b06c9257328493a8197bc24de86830eb
58cc17e634c047f3125f9394e89355d88be7f10a
111468 F20101208_AAATSR li_y_Page_108.jp2
b591fc0a3d2a53f509e3267822c7fd8f
7e1db7360019e59731afbcb430d43396748c19ad
423 F20101208_AAATTG li_y_Page_129.txt
56231574328b08aee43c689d671c6ce6
8735f4060ce5576ec403c64017a61b95b209c023
F20101208_AAAVCD li_y_Page_150.tif
7d12218a0af4062a4730ec02f79e40e9
dc78fde515d6bede9b2f09a22d5eaa805182b1d2
F20101208_AAAVBP li_y_Page_117.tif
f0add23d6563ea98bba74bcfa45b8f7d
3ccc705975e8e2e42fc69f6b3c789faced978480
95471 F20101208_AAAUWJ li_y_Page_119.jpg
09c666d64ae498057a28d0014597b5a1
a9530ac0c570c82d3fae80ae2a4e81a30655e108
92175 F20101208_AAAUVU li_y_Page_091.jpg
953e8bcd2feb4c11107ba8fd228b0092
994be0b9567b00ea7ec68a9efdaca7a8ce7fb326
111478 F20101208_AAATSS li_y_Page_038.jp2
1eec5524667bb1b5626ba90cc21f7f12
2d049ea1eb6036c0447bcab749a81021c70cb0e5
5634 F20101208_AAATTH li_y_Page_148thm.jpg
73e9b331b271901f5161731f6d7be232
4ed1b501f35d1cdc39b5825e1e439d4ce1aae99e
F20101208_AAAVCE li_y_Page_151.tif
7e826ffc704687f85519e9979e0619c4
d58b74df8910686415ce35aea0d0f8b3d2500a7a
F20101208_AAAVBQ li_y_Page_123.tif
f6743daba04ba3c95f5514d70ded7e35
c4844fac9b5e26d003db70cab5ea98516f86fcc6
108413 F20101208_AAAUWK li_y_Page_121.jpg
2feb0ae62a3f90d655dcfe30b7e7fb76
f20c8575bc3290016e65f8c43b170942c1ecff2d
91293 F20101208_AAAUVV li_y_Page_093.jpg
4a9b84f57c120e1ed9c2fb3ae5beaae6
0f2027de5b0cabf321263156ed0625fc00163858
33242 F20101208_AAATST li_y_Page_020.pro
9299bf428d90004c2cf9889bd79fd011
3588d29a4340cabc90e3bc6052e695b9b18fffc9
1546 F20101208_AAATTI li_y_Page_045.txt
aac3dfcbf833d5cbbec6be3dcb2650cc
f4bd62f1d205ca48255a3e8a5ddc01db66e24c42
F20101208_AAAVCF li_y_Page_152.tif
6dc49becb8a1119b79ec919f81c60fa6
b16078a3463d6f0ba2189e499f6981a12b326469
F20101208_AAAVBR li_y_Page_124.tif
6cc89f60237b6e376533f06684b3d89c
e33f13c1c51c3d0aa4386d9fb9d5ab4a90949448
107809 F20101208_AAAUWL li_y_Page_123.jpg
c7b625163bb9981e37643fca91d52912
5b712dd35aff3a58d46f63f951d1a2f52b723f57
102230 F20101208_AAAUVW li_y_Page_094.jpg
64e30ed051a2f994598c8540d3c9e7a0
f54c04209d3157cd0a720f9f6e4c62dd85b04740
35761 F20101208_AAATSU li_y_Page_039.QC.jpg
6ee7c18391e4d956be40c2c3c4223591
e7a147c2cb9644fb4cab07072943f4937a0f69f2
F20101208_AAATTJ li_y_Page_096.tif
ffcf64b5692d555dedf4ac30194929ea
60018187be76f0fd0de82125feb3e28928bdcde1
F20101208_AAAVCG li_y_Page_153.tif
56e940a83df6b36e0fa1e5edbb3689c6
4cd48242645e6380bb520d34a4588c4abf551dae
F20101208_AAAVBS li_y_Page_125.tif
7e4218ccd6c847e015661b370534577a
eba48e698434ecaf79b0f4a73a96793c8e4058ba
28124 F20101208_AAAUXA li_y_Page_172.jpg
01d3c97a29aa096a34e56bdf2178a263
de9067cb715c33402835d6c71b2228cbc8147233
101216 F20101208_AAAUWM li_y_Page_124.jpg
8d8fd28ee03519235ae5ec571f0e39a2
11a312ae43eaad561febef096846e3f5ea47e7d7
103669 F20101208_AAAUVX li_y_Page_095.jpg
53795295b29e07586e0efb5d5af687c4
e830e6887a6f3f1aae88fcabf0ea97a9c8a18088
23788 F20101208_AAATSV li_y_Page_166.QC.jpg
40b10f5d0dff3b46ca603bdcc91fdf4f
91198a82e69fdd4bdf0b1e794822c9f39aa63ae2
41404 F20101208_AAATTK li_y_Page_114.jpg
f3547fb6b7e5529cf9c926159d7e04f0
540ccadfe598ca8e586fb9620658c9d691b2d10c
F20101208_AAAVCH li_y_Page_156.tif
76cb44de25bc927b458900d1eb618836
795799334d4ccf3e6192faa0a8b4f2abc3a03a0b
F20101208_AAAVBT li_y_Page_128.tif
9548584dc37f6496ef3f131ffdc3873a
acb9b9028ad720987800d29574b05b76338b5762
120745 F20101208_AAAUXB li_y_Page_176.jpg
74231f6deee009baf1a47913823a66b9
f4caade35d5972eb30a71c5995370c40af6b4ae9
104597 F20101208_AAAUWN li_y_Page_125.jpg
9d3642f73ff00b4ccf0b88703bc8d854
180550a6958e1523e899663465c615a6d48d1c80
86013 F20101208_AAAUVY li_y_Page_096.jpg
64b68c37c2a5ded7bcbe187885bc3279
a271c7c34328f8c4987f800bcecb119af7f0d1a5
42805 F20101208_AAATSW li_y_Page_155.jpg
946c8e7545dd70486e87f03fa294ad5a
e37311f905ec56087911bb89d4cd79fd8118ae54
35483 F20101208_AAATTL li_y_Page_046.jpg
38ddb10caab8b2278ea757e11d280f99
3d80f226e0ba0f39b4b38d107242baf072fd44bf
F20101208_AAAVCI li_y_Page_157.tif
d62b2678b26ad3de79b923913fb270cb
c0991b403041d07fcd94ef71ae5493e519f7388e
F20101208_AAAVBU li_y_Page_132.tif
88357a10d54ebf9190e673eb4b57686a
32d738242d16732efdde10c5a2d3cae31dbb6c94
116201 F20101208_AAAUXC li_y_Page_178.jpg
910668127d7e9514cce1f1f7473b24b9
6e15fc01f1d143b8787fad3334f69c5aa1485a26
106345 F20101208_AAAUWO li_y_Page_126.jpg
5d34e52cf642ac67f95251081457c65f
7d0874a84f17626af0e9ded94a9a223998aba4b6
93988 F20101208_AAAUVZ li_y_Page_097.jpg
a2ace7fc51e3a3c88ae5ac7abc7e57f6
1640b0e4c74c49edffebc8e1417a4056ba448973
5333 F20101208_AAATSX li_y_Page_082thm.jpg
b181eb0355dabf38020f5263f7d5a68a
2c87c8c3c3eeabdb7a6effc098dba4c85cdae9aa
2079 F20101208_AAATUA li_y_Page_142.txt
cae476e2597056fd5a55f2635daccff4
b1a8ebc7c7cffbec932d2dd5be30e321b6c55848
5136 F20101208_AAATTM li_y_Page_169thm.jpg
71cd43c46a03f332cf01470277ad7947
51db862dbd671cf32cbe69f843c04648a82dcbeb
F20101208_AAAVCJ li_y_Page_158.tif
8c52c1e0e0ee60f5243fb6d951e303ac
d74e37ebb861478491f49d570855da648041950f
F20101208_AAAVBV li_y_Page_134.tif
4634f374691761670e65f9b257e7fb1d
7cebc70cd85828c8fd85f752e088fdadc8451ed4
6309 F20101208_AAAUXD li_y_Page_003.jp2
ce818ac6ee9e1804262ee50accc02749
60e6e5bae645e884c15fa5e01234aadd0599e640
46737 F20101208_AAATSY li_y_Page_143.pro
e09582e984d2de8ddb5adcfd8ecae69b
1cf3c1cf18f70b5812b76a67c2f46ff3ea420480
43675 F20101208_AAATUB li_y_Page_131.jpg
876ee9ab0e41a92b2f38608812423ef3
55698e6cbabd3c29abb77494d6ece9e155118b96
F20101208_AAAVCK li_y_Page_159.tif
5ed0dfabaf64c3cb024ddbac8ab7b6da
50dc5f57df1c09d32fb315c525d598f886183332
F20101208_AAAVBW li_y_Page_135.tif
22443a641c682d459d480732b94d65be
4ec2e693cbf8e840bd799a5167587784fdefb1e9
1051982 F20101208_AAAUXE li_y_Page_006.jp2
d09180dd395d957a66c0233327ef2c59
f2baef933094dad69c4349f0f307d8f0f6a198de
45356 F20101208_AAAUWP li_y_Page_128.jpg
1c06def961a28ff3368cae6817aef497
e42e42e3d918e79d8a20128e804208a384587580
26349 F20101208_AAATSZ li_y_Page_169.pro
c0d224e29f3591a3bd6ba249ff1290a9
1cde5854f173b62a5b723fb25e97f20d4d528972
73880 F20101208_AAATUC li_y_Page_145.jpg
e76ba5079393396284fee125f7001681
b8c42f494e42ca5a1bb7aeedc2020f29a530b3b6
52334 F20101208_AAATTN li_y_Page_121.pro
2566990015c83ae00f281d4297d81bb1
e7e4de3f6a71de1a0d05a2e5c7caca1ace7b50dc
F20101208_AAAVCL li_y_Page_161.tif
11d773c7c88c3e694700f7207867abe1
5350129a8612b5c16190e1d898142c1df28ba642
F20101208_AAAVBX li_y_Page_140.tif
583709b22800e2ca6428031e7b7d6441
e7cfaf1bae4b4bfa26c09c0581e0824ed2eddd1a
1051976 F20101208_AAAUXF li_y_Page_009.jp2
b7a51e477016f666b8650eaa0a0249ef
88a4b26c1643e5e6ba7ca0fd3abbbbceb77301ad
59129 F20101208_AAAUWQ li_y_Page_133.jpg
523a4e0c8124079f9887b1f14ec705e8
0859088a3c17a3dda1df30f981e0c41d4c5d0854
1508 F20101208_AAATUD li_y_Page_152.txt
7c8989241fef9a851382263a1ae7a7b7
32b10e261de66daf654c01f4c19660b4b2daacb9
78334 F20101208_AAATTO li_y_Page_153.jpg
785f79b3615b8767aeae95dc90711e32
a42633496a162112fa9ca79202f8b7821f8daeb6
31570 F20101208_AAAVDA li_y_Page_013.pro
ff08ba449549202a6f67b103818a14d0
6c760e408df2f8adcd81b56a770870bba2655a26
F20101208_AAAVCM li_y_Page_162.tif
bb7b99388b5b1157537ac35d3739b42f
474ef240997c4111eb422d31cc3ea1c8fc7e791a
F20101208_AAAVBY li_y_Page_141.tif
ba5b70d97a160b8cd422991240e70738
44a233937ad711752555b05944a19c2b6db9aefb
1051963 F20101208_AAAUXG li_y_Page_010.jp2
dc8aa360980bb9d147653c102b096c7f
2158ad9adbcb1de4c8f0fa41700f52f39a17944a
26815 F20101208_AAAUWR li_y_Page_136.jpg
684520a3370c539e18b52729f85f6a73
7cbf9ca5651a9f01aefee25058d600e590348f45
59122 F20101208_AAATUE li_y_Page_146.jpg
29e10bc7ad682329996e80850a4c9319
13038a45b8815738baafa1d1a663754f5a0846a3
42946 F20101208_AAATTP li_y_Page_056.pro
d7cf0d0cd9023a92c838dcc57c64a5da
2ac6c3631c7a82c1895a2c8adf6ec6a5ff6d643c
31379 F20101208_AAAVDB li_y_Page_018.pro
637c47747e30fbbeef2d63dbb6004d59
2b08f2ede9ca1f54c4acd1eaed5b2d5657f7a5e6
F20101208_AAAVCN li_y_Page_163.tif
59382e0c35f8e423e84b12185221fdb5
c67462c1fbb6e1b6beb7f5c5ec38dbe597839e69
1051977 F20101208_AAAUXH li_y_Page_011.jp2
27f747ed8b3d65f6ba35df39ec289204
0b7cd2bae94cc7db156f4b084511d404f050d27c
102038 F20101208_AAAUWS li_y_Page_138.jpg
884abdd389a17e3c8a2dfc8353df5c10
fd08d59f0235a84d7a261becb473ae1c2b6ea2f8
4632 F20101208_AAATUF li_y_Page_089.pro
c86747378cc3df108219b242c9df134f
5cb379cbad6aff13c162259981805fec03e05b9c
503 F20101208_AAATTQ li_y_Page_170.txt
fba845d81873484aaab6dbab4a66e763
bda92102ebff30c552919cbe85eb9cc31ffb4812
48342 F20101208_AAAVDC li_y_Page_021.pro
dfe7927873d2eac93bd475ebda375444
85bf66cc93512cfefb541bf4b848a1b0fae7af63
F20101208_AAAVCO li_y_Page_167.tif
b48735da499e7129619e12c9ca449eb2
8a9f3e75ee0586a1c901b1ff3f89705f70ce9d0c
F20101208_AAAVBZ li_y_Page_143.tif
c6b9d02a62785310e4ef796174175276
6887e59d6536cb17ce91ca8b069618e157350b48
F20101208_AAAUXI li_y_Page_012.jp2
2bc1bff5bd64c97b5719700b72f97e3c
9ae2f4200ccdc9286d4c1941883e838f141e7e72
92883 F20101208_AAAUWT li_y_Page_143.jpg
986c4a006a87170e9a1c5ed5e25fe07d
88de7c4ddbd739190bfebb925281c2be85eebba9
85513 F20101208_AAATUG li_y_Page_055.jp2
ddd13b20c8ba16da52a9a80a4c52a196
669e3ac12660057bd68bf824ce5084000e797c09
5815 F20101208_AAATTR li_y_Page_166thm.jpg
a94ff0948441568611b2d59c52e4b112
b3da9eb0de0aaa1717debb57600423e2d8e3c1b5
111486 F20101208_AAAUAA li_y_Page_041.jp2
292b52da02e18b498346ce2372322684
b43588df84829e7a130eeb67adae7882d272da4e
48484 F20101208_AAAVDD li_y_Page_022.pro
3b2688acca76f26a36ed4c7ec47d395f
ef2b4f32c0a244f8f6a1dd44d65dbed0c12e83c1
F20101208_AAAVCP li_y_Page_170.tif
787d27f8b06bc5c76d7d3d5abfa997dd
cfd78e16076ab555a8c396a1183f1723a1d4a92c
100351 F20101208_AAAUXJ li_y_Page_014.jp2
5855e40e7a5e11ea1a96274d6064473b
5ed14a27d9c8fb53e984e360ce18278e7e72da6a
68829 F20101208_AAAUWU li_y_Page_149.jpg
b791b9f523aaa38c1c9d5fad596eecb6
133569401977414b55ec8021a78ec80cdfcf2d2b
5282 F20101208_AAATUH li_y_Page_171.pro
39809d49f815b6e75948de5475a79338
389907a116532c187e98d9e8a35e056768e87a65
F20101208_AAATTS li_y_Page_173.tif
f232b377788b180122afad2b2c022870
39f38116e83c053d621f9b7bcdde15542958a96a
110147 F20101208_AAAUAB li_y_Page_125.jp2
5ee1555f979422a3676ee730660bcacc
9428ecf5ff9f7095651f4ac81362aef50c3b45c1
46062 F20101208_AAAVDE li_y_Page_023.pro
aeb05b1afbbe7639cae3286227ba788f
8036ff59a3765fa2377dfebc3545cac757bf793d
F20101208_AAAVCQ li_y_Page_172.tif
36242acb000033c0ae8d41ba2b274ceb
4909b705876a0bc3f84f048a7ec2a25da3e393ce
69224 F20101208_AAAUXK li_y_Page_018.jp2
5713adf1a720e2f4406f03b5bdc7265d
2711bc2f2d303a6d64654b075fc0cf41e42a35da
60506 F20101208_AAAUWV li_y_Page_152.jpg
7f5d13f7b0863cf0ef9403ed8f7004e0
549a5af125b0266bf73d32dfcdb0b5e724e1f2ab
79065 F20101208_AAATUI li_y_Page_070.jpg
631cdc80af55aac87e478ace15bef7bc
eaa399c2c01615976009ba5507669a9680ea2062
1648 F20101208_AAATTT li_y_Page_071.txt
25065be5f916e000fc5d50540a4c4fd9
a2277b4b06b541ff61a0c20501ae8b3c19d780f8
21876 F20101208_AAAUAC li_y_Page_079.QC.jpg
47ac8a2819c867918f247353bba6fcf8
717b85c061ff225d6913146492800bb9b6222284
8005 F20101208_AAAVDF li_y_Page_026.pro
1e3d18bf6b98299bed87e98f10cc2724
424ae54662055e22a18e405c8c51ecb6d3bccc11
F20101208_AAAVCR li_y_Page_178.tif
0500c6086f555b95cf1eacffd139a7e5
6af5a6bbf66c1aaa6e083c15f5604432902a93a7
69959 F20101208_AAAUXL li_y_Page_020.jp2
959c72d8f5671a5f63f36d465723076a
e691ee8a6c7249f9e868e880159594701a6b5401
27850 F20101208_AAAUWW li_y_Page_158.jpg
c06cb4b39e6d9646881710c632f76d59
7b33a09b91609069abb4ea2fe13ad68bb9ea139f
23644 F20101208_AAATUJ li_y_Page_025.pro
504da613b81bf9d88028b9c02e070eb6
bd19b04b8eb6f3babee64d40144aac994ed8933a
51595 F20101208_AAATTU li_y_Page_016.pro
dceed3cd7e528a62ac988a66bfbe72ee
440e2371cae5523c24a16e2a618aa87ef2e9353b
51646 F20101208_AAAUAD li_y_Page_092.pro
e1c90cada400e122998fc5ca0b99b6f1
a2952bbcde7625f8e860f2411992daa7fee8e7e1
10195 F20101208_AAAVDG li_y_Page_027.pro
f7d8cc50497a357da1d9a5115258a4d3
d6d1a29ccbe78c7fd74f1e161b342e58912fb1fb
F20101208_AAAVCS li_y_Page_180.tif
dfa78279d0a458868a00ab1eab1699f6
e6ee7a487d3c0afe89747e82314ca82d283c2e93
116185 F20101208_AAAUYA li_y_Page_073.jp2
2180d4365eddd8c100af6ee409e2718f
75abfaf49a8698a959e00f70d827867d391fefc3
96160 F20101208_AAAUXM li_y_Page_032.jp2
6f7fb96c97bd74ac6632fbe0dcf4794f
e83b58ae74a6918f584c67aabffb891bf560cd54
37546 F20101208_AAAUWX li_y_Page_159.jpg
117d920f410c71be260f9104fe272c21
99e647ee4c9dfa7091ed2c39c0cdae8e2181285e
8058 F20101208_AAATUK li_y_Page_029thm.jpg
5e86c3ad25a931c2fd67d8169ad0433f
ff1f829bcf308c992017f6ea711b876cd6fcc026
F20101208_AAATTV li_y_Page_078.tif
cf1745c9babf1bf40482e6ecb4005152
49eddeeb7fc2cd638fcdf7e51a59f7c621788880
319371 F20101208_AAAUAE li_y_Page_027.jp2
8f1274aeb8337a975674cd6f9dfd15b6
c080bb3c4c009c4da195ccc83b0f9d5d2dc7634b
51384 F20101208_AAAVDH li_y_Page_030.pro
59188c71b32d9dbe54cd511b661beed7
245154b31cc58f9c72f4037fbd39b84ae74647ab
670 F20101208_AAAVCT li_y_Page_002.pro
034fc21e7c367a10afd4d11484af416f
470f45ed0aeba868cbfb9cad7e66471e85f50383
112771 F20101208_AAAUYB li_y_Page_074.jp2
9ecfaf12fb6e3ccd0564bd86033865d2
6c098a722c999215fd4ae4cbccad6a6f0572fe04
91052 F20101208_AAAUXN li_y_Page_033.jp2
aae61e6d13b060437e48e4a4b51da49f
35cd625051ac72d8fe12ea966337d0a11438d061
62207 F20101208_AAAUWY li_y_Page_164.jpg
4a2b2627d923d5f79de85fcebe89e46b
5840fc9940e6884f90931fa2b144cc513ceb8d85
7036 F20101208_AAATUL li_y_Page_062thm.jpg
fb7f267051a40e2657deebcac67bd8d6
a70aed408b570c179bc6a4b3a536cd2a50a483ab
110232 F20101208_AAATTW li_y_Page_073.jpg
a5950059f24f213c5b8be632c2d90813
e3e142ce1b42ed4b55288a6511fd024b84f33381
F20101208_AAAUAF li_y_Page_149.tif
9240d8f884979a05a85525ef7172bb13
5228c4bec77341a88e124653a569676fdfafd1b6
52198 F20101208_AAAVDI li_y_Page_040.pro
77c63d6133a791966afa2a7fbf5066b3
16cb16ea3fc195c3e73f781f6aa10d7f7c415e89
1242 F20101208_AAAVCU li_y_Page_003.pro
df4e6ddf6b556e9f8ccb17b201982061
06e1acba056a3ea10137ee3efbdbf3215134ca41
116895 F20101208_AAAUYC li_y_Page_077.jp2
fae9a77eda5f88ed4c4204635dda4fb1
4b3a3c69232a71f692e4ca97a1064e57b73ba531
115764 F20101208_AAAUXO li_y_Page_043.jp2
29674d74076850820b57e3eea57e269f
b5bb11bf041da12e8786b24fea6fbb43d9777a53
90508 F20101208_AAAUWZ li_y_Page_167.jpg
4c1f91b4cf9f15e168b6b0db6658f788
9ab214a3550f3e5e6ffcc13511fc6bde527ff91e
8454 F20101208_AAATVA li_y_Page_105thm.jpg
d15fe104cabf208058615e11d83c9a3e
ffffb5eb777cf0a810567609faef21ff232e5447
21840 F20101208_AAATUM li_y_Page_008.QC.jpg
e950688ea2b2148676fb7268094c0e7b
230fc1bf0057248b43b3e1ab91ab9451e778f0c3
F20101208_AAATTX li_y_Page_069.tif
e76dc33ead695db546700f9bdee675be
53d82d67f397c682bcbd55f53016f8c5b2e818e2
9137 F20101208_AAAUAG li_y_Page_106thm.jpg
77f2565a6bf3668500507b04c86b637d
dd1cf431f4dd0dbd5d6f20ba0007d9f3d25ad414
51620 F20101208_AAAVDJ li_y_Page_041.pro
c77e2dd8eec34dc7b0543a7b9a8c20ce
5853eb5858c841a02099b27cffc6098ddde359e7
35810 F20101208_AAAVCV li_y_Page_005.pro
fef0686c89a4623f5daacef1591621e5
785193229f70add3a0782d263190f6467b85baca
67457 F20101208_AAAUYD li_y_Page_079.jp2
b14d1b71b75b96475c9a81eef0d0499d
ef4256979e623d2967e4e0f2428164756baf4e5b
452414 F20101208_AAAUXP li_y_Page_049.jp2
17c68b2fdea4e16278abc865a6e4e044
634a5cb8d247be4edf697561a9e7cef9def1639b
2375 F20101208_AAATVB li_y_Page_173.txt
1d5fc758a3dd7f9ffa1135176c676e7a
4a3bcb1b1f86d466595b7724f19d13a9faf7f16a
F20101208_AAATUN li_y_Page_120.tif
5602d1d8677ed434b3b71651ad6a3ed5
bcfacd68354a8444140a582614c9a48bffb46194
2008 F20101208_AAATTY li_y_Page_080thm.jpg
c549ae45b45c50ae42fff07949c5d239
017134d975b3057b1982bb9a34e1a7f4f283853d
34769 F20101208_AAAUAH li_y_Page_139.QC.jpg
6d536ac812060e281a2828b21e2d59ef
c69cfacb2cd28fc6799abcd8c26c0ce49c38a593
7501 F20101208_AAAVDK li_y_Page_046.pro
6804da5fc1b96e91e29ab19ba72a8aed
996adc3792dc5f4bbfbbeb219f9eef5d277b96ad
76111 F20101208_AAAVCW li_y_Page_006.pro
2cf30b18ff3e7f695e9f5a05a56b4a3e
b4c589f55d635217d1e5d5b76baa2510e19c7d67
451024 F20101208_AAAUYE li_y_Page_081.jp2
5494a298808583f63177d3196d965f03
392794caa51a9a05c629e1d7556a5f1c756602e4
51902 F20101208_AAATVC li_y_Page_132.jpg
eeefea769c709ef06c4d0fcd4532c78a
2b1386d2cd7a434f96bdd1550f14119343ad5acb
F20101208_AAATTZ li_y_Page_169.tif
834abc58bea139becd5497ec62908873
b2c3d815aef9bfb501015aecd86367c0599327d4
39118 F20101208_AAAUAI li_y_Page_034.pro
c9725994f9e77be0d84f99edf61e2588
6650f059daf689a7ee6e9d7076a50096f947e08e
10797 F20101208_AAAVDL li_y_Page_047.pro
fe683dd4fd71e485e6b9c77113f56a7c
6f8e95a586dbc0e52ab09bcf081f3fb908464bf8
80563 F20101208_AAAVCX li_y_Page_007.pro
fd5e9e316946dbe378fd92ae35eba0fb
b29c04d1e87a7de25a1fd0c68752624b398604cb
602773 F20101208_AAAUYF li_y_Page_082.jp2
cc5e8832238ae371cfbc0ee9d1af2d68
261d34b1174bcbd5ccdeaaf816d3ba8398f189c8
503752 F20101208_AAAUXQ li_y_Page_052.jp2
f4c0f95f9caea4b974d184bf314b850b
baca7d6e4edf7a1de416686b919d146538cce2be
33719 F20101208_AAATVD li_y_Page_037.pro
df6376dcc0ab384337a59e753c52675a
9d2e9e72263e6feec5afb3ae760e92fe2f3850f1
122862 F20101208_AAATUO li_y_Page_177.jpg
45b5f305f3634e0b346d3471c6ef8cd3
942abdaabf30942ef92fa156ad9818a4ad8babaf
8490 F20101208_AAAUAJ li_y_Page_137thm.jpg
18b909984bc3a1bb0b36c487f2eac985
a49de1627d50e9446b4f69f977c20fdb197a0f2b
34266 F20101208_AAAVEA li_y_Page_099.pro
01f4239841bb2b9b10c51ce61c1a395e
b4a6b4e2942e72e289557510414bfe5b8d960abf
11458 F20101208_AAAVDM li_y_Page_048.pro
07aef64c7fab080d8f4763f0c0516fd0
365429aa640ebba5f356801155b3d1a74256f416
49513 F20101208_AAAVCY li_y_Page_008.pro
36c7b37bacf63a1e31c44f435febd003
39634555da9048a290b09445ab5e8767e03c5caa
619693 F20101208_AAAUYG li_y_Page_090.jp2
d85a2101b2affd3b9765fff87308e2fd
b14fcdc2e067c30d956e1d4e551a482d65c1df07
98475 F20101208_AAAUXR li_y_Page_054.jp2
955ad276a68ff4ba34cbf09916b05ab9
b121700214cd0f85e5019d3f79185ee84402fb28
50228 F20101208_AAATVE li_y_Page_031.pro
cf4db731b3f1a668081e08ed6120ecba
078561d36122638da742047afce618417a03e37b
1051973 F20101208_AAATUP li_y_Page_123.jp2
a4e7afe4c2d4bcb9fb69190ad55ee59e
f5716c06152b81c0b57a7a2946cadfd8def8f09a
52517 F20101208_AAAUAK li_y_Page_038.pro
203f1d7823e0cfec2e267be6357c07f4
888b9678def310211c0525a8e82124bad9109304
7772 F20101208_AAAVEB li_y_Page_101.pro
8ecb8f1f43a716e7fc2121e60a38df29
492de0ffc7983d993b469ef44b1f12f2664c8ccd
5343 F20101208_AAAVDN li_y_Page_052.pro
7443c7b18ef0e99d0c1a83be102cc002
0780f211271229efadc72851059fc9a521ba32d8
65910 F20101208_AAAVCZ li_y_Page_010.pro
5f5dedfe6557fadbac35cb60baaf7fc7
232db3bbf7aa4e3e258af3c945e2cb71a6363cce
98205 F20101208_AAAUYH li_y_Page_091.jp2
1b3791f3e82c179ec1613cf842655fd6
644f1fe48a4c303aa137c45d7e53eed1e430d3ff
83208 F20101208_AAAUXS li_y_Page_058.jp2
2e9b2bca14805f6457b8d9c7ffbe1667
8ab7e4d207d13f5a5d97a8d9e53a54a309806cf1
24685 F20101208_AAATVF li_y_Page_070.QC.jpg
84393384a7667d5fcbe791c69d92dd3a
8e58876ff097e18d37ea814e87705a35955c4305
721 F20101208_AAATUQ li_y_Page_081.txt
940749a22b0f454940bcaa27f8938fe3
3b7839c6a58cb3d38188a4c30601586931533339
115435 F20101208_AAAUAL li_y_Page_042.jp2
dfc4c3b7061029aa6661d3d26ee892b1
a3583e460271a6ac8de4a2789ab68f1bba20fceb
31420 F20101208_AAAVEC li_y_Page_102.pro
db03861eecab3d97a5a0c759d1b0c635
75a7173204593d07c7e9dc964199458dda958cbd
40220 F20101208_AAAVDO li_y_Page_057.pro
dab1e42c5b645af2d2ead5c5c18fa59e
028015e20fc02eedaaa07105ba1f37a26a8cb7fd
109032 F20101208_AAAUYI li_y_Page_092.jp2
1708b2caf1e1d470cbca99b19ceeca1b
b21376e6f7391f931739024fea951e62325cb436
96912 F20101208_AAAUXT li_y_Page_059.jp2
6b331779bdc53be46a3bb77c724750f0
56d5e1ca2251eff7562d464f5fc311af5ba0cbea
114864 F20101208_AAATVG li_y_Page_039.jp2
cd6e0295702143819732a130a38a6885
56711895343671631034037d17d12b3a3039bb40
F20101208_AAATUR li_y_Page_155.tif
d31731d4cc1f6b11cc45116e934c68bb
4de624b90e824c7c78ce56d5ba16d4c38404b257
47201 F20101208_AAAUBA li_y_Page_076.pro
f77391119fd1744fc418d069d5fcd61c
7624a7304bd0a334f65a996528ef60fa5afce1ec
7070 F20101208_AAAUAM li_y_Page_111.QC.jpg
a57df4ef3141fe265ba1b88ff27940c7
1cd53b91e486115dd545acc024a897890f5d620b
24773 F20101208_AAAVED li_y_Page_103.pro
9bcf4067d136085952bd7f0917e890fb
3cfe248bd9d04714c304b5e4c895da782539fb45
37820 F20101208_AAAVDP li_y_Page_060.pro
b9271207bddd81f8ad4ed83d23173333
96caf356b2e50ad7301530759302d53521ef6529
109010 F20101208_AAAUYJ li_y_Page_095.jp2
ec51cde1c5bef0361a273d7ad0bd5ac2
e31b5a2e06a0bfd957b62949ca18f5369f3d2d0d
92581 F20101208_AAAUXU li_y_Page_064.jp2
7acea0fed8018657f081c521cedff63c
80dac04113e577f9e72fb3813d3aa1865b7d198b
6511 F20101208_AAATVH li_y_Page_101.QC.jpg
4ffaef4c020b403defdf71c58511d812
a3a740afaf013dd7ee97b24e8555e2152fb70a18
16408 F20101208_AAATUS li_y_Page_049.QC.jpg
5731beacb499a4bac7333535c11eb09e
21dd322f349f80d84494d3e6ce92919a768e6f9b
5320 F20101208_AAAUBB li_y_Page_081thm.jpg
207fc5597ba96ddbace9e5ceaa90f8f1
3d50e1e3bea83ced2390c026195fd21783969ec6
58039 F20101208_AAAUAN li_y_Page_176.pro
7839f33b613a530b996e71dc6e94872c
3d5433499fa3222f91d68d04ff47dd892808518c
54866 F20101208_AAAVEE li_y_Page_105.pro
93db682d8855083eb1d63ac421337fda
2b9c127e739426a96d5ab3942b2e6a1c9119920c
40720 F20101208_AAAVDQ li_y_Page_062.pro
6bec3912aaea52028db253a1cd14a864
800d1e280ccc11b108eedf5122ba271872036da0
91438 F20101208_AAAUYK li_y_Page_096.jp2
36589df4782598f4eb0cf533c3b90750
9c805102669d162edcbe57862d6582e065a970df
113093 F20101208_AAAUXV li_y_Page_066.jp2
9734977185a828285bbd50eeb524fe9e
0cf08afb4d88d84f73faac6666accafce733defa
454712 F20101208_AAATVI li_y_Page_089.jp2
55f05bca6d26c0f9bbba78c78cb55c30
1ceac3a03fbeb6fbae152e5bc0e0e79d066f3a07
628 F20101208_AAATUT li_y_Page_048.txt
7eab91c463f4dddeb5eec9954da01e8a
61884e91b0f8100d8a8f37ca54f08e8ac5bfd3a1
23279 F20101208_AAAUBC li_y_Page_102.QC.jpg
bb030894e6af6087c4bfec7b97fcf358
60168b59e46c9ee65aded70fc04e236a5edd5b33
10579 F20101208_AAAUAO li_y_Page_127.QC.jpg
70ef2265ad2c9c04f5f2b17c58c4cdb6
29da62044c5f6a3376f0c2fe2f731cca2860b57e
53963 F20101208_AAAVEF li_y_Page_106.pro
6b8a4dc40561dc892fc10ebe46238e4d
061c65d7635e65c6c7a896258edd1101e0ee40a6
38217 F20101208_AAAVDR li_y_Page_063.pro
2f820a5cf2fea18b21c3b081464308cd
a728669b78b90494e77b6893e3ed183ec63ff8cd
99795 F20101208_AAAUYL li_y_Page_097.jp2
4a4cb5ee36ee407c776f84c2d109b7c1
7e00502c795585e0bd3718e60650bb9ee21741f4
95718 F20101208_AAAUXW li_y_Page_067.jp2
7fe87b43957a351ab5ff75a27c612f71
07459f997d796523df1f8e0afd92205f5d4d5c48
F20101208_AAATVJ li_y_Page_102.tif
e23898b6940e5d3b306325cb4148ac9d
4a698bd4300c4449b4db4a12b92d6d44dc65e5b6
35628 F20101208_AAATUU li_y_Page_017.QC.jpg
edff9027bee02e73bdec37ac45a37857
e7623b19155f3fa34c5312a22c237b278a6dce79
F20101208_AAAUBD li_y_Page_063.tif
6e98f3bb2c9ab38ebc704aa76e9d0fce
dbbffa94a83a4a8688bf3ef2f7cb5c77443eb70f
91018 F20101208_AAAUAP li_y_Page_032.jpg
e16391bce2957d4b5098a261005ad90c
6b7498a0fe40305dada2300f84eba652380d8433
54974 F20101208_AAAVEG li_y_Page_109.pro
8c21d9ad8ea5a66293628669c1c492ba
526ff9eca2ba1f2673825b4027a4b7735fc58243
52977 F20101208_AAAVDS li_y_Page_066.pro
d205fced82ccc18d52748ac6fc85f307
16ed8d0f771f3e25fa3ebaa7eb8adb95f7ea98da
57419 F20101208_AAAUZA li_y_Page_148.jp2
d00fb3f04f78aab34615f4e2c6ea4e24
d5b853bfc482144b0a86aab5c3509abcdccf4d40
93527 F20101208_AAAUYM li_y_Page_100.jp2
db53d99e48ccae3fb1643a295f8599b1
ab685e7ad0a5f17aa350d3994980613802fbfcde
82027 F20101208_AAAUXX li_y_Page_070.jp2
5f018b7a8106fd839918c4f5cd397db0
5f0eb5bbfe28a70fe75f47ee3fabb6a9d7c522dc
41381 F20101208_AAATVK li_y_Page_069.pro
87a92d28414573e29c5dc85174c1d8db
13541ad9724290e1b1009d816449c8ef2b849b2f
137056 F20101208_AAATUV li_y_Page_012.jpg
02d76ff8373b9ca3cb29ba6d761a2cba
d542a4dfd7a8191acee9b66859f704cc3d5a8369
19519 F20101208_AAAUBE li_y_Page_146.QC.jpg
3064ebeb68fcae33f6464363f432e3ad
43c48b6ac7c3b9eb09cdc1a695ac22e3d57d0c9b
667 F20101208_AAAUAQ li_y_Page_050.txt
725512be364821d70f7fa0c1e7ccf4fa
2ba5d26b381833aa0426b809e0526bda8f2916ff
8515 F20101208_AAAVEH li_y_Page_111.pro
f03afbe5033ae9796a485c69276ed309
75ea6bba57c4d6ea1360e509392c176d12070de9
34447 F20101208_AAAVDT li_y_Page_068.pro
76ed1b4cb5d4e125ef37f7aa7f91d689
4e97ad8823c6ca1c96e65520a4b19a4b78c37d67
84354 F20101208_AAAUZB li_y_Page_151.jp2
dfd1af8b75772b5e81e4e2b9c0e9a67d
7f114da0055685c7a060f0a351188202bc957534
115048 F20101208_AAAUYN li_y_Page_106.jp2
1acd9d7c7d2e10224ce547c4d4279a1d
42ba844c710424ae00d6428afb0110e2f79f9c3f
81680 F20101208_AAAUXY li_y_Page_071.jp2
b781d64b121cf9bcf80f79c876a198d6
d79e63f068a88303791c21d03f11d016ab1391fd
F20101208_AAATVL li_y_Page_139.tif
fe1cda9f441ef599f0ecdb6f99b2835d
5ee6b9f7566bbdc5abd58296b6f2b18b9beb0e26
99373 F20101208_AAATUW li_y_Page_093.jp2
033cd82afbde428c12de4e0ce53394e8
e55942624524630db6eb4efa368b454d87d5d8c2
571 F20101208_AAAUBF li_y_Page_027.txt
5b46563f4899a9a450b30a77caf44160
5bc8949121869966ea06d786aaf4a569a4e9b72f
617 F20101208_AAAUAR li_y_Page_003thm.jpg
b9586eb4ec59a7633477652c2bbbefb4
eafce688bd832f45588c941243fb6133065a3cc3
32781 F20101208_AAAVEI li_y_Page_112.pro
639d7479738fc88430d9a8035a69f2d7
3d5d0f8459fb18f4db450b39ee1076070f0f9556
37547 F20101208_AAAVDU li_y_Page_070.pro
7e89cc5cf6594056f68db3c4a874732b
50f01a76a69260c18acac95c4d0ec80bcd75558f
64595 F20101208_AAAUZC li_y_Page_152.jp2
e73a6026102e1f59970bc3b9dfc1dca6
e63148c2258c482d7242e9601cb880784ab7e64c
116303 F20101208_AAAUYO li_y_Page_109.jp2
ad390db4f9ae3513821e0184b1acf77a
01a5c9222c3b28700c57abb048588f97dcb786bd
79268 F20101208_AAAUXZ li_y_Page_072.jp2
d50e91df52bf7fbbc011a7399f3e64f2
9870265bb102ddbb4bc8e77ed02bb070c3182a34
F20101208_AAATUX li_y_Page_104.tif
606f40612a2ab770d4594312ee3d2516
4a25692419560b5f232e10050444a96a2e6be08c
47721 F20101208_AAAUBG li_y_Page_098.pro
cbeaa6214438d476bb41f5218307b409
d04a41e55ab1c51d530f4cef6c0d1358c7e35794
43791 F20101208_AAATWA li_y_Page_065.pro
3b14f60b7cbdb2c1f21a4816a54b2c48
0afff8f0c88dd06bf49ad192903986fdc8597923
F20101208_AAAUAS li_y_Page_067.txt
fb6ba35e1f5f13a1c127eb4bb54cb499
63023440ed4eb93aec0dbe4cb00984a42b974294
101306 F20101208_AAATVM li_y_Page_076.jp2
97dab2366c8c25616921a34b77c10ef3
fc0d0240067579d4a0940ce3fd3687f67f87c2a1
5230 F20101208_AAAVEJ li_y_Page_113.pro
63ceb8ced3184cb11363d6999c5abccb
729ba5cda274665f47214e472fc41fb2a55246fe
38196 F20101208_AAAVDV li_y_Page_075.pro
a6a2d418977b11a69e5bf6abce2ae848
497b3480b1d6563c74c19983a91915f1ba9a848a
71816 F20101208_AAAUZD li_y_Page_154.jp2
98e8366cf6480a27c9abb4f56f5ea8c3
db2ead5fe25b4308705b40f2e1acb7110b89ca53
732676 F20101208_AAAUYP li_y_Page_114.jp2
a75c4d68a0068575185d69d44dcee975
83adac71961af4bdf2535c6612a9d02499514bf2
16099 F20101208_AAATUY li_y_Page_085.QC.jpg
a46fea18e3ebe8b55436920dcdef1f8c
cf4831fd864e03ecfd5246b0e21a5d1b3bdae0b7
7437 F20101208_AAAUBH li_y_Page_054thm.jpg
2629669ff7a77358e15a09806573b7ef
79d0ecdc39ee93140e40d7aa6281a90c257763d6
76915 F20101208_AAATWB li_y_Page_168.jp2
464a5d2f26b9e7a22cc163aead526041
d36e88acc3e197a318c72b479f7e087cc986a2fd
63163 F20101208_AAAUAT li_y_Page_147.jpg
0777a2cbcbd91396d4464a6ebf05bc0f
914a8eed8ca716285fce3bd8a0324d6999f2dd70
8874 F20101208_AAATVN li_y_Page_038thm.jpg
ca747d61f04a998fbb5ea745056b1d13
3268e5b80292c9a4ec4613a84d240f7ed7c77335
5912 F20101208_AAAVEK li_y_Page_114.pro
08e4a6232f245fe3511dfbdb4aa53f67
fa1486398347c3f590d7a7a9bed1e15ca3345979
56333 F20101208_AAAVDW li_y_Page_077.pro
77ad23ed1fc61d90062e481716389445
3a40caa9596a1f1ddd25d6e6f2cda8e3d2948157
65173 F20101208_AAAUZE li_y_Page_157.jp2
bba9c85d2abb3b5db50cf558a2ec34fb
8c4d1b167ee143eba6bdcabcf4a6915bdc661bbc
98713 F20101208_AAAUYQ li_y_Page_119.jp2
31e5539e79fcc633d919c293b30aec49
540b29d070b033cba498f940c9eca5e5734eb38e
109590 F20101208_AAATUZ li_y_Page_109.jpg
8917d6c0298abe7d383aa36e164d91ad
6e8df15254151dc8a175703cf0acf1e2fe5a8298
57777 F20101208_AAAUBI li_y_Page_103.jp2
3ea224ab8d546c1b8064d4b4ac4410bb
6084da207f266d03349522ca129436d9a61c7681
1863 F20101208_AAATWC li_y_Page_120.txt
6473ae14898103aaed05f78ab8dd0f85
c8c04f961b29589ed58dd9d53bcb7ceefdd33528
7265 F20101208_AAAUAU li_y_Page_080.QC.jpg
1110f322bdd3166aeef3d8911d51eb40
d4cf43964cd7684406cefc9f1136636d7b7583c6
58010 F20101208_AAATVO li_y_Page_150.jp2
750081b6bb4ca65a2e1435db0434182e
0375ad471f812f871411476661fe09c3bb80767d
8355 F20101208_AAAVEL li_y_Page_117.pro
f74d0773287f8ec697bcca5ca2a7cb49
7f4b8f2e08f0e967f7d9611ec869f47b21146476
11985 F20101208_AAAVDX li_y_Page_082.pro
613e5a41408fd51f99c0055ce1d71f06
a515d44bee00ea6edfe3b8bea2302a1fbdd64cea
57249 F20101208_AAAUZF li_y_Page_160.jp2
f90328a74ec90d9b5b86476df5e38d38
2daac8531fc29d0322ed0218ac7303b069852bda
95291 F20101208_AAAUBJ li_y_Page_014.jpg
790ab0668192e0f376aa9ad6fe9c18e1
69b42f865c8c3b2c6f4c7a1c5657fa96b4b07502
32616 F20101208_AAATWD li_y_Page_122.QC.jpg
a770d4121d319a895f9f07598421cbe2
521a3ff034a237d1a91ba91b61e1cfc73563a1dd
20824 F20101208_AAAUAV li_y_Page_133.QC.jpg
8b5792fc3b81b740e6e69c188702782d
8fb425ef173a47e5baa0e8ec147607283a776851
28960 F20101208_AAAVFA li_y_Page_147.pro
04c4a129017c3c5a53846175e8f8f96a
fb302163acf5ce010fd273fa99d011f3ce3c6592
51445 F20101208_AAAVEM li_y_Page_118.pro
90da320bae4119133b8c10476e44c99b
a2e75f110f65e204fbbdf1e77d7f499537ce3cd3
52381 F20101208_AAAVDY li_y_Page_095.pro
70204282a31e005da30bee70ff1e2356
e822bc8c859359ed53f250599e92b4b327a3f0ef
84094 F20101208_AAAUZG li_y_Page_161.jp2
313ae7dfda565b5e79668fc4e72a8f63
ed679a77b734fa441544ae4f8d32b4980bd6aadb
98843 F20101208_AAAUYR li_y_Page_120.jp2
f1f6d4dca03948308a3f7dd7f3a532c1
f8e9a1f6c7244e7bc2387c938d86a9f05e1b0035
20581 F20101208_AAAUBK li_y_Page_157.QC.jpg
f2c2ef1ede87bdfd8827a2aad06f74dd
eb1f1e488fa8bd77c447caff7eb0e0cf8a05be26
17366 F20101208_AAATWE li_y_Page_089.QC.jpg
07b1489019daa74ef846fae88fcc2b61
270c710c86e6b87b4424ae53dd12de0ecf102a47
1979 F20101208_AAAUAW li_y_Page_061.txt
ff3a15688e4ffc7e428a9abe3c219a36
fccb779d03182cb970358932a67f4115525fe3cf
60962 F20101208_AAATVP li_y_Page_134.jpg
44f43192986ddee229606e187e834698
6d9ef9d0dc41d5de846b86bf0da738acc6d9cafb
37995 F20101208_AAAVFB li_y_Page_151.pro
c66fda7477e0e16b17101df88714f247
5faf6e8d9bef8fef21c59e7c1a2b092209cef0d2
50648 F20101208_AAAVEN li_y_Page_122.pro
a1fcc7745d52b6f48b4952a8cd7d29d0
06859b353c503c2424abb3531f622bd627bf3881
46234 F20101208_AAAVDZ li_y_Page_097.pro
d2c328feac5f0a0f9456eab4550fbed3
617133197c72b7973d8d6493439997566e3e1fd5
73822 F20101208_AAAUZH li_y_Page_162.jp2
9a07afc3965b1ec63b08f11ce8fa47fb
879764dba18835507582e4e58f10854447c8c918
114415 F20101208_AAAUYS li_y_Page_121.jp2
8f9d3fc6400fa14ae48b5a7f78a91db0
45a91124d97654fc00892731ba004dec60c1a028
6385 F20101208_AAAUBL li_y_Page_090.pro
f252fa26bc59e0d9547d763023291793
d622a2992d04f780ef933e4b1b4440ab27a2d118
37322 F20101208_AAATWF li_y_Page_140.pro
a606d71bdedf0b10957b2f8b96d74946
a321aa97aff4c34979edf55a25c25d4b659989de
69087 F20101208_AAAUAX li_y_Page_102.jpg
a94ce5dd7eee3359c132e0571d677ef1
ec3300d7ba779a28673e79c95300588148c8304f
25249 F20101208_AAATVQ li_y_Page_005.QC.jpg
b9a60ba0320ab2626972e47a42908bb4
ef22e8b88b87d13e4e1cec3faeb7af981c72c0ce
11051 F20101208_AAAVFC li_y_Page_156.pro
3edb0d7112f755f983bb283aa999c15a
1dd92314c9069d04ab63e288d398cd7c91e4280f
52271 F20101208_AAAVEO li_y_Page_123.pro
54c411a31da871b290edbd72d6ee15fd
d90f53914b05609e67b72b244b2ca36161b78d3f
75516 F20101208_AAAUZI li_y_Page_163.jp2
cccfbaa91eac044ea6960b5d0c475e15
db965e1ba0371b9f405f8f1e3fff6d07506e52c9
732297 F20101208_AAAUYT li_y_Page_133.jp2
ff3d99cb0434229275dfec090bf076a5
10ae0ddcbafa4fa39e5f8d6821c0b26fce8d1608
63896 F20101208_AAAUCA li_y_Page_018.jpg
436b29b8c0d65fd65e872ab212b32e52
053b3538aaf0fafd3aacca604d1e942982468973
21758 F20101208_AAAUBM li_y_Page_163.QC.jpg
5985f5e0f74e71ce54fd9cbb95abce43
59329368c912184129d90a19c61b2c4c9b52b9fe
20000 F20101208_AAATWG li_y_Page_101.jp2
5a651754c0d995c73b29ce72d8939e58
3e1a571ee7910fa5a05c696d2b7141cdac6e26f6
5139 F20101208_AAAUAY li_y_Page_172.pro
06195d1ecd4189072ae32ba0fd8bbcbe
eec1a3bc1ac1cc8b1b8c5ccf66ba7b39025816f9
26197 F20101208_AAATVR li_y_Page_006.QC.jpg
a3dfe54c2cd07ccc7aa0f54c6df3b5fa
264e64285a55a3a005c7a087128c297456cec799
24690 F20101208_AAAVFD li_y_Page_160.pro
82aae905f5474db82eb60ab7bd0b0f1b
a4faeb473b1f9550f00e992d13187da61b9991b0
52298 F20101208_AAAVEP li_y_Page_125.pro
a86a79ede170dbb967314ef1c90eb396
02d09f0ff7a161d86e391e281fd917b32321565d
62982 F20101208_AAAUZJ li_y_Page_169.jp2
6f8178e0a77735192ad8a7322d4b0e07
e1ee8a03ac5bf157964cc86f4c2d92c2ed88ba56
624338 F20101208_AAAUYU li_y_Page_134.jp2
f82d230f0c8451e1fdb32dc55138121d
eb9edce2751bc1e08fca8f4e5dd37da29b881940
29356 F20101208_AAAUCB li_y_Page_053.QC.jpg
391f82ab21a8867ffc488fb5de4fd787
2034c2ea31b6e44032eec9af5a108fe2dd1de93c
6456 F20101208_AAAUBN li_y_Page_006thm.jpg
946215c986547271665ff82ede939b9b
67fed8ac06d8a2f9d890effc4d4d65d9545e6729
1428 F20101208_AAATWH li_y_Page_003.QC.jpg
4778e52b104f2e2761f2c5dfe353bb7d
b3c1fc00f21276e8c4449d719f15aeaba6230ab4
49753 F20101208_AAATVS li_y_Page_141.pro
1154ce5c4be4ffa5986d40e06aeddffc
449cc2cfa8c6adc67532a4091ace04a9470ce616
33330 F20101208_AAAVFE li_y_Page_162.pro
e1e770e85a4747e96af25a030a6de884
1cdf7d536ffc977c3c571b2e8d0be6061630c3e5
14082 F20101208_AAAVEQ li_y_Page_127.pro
667cca03eb2e25f80fccbba696981ed1
63cf6fe622dfd4b72b20db45036be1d0c8085c8d
435226 F20101208_AAAUZK li_y_Page_170.jp2
1ae2185068ed62e35572d984166970fc
613b24086bc4afdf86d50ca4fe7c2fdeef699cb4
236647 F20101208_AAAUYV li_y_Page_135.jp2
cc43b27d459073d36ff6c13659c9bff3
6edc7dd8e04fdfbbd1b8013bfcc84158c283aedb
14524 F20101208_AAAUCC li_y_Page_084.QC.jpg
ca09255aa4c24a7e12ffcab6363f3279
3e903f1b092007154762208a630db319fb10b589
1320 F20101208_AAAUBO li_y_Page_164.txt
3a77efe538fe2f471b39df9bec0a52aa
3095051017076c485d45d9bd121a5277e8dedba9
2281 F20101208_AAATWI li_y_Page_178.txt
b98a26f2c402629ae6b82be93184bffc
ae8c4195735eb8890b98d5f12be8709cf29c83e5
80168 F20101208_AAAUAZ li_y_Page_063.jpg
1538fc79daa8e246d054cc84e5517713
1bde28545be3be4849cc8e68b154c2d69b55b29b
1202 F20101208_AAATVT li_y_Page_160.txt
ce9425894dc0db07454dc843cc0281dc
b758b06b2c7919c1e87e68d84345bbb323371026
26833 F20101208_AAAVFF li_y_Page_165.pro
96c1b629be98eedb2b2c97c8f65402d1
f1dd1b38ac382dceab56002fb3d124af4f841644
17637 F20101208_AAAVER li_y_Page_128.pro
ef3c5923d060ab9c61e68569c0ad9d46
8d21e5988b2131b11932ac05a888e0329da4a1bf
290199 F20101208_AAAUZL li_y_Page_171.jp2
606565b7d652f0af418e2f612f537aa4
ab6b4de49b5cc9c370e2c5695615a88b2a48b044
84957 F20101208_AAAUYW li_y_Page_140.jp2
1024fea260d07c2a1265ae0ec2e5ee78
cc8ff74b0c29a2efb53e8ec56662fde4c0a24609
91226 F20101208_AAAUCD li_y_Page_062.jp2
f532ee6382ae19aea8e8b9843abe8284
e5db810831d366f747b13052f083a0718ba0c8d3
37928 F20101208_AAAUBP li_y_Page_010.QC.jpg
98cd96e40b42b06bb331bf093be1fcd1
76746e79e7be080dbae598e5ce3bbfc1ae54e9dd
106718 F20101208_AAATWJ li_y_Page_074.jpg
157160305bc0fbc217e3161508439e12
120520872a147cd4523496f2d5d7b59fcaee521c
109883 F20101208_AAATVU li_y_Page_042.jpg
f73a8935f3a2c5240166e00798cbc314
837f42e336cc1f43fdab6bfe30fb529ad2bd67a9
38060 F20101208_AAAVFG li_y_Page_166.pro
2f0ad36a9f5058cd16f98d16f5df6294
84832074b3fdbbe280d833159d494a9f30d3ec64
8898 F20101208_AAAVES li_y_Page_129.pro
09fda305a05977a711d74dec9ab78b0d
abdd3bf1b7d982119f82eefc21711ea764dffe2f
267790 F20101208_AAAUZM li_y_Page_172.jp2
8d5eb0103e4c5dd7bb88311b5b62194a
9082ce35b12011e5eba67e6905b89d4daf995444
106448 F20101208_AAAUYX li_y_Page_141.jp2
199455d946171e65cc813dbb239cd7dc
cd3b5fe62138028c71a6f13d12dfd78df63cbc59
379783 F20101208_AAAUCE li_y_Page_028.jp2
c10d9b03034ca911a5ae7e5917c0804f
bc26a5bcb930e36ed26ddc0e6373b2a0f4b0f010
19212 F20101208_AAAUBQ li_y_Page_169.QC.jpg
e2829549dbba78c9af64d41438d5b82a
63ab31a4aa37264fa4b634c6144c717bd433fbab
1375 F20101208_AAATWK li_y_Page_102.txt
a0656df89a62a8f593cbce1a11163051
1469513db8f8b40cf6fd69afce8132082bd18008
1927 F20101208_AAATVV li_y_Page_097.txt
3b88397593bac539370c7963b87f8dd4
ea0950f7590752e697af14a84f3c6883c8d8638d
44716 F20101208_AAAVFH li_y_Page_167.pro
290806a2ab7d14c342cdd58f3e600b5a
b3bc280a91ccb4f205ddd9ad8a1156c865e93fe7
10627 F20101208_AAAVET li_y_Page_130.pro
8d40fbf3da6b650895efb571853bff85
cd7c9d81add34f8be7e025dc98e6376a9e185e37
140996 F20101208_AAAUZN li_y_Page_174.jp2
e8c63bb1270caf210cade977804cfab6
1a74d5c86b752fb6a94313051b30b120eb94d9fc
383958 F20101208_AAAUYY li_y_Page_144.jp2
8162ff19000f5f83aa1b109f81b8b233
2d99c4a40197963a0eebb7a572fa4b99d1e20900
5032 F20101208_AAAUCF li_y_Page_003.jpg
de86f67d77361ce2ced25e30555a70f2
3b787a0ab40d93f6efc6dba4bc4a16ee6a1ca9fc
106772 F20101208_AAAUBR li_y_Page_124.jp2
7554549faf393713c11adef3bea5a1ea
5fce948cc0ef62a92dec5297afbaeb9f290e1f03
27415 F20101208_AAATWL li_y_Page_033.QC.jpg
39a8f7f60df18a0a3571e7e8ee646a41
0e976027560d0747a80893b1511bfe15678f1ccd
7626 F20101208_AAATVW li_y_Page_075thm.jpg
73953042d19ccc7254d74be4d191a0d9
215dde3f4795b4186f1d16816b25f3d177192c86
10353 F20101208_AAAVFI li_y_Page_170.pro
7c7757576328c9af91254a6cc3e6dcde
9662cb0f3f3c4620a13fc49cfe46530c81403e89
12421 F20101208_AAAVEU li_y_Page_131.pro
8d92b4cc44e4cf7981fa0f23384ea615
2ae6df137d88a461a6d2927782c3b6cb5f7a96e8
133266 F20101208_AAAUZO li_y_Page_175.jp2
c64cd328b46ffcaa7be4fcb1af78d3ec
c2ca7b04c555347fda7e5bca18346308f46bbf9b
66439 F20101208_AAAUYZ li_y_Page_147.jp2
87c7d52f5bce0c173136ab6f5ca32237
696160225306e487abd6d604b7f8de031904af10
2411 F20101208_AAAUCG li_y_Page_177.txt
fead87de358138faf921ff9fc5273bec
7a8c4ff8cbb9fe61d4154ee312a4730f9193880d
4919 F20101208_AAATXA li_y_Page_136.pro
93fc0331b24c1034c71cd9af82162c98
9a78bdcd8d61c60f6a96376c6c738c8bcb453535
24118 F20101208_AAAUBS li_y_Page_129.jp2
a1090a1cb0a53ab98567862edd399185
5f0544d205f4870dd539624e112dfb045e2cd299
24274 F20101208_AAATWM li_y_Page_071.QC.jpg
83d3a0947f4fafc12a3d316fb3fbad91
567139ae837f5519400f103ef511c59b6fa47348
2158 F20101208_AAATVX li_y_Page_024.txt
f7c4744ad1ed3a6c23f3ab290daf1cdd
f1f1764b45145f58040380cb1f920d2b1ef94326
56733 F20101208_AAAVFJ li_y_Page_178.pro
f08f456df71674bf41463400e2d970f0
834b89ae02f1244f88c29146294e144f6b353d7c
14099 F20101208_AAAVEV li_y_Page_134.pro
3661e17bbf06ba75c1eb0cece3c6fdb3
7c2c520df03d94b85a1471993193f9a0bce54acc
1051923 F20101208_AAAUZP li_y_Page_177.jp2
fcab9d266688f664e529b35ceb7cbfda
d48876418dec81f203547c707652e7eaf7649bb4
44806 F20101208_AAAUCH li_y_Page_091.pro
6fc250a71f0616b5ad03975bc0257333
827caa43bea20298c35f75d8bb2880bceef7f808
1134 F20101208_AAATXB li_y_Page_165.txt
a27c2f061b3cf3cde971389fb082da62
318a0728b211afac8e3f359ff258538c22858b89
F20101208_AAAUBT li_y_Page_099.tif
bf4d836f02d4426691a152127a0377f6
1bd8bab509221adfd1627b6ae7e19dd35923a702
25197 F20101208_AAATWN li_y_Page_037.QC.jpg
e1c589a4d0498542916f44a714f5e242
fb5ab1a9d55d43196c7b26b4fa1d28f61147a060
104861 F20101208_AAATVY li_y_Page_038.jpg
9d4bbf6421a65d255cf7bbff3d321be0
f6c20513217f7ce4beeb4077f4521e9e066058f2
28061 F20101208_AAAVFK li_y_Page_179.pro
756bcf98ce2afc576582796000c91527
8d93451a5f7049583b134d719355cb1d7bc43f82
5256 F20101208_AAAVEW li_y_Page_135.pro
4579c7266a9130bb776423b69e30a459
4601abd47bdeae675d57b3696cd96c1c0d8f5803
681789 F20101208_AAAUZQ li_y_Page_179.jp2
3ea3125fc3d4a0337367380f0d71573f
f6790dbe10e202f971884fdabe3b6743947a5e86
101444 F20101208_AAAUCI li_y_Page_141.jpg
83ae6dd3ded25a5c7bd6a538f9c0b132
c475a9571263262f23fa03d5e042023a8b35ee0d
451 F20101208_AAATXC li_y_Page_104.txt
4358c6d3868e2d93fbe1b81ad6e4b14b
fc0987c8f24db3ef3e77e6f82e5ef28c6663fa21
92291 F20101208_AAAUBU li_y_Page_056.jp2
bd688d96ad688a38e8d276e67807c1de
e8eebe478805812e06acaf35487cf611d65fb43e
54404 F20101208_AAATWO li_y_Page_043.pro
5b5cfb132a6fffea189be7a526760e90
fbc04f9c01f3c923245422fe5adc8a17c2d72d7e
4201 F20101208_AAATVZ li_y_Page_115thm.jpg
066e9283bdb15d5764c7b2284fd9696a
1bab6823f4b4eaaef86b7862781afed39081dbc0
487 F20101208_AAAVFL li_y_Page_001.txt
7878300b3a8f877ae368e729d2f36e74
53c1f2b960260c9afef75eb83722c40ec385b2aa
50459 F20101208_AAAVEX li_y_Page_137.pro
b879ab3a2ab7cafd9aeeea2de0c78d35
ba51911c2450842d6e0a679391ed0514b2cd65bd
45202 F20101208_AAAUZR li_y_Page_180.jp2
4b8353bfb82a768247aca1d5eca9d99e
ba683155a97f6e896d7fc96ce7bae1675f9b4578
120257 F20101208_AAATXD li_y_Page_006.jpg
52e3ec8e3a6f29ac26241cac5f427734
2edc4fa2e449c2d527f73b1ea25f59dbf62f93df
8202 F20101208_AAAUBV li_y_Page_022thm.jpg
ca0e7a404037605687a835f84585b49a
2ad6a98d3a617af11bfcedd002c8784eb330670d
53010 F20101208_AAATWP li_y_Page_024.pro
36b6e16dabd5b4cf43464b053e99c49a
555799e00509cb9248b38f7d6623e59ea4cf2472
3591 F20101208_AAAUCJ li_y_Page_007.txt
ff248b048b0873a17b117948937c1a36
be4d2c0f1ca8f03c952f757bb15ffff78395d08c
1985 F20101208_AAAVGA li_y_Page_031.txt
06df046305d48cf47c7d59042f66041b
317e630b04cea2f3681c4ae170a75002f3933ddd
86 F20101208_AAAVFM li_y_Page_002.txt
7ca1e3e8529f5a6981a7a84a0c3b5544
198c74fdfe3ed85ab4d2c20128a0961a25aafdf6
49868 F20101208_AAAVEY li_y_Page_139.pro
cd776664c75c97acd3ed2c8c6302c132
2b01581781e4001860aef7e3657ea4e3028e6560
9390 F20101208_AAATXE li_y_Page_174thm.jpg
27ef67481507d1986942578e43f814c7
27a0760ab3f1c5dcc9f13a3a5850ef482559b05c
6578 F20101208_AAAUBW li_y_Page_068thm.jpg
7bcf0cc09d5c245caa115de069edbbc8
06dd0a507f38b369bd1a8d8040783eaa1683f590
103872 F20101208_AAAUCK li_y_Page_030.jpg
8bfe47a3f0a0260f3f0f3db94e074694
88b6c084598ef4cc261fe0840cc40b160990dbb2
1840 F20101208_AAAVGB li_y_Page_033.txt
4fede4431cfc5cc231429f6863267cc8
9d83f9863aa095259347a15129a02248b64a721e
106 F20101208_AAAVFN li_y_Page_003.txt
4400e438128beb04ca54218fb0a98ba1
fde1e20fb0dc2714e4d8ed35185304c1962e59a9
34611 F20101208_AAAVEZ li_y_Page_145.pro
bd0ea6dc97dc802af5e40804c47026c4
975e9dc5dbe2f847b56dc354d33c3c0d6450ad8f
F20101208_AAAUZS li_y_Page_002.tif
7cb7f5e7a1c553a1a2a683ad84b002ec
de4d54bc03fe74db9d8e1a361a7add92e6f4af1d
17419 F20101208_AAATXF li_y_Page_047.QC.jpg
d6c5cd76bb65344936d911bfbc7475e5
b3e8976a4ef5f6fdba8f4a9c0a8883fc87664770
67256 F20101208_AAAUBX li_y_Page_164.jp2
0f5863f8ce8094add297ac0860135f6f
473a0e0dd8327cbd928d854341805b590292d3c7
7342 F20101208_AAATWQ li_y_Page_057thm.jpg
fd58f77399e39a27e7dfad3ceab73820
2d1be8ed03d98e4d07b7249c78b41d9ad94ac492
78487 F20101208_AAAUCL li_y_Page_151.jpg
ea96b1e2db5417cbde2d1a133832fc72
4984900861a6788f313cdd96a28ef486083fb91b
1629 F20101208_AAAVGC li_y_Page_034.txt
0223c1aedc1d32741b45d7b284a2eaeb
58152ad91cf5bdeea66ab0fffd3930df6491a803
1968 F20101208_AAAVFO li_y_Page_004.txt
95ef4f8ae40e2b7dc8ecafbbbdf8d06a
338dc447bb8b3c1e2ca15b571748996421a3f66e
F20101208_AAAUZT li_y_Page_003.tif
48506e4470b538c9369a18a93ecca8d4
b41e3bb384c0ad5b9a7e659aa1574aa6a9514dfc
23859 F20101208_AAATXG li_y_Page_068.QC.jpg
8b6597959048db2f309462197d22840d
3c661268220aca3aa67ded18240b59f6f02218e5
105820 F20101208_AAAUBY li_y_Page_061.jp2
26181b698d33bd27f537e941569069c2
0bc6019ba2ad5f6fe06587373fbef3acc25a98d2
27376 F20101208_AAATWR li_y_Page_055.QC.jpg
d0501556e9cf91f9ff1e6d82a46b8150
cafbbc20cb3648a94897edcaeabc4598d4092821
52848 F20101208_AAAUDA li_y_Page_074.pro
565ad84d73bea5d5ded4575260728939
4938befea39614af88c53cf4e8c402d923237ec7
36582 F20101208_AAAUCM li_y_Page_153.pro
f60ff1cc86cd0fc886f678a1c20d6028
622a5f57720ad427abc2a24843aa17ea97cb01af
1822 F20101208_AAAVGD li_y_Page_035.txt
961668b228c1ae4a33d28820b4a58eb2
b09e11e0b4fa8b8cdce6d4bdbfcba6bb3da0fd8c
1432 F20101208_AAAVFP li_y_Page_005.txt
a85182480533b9092bf1b1e6958c8398
a1b62f165ee8e3975be4e1954797a1d93ab43cfe
F20101208_AAAUZU li_y_Page_005.tif
615c7af96458213b4739d149c414c033
dbd21de25a06195f170f09fe60df61c9f9036194
33857 F20101208_AAATXH li_y_Page_137.QC.jpg
cd4f07d57b000625bddd1f2cedb2b1df
14c009a649f87e0fde3979b5a52ce3041320d6d4
2741 F20101208_AAAUBZ li_y_Page_174.txt
4c23009b07fc963ef1be9a298316813e
fdd08bee90ae4df0b8d2cbfd0d233aea430ba3c0
655570 F20101208_AAATWS li_y_Page_113.jp2
0d2b1176492ed7461e02235772550990
958d77c384abc34be39f4b921b7869db0349fdbe
39933 F20101208_AAAUDB li_y_Page_174.QC.jpg
60ea6e01e30d3145af6a82440c557e81
3935b0aebfde90b65d6694986aaa5416a0967524
1043 F20101208_AAAUCN li_y_Page_002.QC.jpg
ffb04869c06e7f135a3d4bdaf6dad7ae
72918d5ac961d065dad62617c4659c911e7b3f3a
2055 F20101208_AAAVGE li_y_Page_040.txt
bddfd2070e7d0de446a2815defd42033
65f086a91082d24d5c5a8e5f1333b934a10add65
3349 F20101208_AAAVFQ li_y_Page_006.txt
0f2c52b688c6f5572301e6bf3869ed24
a267aac6c04b690502891b52193ea915667782d3
F20101208_AAAUZV li_y_Page_006.tif
8b16e5a02c4485fa145d0996c608ad6d
6ada5d6b0d72a849db0912736a8c8e717c1a2697
51842 F20101208_AAATXI li_y_Page_094.pro
13b196f648380691d6a665381bf92379
996051e336a2bb78370b531f6c249a78cebb181d
1753 F20101208_AAATWT li_y_Page_060.txt
163f4ed4769f94fe33aa25a381fba266
946380588c4c666d83495d226b75ad537f3fdc9e
35095 F20101208_AAAUDC li_y_Page_040.QC.jpg
518952aa2e2f9d621ee47e257627b0da
729423a5fc3526702f12c7ef9a4583ea8759f2ba
8550 F20101208_AAAUCO li_y_Page_042thm.jpg
f1fc6d7523ffec159ec9404d1dca5d97
95d46c3565d0d7e7c46bc4ab71c9f94d2fdc887f
2149 F20101208_AAAVGF li_y_Page_043.txt
6b5485f8ac93016940d11a40f1b8b366
f2dc8237d1b573a0df23a86ab7ff7c4ef88c7493
2049 F20101208_AAAVFR li_y_Page_008.txt
7d765478b47237a5f6e981986c1d76dd
aed554cf96dcf9a1ff07a187601ab2cbf51154d0
F20101208_AAAUZW li_y_Page_010.tif
0753217c5133e56a12bc13c5e9fe18ea
db210545f6bd08db65ffa435b44635023c2fc3fb
5421 F20101208_AAATXJ li_y_Page_008thm.jpg
1a1dd4bcbc589765cec23b45e4e78816
7992217a95cbe4b475625131749894a28f577c5f
52170 F20101208_AAATWU li_y_Page_142.pro
5f3782c955e723b51c3bcf875ec36c38
36982547beb5c0842b9cc054a526884dd56fc36b
F20101208_AAAUDD li_y_Page_044.tif
6ab00f2b1ee3f4f0e0952dadb7cf013a
964daec7839566dd1dda96774149fc43a39f1ff8
77463 F20101208_AAAUCP li_y_Page_145.jp2
d1e00720f64ac0c997af07cad7cd0b2a
3ce1b8ac999f7fb105a68265af220232cdd19f9e
2229 F20101208_AAAVGG li_y_Page_044.txt
1a282c89108a260a8206d18308ad0c6c
0ef37ffd297dd2121fe690a0464c1450c3aa37ad
2932 F20101208_AAAVFS li_y_Page_011.txt
faee33d7c302fbcd261447b6e66ca9fc
4127d51813fa4bec777f1502364b208f3ebf5386
F20101208_AAAUZX li_y_Page_013.tif
f8e976bf994390a909419b60d546b133
00e2190c07194af143da9421598ecd8f2e18132c
1799 F20101208_AAATXK li_y_Page_057.txt
09bfcd41381bc2024857d07609015791
935d682db3a944813ef3f2bb74ea0751b685b293
1051768 F20101208_AAATWV li_y_Page_116.jp2
ee71142aabf480638401a00740bb7a21
5ea48f53f2ef34c37a90abce6678d3bf7b36aa6f
34482 F20101208_AAAUDE li_y_Page_042.QC.jpg
cf822d6c94d4498a0d776d6c269a0f01
74768cdfa1ab4fcc7ed4037f98a54e7adae20752
F20101208_AAAUCQ li_y_Page_171.tif
3b3f4804e5f6e482270a069f55441073
85002167dc73199b60981980da7639af3ac4211a
724 F20101208_AAAVGH li_y_Page_047.txt
ad7fbed9c2516f29df2bc39e205bf8a9
42cbd97173470fb7f087c5f6217571a2b46422ba
2699 F20101208_AAAVFT li_y_Page_012.txt
b7e4ecb264d6ff15651ed95b271b4fcf
faf3e95787af1ab20e2f6402bae112f3dabae99e
F20101208_AAAUZY li_y_Page_014.tif
f39d32d56fa97a5af0bc180b0025c5ef
42eb295b289fac6ea217ee0b599110ecb645e76e
F20101208_AAATXL li_y_Page_130.tif
455174c9ee7a532dec964bdb4c683694
9e4960f4c39ae2385b89b8500b8837872ffca32f
79655 F20101208_AAATWW li_y_Page_005.jp2
792d642f18ef72f0e2131b0a3ef9627a
1dd9e2d22bcfb7a0af17eb7a048a3c930c6842b5
F20101208_AAAUDF li_y_Page_012.tif
6bd4941052a94c40ffc9ce72516acf35
035e0e7175b1e1656f1e19371201bc122819871e
76455 F20101208_AAAUCR li_y_Page_019.jpg
1d6ea51cc8bb16d7c5b545925ec668a9
4a0767f15f30b02dfd38152d1cbcd511f30eb179
733 F20101208_AAAVGI li_y_Page_049.txt
dde2cea6c819b00e09f31f8ecfdbb291
b7ce57cf113e58fe2f9d09fdb33f8e84b1864512
1994 F20101208_AAAVFU li_y_Page_014.txt
a02894103a4d55a47f6344b2046584f7
0340a2e5f83c5960fea6d7d8a33c5a01b0db3d81
F20101208_AAAUZZ li_y_Page_016.tif
9a4c8ead458f82e0f424c790a6d0a03d
6b724919e46570c605f7ac822bd18783d1e87145
1575 F20101208_AAATXM li_y_Page_166.txt
42c69d7df1231034ff914d6ba9e1ce12
286c954d97dd718364001e70eea35d4adc18996f
20480 F20101208_AAATWX li_y_Page_111.jpg
0b5ecc35258db7143001da5eb4f9c1c9
597d64cdb756db9bb8990ef0ac5a319259117378
1952 F20101208_AAAUDG li_y_Page_099.txt
93d102c21a009d60c9203ae34417ba5a
fa71ffcc129beb8c1c3a39a7806b0b1bcd276f51
64395 F20101208_AAATYA li_y_Page_179.jpg
3939f57cb55d0c7a3b708388dd255311
7e0703c89967749c1ffc9e75ada1276958225e45
F20101208_AAAUCS li_y_Page_111thm.jpg
e9a0409616eb98015876bea0e7fb6760
3eba6337debd5f423062338adc7e9efb77e00ab0
1845 F20101208_AAAVGJ li_y_Page_054.txt
1e27c1adda961702d2799a273d4d20d6
2557217e9b8a73bafc37ff6e37479af0027638fe
2130 F20101208_AAAVFV li_y_Page_016.txt
a90cdc4598937b559af1cf084267132b
bb7f1f4f3e57afb54e6f91a830cc975a57e85e6e
8945 F20101208_AAATXN li_y_Page_040thm.jpg
4413ab783c519d8b157e327a52a9e3d6
b9963b900310257193fa7dc5dfff3a76fcb9a94e
40236 F20101208_AAATWY li_y_Page_055.pro
42b9006df0bd22a5a03eb6a583c757d7
37570bbf300a9a4d49185d64597cf1ad61ee7bea
29049 F20101208_AAAUDH li_y_Page_164.pro
6c37fbb3612f064954e8d2ec07571410
c55377b5d0dfb7af0cf487e17eac05ab31f63c6a
40182 F20101208_AAATYB li_y_Page_144.jpg
4eb63f796bf0da80cd5974428ca09332
7bd6d6a9a3dee24a099d2bbaa175d82cbdee4491
44921 F20101208_AAAUCT li_y_Page_032.pro
e53ba6d2b251e6caaf7c3898479271ab
e39b7624fe21d79b769b63fcc76ad134e8a09d14
1823 F20101208_AAAVGK li_y_Page_055.txt
719cdf0e7dcc6aa59f1c6b19bcdf1a52
468b5c2abf2c81d775d0afb63d3198b0c2ba4ea2
2100 F20101208_AAAVFW li_y_Page_017.txt
341fcd74335aebec53529a6c26bd8ed5
f9657e482676b6979d2906bbfff6426d50506a57
89088 F20101208_AAATXO li_y_Page_078.jpg
7484806921b1434846c38394384f3674
2ff66aca67a5964ac95311caf79426d8bd1116a2
107903 F20101208_AAATWZ li_y_Page_122.jp2
86cda5037b7fcd82c9196c2300b0fdfc
6a16eeee60d382f25065ee7c00c045fdb9109e64
52318 F20101208_AAAUDI li_y_Page_108.pro
bd6ff56a4fb7b3f7d10bf294994a07da
b6c81c551a9fdcb10dec68c7d6e9b96311c2ef6c
78500 F20101208_AAATYC li_y_Page_075.jpg
7586ca15d2cdc5eec456408503a4e95f
59849e2213b39e196db71756261723a07b0271ff
2031 F20101208_AAAUCU li_y_Page_041.txt
90193302b04aed8423f7ff75be11bad3
a2378015f239e051a81362c698060309889e05fd
1778 F20101208_AAAVGL li_y_Page_064.txt
acfa274381126e140b83eeb715c5e259
af9e91b74ad7a15a548bc81452d80704ee09a2ac
1758 F20101208_AAAVFX li_y_Page_018.txt
17b4645894c59b529a1aaffe9e04647c
7f70b462b2843bdb4b12b39e5d02091b232c347f
31218 F20101208_AAATXP li_y_Page_079.pro
56673565b191efe9e60abe8e37cbef62
65aee79e3c9dc8a229b3cafae02d10594a5640b3
1365 F20101208_AAAUDJ li_y_Page_025.txt
dd8210014f62e4db426942f56ca60327
bc22dd18173241e7eb7e48510facd0e1e87e0109
782181 F20101208_AAATYD li_y_Page_115.jp2
e67c44c8f9ee5d6abb8b0b518acd307f
53352f5dc5a5c136c46cd0d6b59e2ec12b2e8319
20849 F20101208_AAAUCV li_y_Page_134.QC.jpg
edc449dd73695dba4fea2e336962278c
940c4904db37fbd18352e2f3a78d31dfc9a8be9c
2107 F20101208_AAAVHA li_y_Page_106.txt
8fcd51d84adc42d016b9b4bf1a9a2a93
45541a45d77267129a1507db7e8613e0b6ee3754
1774 F20101208_AAAVGM li_y_Page_065.txt
3d1c6b19793682d47ac02ccb0516c343
1908a4062e36ed96068223a6b6518ba6c6d99df1
1782 F20101208_AAAVFY li_y_Page_019.txt
70affc78ef19348647ec0ef80be734f4
f3d24aa2173d77e2dcf8b1fcdcea4e7bf723e8ab
85709 F20101208_AAATXQ li_y_Page_064.jpg
065efa46d5f436644a64de11bb6011a7
0d0646666e4d7d6f55e65ed8795adba3e353f6c0
102057 F20101208_AAAUDK li_y_Page_021.jp2
6dd276cd3ca0076a59b8be4bb2ac0230
12f06e5e4af9177cb6fa716679c274c4a1ad266a
84678 F20101208_AAATYE li_y_Page_153.jp2
ad661f9d15d32e3758cfad7d954ce29a
942ee2ecd360c304c49cbe65f3bfbd995a2fe6d6
625 F20101208_AAAUCW li_y_Page_087.txt
0648c02adb97731a7772b0c7c2227b5a
7962197cc3e241f5e5b1d8a54f018139e3208082
2062 F20101208_AAAVHB li_y_Page_108.txt
b1dac72e09f1f4fde1a5c5b55a3a9b38
9e732dacbf4dcdda5380dce4ac1e317281331e4d
1748 F20101208_AAAVGN li_y_Page_068.txt
2cbb527488765ee7cf20805bb2d0b69a
50796c62a1b831057da10a2fee1f646049709c0d
396 F20101208_AAAVFZ li_y_Page_028.txt
ea24dd9909b1d812219d20b316769882
d3a7f58734608c43d4c406f3ccf8550fe870c37f
887479 F20101208_AAAUDL li_y_Page_034.jp2
70f19cbc3de168c8d87dd7f153a0a4d9
afa87182005f87f84bec7545cda5da6a3cd22e38
4893 F20101208_AAATYF li_y_Page_131thm.jpg
aa71bb085c234896479aaed57b276a16
d11a2cef1005e41a2694fa4b7fe3990fd95e1831
9993 F20101208_AAAUCX li_y_Page_087.pro
51e44b52a9f30204268a9f564f531360
5abef7c5461b5b6c4852306db00135e5cf974c61
1554 F20101208_AAAVHC li_y_Page_112.txt
7a4a173ba1e7bc1b3e62509331092a4e
cb34296df41cda13fbd388490dfff684cd2fc1c8
1947 F20101208_AAAVGO li_y_Page_069.txt
b36e02e47256ab2637eefb54b436e188
653a8518e14de0f6c18f50acaa5181f5164d8544
F20101208_AAATXR li_y_Page_063.txt
35713df6544abc44b838f856f90a58ef
64178a4bf6e3c80a19c0e386bd1bf7ff117b2d4e
79660 F20101208_AAAUEA li_y_Page_166.jpg
ba565a7ad44fc84e1061810b6e308f7e
8a2a5281878a1dc163cc00f88f9bf4009d4867a5
61622 F20101208_AAAUDM li_y_Page_165.jp2
93ce047634254b97c1015acd961f53f5
b7af12985a871dcb08ac3cf2a5302b62b1d8236c
F20101208_AAATYG li_y_Page_090.tif
ee6a526036920ba90087d2160b1c9aa6
b42d91bf550c03e1644c241b614c888b8659861c
79207 F20101208_AAAUCY li_y_Page_058.jpg
154eb820d5dcb230b8c62f56c3ca4b71
bb0e34eee23663ef04e41d3bbae1ae95c0fe8113
502 F20101208_AAAVHD li_y_Page_116.txt
6b707ad3ba55db4e2cb7dd7d32d3f22f
c2daf67180894b12e1cb388d44ae434647c5a743
1621 F20101208_AAAVGP li_y_Page_070.txt
fb8aaa7300cec216ff662c140889c189
27c4324487c0a67c152bdb5573abb52ac8e3a910
F20101208_AAATXS li_y_Page_179.tif
8ddbceb70ca92b63e4dd2aa828fcef20
6804468a1af0037b32fac3e318206dfd85d8591e
F20101208_AAAUEB li_y_Page_066.tif
221bbd2bfa5746d01c2ee3ad77111607
8585baa2e38eb4aaabfecb693578c5142fbd814a
30954 F20101208_AAAUDN li_y_Page_065.QC.jpg
3875f7a7d8c2075c42434cbf1d78d10a
dd9d524e088e80f7e50e1d93c273d7b99954b709
11929 F20101208_AAATYH li_y_Page_113.QC.jpg
3e0fed959741ce2c4b7719626128b229
7f8f75c229eb841282796f0f107e7eab3e2d16d1
20952 F20101208_AAAUCZ li_y_Page_148.pro
993a69cf306da04ddf518b959a48a3b0
efb7a0ce2b28e961e0119bc93d17c42b70e52d5b
2064 F20101208_AAAVHE li_y_Page_121.txt
c485187a33ee54c84566c7b6d69d486e
58c54717bd56ddbc0f3b5dd449ef37dcd16236c1
1708 F20101208_AAAVGQ li_y_Page_075.txt
5a56397e6b23129e32a597e6fdc3ad71
61bd41fd3d72a8d5f6677f35919986d7b3b0cc3d
4092 F20101208_AAATXT li_y_Page_128thm.jpg
443e7cb75b05bada5c8a300822ab068b
cb0cbdc20b20d7d93c935e967ec99813f8a6e396
7484 F20101208_AAAUEC li_y_Page_055thm.jpg
e115b77fe0ce519d188c81619bc6696c
143355f5a574d48ffa84672a37e4142adb8576a2
12266 F20101208_AAAUDO li_y_Page_086.pro
fb8417db02fe22f54a03aa2a62b0e1c8
fb4babd8508adb58a79b345f66cadd23522bc24a
F20101208_AAATYI li_y_Page_019.tif
0336400f714adfa87016f44d88caf565
f938e9631fceb7ab9704381a4c348b618d633da6
2094 F20101208_AAAVHF li_y_Page_123.txt
0710b3f0efb4f4fd2262602444fd2df2
9de3e7d5e66d77a0b0ee5de5aa04d64c5e9c8697
425 F20101208_AAAVGR li_y_Page_080.txt
ba393c84c2d3d8ac93d42b6ac8be1f8b
86c632a524391d9fae630a16063456db4483b91f
490835 F20101208_AAATXU li_y_Page_048.jp2
1b519a4db536574bef48fdd4acac69c2
09d82f7eb90cb486222ad6b7310daaaa96fd07b3
26433 F20101208_AAAUED li_y_Page_060.QC.jpg
a66048b5029c3a80783205fbcd083e59
cca9c3165a3f76de804bb54debd8032c0d3945f9
6610 F20101208_AAAUDP li_y_Page_161thm.jpg
ba468262fc758dab7177773432e3afc1
fddf57e205a30b81e7086a3d3767ed6b797963fe
250 F20101208_AAATYJ li_y_Page_115.txt
843398b6082dde0ab6840ea610bde372
7d79fc13940c1797e19a3d321cee5ceafbf725f2
1963 F20101208_AAAVHG li_y_Page_124.txt
0d355afb24cf0ab684587346d575d924
af6c292f4bcb6a55a64b556b4bd753b59346a6d1
522 F20101208_AAAVGS li_y_Page_082.txt
59c2d7ad912dd992c6eb445570de5e5c
7526dc62431bcacfeb5d14b4a014b8640967e168
713401 F20101208_AAATXV li_y_Page_088.jp2
5dc08662f2837381ef51deb4f990e05a
9e2023189d28099f0eca70f1ae0ea68d92df00aa
22277 F20101208_AAAUEE li_y_Page_135.jpg
ca3c5bd4318ff3b54d35e8e8f1a9e538
a65a1ad7e3844446820108fe7748e1e0b3745440
F20101208_AAAUDQ li_y_Page_160.tif
6191e6dcd379ef133839928658bac8c0
31b03ad7615b90812ba4a3395ba30e1d864a208c
84739 F20101208_AAATYK li_y_Page_036.jpg
75c0fa379dfdc92f7267e2363b603ad4
b580a57eedf5209308f9bdea5e7a291e3b34c3d2
F20101208_AAAVHH li_y_Page_126.txt
d04c38571784639cf199a61a367dc54b
974a84be7d4b2ef55e32c6ecf0753a4c93ed7d66
436 F20101208_AAAVGT li_y_Page_085.txt
b1ff57f593c03778a9b5a4a2203c4b17
465ca01f9a308c8c65924f83652e047b7a8b36e5
2207 F20101208_AAATXW li_y_Page_077.txt
529bd61220d6f711f27958c64516be6b
3dbfc75a4d4bfbba258ba96329f0fa474f5cfc36
84961 F20101208_AAAUEF li_y_Page_060.jp2
7092915c1be00574fd0b61e205449e5c
fac284c117fd0799795782e11e8cb58503755b1a
14317 F20101208_AAAUDR li_y_Page_155.QC.jpg
1df0f66700ceb5981dcc613a3f31371d
ff7c01e6689f711b00fb115d6dfbfaf862959afa
30422 F20101208_AAATYL li_y_Page_093.QC.jpg
7db550fe5f2b716822795ee73160f3b3
a3358a7c4528877221f0353131597f1b47d8f56f
560 F20101208_AAAVHI li_y_Page_127.txt
8ecd8f0b6ffa57cb627ecf3d49ef015b
40b87fae48d961cc03118bf4ac9de4704eef8166
375 F20101208_AAAVGU li_y_Page_089.txt
1d9aed16e9ad38ebd22232fac81978a8
d90d2b76c3bd4624d3b197ca8adeb5ded6346193
109053 F20101208_AAATXX li_y_Page_138.jp2
ad271a3ed0fe67c691d6b6ebef9e9692
b0fffb3027e992a96c56282ffe30c49c32f5ffa8
1711 F20101208_AAAUEG li_y_Page_154.txt
c47f3db9aad1b449dc205ef285cbfb13
2f33ce89733d8afa3d15a951ee387b4dec9435ae
F20101208_AAATZA li_y_Page_042.tif
9feace24535281facba63eec3a3eb5a2
8ca2119a473402e8da06d2fe38682a0ef9e26021
1400 F20101208_AAAUDS li_y_Page_168.txt
d7e3736024fb7d9cdc7c866ee88c4bbd
f3a97a40bf498693b2ffdf3bc8380a2b9f83df86
3422 F20101208_AAATYM li_y_Page_002.jpg
9c0aa110bcc8961c00fb61e747072330
091c363dc4d1085d703f1816fa53d7fffcd8b49a
935 F20101208_AAAVHJ li_y_Page_128.txt
3243086a1ac771d6b8fd6490497b3caa
f02f82b906fc4dbf52e852a5d752113e69ceb45b
1888 F20101208_AAAVGV li_y_Page_091.txt
873f40f66e8a73725552c456c971ea7d
4755936968fc0f06645b5f78aec9176df6475293
7627 F20101208_AAATXY li_y_Page_080.pro
9d8b8e8cc6b13aaef6accb2012794052
93683e335126796ecf4a28ff04bcedb8a0bbb2f7
115955 F20101208_AAAUEH li_y_Page_105.jp2
9b838f77958567301e5fd8e7c123dc88
d21e09e58ded75023e433d1daea981c785029e4f
F20101208_AAATZB li_y_Page_119.tif
9dd00e23d38912928969c00f65ea4813
d602e72a579cbfe1e5b3ac670811f01bb2157cdc
12699 F20101208_AAAUDT li_y_Page_027.QC.jpg
47c11ab81e2d545f24a799433bc12696
87996a8522e0c70993f76d6a9275c925171826da
45414 F20101208_AAATYN li_y_Page_104.jpg
aa0c0a210223e75fcf79ac435fb597dd
e9babb646529c6e7d92d435d1c6f3e51340cb23d
840 F20101208_AAAVHK li_y_Page_130.txt
867ed7570241711b59807af61541caaf
a430e5e644ed6c1f22ca044aac70f4879f08b1f2
1825 F20101208_AAAVGW li_y_Page_093.txt
40ae921704b5f05fca17a6a004696a04
4caa919542c4d6ac4a701a047107ec5e83b862c9
5913 F20101208_AAATXZ li_y_Page_163thm.jpg
0bfaedddbb8f04057b44c89cf8f07900
513565526b90842ae1e6d6e4f7da38e224ccccf7
44237 F20101208_AAAUEI li_y_Page_053.pro
295c6806e5380674cc4c81af54e88900
21d78049c20dfc00c62403399d7885d5e1a8a8b5
49274 F20101208_AAATZC li_y_Page_047.jpg
da024007ac7a8584cb49ab58642f599b
d9bcc4bf5cd0688d6dd6b167aee6632a3bbfd58c
111016 F20101208_AAAUDU li_y_Page_173.jpg
2a69164f62e65b21ddfd821929a9125b
44b71fb04dcdb7b402b2648c95f36448d596815e
8941 F20101208_AAATYO li_y_Page_173thm.jpg
ca5b23c0c5fbb9fe2fe6ae7a19448856
0dc5d4e200d6d395ff3c8a070f6c995906a0d35b
1055 F20101208_AAAVHL li_y_Page_134.txt
2b66b05f3adedc1fc0ff54f7e5a11cca
415a4cbea73e635af0f2fe93f61eb1b4c90dc0a3
1729 F20101208_AAAVGX li_y_Page_096.txt
268c8d3d29c2d613e2bf5d5a9ab40648
f89e2eadc9da5a699a25ee2555cd260af126fdfa
1138 F20101208_AAAUEJ li_y_Page_179.txt
b7435a484a6f0d162dfb3cbf77249c41
986cc8d2bad4ec808d848bdfa744ca7cfeb03820
37840 F20101208_AAATZD li_y_Page_177.QC.jpg
f0dffb85fbc5393994b24cf624fb3f6c
35030a7d5cb234341794207fdb2ef6c03545f945
111498 F20101208_AAAUDV li_y_Page_137.jp2
2e88c61938a9566688d836d8354667c3
ff00ea11795ccbe6daac7e8554eb4bf934bb2a63
F20101208_AAATYP li_y_Page_021.txt
5ac0c7071fc0f235547ca370f43b7733
f8c3f399ed657cc360a449b003288394ac301e63
2071 F20101208_AAAVIA li_y_Page_001thm.jpg
f5870263bf4212a2c13d22b41412d0d5
dc1fd9377f9785a1c5516104b43595e015d1f168
2089 F20101208_AAAVHM li_y_Page_137.txt
addd4de9d2e88751c04a56cd71856d22
cce105225edef5132d24e19c7a2fa7b98ea6e959
1892 F20101208_AAAVGY li_y_Page_100.txt
8aa0fbbc3c8f18db54639a80b33968d0
fb24e92cfcbba339ee1138c39a50ce897a4be0ad
103412 F20101208_AAAUEK li_y_Page_022.jp2
77533b958ab4c546851c18963b74d2c4
ddd440b1e330ffa03212c7a902b4fb49514d6697
1051972 F20101208_AAATZE li_y_Page_008.jp2
7059fc855ff9173c309dc5d96a0ad391
feed16cf681e6bf57b2a61c1c196548c374da7fe
108322 F20101208_AAAUDW li_y_Page_142.jpg
328cd783dd446a60c957588890edb04a
c5ce318b76c01c050f7af6ea8c2bdb2923096736
6587 F20101208_AAATYQ li_y_Page_103thm.jpg
4fe2a9b7e49ff587521a872f815b3afa
50c9a56357ed32371cd6bf673f6804d94f927b6c
2376878 F20101208_AAAVIB li_y.pdf
933e9cf2886f5f3ae7ba2331736eb734
6acc32627fad21b96fc4fe0a091b356ed5b9e2ec
1620 F20101208_AAAVHN li_y_Page_146.txt
149467741c88ca2bce796a6d56cd2da8
c49101966491dc28f1e8ca8b5163194c66bfbce6
2324 F20101208_AAAVGZ li_y_Page_105.txt
9d279933e619239f9280c7d96a026b82
e61767c8d92230da85e74fac7f621cc2fd65e08d
111339 F20101208_AAAUEL li_y_Page_126.jp2
b021c29b540ff62281702d314e413727
acddcf5324ae70270c13974321566e3ac133e99f
35797 F20101208_AAATZF li_y_Page_168.pro
485ccf986819d6c57eb5f8a7d77ae0fa
60e55f2e4092dbb3f69c7dad91c9347fcf578ff5
21731 F20101208_AAAUDX li_y_Page_020.QC.jpg
60443dfdf5e925becd6a1d1c6c2cad63
f22acb59580677d63a022befc42bfcd238c19ca8
31683 F20101208_AAATYR li_y_Page_154.pro
46c1a750b84273a73a172cb8d0f5c966
b713cd3c2935a075ddd78ee95d7d05f870b5f2a6
8249 F20101208_AAAVIC li_y_Page_001.QC.jpg
2b53db99e18fcd65fd48cb53155bdc02
af2692491b697f9428c265d400dd0593ab16fbdc
1510 F20101208_AAAVHO li_y_Page_150.txt
6ed956bc37a2c2dcda966a2c6e837968
9736ecc83a4b846d65a4e37457dfa40ad4d54180
409952 F20101208_AAAUEM li_y_Page_087.jp2
a9226770630921c97aff9d53231b977b
ed2ad6b1365fc3cbdf16c5b61fd0c55379223c98
13544 F20101208_AAATZG li_y_Page_046.QC.jpg
3257f9337a559eab63ade8085f15cfb2
c8625c35d65319add31fcbdd46c8eec28ec7959d
839 F20101208_AAAUDY li_y_Page_155.txt
a279b365a663d304ff8b89b924b78bf4
0e674180f9c5edce1e83eae756db18e8747f546c
F20101208_AAAUFA li_y_Page_092.tif
e1e4aa66686b0ccddeb44e6076a9bc29
bbc405e37d42e227f84dbfa8afd454f6db6c66d0
F20101208_AAAVID li_y_Page_002thm.jpg
e99a2d9aa6f942e128e43f83a454a4d1
125985739fcd79881b964751f69ec579a44e0345
1862 F20101208_AAAVHP li_y_Page_153.txt
8374325a20f6a445d0919f7c8ab9a746
148c11950dd800d194e6df25a40e8e113dcda5ac
F20101208_AAAUEN li_y_Page_176.tif
f753a62580625c7a8560d41ea35c986a
10537b84b026307452b589c23ac60031bb25bc96
8689 F20101208_AAATZH li_y_Page_125thm.jpg
8c1e7760b30171761e26bf20d8e5fc8c
a16aa6224c78d22bbc7bde5ee5f5931970ede1d4
F20101208_AAAUDZ li_y_Page_178.jp2
5fadcd1f39f29b7ab8a0ca6d3ad320ae
8bed0d7dd62aa31338f350550d3c684b0e3dc687
2112 F20101208_AAATYS li_y_Page_110.txt
cd536460020565d0943e2ddb1f7625f1
c42dd5291ae8bb4945f0bebbe0ea81c2c9b73d0d
58069 F20101208_AAAUFB li_y_Page_025.jp2
95e853f7529be8fbca33248acfbd90c5
6b320aa55df895afa41ae425a1411d71b953efed
6429 F20101208_AAAVIE li_y_Page_005thm.jpg
730aa33bc80a88dcaa30bf32eae547bf
f85897d3343fd665267827bb066394ef8029263d
1437 F20101208_AAAVHQ li_y_Page_157.txt
b8f50b6a5ab6b67ff9f3bd77a1ae9572
64cf457a43dd0e0f759d368befe69ba46f22e6de
85497 F20101208_AAAUEO li_y_Page_100.jpg
3664330da22c3dc79af3251ed4f0b52c
0c00107d0606080f27e1ef0489375c6f632cf9a2
4069 F20101208_AAATZI li_y_Page_114thm.jpg
28f95321402baf8a034cf35f7965e4ae
b0b3ece7ebcefcb4a3b4fa3dd1c90467e6ae43fe
F20101208_AAATYT li_y_Page_097.tif
ea493f6f0a9be7c32f27a7ad6d7c1884
ab8b1e075e709685de0d66c3898136215beb13f0
1746 F20101208_AAAUFC li_y_Page_140.txt
693800a7ef6162739a8082dd032549c7
c1a46361c7c7e55c3d1a2afae9f2ce7cbac654e4
26275 F20101208_AAAVIF li_y_Page_007.QC.jpg
1dc7208626bd37bbe032a97def542c0f
2dcbf5f7bfb5fe03fba2a9d4bb93166f8ab923bc
643 F20101208_AAAVHR li_y_Page_159.txt
21f97bfc0ef9c928745a421613143ec1
82832ac881e4f85bb064ccbab2760b8515c16fa7
2003 F20101208_AAAUEP li_y_Page_122.txt
8944c053678d623e6ceb6ee7eeedefba
eca8b8f764af67ab97f9d8137a6f30ae3470de46
341 F20101208_AAATZJ li_y_Page_111.txt
07acf5c758c9b169863cf85107281bea
0fe23a17559aad4baac47dc144fe63a89be03978
20387 F20101208_AAATYU li_y_Page_152.QC.jpg
fe091baee09af1f5a0fcf0eafdc0ce3b
9cfbbf32957c3e2d6a6bba10269f14256fc26048
8959 F20101208_AAAUFD li_y_Page_043thm.jpg
f5749444a5ff2bf5e3b43ef40350ff2d
c81af740658245ddb8f89931dc074015be536559
7324 F20101208_AAAVIG li_y_Page_009thm.jpg
8bf3af4c7210a0d616946f3be14a4ca6
1ef46e664405797002da9fc0005a6b34cf510c63
1674 F20101208_AAAVHS li_y_Page_161.txt
c923ec2c2b8cc58b10bde0d1fbe77db3
5e15af9a01faa9a8cab6f54c80788dc6a2d88e82
26405 F20101208_AAAUEQ li_y_Page_058.QC.jpg
8cfeed72bcac874541f58ff809428ffa
78de63a3e7e6a4eb7c1386defb8b7322dce17d39
1570 F20101208_AAATZK li_y_Page_037.txt
ee956cfd99988283a5ff64ec30c4a416
15500cc945206ab2b18ad6ba846ced9a1d3747ed
8921 F20101208_AAATYV li_y_Page_077thm.jpg
6809c67f97f788a23a5804d4690789dc
7ed14fd00ad4a552a480a777e8f1395f5cda06e3
50375 F20101208_AAAUFE li_y_Page_009.pro
bc16cb17ed8720bdf3f4f0516cb41f12
f308379390a720b0a01d213f6c4476b626481d95
9491 F20101208_AAAVIH li_y_Page_011thm.jpg
a498780592b7e445dc2e943a48406ddc
dc0a3562ae73c71800ed32995beb8739906edffd
1535 F20101208_AAAVHT li_y_Page_163.txt
d538ecf842ed399b6fc3c0409f4ef87e
d72cdc4d3a91dfcda2f734e3c3eee6c9a490bf1a
24731 F20101208_AAAUER li_y_Page_099.QC.jpg
689e72a61c09ba9ba878d64959eb07c8
90b5accc6f04be637c6beb5f67bd6483941ab972
8465 F20101208_AAATZL li_y_Page_092thm.jpg
cb5f53560f1aed427127de1c7c9b4b27
fb7c44160d473a8f6443fbfe9081944ab79fcc72
2096 F20101208_AAATYW li_y_Page_141.txt
1ff66322632bbb385d1e2e077704980e
b1a37fe53edf930363166c3ff91283aaf27eb82f
63640 F20101208_AAAUFF li_y_Page_169.jpg
e3fa64f90d2dc8095c50a4e4e814abe7
1ca6b1eb95842b8c331c278d85764e822610672c
9545 F20101208_AAAVII li_y_Page_012thm.jpg
663b9cc094d71fcc3349fd3611a7a1bb
77a8c4be9597acc4a264b541b1544d9b245098b9
1349 F20101208_AAAVHU li_y_Page_169.txt
0847f517fdca2400b6265252bbded3ed
5bfdbf831eb7688ed6c63ebc91218ecd079a1ac2
30195 F20101208_AAAUES li_y_Page_119.QC.jpg
8744e94997b132e64900db575be4a6fe
59b3f64d26c7d3e05132141d99d8ec5b7a2540da
45833 F20101208_AAATZM li_y_Page_128.jp2
2df1303224b3ef6aacd1ab16a420285b
e27475f0658a23536f428671ba3d10511faac6fb
2034 F20101208_AAATYX li_y_Page_030.txt
cd8061f6d241fef841c5e5eb334ba712
0d232cb2b86fdf5a1e08062240b6a85b5b86d6aa
53220 F20101208_AAAUFG li_y_Page_110.pro
c01b3149ad0d80218cab7461c8a0a0b2
de6445c2cbe59423852bd147f70fecc323a8aa65
7653 F20101208_AAAVIJ li_y_Page_014thm.jpg
d4c5da804ef2ff63342878919da0e29e
91b547505f413fb067f386d22b4ad88954449536
242 F20101208_AAAVHV li_y_Page_171.txt
e2b97ee128787904ff4ec6b33b16f855
1bf0e029bc298b2fdcf3fd663da1d0c7e4a2fa97
13779 F20101208_AAAUET li_y_Page_128.QC.jpg
34828ced54de3d268aa8bd04b0b6c170
5a9e35030aa956cc176b6c1b962957a717ec8ccb
5457 F20101208_AAATZN li_y_Page_132thm.jpg
ee49afbe99124245995b96a2cb284595
8cc545a933ff8b8a68ad32fa7eca4e80a53dda06
21981 F20101208_AAATYY li_y_Page_111.jp2
333dbea001f128aec02f3c7cf6fcf4da
cce04c9e6e1392dcbeec4c074b357595232aaff6
275 F20101208_AAAUFH li_y_Page_052.txt
3a3613042c4feb67a82d23a6f1c35685
a65624ee761a0a76df7ed740540576c1fa0afdc7
29540 F20101208_AAAVIK li_y_Page_014.QC.jpg
861d69791af4a4d99eb5cb3fa3a32299
f61ee0651211a595429581c89052c59b9b3278da
305 F20101208_AAAVHW li_y_Page_172.txt
1e239955b78a2d05e440099f83611641
e95088185a8ea8f7aad49023576061c24a553f3e
29386 F20101208_AAAUEU li_y_Page_152.pro
696c5b2066fff29aa12523edb97bef56
207a83af2ab6424bee1970aff0559b0cfe499fe5
44447 F20101208_AAATZO li_y_Page_067.pro
b3988ab99d6ab5743d9acfd18dc47635
b60c95509b48229fc5b3e096063dffdb957ea443
8709 F20101208_AAATYZ li_y_Page_124thm.jpg
28b91ca3b790f40c6d85e188a5697586
3482f7594d4ca1f303cbf8f5df1b1303edfa8f7e
F20101208_AAAUFI li_y_Page_071.tif
13ba719c00ca31694680a8f519c4e456
ab5d67fd532ab4ccfebc14636719990ab240c879
24175 F20101208_AAAVJA li_y_Page_035.QC.jpg
b89eb05ffce721d0ae62a4fb290ea113
b790b5e4645de70233d487b0e3e781614f45792c
7528 F20101208_AAAVIL li_y_Page_015thm.jpg
6d0e7dc9a8ff3340743e4910c48e1864
a029c3a8814e5756bb6d872566afe48b12b86673
2595 F20101208_AAAVHX li_y_Page_175.txt
066095578d0c65adc1ac63d758a97c2b
e1327c08a6ec6cf610a21181ef45acdc23842c12
F20101208_AAAUEV li_y_Page_021.tif
238f8895def417e267bb3e4eefe84743
25c51c2a09a3efc6f523f257db682ac5bf7fbf34
15189 F20101208_AAATZP li_y_Page_131.QC.jpg
1a3e05f10a0ba028a4474dd5b485ff03
080ac9542bf48ceb83ec8d4e8e879d5622cf3f87
3451 F20101208_AAAUFJ li_y_Page_180thm.jpg
8609446848f66536bb3cd568b13830ce
a9d94ef291c0dd8cee99aba9120407f498069962
29971 F20101208_AAAVIM li_y_Page_015.QC.jpg
f4824555e3fb5cb7c9605beb6a2cd304
a534d4970ea8f86cf99dddd67e62db1728436cff
2351 F20101208_AAAVHY li_y_Page_176.txt
12028a65334aabf272a2f5ae3ff6fbdb
8249d244a3e5d68d86979f9848589319c2d3a472
4339 F20101208_AAAUEW li_y_Page_155thm.jpg
abf0d48d41c60e0ca3b5f3eab93bf282
7980445cc75e96f5edf055c535a3d0bdb4d5c13b
102159 F20101208_AAATZQ li_y_Page_040.jpg
2d4c45fd854ea7ba18387727265bed13
16be5e735cdcd414f309473c856dc90b28067ce8
110393 F20101208_AAAUFK li_y_Page_094.jp2
05b1ad2792ba574f571ced3686de5729
46169bd3869699e0e7c513b6f68335197c629937
7586 F20101208_AAAVJB li_y_Page_036thm.jpg
af485c2954be6983703866974efc662f
8694378b765cec6d76a192124dcfb4b62bc8da0b
8624 F20101208_AAAVIN li_y_Page_016thm.jpg
8d5ab3d15c6f06ddc3ba228f2f7e4b7b
f778a9e57aa2e3217f42a276affb625bfdea8fd7
793 F20101208_AAAVHZ li_y_Page_180.txt
12a601782dfddf55b6612efdb2e19a8e
1cbfbcf1251a110c84b2938b91b6f8f8c510d7a8
1712 F20101208_AAAUEX li_y_Page_145.txt
65be9a5d19dd23bfaca00600019e701b
ac57d89791d953fedde2f7af398ef88d410e6de1
7543 F20101208_AAATZR li_y_Page_065thm.jpg
7d39494bbf82f64d6d9642e569a078e4
1629283788cf82f9a76fadbf3bedde1ca8c00403
29937 F20101208_AAAUFL li_y_Page_009.QC.jpg
0a2d9f97b42137fdaac0c8fa95226c69
fb1614a514dcf61e9ce67067293166596d4bce66
35598 F20101208_AAAVJC li_y_Page_038.QC.jpg
0b21c1cb54ce92b1f27fbcb871398cb8
5d57fd6b20198a57f00b88b35de73e786f8bfd08
8770 F20101208_AAAVIO li_y_Page_017thm.jpg
008160a91c0932f88a72f240e0dcfe7b
a0fec5b237ccff34a640c4c70c1ba48ac9f69229
104524 F20101208_AAAUEY li_y_Page_029.jp2
239eb65a35b20fdc4d40f9f89d3c5b3e
230d1f65de8f89b4b6ad9e82eb41adca1795b4df
4424 F20101208_AAATZS li_y_Page_051thm.jpg
5c8b5dbc8bb0ded9ab25dfe94a1815a3
828a6e959746ed2b5387f5f76c1e85245b2f7f26
89905 F20101208_AAAUGA li_y_Page_067.jpg
094b151835cb1418f74b08f4c76a3df8
ad5b7a04d151821983eef9f33c47b3ce80f958ab
5884 F20101208_AAAUFM li_y_Page_102thm.jpg
f8902a7612a2d666d5e71bf49b233487
53e2ef30586765ebc649ec702a59ade6daf38c3b
8810 F20101208_AAAVJD li_y_Page_039thm.jpg
777e3370bc573fc3857eb570d2566825
6527a3108c9e3bd65d12d7602ed2524cdd66fbc9
33790 F20101208_AAAVIP li_y_Page_022.QC.jpg
0b8cd5e04557b39d4768e8e2932d8002
66447bb443a066273275f2d1851c0b6226ca253e
2105 F20101208_AAAUEZ li_y_Page_039.txt
c9f5102d1f3fe6341f299562425f4261
ed4fe898e36e41c52b53846016157b5cd22c26fa
8667 F20101208_AAAUGB li_y_Page_158.pro
68f80665d8dbead28957148ab9699a3b
31db939982a2f65c130bab6d4d6d6a2595e56013
9079 F20101208_AAAUFN li_y_Page_010thm.jpg
ae84c2fd1f71d6d1f7e03dff7561df35
a0f674fdaa427208e3d0dd76eaef0068ae2c1745
34113 F20101208_AAAVJE li_y_Page_041.QC.jpg
cfdbc0a8894fdf24ec1304e23ba46253
d0718896ad7fa931f447b76fd65949c7783223a6
34285 F20101208_AAAVIQ li_y_Page_024.QC.jpg
a26f9e75222cf4742059b5d8ab699d88
8c40d6a8a4585851aa3827a62fd7e143b582a8fc
1733 F20101208_AAATZT li_y_Page_101thm.jpg
b9eedf7bcefbe27477eb741e44afb825
27cd8fcb18f9a56b24ad1efa49004754dbf695d2
7052 F20101208_AAAUGC li_y_Page_070thm.jpg
02385f73ff755fbf5067a9c77c029c5f
ffd14fe69ccf06246eb5eeb5fa320948d0dd620b
111361 F20101208_AAAUFO li_y_Page_106.jpg
4a6f121825d7290ed813e303dd9395e2
ee7c7b547b9d2e73630d917edead5ea849e5385c
36358 F20101208_AAAVJF li_y_Page_043.QC.jpg
581a627d98f163bbb27fc7541466c8cd
32790b7f41c0a131351709e76ace9b419c326c8e
17674 F20101208_AAAVIR li_y_Page_025.QC.jpg
2a2ceccf992a383be2988a62fea15a72
242ebe5bee6d90bf15f46397d4c46ea3711ff5b5
574791 F20101208_AAATZU li_y_Page_047.jp2
bde9bc5528186cd4207260f4d50d1971
3216f38fdab9790a3d8aee4e00a87778f51fd569
537595 F20101208_AAAUGD li_y_Page_156.jp2
7e042124934d4041aaf6d8a748392225
1d30866a9927be55585429fce5251b45bff012ea
66988 F20101208_AAAUFP li_y_Page_154.jpg
1b2a1de9d94cc1429236e95a2cfef749
2c2a891ce6d9b3901d430dce43bc212af3200e44
9032 F20101208_AAAVJG li_y_Page_044thm.jpg
6c8be35f5e949967aa19af7068ceb653
98320377c323d3f3497515f1628e5219802e18e7
5130 F20101208_AAAVIS li_y_Page_026thm.jpg
c630f601e77b73e87ded68e6a68281ef
6295e205b0d7e53728ddbbc02ce24afb87272890
72798 F20101208_AAATZV li_y_Page_163.jpg
6a1236168055ffbbcf2048419a2449e6
0679562727b8551264bc8b42e3b0d8454c0dd5eb
25177 F20101208_AAAUGE li_y_Page_057.QC.jpg
1c3d3b2acb0afa1b6d79ff382320a5bd
ec9ac35b731dc8ecb4e2b4f7807d8679131317d7
48717 F20101208_AAAUFQ li_y_Page_004.pro
7c20aa6a7180efa31008e0f770689e8d
7cb8eef7ab896a18da55349eaf13d157243f0ec5
26344 F20101208_AAAVJH li_y_Page_045.QC.jpg
13343025bc3632a78577b1be2fdd7754
fa60715705e71a02b714e2f9fde4da015790fbab
15747 F20101208_AAAVIT li_y_Page_026.QC.jpg
233a02ba1bfaad0ddd4df9c4cd33710a
9ff43bc79d75c6d077306ba45bed8ba1ee0c9692
F20101208_AAATZW li_y_Page_084.tif
52f9f270186ec385a44365b40a8bb8ad
f29b9e9a770f3172b5392d54bbc00b38f6707671
23780 F20101208_AAAUGF li_y_Page_129.jpg
09e50fcc1c967c283a0a53c197451e85
a8a8cf9e06cbe55c0db411a80ff3bb0398242f7c
63834 F20101208_AAAUFR li_y_Page_088.jpg
583336599861b0f204f24222cb667391
5957ee38950b41c2bd57390958e068eb8d8dac74
5049 F20101208_AAAVJI li_y_Page_046thm.jpg
fb95fa792925eec667ca61f3887441cc
81418e2ef749cc45b7158ea313c41f6332e56a26
10332 F20101208_AAAVIU li_y_Page_028.QC.jpg
9fce595f14539c307080a5b224464f79
704008d5f9b1c57888440f86281b874ae80cc6eb
94056 F20101208_AAATZX li_y_Page_054.jpg
eac86e3d6fcf5873aff032eecb0e668f
0633f3742f11d111f8ed9c2a7b9e2193939906e9
F20101208_AAAUGG li_y_Page_094thm.jpg
f3be8d0c1b858cc3258afc1ddcad66f5
bb31f9509ca24380d455dc93e89e1049021e5bf5
582 F20101208_AAAUFS li_y_Page_132.txt
3d4a78ab6f48933e902b1c359c567bfd
5f2420d50cdbf5bb61dc11d7347a715dbf04369a
5497 F20101208_AAAVJJ li_y_Page_048thm.jpg
b574614472a2e58f2594c5d0b8628131
3a1ae20bd235d347fb7efb77686304bc1727a096
32085 F20101208_AAAVIV li_y_Page_029.QC.jpg
706c50ca3af272ffeff3295a43419ab7
d4d5f954e4adb0656f111ed8f53b33e978e05a84
F20101208_AAATZY li_y_Page_011.tif
a72dd84c8868704c3f2103dd2fef516c
cea97889a6606951f3a8229878f0f84e890d282f
F20101208_AAAUGH li_y_Page_008.tif
d687779d0ac18bc377bd0a0cc510be7d
ef2b549ec0bc9bcc25d3bd7453085f403add5c8e
F20101208_AAAUFT li_y_Page_001.tif
dc88bebbb40eed4572175139e75b4693
e0cea0f28ed95e45268d2ac3d103a6c41784785e
17137 F20101208_AAAVJK li_y_Page_048.QC.jpg
27547785d804825042bab29635e7b66a
f6efb0344da6fad512885a34713519acdbf5b743
7716 F20101208_AAAVIW li_y_Page_032thm.jpg
3ccb3d3a6d6fd226d229d749dbfbac1a
e718986bd86177f4c90f9ecb4ead7bb350f22d76
79260 F20101208_AAATZZ li_y_Page_140.jpg
9108edb67e7b168c64758e025e6ae1f1
000544a72e503280849a1f82415a4d310d09da5b
F20101208_AAAUGI li_y_Page_070.tif
a26c1f3718dd6edd3d52a6525cc9aad6
83ab755775f99904afd074a53ee0ac827ed0b0f3
92009 F20101208_AAAUFU li_y_Page_053.jpg
1b34f88d6474808e72b90ed291a3a6ac
50f6fd9383d849731c55eddfc4dcaab11cb300ce
6903 F20101208_AAAVKA li_y_Page_063thm.jpg
16b731f70e2fb926f580b6b12c851c14
c3805e5a9d3630d05e2ed5246bb56af96dedccd9
5496 F20101208_AAAVJL li_y_Page_049thm.jpg
d7f36b011784179c875dce52c1bab3ec
f34480be42d9c2643ddd449e54682cdd7b3a0df7
7674 F20101208_AAAVIX li_y_Page_033thm.jpg
58d93a3ae4cfef70896562ea86b71844
3dbe0fcdec23c65c9c992178d45b11bac73d1395
22334 F20101208_AAAUGJ li_y_Page_147.QC.jpg
03355fddd13875df6757ee14afe3633d
4593fe3bf0b7bfb4430ade8e927aed3795a654cc
F20101208_AAAUFV li_y_Page_051.tif
3814fffe58a29424de202d9ed75e69ef
31bbbc0e5a9e28198f2e32308ce61aa63b6b471d
25119 F20101208_AAAVKB li_y_Page_063.QC.jpg
89eb31a5478812fddbdb0c025d37a2fe
91716fabfac2f6f08ba4ef407e35b3fa4e617b48
17804 F20101208_AAAVJM li_y_Page_050.QC.jpg
b2547344e2d65a4f6d109cc24e387207
a1085c4d26e41bf87b49a1f11e3e9be1b22284b5
7067 F20101208_AAAVIY li_y_Page_034thm.jpg
70bc3f4f5246014c6234c1ca88a8a657
dd078fa76bfbfa06cba6a9b382bef100f0749f6a
19919 F20101208_AAAUGK li_y_Page_168.QC.jpg
8141e3d12cf4e42f02859f60119c0f94
a026d0ec0ecb21be85a5f207f6e4850a9128a33c
30159 F20101208_AAAUFW li_y_Page_120.QC.jpg
fb05ebb481a75726b37dd4c9049e8c05
2800bc3a74eee720fef0b47bd36a3cf8e7a4d615
14688 F20101208_AAAVJN li_y_Page_051.QC.jpg
b626a591c36b1083b7242afccef72343
bbb8000e8ec08be8f24bef0906b3f23679b25e5c
25678 F20101208_AAAVIZ li_y_Page_034.QC.jpg
6b3bf57116ebac5ffbdb6370c527b17b
734d6621b2160107bd8444345c877cfcae7d7b04
F20101208_AAAUGL li_y_Page_022.tif
03cae9587c504eb40979a5f270e462a3
c6eff665fe08d9ae126a0be71890845cd036caf9
1946 F20101208_AAAUFX li_y_Page_059.txt
2634a57ccbc534e40f0855cf11712f72
94a8c119be991a77546bcec92862c955225fec4b
7645 F20101208_AAAVKC li_y_Page_064thm.jpg
a1e4a4d8abea432d61491b6b4d75084e
74f6e3960cf1bc185ce2af5ad429656b74524f1b
3956 F20101208_AAAVJO li_y_Page_052thm.jpg
fb27fda9709c4b29c8374c95eb356243
3f467a8fcb0a6a76d655d852f626cc22a15adacf
105384 F20101208_AAAUHA li_y_Page_137.jpg
62fa5ddeb75784af4898100c0ffc189a
7ab2cb8ee6f626502439a10cd7e850acd0164e48
486255 F20101208_AAAUGM li_y_Page_050.jp2
1e92ccde30834edd5eddf632af909747
ceb488018e13e091e1829e1fbe77a1f36cac08b7
75479 F20101208_AAAUFY li_y_Page_099.jp2
cf38784adf53bba686b978ad2047a9f8
c9360ac5dc194ce8602cc6a935a9b70fe26c77fe
F20101208_AAAVKD li_y_Page_066thm.jpg
6611b6ef30b6ef29aa305170bc26565d
536fbf8b15cec075e4ec7d0f2d65046b8e45b8a0
13078 F20101208_AAAVJP li_y_Page_052.QC.jpg
12cec19db737910b20668de8f5a6a69b
5a2af481fe59c5c95cc2220f4aae8d28042f5074
3201 F20101208_AAAUHB li_y_Page_028thm.jpg
626680113b92a75d3d1250626dc13b02
5ecdd9c29177c91fb93dcddb980221ad264b3a66
1550 F20101208_AAAUGN li_y_Page_079.txt
39bec25a8cec8dcdb2de5145b5507e50
46137089c2ce2e03eb0928072ae434837769de96
58599 F20101208_AAAUFZ li_y_Page_165.jpg
ab17c0ee33fcf8024e0eba5f5b8c5f90
94742080c15d15bace3e6d33d434486d2e94f618
7860 F20101208_AAAVKE li_y_Page_067thm.jpg
db9e1adddbbd557c69fce7b6e9f88037
f0da2851a11ce993b0a3729942f93a2dce86b2f5
7362 F20101208_AAAVJQ li_y_Page_053thm.jpg
0c7448d9aea9512529dac7f306ad1401
ea87c16c60a5d1367519e63a72696ace105bd3a6
1194 F20101208_AAAUHC li_y_Page_103.txt
b74a1406a9434f30a9447f0f218e3c54
e25b200ebc087e092ad4923b73741924b5448841
5448 F20101208_AAAUGO li_y_Page_165thm.jpg
cefb5dc83f21bd492f6e44cba6a87b7e
181e199cbc1e87c75d720dbbf951e63af62eb865
28805 F20101208_AAAVKF li_y_Page_067.QC.jpg
bc1dbccddb83a9d7a269fd56160f4220
3b501c42ce5ef6d6362dc653d97ec49b0c25e9e8
29281 F20101208_AAAVJR li_y_Page_054.QC.jpg
9c3c2a24ccf9313efe8f678b7d1eb9c9
702cd75cd9778de29bbf0cf9fc800129371dd102
8456 F20101208_AAAUHD li_y_Page_004thm.jpg
abe3249e96997cbd87b15e47ae046361
258ae30e298ec648604519df68ccd173da87f7c6
17455 F20101208_AAAUGP li_y_Page_090.QC.jpg
951d8b3d67d7a7aefa92a22b499bcffa
2f2bf6fe97a359349bb62777f6ec2ab7b84b369a
7165 F20101208_AAAVKG li_y_Page_069thm.jpg
cf91c57569c87c4afc90f8f85f44911c
8f81d6dad973f1714aa50956b6fb7c732358f48c
7690 F20101208_AAAVJS li_y_Page_056thm.jpg
87dae04944bdf7f0b731cb23709c3e53
7e36eccab9e8a45f3be3ac08ed00860383e41fb8
F20101208_AAAUHE li_y_Page_167.txt
77422832fde38d5da08fd47f675dc175
2eca1044864e508ec310b2a1568ac62713131db1
15704 F20101208_AAAUGQ li_y_Page_087.QC.jpg
2e9a685294cc2d21874fea27f48c52de
c9506af7e27fb8d244ab004207e2471756d4dbc4
26829 F20101208_AAAVKH li_y_Page_069.QC.jpg
ab6df02016ac378960fcef8999444ba8
040da51b6d9e261ee7ba9a066465b7a2a331188b
6966 F20101208_AAAVJT li_y_Page_058thm.jpg
07f4e7a69d40de31f5320e74aee5598b
e6bb50ba600e9b6bb74382859534c3f2e5d1c6e4
6183 F20101208_AAAUHF li_y_Page_018thm.jpg
7967b2cb0763cb65fb23124182676e64
47ccd669ee90390d7328c8f61cf089cdc6d01d80
299 F20101208_AAAUGR li_y_Page_135.txt
7de4e6410b7f2ea91efb09c9f8e642c6
1ecc7296d9fbc4db63924d3934495f49494946d9
7403 F20101208_AAAVKI li_y_Page_071thm.jpg
647e54e878eeb90d0e06a4ac0adfdc05
5f84820805ce4c7930e3ab6c6fcb12c6d9ce4611
7669 F20101208_AAAVJU li_y_Page_059thm.jpg
15eb4c5a96fec37730690d26a0341e27
72e9286bf5e8f1441f4fa7a9acb0503d9bfc56a8
13884 F20101208_AAAUGS li_y_Page_115.QC.jpg
ee4f3641bdc627bd3f5a4a529da29f79
ce10b9839e41ab4afdf318eb5f07dd18c2d31b88
8122 F20101208_AAAUHG li_y_Page_104.pro
187e851e2367c69ff0af331798fd1901
7c426ce5dd898b1b236541fe79426719a18218ec
6653 F20101208_AAAVKJ li_y_Page_072thm.jpg
cba357a0345c5a70f38259699e7127ad
42a676f1a4a9db9b688c777733f13ce3bbdea926
29672 F20101208_AAAVJV li_y_Page_059.QC.jpg
75c03e5473827869c1204e051a088f2f
a87d8a5e69ae9d4a149627c89b35b04c3672289a
67819 F20101208_AAAUGT li_y_Page_117.jpg
1a48cbf6547293a44d0737f6951377d0
a2c7d393e8b6dce31de155e7f174fa51d6a44ada
F20101208_AAAUHH li_y_Page_107.tif
fba0ad995ac2a8e45fed999a57beac19
10da7fd43ce4a007d41193c683cc115efe75ec8f
8851 F20101208_AAAVKK li_y_Page_074thm.jpg
fa44d0c6a291dc71f5b456748476e7d6
bf6f006ee9974a50af8bb71868321187def79aab
7218 F20101208_AAAVJW li_y_Page_060thm.jpg
cb3e0a29283041d3ce5e90a796d0b946
2afde3e7c7d91bb4498d44c69359f5dcc7e380ed
F20101208_AAAUGU li_y_Page_032.tif
90dd5201f767698797a89cc8541b7c2b
9b990610895c717797f582be82fbdcf8e643e7a9
17073 F20101208_AAAUHI li_y_Page_160.QC.jpg
3e3d746d92dd63d33f1b40f2932e051f
a3b1149268cebda82575daf450855c51070628d8
36750 F20101208_AAAVLA li_y_Page_106.QC.jpg
88e971ec024fd658291a481d20300b04
4e29ba7ac913b49300b00ea79ad1bec76937e0e8
27669 F20101208_AAAVKL li_y_Page_075.QC.jpg
85d699638c3ba80aabdd466693b8bd1b
126a5495f13edddb27901a3bcb9f4d01640e7b98
7945 F20101208_AAAVJX li_y_Page_061thm.jpg
a3bd18e23a6f1bbf865532f61b5bc899
353e2e430b9cc3580837d02560f0494ef45cda9b
380518 F20101208_AAAUGV li_y_Page_130.jp2
0a99d5ee848c576a35251bfc376080f8
6376348ab0620a8424ba75051575debbc0a93d77
88619 F20101208_AAAUHJ li_y_Page_069.jp2
aa2d351d243f5a6a648010b1d47a2ea9
cb23ccbf62eb3acb247ba319a1de4eb2f34310e5
8629 F20101208_AAAVLB li_y_Page_107thm.jpg
ddd9d7e84c28b700c2531b76f044afc3
ad1c244580239dd3a780259720ed4c0635c26eb4
8714 F20101208_AAAVKM li_y_Page_076thm.jpg
7e6c09819f5b66b31fb46361accfee8b
c9f871e97b1a49b4a6cd95efc4a2b4b31eb1e553
33624 F20101208_AAAVJY li_y_Page_061.QC.jpg
66e336985fa39bffefa47f4b22876b8b
67edbb96653142165e30b3c4bbafed2c43cd93c0
44838 F20101208_AAAUGW li_y_Page_119.pro
b510059f2a28fc31f04f0a1a5735c755
a89e21eba7f25e6315936ff3cf1b7b515d246051
F20101208_AAAUHK li_y_Page_067.tif
b0ea1ab68f299a19b27004482c674842
a79e8cc73b0dee6ebe7dcb8881c19d55eaf467a3
32707 F20101208_AAAVLC li_y_Page_107.QC.jpg
ba3f68674e6cb3a49bd85214519c7f29
e7b6f456f18a89d1be3d04ee2dc61af2f59dd2dd
7097 F20101208_AAAVKN li_y_Page_078thm.jpg
2cbd959d08efc766112a03727dca9014
4503381d4925f9d7820eecccaf722bf0528ead5e
26121 F20101208_AAAVJZ li_y_Page_062.QC.jpg
7883eb83a2e06f580e14b35804c5b63c
e618df3abe7b9b119254aa50595c9df2b33df69a
9704 F20101208_AAAUGX li_y_Page_116.pro
6bb269cffe5e6068089a0cde3431bca2
797ab17c7d57429fb4a92c94818f04c24eab6969
9714 F20101208_AAAUIA li_y_Page_085.pro
95b2e57835ed5d4ac8fc1e753c76fdc7
4acaf782d1f307ac1b290283f68f88b2f4c023d3
F20101208_AAAUHL li_y_Page_049.tif
3218415e2382de4db5e598abf007e128
ddcd9f4db6a62660c89913c80f00de69a43dcbb2
4294 F20101208_AAAVKO li_y_Page_084thm.jpg
9d211764f400ff96e0c991c06eb84312
96cf99b4dc208fba6862ec0cb829d927248f088d
F20101208_AAAUGY li_y_Page_085.tif
6ef45df3313a949da2de080ea7ac8571
d2de251c30e9befb537575314f41752d0bfdfc11
16316 F20101208_AAAUHM li_y_Page_081.QC.jpg
f5317cb5462de12ecfeb10d0ace5e3c8
b26c4ab1777a32a1c487ec5c060c81fdbda99224
8484 F20101208_AAAVLD li_y_Page_108thm.jpg
5208d410a72cccdab8b923c1220abdd9
8c50ce71a3a49df1207e3fe6209d2434a9943670
4854 F20101208_AAAVKP li_y_Page_087thm.jpg
7b5d01c0f2af3b5455a5c0df85a62aac
ccaf01be1473f76eb90cee5ba6c382b1fe3c51d6
1893 F20101208_AAAUGZ li_y_Page_056.txt
fab0433829687138218658615be6eb20
5b1a3ad839bece61ab46437a182187c3540801b4
F20101208_AAAUIB li_y_Page_042.txt
022953acf3e30f6cb673a3b287053e77
124c9479870d2bd237e0e22674bcfb1bf68e0f88
F20101208_AAAUHN li_y_Page_144.tif
c2cc8dfe488e49b983ee34502f454d3a
55941617f02458172b803126192018132c74f32e
34887 F20101208_AAAVLE li_y_Page_108.QC.jpg
e4202c332596cd00a78aa7115c701a8d
ca359bb12d2dc6852eb5b7fb434e3f1626e1e535
20248 F20101208_AAAVKQ li_y_Page_088.QC.jpg
8a7f5b1b48d02f5f1fb44e1be9a6c505
08d4f8a0961ac52e4928a6e3eae52316cf34ab09
104180 F20101208_AAAUIC li_y_Page_107.jp2
4b56cae8da33dbe21bcd7bcba462319a
918bf51cea868ded41ffa05d5c8d9250bf05f030
7685 F20101208_AAAUHO li_y_Page_091thm.jpg
23bc8263d1898265c9036aab48ecfb0e
82375e896c1f97094d445af9e71e76d093798ade
35851 F20101208_AAAVLF li_y_Page_109.QC.jpg
6ead67d89fcbbd9314cfef8588ff8bb6
b72edac27ed002d37810da58ab7863ed0c6ee869
5120 F20101208_AAAVKR li_y_Page_089thm.jpg
55f475867ccfa6df6638496a69c6a16e
39eb82439c8ca4f57bbc4712efed5ccbdb702e35
85350 F20101208_AAAUID li_y_Page_057.jpg
d87c0658b2371e86673afa891f9def87
b682ad2afee4af74d29a36fd4f341b1ad42ad628
111138 F20101208_AAAUHP li_y_Page_030.jp2
eab8febc24da8d90335192a8e24efddb
8bc46f3f009e56f19f1a6311cd35d5b34f6bca9c
9081 F20101208_AAAVLG li_y_Page_112thm.jpg
eaf7a742cb20ccb2bdfc9305cd9defc0
bc97494e022a7e0499c5c4246657e793763ca223
28998 F20101208_AAAVKS li_y_Page_091.QC.jpg
fce356193dc2f61410ab97e8c51db4db
000aedf1605405df2a6d6e3e32096fa06b30426f
102659 F20101208_AAAUIE li_y_Page_009.jpg
2b5fc9b20375092178f69bc9d7a1ce7c
7be33c160ad7e0a76e0c2ddb1a5aa163319a13d1
108207 F20101208_AAAUHQ li_y_Page_004.jp2
7fccb26bfd04657b1d1021fa35f436c8
ce9979a8c7c5ea770d4b93f091e283a21b74de2d
29118 F20101208_AAAVLH li_y_Page_112.QC.jpg
84975f09b0e992a1bb9e728e3c5c419a
f80f3ee17384aa1a4b1be5e644c6b27ebdc7f892
32968 F20101208_AAAVKT li_y_Page_094.QC.jpg
d578f6042a031a01a42bc1486a9c4800
c25a6efa2bbfbd62b7cb6a72367f13272690dadb
F20101208_AAAUIF li_y_Page_018.tif
964d4a0bfa0e1999ea2dd3c5d0df8d83
5884992a50fa41d0afb42d6709014962ba398285
1638 F20101208_AAAUHR li_y_Page_147.txt
0c2e78e0c6c8b6c6211a2259250af62f
45a76c8e24b5e837b8325327f900a4711ea4938e
24417 F20101208_AAAVLI li_y_Page_116.QC.jpg
e8a4644ca0332da02945ef581bff2d20
bdbdb5e8d566166f7288656bf3bc872e47b771f6
7744 F20101208_AAAVKU li_y_Page_098thm.jpg
d0ab6a714a50a3148d52fb25f3ebb652
b61943c5eca886fda1e07aebe79427954742c9f4
6024 F20101208_AAAUIG li_y_Page_084.pro
fabefc9d2424bfeeaa0fe0dae96d041c
f4a1b95d465ba803650fc07d2335cdac72a46624
1051965 F20101208_AAAUHS li_y_Page_007.jp2
ade20f43c37998ecdbe91ab5bde06fbe
daaa5665101073b43b7bb758ccdb479348ac1672
7889 F20101208_AAAVLJ li_y_Page_120thm.jpg
472ebbfb62c774ecc0621b2021f5f286
5f6557369dde58c7542dcb97103afc309fe9dddf
6412 F20101208_AAAVKV li_y_Page_099thm.jpg
56f1e0389f8a4ba7fe640581b245e172
b80fedbb948fe0532c87b8fdd9e674d3be6b98dc
54819 F20101208_AAAUIH li_y_Page_073.pro
455b3b1b53fdce93d515d08c3afa43bb
9caa556c93051c52ae6946e390fa5f753d989db9
54377 F20101208_AAAUHT li_y_Page_160.jpg
4df80f617c331fb048a53daf526d104a
c2ca8a7a2f19b94b5e3822264ca52f01ae3f549b
F20101208_AAAVLK li_y_Page_121thm.jpg
091112d45d0c2a8c13c14f8357ca6b74
3dd0cacec7e7c8efd4069a24d86aa7713385d6b6
8224 F20101208_AAAVKW li_y_Page_100thm.jpg
9d1224283f3c0931187326534f785bff
db4cb2ecb6a018d27f329e4463d5e444e4fc48e3
F20101208_AAAUII li_y_Page_118.tif
8199f16f40c5587ca0e794bf3ed9fdbc
34ec0ce37dace25823b9e171067d5369bee0c29e
34688 F20101208_AAAUHU li_y_Page_074.QC.jpg
41ac757a9b07cfe1d54474f812e9240d
84c7b5bb83a1e1d5207c912778c99e13adef9d65
14581 F20101208_AAAVMA li_y_Page_144.QC.jpg
14e2d5c1470c94e247d13cd70cc125f0
13a4d3824238c427396ac7d9c91e6177a947efa8
35800 F20101208_AAAVLL li_y_Page_121.QC.jpg
a73a20617a982b616b495ce280f2fd71
8b51a07eba401f9bad84dd2d5ae5f5e034b34421
20791 F20101208_AAAVKX li_y_Page_103.QC.jpg
f0077710c408a9c90be355f71035f046
f1d378aa443c7a9329efdf59e0069ec5ffd96dd3
25655 F20101208_AAAUIJ li_y_Page_151.QC.jpg
61043da250db490cc38b83d126b24295
610420478faa5ff5453badf7aaf4f7fa2b9da362
88842 F20101208_AAAUHV li_y_Page_056.jpg
75e98312d17efbf0383ad457bebfd4c8
1953ef81a41f8718a0d1f55b482b00e8d49cb7ec
6600 F20101208_AAAVMB li_y_Page_145thm.jpg
319a2c6642eeb80cd513afa746e8234a
9a93a8e6fdda8f2a89a22bb8081a938c6555c65e
8548 F20101208_AAAVLM li_y_Page_122thm.jpg
41433726b9f26c1b05fdaeb6de820b9b
be8a79594d7a67eea189d3d646115755ae4d74e9
5348 F20101208_AAAVKY li_y_Page_104thm.jpg
da782d0826888e7eae9f497d8df3873f
d078e60d8551e9309ff87ec1efb47bd5c264e1b7
F20101208_AAAUIK li_y_Page_122.tif
797d451458b837c1ab66c510d3ea1ad5
705744cbb9110d879c43a6b04d45a7c2050d6410
F20101208_AAAUHW li_y_Page_030.tif
84ef5ce11304e7093570cb69526ed0d0
4d4946f01f1e68043fb18b9b177ec0e7b689e01a
6245 F20101208_AAAVMC li_y_Page_146thm.jpg
037a69e1d6f6bfe9714cb21bb3f696ed
e89950c032f16bd8848f9039232baf3515835f0b
32252 F20101208_AAAVLN li_y_Page_124.QC.jpg
074c1a376c6cc71ea7afa5cccc100bac
d7d636aefe7f58f33978c058bc593e92987dad04
17052 F20101208_AAAVKZ li_y_Page_104.QC.jpg
db2d72b338f528a7ee0ef327897744d4
369bc72deb02b83a08944ad6ae0d7b878f4b4200
43889 F20101208_AAAUJA li_y_Page_084.jpg
5a9881f2c3c761ddb030f5c7bd7bad3f
fbf961b09be54538c53f4fb76ec328490862261a
35177 F20101208_AAAUIL li_y_Page_095.QC.jpg
24dce402fee8b1b9c26069b64c6f8169
adef29142aa6fc6e0c04648093199bf8d95ca521
30939 F20101208_AAAUHX li_y_Page_097.QC.jpg
6790b02fb8a61bbe9137a27f3da50cd7
4f36fff1da5050ee3ebdd654003bc0e43f56c240
6054 F20101208_AAAVMD li_y_Page_147thm.jpg
1fdb4fd3b314b10ba4cd5e95986fc172
f16e24ce926eaf189f22a38fc886ae1c79aea957
9067 F20101208_AAAVLO li_y_Page_126thm.jpg
e06a11287f6f8d849f1d4642bfc965f1
43e5958fc4a54601e97e998fa46fcc3ec18ec1cc
F20101208_AAAUJB li_y_Page_073.tif
07a9da50811aa427ae9a287929035853
496743b9f285ec6d285d8ee568dfca73bfda2d5f
14527 F20101208_AAAUIM li_y_Page_050.pro
3cadd7cd635dd07208da35e4de182e2f
1d3a128c1d9c5b284c491f9a1b96e0cfef891c57
76620 F20101208_AAAUHY li_y_Page_068.jp2
bddd8d851e02bb1d825e660609735641
d28587bbf38223580eedb1dc09d3bb9d602cfe02
34142 F20101208_AAAVLP li_y_Page_126.QC.jpg
0ef17f53dce18ab31113d75da5648113
01f0e144b99624d8bae77e015074d4a1ed8ad1ae
122065 F20101208_AAAUIN li_y_Page_176.jp2
4c2a5dfbf342991e03419cf5a6ca59f0
7eedcc4cf4b34ffd8af1c9325c97833256ad642d
62243 F20101208_AAAUHZ li_y_Page_083.jpg
9268625f2432c309d609b9e7a2685119
76c14d898031d33351fbb2edbb31674ff27107e3
6813 F20101208_AAAVME li_y_Page_149thm.jpg
e34eb6a9e4c1b2d77e547db7e16a4b74
4e5e18c1a58c06d67104c514523030b4bba20f66
2202 F20101208_AAAVLQ li_y_Page_129thm.jpg
2c906c691f498e889df04a4337ad8564
43e3fa9c2b13db567dbfcffe0c85e69a31cb91bb
F20101208_AAAUJC li_y_Page_091.tif
79d3e50133613a5b5757d7a037bf3373
8a80928caf17f2c0a35a3394183fb1ac79f3d2c3
58210 F20101208_AAAUIO li_y_Page_173.pro
f883f0fb336cac8024f27413875c4f9c
b0f3f2405ad91fd2cf28f2a3645973eee186aa57
22118 F20101208_AAAVMF li_y_Page_149.QC.jpg
ef282a4f96a592287eaae86468a41e4e
2180cf3643dc00b5d823e68251bcafbc063a7179
17602 F20101208_AAAVLR li_y_Page_132.QC.jpg
f5882171ff81e698bd7f76563ac2dcd4
24550e08a3350b769504a3589864842046f6531e
6063 F20101208_AAAUJD li_y_Page_167thm.jpg
761afb37dfabe8b0a1aa1e88ebfaec66
1747f9ada1877fa9bf2ea180b4ed4b13d8a72541
84996 F20101208_AAAUIP li_y_Page_045.jp2
6de11efc1ef2d054d7adaf34471229fc
fac873335e5296b79a980bf4e0a403ea0840a6b8
F20101208_AAAVMG li_y_Page_150thm.jpg
0372fe963adee8f32374308e7df7737d
f9a033e8a9252bf0dd48bf949fe3f98ac48b3d0c
5775 F20101208_AAAVLS li_y_Page_133thm.jpg
31b64a503107cbc3d22e00f3fe9b6489
f1ef5a9b377d0d244e89c19485fa57469487266f
12020 F20101208_AAAUJE li_y_Page_049.pro
0f7ca5d6b4de054aff05e9e4c834ce9c
1d560849b721e465faa1d2af8f927cb12fc28d55
493 F20101208_AAAUIQ li_y_Page_156.txt
f87b24d925cc4989dc1a0b537b69e927
d861b0f56dcebc9f268e3130754c3af507ee77c6
7367 F20101208_AAAVMH li_y_Page_151thm.jpg
0c0fd606bd89cbfaf998d36ad902418a
a4c900f51a510c0dddd421473760242eff5e7fc5
2844 F20101208_AAAVLT li_y_Page_135thm.jpg
11a9238550e81ebd2c5419e3787423c9
b1c2476ffef3c678e011953fb5ab62eb23d3c448
5823 F20101208_AAAUJF li_y_Page_086thm.jpg
b5ff63c524c61d18a746c5d456d354ca
5f3648e375c3ff3eee01eb1fe12e3af01133edb1
F20101208_AAAUIR li_y_Page_133.tif
560e429320c7878bab35bc4b570abc2a
3b5c9e0203c4e800da3d28dac3be4c3e4e496076
F20101208_AAAVMI li_y_Page_153thm.jpg
89ff86545664c6ed1e6db8634bdc4526
39dc3b83bca838c0c6d2deb156562bf4bc00cca7
2894 F20101208_AAAVLU li_y_Page_136thm.jpg
e2dbd86c93ab7d41fe48639723575890
2541a462bde8bb0575824488185f1a19ba7d5a6e
8578 F20101208_AAAUJG li_y_Page_024thm.jpg
7bf7ef6fc4e7191dfd0adfdca1abcb3c
d288ff8fee23a8e1d8d069069affee4fd608193f
F20101208_AAAUIS li_y_Page_133.txt
8715e23f26ee83d781f591753ecbe163
cf47f08298f3839e6857056aea8eab122638dd2c
25966 F20101208_AAAVMJ li_y_Page_153.QC.jpg
8463ab045f8d49b3b36bcffffe1fd780
853a620c9d679321b06aeaf03380cda3043563b8
8863 F20101208_AAAVLV li_y_Page_138thm.jpg
640cebabcf22b1c26e0816584ff26048
49a6ba0bf4efc4639a041e0d07f74bfa3effb8ea
1586 F20101208_AAAUJH li_y_Page_020.txt
9386353a088a7ead7915fe187864b576
8fa30c7b9618b3bd920dd93e7f895dc44b7305ac
2035 F20101208_AAAUIT li_y_Page_092.txt
84ad5fbf61d49a8b8780c1bc15969b31
4c57cfb37adfcde5a5e679ca8bb1c563873a0c4c
6480 F20101208_AAAVMK li_y_Page_156thm.jpg
bc79c28c38c873022a9def6360d28e4c
c3a3d33046a5ce7f11c98d0e8411b3aae850f2a0
8712 F20101208_AAAVLW li_y_Page_139thm.jpg
f4ed5d90736cf39c16f9775fa392edf8
a9eae3068546f54c29500e1e4369e80c1a1c4228
6798 F20101208_AAAUJI li_y_Page_117thm.jpg
c8a093a6e1d19625e31dcde76dd5de00
bbcb689686370988766fed52c05be2e850a68786
97349 F20101208_AAAUIU li_y_Page_029.jpg
b425d8bbdda3b39f5b632645b9b5fe97
804622f7b5495f4a3446bead7ae4d469424384f9
8728 F20101208_AAAVNA li_y_Page_178thm.jpg
71619a7bc549d997bbe8b86543999ef3
52ae9b89f97e86abad10a7c91dd505408ea73120
19447 F20101208_AAAVML li_y_Page_156.QC.jpg
78f3e7350c07253f41984fc040f60fba
042776a419b67b07ed0b0130a007e83cee3c38f7
8839 F20101208_AAAVLX li_y_Page_142thm.jpg
d44f96880b675f98cae8e09c9a6cd80b
67525f2d9239da2cb8791471b1d9d564f9c2af93
8338 F20101208_AAAUJJ li_y_Page_001.pro
3536f498fdac0cc4f8e9dd26271c1b70
7a0c9825322ca99f7ff9234eedbb2e0310443a2e
74415 F20101208_AAAUIV li_y_Page_072.jpg
e2ee0daade0f4a984232d12f00765537
64e00b6ebb8ab55343bb9889a260420b9aea61be
203487 F20101208_AAAVNB UFE0017550_00001.mets
13a0c588035dd79f139e0b079ffd035c
6cfbedb71b88c517acba67a41b4762c1eed4b640
2783 F20101208_AAAVMM li_y_Page_158thm.jpg
eed143ebd33672ee9df145134ae89c58
d041cb910cf53aaa3e4f825b7a5caf4f01941102
34945 F20101208_AAAVLY li_y_Page_142.QC.jpg
2bd9c985eb1fee377ebfee4406789ea8
fa6c9834796edd5fcf5e5e6f263387ee49af1790
108967 F20101208_AAAUJK li_y_Page_024.jpg
2fa30eef1363d665c2d2228fee3ecd7f
431ddfdf835f2b1dda5b35c10aa9ec2700908b10
53411 F20101208_AAAUIW li_y_Page_048.jpg
4c54da311d15317e394f64fa42d1e863
d0b35f2162ddf4174dfbfff730f9171a2902946e
13325 F20101208_AAAVMN li_y_Page_159.QC.jpg
4701a2996eaca4b6e4b61730ef84c299
937547616a38939a2ddd16e1318ef3db8cc2f2cd
7542 F20101208_AAAVLZ li_y_Page_143thm.jpg
67d12d5df0b2f9d5a12d6d9c2ff68ccb
4f4cf597169c6f3842714912421abdbbce1dc8ce
96123 F20101208_AAAUJL li_y_Page_098.jpg
36404016be17c3bd169e4007efe3b10d
cb94fb2bdef1132311e3d6bfb3a2fbb1865f2736
F20101208_AAAUIX li_y_Page_009.tif
b31883c3cbc665a7b957b6f23a3a615e
5c59a1ec415ec1e54eda55e3c609a6da8d0b7a0d
10245 F20101208_AAAUKA li_y_Page_132.pro
68b0bafb74322d1c1b70ab0d7e0f0f3d
cc25974b900a7148ef1405147123fbae2d006b99
5175 F20101208_AAAVMO li_y_Page_160thm.jpg
78ae2929471c9463fad38193584f0532
ecbd61ed75912bc54ca4684eeb047c8abfe5503d
29557 F20101208_AAAUJM li_y_Page_028.jpg
06478f3d58a9187c31566760b06d70c4
0ff092919702579886c008149f5ff8df547f49dd
102451 F20101208_AAAUIY li_y_Page_098.jp2
779416bcad86d3f0b926f5a76dbe45d8
b1ecbbc825fff3f0c92a705dcda3987135cedba7
39561 F20101208_AAAUKB li_y_Page_011.QC.jpg
a5bbf96789f0a18b2fd90692e3333c9f
b03c79a37ec104ffd98fd78ccbf574ec25627a8d
25407 F20101208_AAAVMP li_y_Page_161.QC.jpg
831da88fff90a1e10e9a6eb54721d96b
f7cb39d87eacec43484f62320fcf357d6e6333c2
93632 F20101208_AAAUJN li_y_Page_167.jp2
e8572155a8c74c9520a791d8831ad3ba
24392368a28b53ab009d1d46b9805f2996e282f6
38406 F20101208_AAAUIZ li_y_Page_077.QC.jpg
a6f969df6c3c2c5d318193319e46239f
2f0de0e558c7ca238a654679db35316b074ae24a
533309 F20101208_AAAUKC li_y_Page_085.jp2
193c17323a5adaf4d442ec73f85ad0ba
93f276d5ee945355098cd5af81cac9dcef0885c0
5382 F20101208_AAAVMQ li_y_Page_164thm.jpg
145fbeb998b15a879a7a2f7dc97de793
bc4a547ed010de8bd890ce1fe2c4e6874a3df437
4247 F20101208_AAAUJO li_y_Page_113thm.jpg
5c96def2bef1debdcd75dc56030e77b7
14f7d938b901b272b545516ce59e7bdc31bdac23
20142 F20101208_AAAVMR li_y_Page_164.QC.jpg
987b34c45ddd6ebb3ab9624976356236
7500862fc549cdd2514c9b6c25e898d450d4f42e
569510 F20101208_AAAUJP li_y_Page_026.jp2
3aa0d5b2ba0072619877a2734f67f1b0
db9bc1cadc2534652d9c48009a485581d0953e96
103099 F20101208_AAAUKD li_y_Page_016.jpg
b90a714f1833d593d3953890046e9b8f
0a72f1116be1ba2168a6a22eebc08566de22a0c7
20261 F20101208_AAAVMS li_y_Page_165.QC.jpg
91ac27c6598b1ee28bbc82d12db5a215
9680e86c81031ac0b86865d56a3fb2e53b0ae3fa
F20101208_AAAUJQ li_y_Page_177.tif
844701a84266976849997f84d76e377f
bd2a83807a638075ebc533eae0f3c340079aacf6
F20101208_AAAUKE li_y_Page_126.tif
1c884a87a257aa1e4579747619d51a48
94646fffbfac12a819c8ee53c6873698c1695696
4776 F20101208_AAAVMT li_y_Page_168thm.jpg
63a1f898b177c50326703c0714e1492e
0fb4abc12b8bc22e5cb70b6c72fdb512d51b820f
36364 F20101208_AAAUJR li_y_Page_072.pro
b79ac627b181a6385ae073f7df03d9c7
7fbb8c96452189c16081cc103347355cefee78a4
41793 F20101208_AAAUKF li_y_Page_170.jpg
b94e74c6c4e60ea0645aa1cfd0bb825c
e9e03537a79f271174562174750e36ddef05a78b
2734 F20101208_AAAVMU li_y_Page_172thm.jpg
067262470e3a3f4aac8c9ea0e7b6ce0b
3301bf799845f396107f77e4453d64b344ac6cbb
F20101208_AAAUJS li_y_Page_098.tif
93c6c7283fdf1e8b95828ca96e696ec0
700c2d84c2d4fbada151446a7ef2ed3f5e177d2e
72721 F20101208_AAAUKG li_y_Page_149.jp2
5032dbe8fbf246ecc52131b34419e77f
d6f33da2dc23a3ad505eb6352bfdf6b45911df11
9007 F20101208_AAAVMV li_y_Page_175thm.jpg
4bc085d26be3f8adda54d429e7ceab66
6a7c07bc9e20098091637872a8b5f0c6f0cebb1b
35033 F20101208_AAAUJT li_y_Page_173.QC.jpg
59429724815435c02bfb5e6813afad79
a834fbd72b638298fe57620a6d1fa8e21b50ad17
1695 F20101208_AAAUKH li_y_Page_058.txt
c07109394c4e559b8bcf35a45ace0228
6532a38bee55fd65fc6667a9f08678481655a865
38227 F20101208_AAAVMW li_y_Page_175.QC.jpg
125b587f76403d17c84fad390ced5def
866c394bf43456134484e9da5d9ffeac21d43486
24213 F20101208_AAAUJU li_y_Page_072.QC.jpg
0373041b50954644f1029730b8d5b6fd
6670f44a628e7198ead1c465b45f79da00cabee4
741 F20101208_AAAUKI li_y_Page_088.txt
2b60023b17f1a171d4219e9f46850254
24278ece327aed697bb68df05089fad39774219c
8274 F20101208_AAAVMX li_y_Page_176thm.jpg
d210fa312852ec7feab28f81103a2c3b
1d76fd2cbd7c9f33274bac93958b7fbc9e7a3e47
555 F20101208_AAAUJV li_y_Page_026.txt
d358ea1dfe9b633e9f09bf75846b98b9
a437e0ddec3490e4fea140cd810d53398499ae71
2020 F20101208_AAAUKJ li_y_Page_029.txt
517a724b0cb6abc5aae7ca39c681c8eb
8ddd758d4de59080b952c7d298fc932f3d426217
35330 F20101208_AAAVMY li_y_Page_176.QC.jpg
2c7353192384c9719bce4d416821d59b
1e897709b9357a9bcfff5759643218fd99bc05ad
5388 F20101208_AAAUJW li_y_Page_050thm.jpg
55103f62d96c2dff1447828947366943
4b217d8fdc34f6a84a5bc1e492cf39f0d7c7379a
547 F20101208_AAAUKK li_y_Page_086.txt
d39a7b54741cdfff7892fc2c93e018ca
ed067808f7e51ee17d3b17496c85c3b6178c7fb2
9459 F20101208_AAAVMZ li_y_Page_177thm.jpg
6790fdced6c69abe6560b68a852e823a
cc76d0875fbdece813f6c90c845b8e130a509fc8
35915 F20101208_AAAUJX li_y_Page_073.QC.jpg
f672fdb1c91293238a7427c66ecae23e
65b3411d78235e716d78d02809e15d30985616e1
86220 F20101208_AAAULA li_y_Page_075.jp2
fdeb85cb559d2076274d3c8873c21b1f
0ed72b1e31c7165c0a0cc1ad33ceee53d6dfa1ec
55493 F20101208_AAAUKL li_y_Page_156.jpg
c1d98dde6abaf310fe4d06b68985b1f9
815f97d3ce43e75b38f57424fcf6da5fe70718ce
30153 F20101208_AAAUJY li_y_Page_021.QC.jpg
b3a766c5cc1240be3264f9b777909cf6
82e2711581cfd879de7685176bfb71fb7b4be573
88901 F20101208_AAAULB li_y_Page_062.jpg
20757b3d01846b4cbb87e81b1983d598
6a36e18c3a04eb9837c4f92b2250b7101e800ba4
43063 F20101208_AAAUKM li_y_Page_064.pro
34760d3b440a581e57677890cdbcea05
d2f67baca07239466d0306ba7cd3f8d8572cb8b7
7749 F20101208_AAAUJZ li_y_Page_093thm.jpg
365bb7efafd560a7334c1b4639da55dc
46e4d467581bfaf8b291c79d46428d782e4dbcec
1938 F20101208_AAAULC li_y_Page_098.txt
000cdb8e448636d7c4fc0007d0308f61
82b1cb3367f923b866c6f152474a39778d1979e9
110831 F20101208_AAAUKN li_y_Page_016.jp2
1963909f68b26981a6eef384ef4dea3b
47f41a580d5f5447a11d8e64446fadf47bc95080
115108 F20101208_AAAULD li_y_Page_024.jp2
ca4d9f5c97e745c6ea7762211b27b750
0b58035c1107a9da35b62e58b71c7a53c796e445
6091 F20101208_AAAUKO li_y_Page_152thm.jpg
d1a53f1b4bbf270641205406d4c08216
b831438f70b1335eb7db4b6f3445616e1bac6e80
106981 F20101208_AAAUKP li_y_Page_041.jpg
e382fc659e221c3fd3a4d8ec581c0af7
5f5b0730955d5e04c9842ea287cc16bf4d3e892d
121133 F20101208_AAAULE li_y_Page_044.jp2
a49d72e1a69f15ef83dcabb30e99a2c2
bf95537fff0e13023f8feb5dd6f7bc7eb27e293a
133588 F20101208_AAAUKQ li_y_Page_175.jpg
108e9236ebb6696128e68bc925d0db0e
25b2f338633b5dcf160fdef1bc4cee052737f629
65886 F20101208_AAAULF li_y_Page_020.jpg
80ac0a2e3ad0598f053cdec9d452f83d
bab9ca8a5848e5a39cfa55c7ee30f8c96d280499
64584 F20101208_AAAUKR li_y_Page_102.jp2
6de84625427f3d57862dd7b3f826a5b5
e78d443762bf97a887d7cd000782f32b823ca4ce
35202 F20101208_AAAULG li_y_Page_125.QC.jpg
32cd68fef4c890caef9b20220f81ff10
50b55b2dbb0d37c5d7f6d218a40b900eae003dc3
22086 F20101208_AAAUKS li_y_Page_162.QC.jpg
4c4a70f1ad2a7cad978a2da55bfbe233
041a6dc667ad08df78cfc60b401f538498dcc684
87653 F20101208_AAAULH li_y_Page_015.jpg
4dcabc7e948e67f751127e71e2b1dbc5
a0958ea2ff733a83efdf1a5e9c0d00dd75c2d484
F20101208_AAAUKT li_y_Page_037.tif
411784ac914accfe449190d57c4b135c
0a477725bde77337ec9eb7e620eae0b26c397a7e
F20101208_AAAULI li_y_Page_060.tif
d0f100fb814b4a7c11452917fc7b9b4b
43665de07a9fcc758cb8f138b630f840b537e254
F20101208_AAAUKU li_y_Page_129.tif
fdd23ae9589a6be5168e548a13b6e68e
f21380f270e61a0f1cc338d689d2fdcaf6692407
4707 F20101208_AAAULJ li_y_Page_002.jp2
5c3e6bec6f6f0cb1ca42cd805a17e150
5fa6d570c4873688ba7dec7410bdba8b498059ee
134093 F20101208_AAAUKV li_y_Page_010.jpg
aa8fc487c6128fc2c5f4e15e73312c12
b26a48a9fcc389fbe9642a2126d6c04aa3872985
2026 F20101208_AAAULK li_y_Page_138.txt
2f792e6023a2f71d98019a496e447c2b
07b59d4276af09ff966e570d79efee197353a7bb
F20101208_AAAUKW li_y_Page_166.tif
98ab258184b7be5c2181f063f5a0470c
f71ca4327e647c593cf79cedccfb3ba00140817a
F20101208_AAAUMA li_y_Page_029.tif
f54f24995859a15f61c03dc8e97b2484
3aa022eb0af72985547e352f643f5cedbd36270d
1908 F20101208_AAAULL li_y_Page_076.txt
f2014fa7b36aa27dbc6fe22f2540e963
98f5f13e0766e2d825349a564e024128275b3004
7327 F20101208_AAAUKX li_y_Page_116thm.jpg
5665d08bdbbea29dd57f68b5851793cd
981a78218b8272f2ca5bd29684c41ee539153a8a
11943 F20101208_AAAUMB li_y_Page_088.pro
4a60da9ba2cc2e5cca8a89057cf635e4
1fc55e8a1104104485dcab5688783c237232e715
104120 F20101208_AAAULM li_y_Page_092.jpg
28da26f86c26549c8eb870b705df0825
e333027881eef25b24458844602aaece41b2c246
95648 F20101208_AAAUKY li_y_Page_021.jpg
0e215ece98406a27e210d1720578c27f
f585d499784daa1f0bb462237ecb291cde65b9a7
18860 F20101208_AAAUMC li_y_Page_180.pro
801751b7087726d5c46064dfbf479894
2b05d39fff75f0c97e9c4c2d227c7b9e5479ce78
91251 F20101208_AAAULN li_y_Page_065.jpg
327a55ddc48551616525d73e3330a3c5
be6505f2661da2e54a21bd5fea786ba23565a1b1
1715 F20101208_AAAUKZ li_y_Page_015.txt
61442baf21df1ad204727803153cf58f
a54fdcf9550b2c48642efe2ac7785312598286b3
23657 F20101208_AAAUMD li_y_Page_019.QC.jpg
09efc8130a3fb2f0a89bdcfc4e611f6c
8c5a8b2b00e5e11dd84789c8d9e645e47e76b181
F20101208_AAAULO li_y_Page_089.tif
6ea3ad6a0cb90a3195462e3f857fd05b
a4724cd0d6cc3dbbaae6e8e8b533526d110d35ec
3918 F20101208_AAAULP li_y_Page_170thm.jpg
c5b434772f3f36edf15dcb9fd7fd8ec7
2a774f60402693a87f13350bc8f6b5f718546ab2
F20101208_AAAUME li_y_Page_007.tif
2d08e8eb04927c5d716cb876c731e4c9
99c8d49cc73ed082db778e65cb67b81e3c9075da
34193 F20101208_AAAULQ li_y_Page_138.QC.jpg
95f3aaf3b018f6a005f3a0fcaf3df1b8
87f4b15707d8c194fa6886937749a6067b4c3a2d
F20101208_AAAULR li_y_Page_037.jp2
ee9608006765f48d47d3e4d1937a3ccf
2edcb310dd8ec0251740b30e41100068640d0889
8336 F20101208_AAAUMF li_y_Page_095thm.jpg
951ab493a0021cf95f0ab90d025b8a38
869391872d0d3091709537e4e0213496843ae01b
1470 F20101208_AAAULS li_y_Page_162.txt
c2d5daa023bcca0826eac8a4182076f0
6aa681813fa3bd68121d8046f32ab111337ad9b4
1970 F20101208_AAAUMG li_y_Page_139.txt
b5d19fbb8ee6056f177b07ca2d44a1f8
35c8531423871cf6ee8e4f3529c74144ef15ffc2
393159 F20101208_AAAULT li_y_Page_104.jp2
f2281b2041a0dee24f92b8aa3f8b8b83
447b846b647643049b7c430d4454f8d1d07f4d20
295 F20101208_AAAUMH li_y_Page_113.txt
c3d5ed560bdcdd4366a151ace56fb582
fef3c13dae43c670e98b7c8815ee53b05d6b92a1
F20101208_AAAULU li_y_Page_045.tif
2de42f9f4b0121d1b122aa128aeb7404
c92ebde19d84266f9cd68b7ed63783cdd15ce193
29784 F20101208_AAAUMI li_y_Page_032.QC.jpg
55f716def6990b3a6815b458cd737ce3
cfbfc421d0451e01db2da9c60993719124fed02c
5639 F20101208_AAAULV li_y_Page_090thm.jpg
77e9356583fedce9dc5f19df394401a7
30ce0a96250704a67703e1553abffc3c5b32bfdc
F20101208_AAAUMJ li_y_Page_141thm.jpg
e1100f585bdf0d8ef23a5f02c5dc9fa8
26491c552b1cf0f12cc69b9f505cd50b14a33975
53359 F20101208_AAAULW li_y_Page_017.pro
dfc1548eb49af379ffe25524b858c72e
b2ba6aefe683d7e688269aa9c19722098a53f706
33015 F20101208_AAAUMK li_y_Page_127.jp2
4faa70253ff1c83834731e9357fc3201
80761e65f97d69fcec40ed6f243e11b220d80c08
33159 F20101208_AAAULX li_y_Page_004.QC.jpg
a298772c9d0f700ef62c963241d5255c
208d07f9bd1b8bf1d40e17704c416178aae14485
4604 F20101208_AAAUNA li_y_Page_179thm.jpg
30e3737147d17d99b44098c954440f3d
d93ba2972776020b2163cea29df9e65173798659
1880 F20101208_AAAUML li_y_Page_151.txt
6f10b6c75e06fce2db068ab8d10a8b79
222f9226ca021c07ed8639ffd262d30d739d9863
42497 F20101208_AAAULY li_y_Page_180.jpg
48f24324fc2f9b618a2bc80bf22462f0
e0466b11e3d99043d7fe66eed15c1479e1a424ee
F20101208_AAAUNB li_y_Page_058.tif
f620ccebf998db54b639c6f9ed5aa98a
bce5021b7a2961407c2af94b6533080e5c85285b
F20101208_AAAUMM li_y_Page_136.tif
4dc90a1beb902027811b2bc33f68e1a7
e2f42a3532d8aa9260a6110575c34921d5132885
427369 F20101208_AAAULZ li_y_Page_131.jp2
61ee9efefc0021fdfb11551df2d6df3d
367ae98277e7a84fff968f88fd77cd1d17a7b3c2
1762 F20101208_AAAUNC li_y_Page_072.txt
92d143eaa9c112f6ccd48f4adcfcc44e
bc30a7f1f937509e41b8e8d9c06aedf36e9d855b
F20101208_AAAUMN li_y_Page_046.txt
6f0fd9f5879354e868ee42c17b71ca2f
761fa5d9287bb072aafe2f25a8533453deef73e8
31565 F20101208_AAAUND li_y_Page_098.QC.jpg
8fb554bac69bedaf6326a7ebb4ecb75d
40e5d8f71e39c14edd12001c6ef43a5bc9e48446
34610 F20101208_AAAUMO li_y_Page_105.QC.jpg
1ff77510f171475906ba5682a2eeccd5
1dca406b87e8f02ae6f268b221e257027fc35c9c
889578 F20101208_AAAUNE li_y_Page_083.jp2
6af3b0b6d2461a79f91e0d578c06b895
cabfdcd5e79b5242ff42a3c7d0dfeed0dec847c9
1819 F20101208_AAAUMP li_y_Page_119.txt
7b2b8f50413fec797876e6760d4a8f7a
4e12f5a05fdf83e55a1dc9e2aec0b685b1713fae
49382 F20101208_AAAUNF li_y_Page_081.jpg
56254a57234b5ac99e816074e4f09570
e71efa539b168c56fee42b69e99dafb2ec8d6691
4314 F20101208_AAAUMQ li_y_Page_130thm.jpg
93f64dfba78fd8a3e053cc620cebe384
0c75d19ae7a4521aefab89e8afd5fa1ba8e58307
101221 F20101208_AAAUMR li_y_Page_143.jp2
ed8352f8948c5c6cc634d23050c63b3d
ffcecf4ef5f28e79ff6b5ade553c8158529ab00f
F20101208_AAAUNG li_y_Page_072.tif
409646f3fbfd0e9efa9e8b01703ce187
d9cf79277042d469d3511d19e5e110d88667fe0c
1835 F20101208_AAAUMS li_y_Page_023.txt
2db8ad5a74d2e9d2180ce884f1152844
bb94d65c551d13beda6d6142bd9cef1c515d0871
28395 F20101208_AAAUNH li_y_Page_056.QC.jpg
0b96e088f832811b327b8f6e4f452c07
5d14e7f19d6e980e115bb49b007c6a6d24f676cd
6284 F20101208_AAAUMT li_y_Page_154thm.jpg
1b36269535c2b7e4f5355ed830900e43
787a0883a743ecf2426295e55087c31f50a71852
8909 F20101208_AAAUNI li_y_Page_109thm.jpg
32c23a2440fe5248c037c2cbc58438e0
06d057ba41559795b3e94e0d5f46ba6bc5c5d608
37291 F20101208_AAAUMU li_y_Page_058.pro
b96d69da8b65eef5c13d9c1da3e4f06c
56fe55a4fb005dcb30f3f4da6498cabf8c7bbe39
F20101208_AAAUNJ li_y_Page_004.tif
090a1ca07235e3eb6a25198b95c2c3d5
0930b0d714cf0cffa5ad1cafad14a2051d0835b3
26842 F20101208_AAAUMV li_y_Page_064.QC.jpg
4daedd32467075dda96330632ef0da9d
e38320e1c48209368e3e0d917814e833ba075526
8837 F20101208_AAAUNK li_y_Page_136.QC.jpg
e79b0ca98a8b2c5e6125d072454613ce
10c88042fc5af8f8e458624faff80494a97aa09a
314710 F20101208_AAAUMW li_y_Page_159.jp2
b82f2040b037ca704df1861f5bdbcda2
a3adfa6c59408b8c22636cb2dea3e5d8aba62ca6
96838 F20101208_AAAUOA li_y_Page_078.jp2
15efa06d84c99071375e7fd304443d71
03559a2ac4111b2817af867f0e1b13ad8a9c72d8
111963 F20101208_AAAUNL li_y_Page_040.jp2
0be162f5a355f575455391bcf1860b0b
3126b6f823cb89e5c8baf150b956dde6077df878
370 F20101208_AAAUMX li_y_Page_117.txt
53cdacce41b61ad28d37dc9a2b34c7f3
50fc797ca535c1cb32fc022d17c5f50626243dba
7682 F20101208_AAAUOB li_y_Page_140thm.jpg
ad9164b650947660113c4c4777aca7b9
f46fe7f245ce1cd0098a15918ef8cfbf6f864b7f
F20101208_AAAUNM li_y_Page_114.tif
6821ef38a9266f720e95ab753dc7d1c5
c43c7bb62665f0e7662068e1eaed80e2481afe99
F20101208_AAAUMY li_y_Page_137.tif
1e49f95da2fc46524eb1518f0d59547e
193b4121d29ab9513545e4edc37eb11f9a35fec8
8777 F20101208_AAAUOC li_y_Page_041thm.jpg
05d83f8d0f031cbec11a8aa334e36089
fa2df8e1a6cb4bb07f2154dcf608040b40f3ae3a
5265 F20101208_AAAUNN li_y_Page_085thm.jpg
586b77fca1656609d46261c456396e6e
d2c30c01df612d2d3c4dd65212ef46a22a012bee
115710 F20101208_AAAUMZ li_y_Page_110.jp2
9482c6578927e6489432b5ab54cd0804
1a57172e9e1b09eba99faf4bb6e0b72503892ea4
36324 F20101208_AAAUOD li_y_Page_123.QC.jpg
95e00a579ad6be0ec8060484784a4f4f
fd898523c6fd7c104d2eff8da4a33eff3c92007e
108105 F20101208_AAAUNO li_y_Page_077.jpg
b88117e7fa927827741fe10bb6d43de8
fb3b3e4aaa5adf74cd0d45adf588a9288ba47d51
4974 F20101208_AAAUOE li_y_Page_115.pro
9bfb112a063e3ba3cb71af21649f9d3e
c58b2e12d1132372be18d0d6ed225febff4090a2
110640 F20101208_AAAUNP li_y_Page_031.jp2
004e93591e1fc819f9e1c97717972b03
5ccd5c4a94add8b144fad25e6c1e88e6ab317163
7805 F20101208_AAAUOF li_y_Page_119thm.jpg
d562aa93d222d6b484f128239e18d765
cdf8270efaf4b405e140276bf46335cfdd4a6cb0
41212 F20101208_AAAUNQ li_y_Page_033.pro
65deea75f2652c7565790e018438d633
94ee2a7bbe37146ff9c5de3a803794e15ac014aa
38536 F20101208_AAAUOG li_y_Page_161.pro
9d93b0195c117fb23b76e4b8f78a09d5
e238f0de6b0261f30833968841eb8bcd4a5ab8a2
5880 F20101208_AAAUNR li_y_Page_088thm.jpg
cd341246eda22785c6228d524b1069e0
cb68ca3413f1956eadd783515b0a7580200e88cd
38661 F20101208_AAAUNS li_y_Page_045.pro
bc52cb26d4ecf780b1ccea0ba9c7855a
9c3f0ac5454f62002675b766f09e59e606daa4ae
2153 F20101208_AAAUOH li_y_Page_109.txt
a4e171ce8feaacefd1d1dc2d48a82aef
d73ccdf8a6b7e079911972ede5e6d260f66e89e2
428 F20101208_AAAUNT li_y_Page_090.txt
ad3e7c31bb7f47262c125a613430c036
ab5083cef4b6e43bd27e31686f335f9bb83680e2
45371 F20101208_AAAUOI li_y_Page_014.pro
357f2644d4052bd5de00d6a2da8c8c39
1cd4a5fb95e280c0c6970dd853d725e6d3d188ab
F20101208_AAAUNU li_y_Page_175.tif
80ed12d72021433c8feae339eeffc0c6
e0b393fe00a36bf2fe5740b34bd94835add68f1c
29267 F20101208_AAAUOJ li_y_Page_076.QC.jpg
415c38ca4b394069482087ff9a6c8891
8b04f542a36336db3435ad3f66c87e61517a5d8b
81519 F20101208_AAAUNV li_y_Page_069.jpg
35835b8b6347f2982966d62e1de9c3a6
e94e24884c4f66758aede6574ef460e8ddc4e1a7
F20101208_AAAUOK li_y_Page_064.tif
7582304c6869162f160c86f806115efa
f667ad69a9341ce5e03fc65bce014cb29adcd694
14369 F20101208_AAAUNW li_y_Page_083.pro
90a2619e085e6d0bc78d182ecf23d2d9
3f593002bebde38113247157caf2bea9596b1a9e
4826 F20101208_AAAUOL li_y_Page_013thm.jpg
8112ee30cbbb119d2dd59114ef86bc03
d9d3238c2061c494348d4fdf72e37dd02c0ed5ab
38055 F20101208_AAAUNX li_y_Page_019.pro
c2c9a939b2b98c945b0c4892e910f21c
d695d7a1e5986fe07c39b0a9f74d987912fc5cd9
F20101208_AAAUPA li_y_Page_009.txt
ebdc62f24ef0d727d0444662ac960983
a09989845882243b6f98f159ec0409c10919a97a
F20101208_AAAUOM li_y_Page_024.tif
49e53d0916dd50368e3691a0896be025
8e70a331a25c7b96e07deaf348359542cec31c37
F20101208_AAAUNY li_y_Page_113.tif
a166c16f8d78d20c5ee3e60e27a42d1d
e5b221d634ae9b115c05498233aad067263f9f19
52944 F20101208_AAAUPB li_y_Page_150.jpg
b5be7b54f866ce61a53187786e87808c
e2245d2c0a0924704251757659be481662e7a56c
F20101208_AAAUON li_y_Page_076.tif
bbe74af8ef38f696c8a550158ea20f00
90452193e131bd3af97eae6db332a9acdbbfed40
12456 F20101208_AAAUNZ li_y_Page_114.QC.jpg
7ee663b45b4acb5eb21f7f92a1cb5ae1
cf5939283f09758070bb2113f5887ade39943379
520074 F20101208_AAAUPC li_y_Page_051.jp2
fda5ef105f7829c334841b5e281d27b0
ca02193f61f6d1c93b9fd6c281efeb74e76a3224
77691 F20101208_AAAUOO li_y_Page_045.jpg
693f34b7d1914cf7afb3f3262432890c
7df63fc8dbc5b20d803723cfe55d72edb2ac8ef8
70654 F20101208_AAAUPD li_y_Page_011.pro
5ecd438dc3f0a5909c28d5e4c954b111
e240e723afc2138e5816d3c3be1d470df28de0d2
93917 F20101208_AAAUOP li_y_Page_015.jp2
04503c7f746d99b3b876551432821f3e
b31ebf0be5decb85543bdedff3995dcb23145b95
6770 F20101208_AAAUPE li_y_Page_019thm.jpg
49b39beab338d06633be8bbaeccc8657
a7bc438823c5fb9d349d20d444ecbb0f620e1bcf
49279 F20101208_AAAUOQ li_y_Page_107.pro
8cdb11a71ccd80cdb29db834e2e27263
f7ccc159862fc5865437fcacb2b2e71f59ca444d
2151 F20101208_AAAUPF li_y_Page_073.txt
5c860b91f5e33250cc6d36a8c22930d9
49919dbda4cc61faacfd776c46a8614258057037
29928 F20101208_AAAUOR li_y_Page_036.QC.jpg
a250d84cdd86e29c19d98fed5e0f8abb
7367ecbd6caebeb259fcd307b215d2b6cb64fc62
77644 F20101208_AAAUPG li_y_Page_035.jp2
105546937041fc54c0ff503eeab4f967
dc032fd2f6fd746042dbb7af496373e5dd80a986
F20101208_AAAUOS li_y_Page_046.tif
188b7dd956ddf7e1985d9981e39a49d5
8f3b711936225dd1db918418b3c085e05f0296a8
2714 F20101208_AAAUPH li_y_Page_010.txt
5c1deb520af4ae346481888c8f12789e
9a38fbbbf02b45e04b01ffc0fe9d25bbdf172f33
6802 F20101208_AAAUOT li_y_Page_035thm.jpg
376c956d287720238099f53f76fe3620
b1a8e53c5f8a6ab6a5ff0b27640c264f37a85b2d
46435 F20101208_AAAUOU li_y_Page_049.jpg
39f0d4d14b729af406d02bb16a724e71
91474a557095ad6da61fa2e9ea4f93ce8c993a43
F20101208_AAAUPI li_y_Page_038.tif
f119b1971d26a1167fa2049cbe31c526
d2efc7b84cce45b307de3074ec576f92035b2463
F20101208_AAAUOV li_y_Page_131.tif
4b52efdade5a6ec507322ae0696d61c4
00a592a4b764bcb09390698de22b870b57210b12
19773 F20101208_AAAUPJ li_y_Page_080.jp2
7bb20d03523a6f05d5efc8003442b06f
cddcc9e047ccd166476e8e45f465ff6461c2e4e0
22342 F20101208_AAAUOW li_y_Page_083.QC.jpg
9e0248a9853789436bc9bce330e11c3b
b9b23cce39f965fb5474de1fef810d339bf6dda2
109194 F20101208_AAAUPK li_y_Page_110.jpg
db4b4cbc2b902e146d8d8124592eed25
c4c6f1c3d5cda6e1a052f40759627478f46dff89







SIDE-IMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT
BOUNDARY LAYER MEASUREMENT





















By

YAWEl LI


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008




































O 2008 Yawei Li



































To my husband Zhongmin and my parents









ACKNOWLEDGMENTS

Financial support for the research project is provided by National Science Foundation

(CTS-04352835 and CMS-0428593) and AFOSR grant (F49620-03-C-0114). A doctoral

dissertation is never the work of an individual, but instead a miracle that encompasses the efforts

of many people. I would like to recognize a number of people who have helped me in various

ways during my time in University of Florida.

First and foremost, I extend my sincerest gratitude to my advisor, Dr. Mark Sheplak, who

gave me the opportunity to work in MEMS research field. I sincerely appreciate his guidance,

continuous encouragement and support in my research, tirelessly sharing with me his expertise

and wisdom. His profound knowledge in MEMS, fluids, acoustics and so on is the invaluable

source I always rely on.

I also wish to extend gracious thanks to my committee members, Drs. Toshikazu Nishida,

Louis N. Cattafesta, Bhavani V. Sankar and David Arnold for their instruction and assistance on

this interdisciplinary project. They are always generous on their time and expertise, and I am

grateful for their efforts.

I would give special thanks to professors in Department of Electrical and Computer

Engineering, Material Science Engineering and Mechanical and Aerospace Engineering at

University of Florida, especially Dr. Mark Law and his student Ljubo Radic, Dr. Kevin Jones

and Dr. Raphael Haftka for their invaluable suggestions on my device fabrication, process

simulation and design optimization. I would especially like to thank Dr. Melih Pepila at

Sabanchi University (Turkey) and Dr. Jaco F. Schutte for their suggestions in optimization

design.

My thanks go to Dr. Venketaraman Chandrasekaran at Sensata Technologies, Sean Knight

in University of South Florida, Alvin A Barlian in Stanford University and Core Systems










Company for their help in device fabrications, and Keck Pathammavong at Engent for his help in

device packaging. I would also express my thanks to Al Ogden, Dr. Ivan Kravehenko and Bill

Lewis at UFNF for the facility maintenance and help on the fabrication.

I was fortunate enough to have great colleagues throughout my graduate school

experience. My thanks go to IMG members, especially Hongwei Qu for his suggestions and

discussions in device fabrication; Brandon Bertolucci, Alex Phipps, David Martin for their kind

help and assistance in device package design, Vijay Chandrasekharan, Qi Song, Benjamin

Griffin and John Griffin for their kind help in device characterization, Matt Williams, Benj amin

Griffin, Brandon Bertolucci and Brian Homeijier for their great editing and suggestions in my

dissertation writing. It has been a pleasure to have work with them, and I will carry these

invaluable memories on rest of life.

Finally, I reserve the special thanks to my families for their support and encouragement. I

am always grateful to my husband, Zhongmin Liu for his endless love and support in my life.

My parents always encouraged me to be the best and do my best on what I want to do. I would

like to thank them for believing me every time I said I would graduate "next year". Without

their love and support this dissertation would not be possible.












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............4.....


LIST OF TABLES ................ ...............9............ ....


LIST OF FIGURES .............. ...............10....


AB S TRAC T ............._. .......... ..............._ 14...


CHAPTER


1 INTRODUCTION ................. ...............16.......... ......


Motivation for Wall Shear Stress Measurement............... ..............1
Wall Shear Stress............... ...............17.
Turbulent Boundary Layer ................. ...............19................
Research Objectives............... ...............2
Dissertation Overview .............. ...............24....


2 BACKGROUND .............. ...............29....


Techniques for Shear Stress Measurement............... ..............2
Conventional Techniques .............. ...............30....
MEMS-Based Techniques............... ..............3
Floating Element Sensors .............. ...............32....
Sensor Modeling and Scaling ................. ...............32................
Error Analysis and Challenges .............. ...............34....
Effect of misalignment ........._..._... ...............34....._.. .....
Effect of pressure gradient ........._..._. ......_._ ..........._ ........ ..............35
Effect of cross-axis vibration and pressure fluctuations .............. .....................3
Previous MEMS Floating Element Shear Stress Sensors ................. ......... ................38
Capacitive Shear Stress Sensors ................. ...............38......___....
Optical Shear Stress Sensors .............. ...............40....
Piezoresistive Shear Stress Sensors ................. ... ........ ...............42.....
A Fully-Bridge Side-Implanted Piezoresistive Shear Stress Sensor ................... ...............43

3 SHEAR STRESS SENSOR MODELING .............. ...............53....


Quasi-Static Modeling ................. ...............54.......... ......
Structural Modeling ................. ...............54.................
Small Deflection Theory .............. ...............55....
Large Deflection Theory .............. ...............56....
Energy method .............. ...............57....
Exact analytical model .............. ...............57....
Lumped Element Modeling .............. ...............58....












Finite Element Analy sis............... ...............60
Piezoresistive Transduction ................. ...............62........... ....
Piezoresistive Coefficients .............. ...............64....
Piezoresistive Sensitivity ................. ...............66.................
Electromechanical Sensitivity .............. ...............68....
Noise Model............... ...............69.
Thermal Noise .............. ...............69....

1/ f Noise............... ...............70.
Device Specific Issues .............. ...............72....
Transverse Sensitivity .............. ...............72....
Temperature Compensation............... ..............7
Device Junction Isolation .............. ...............74....
Sum m ary ................. ...............78........ ......


4 DEVICE OPTIMIZATION ................. ...............91..............


Problem Formulation ......__................. .........__..........9

Design Variables .............. ...............91....
Obj ective Function ................. ...............93................
Constraints ................. ...............94.................
Candidate Flows .............. ...............95....

M ethodology ............... ... .... ........ ...............96.......

Optimization Results and Discussion ................ ...............97................
Sensitivity Analysis .............. ...............98....
Sum m ary ................. ...............100......... ......


5 FABRICATION AND PACKAGINTG ................ ...............105...............


Fabrication Overview and Challenges ................. ...............105...............
Fabrication Process ................. .......... .. .................105....
Sensor Packaging for Wind Tunnel Testing ................. ...............110..............


6 EXPERIMENTAL CHARACTERIZATION ................ ...............118................


Experimental Characterization Issues ................. ...............118................
Experimental Setup............... ...............119.
Electrical Characterization ................. ...............119......... ......

Dynamic Calibration .............. ...............120....
Noise Measurement ................. ...............121.............

Experimental Results ................ ...............122................
Electrical Characterization .............. .. ...............122..

Dynamic Calibration Results and Discussion .............. ...............122....
Sum mary ................. ...............126......... ......












7 CONCLUSION AND FUTURE WORK ................. ...............137........... ...


Summary and Conclusions ................. ...............137...............
Future Work............... ...... .............13

Temperature Compensation............... .............13
Static Characterization............... ...........14
Noise M easurement ................. ... ........ ...............142......
Recommendations for Future Sensor Designs ................. ...............142........... ...


APPENDIX


A MECHANICAL ANALYSIS ................. ...............145...............


Small Deflection ................... ......... ... ...............145......

Large Deflection-Energy Method ................. ...............147................
Large Deflection-Analytical Method ................. ...............149................
Stress Analysis............... ... .. .. ...........15
Effective Mechanical Mass and Compliance .............. ...............153....


B NOISE FLOOR OF THE WHEATSTONE BRIDGE .............. ...............157....


C PROCE SS TRAVELER ............_...... ...............160...


M asks ............ _. .... ...............160...
Process Steps .............. ...............160....


D PROCESS SIMULATION ................. ...............166...............


E MICROF ABRICATION RECIPE F OR RIE AND DRIE PRO CES S.............. ...... .........__16 9


F PACKAGING DRAWINGS .............. ...............170....


LIST OF REFERENCES ................. ...............173................


BIOGRAPHICAL SKETCH ................. ...............180......... ......










LIST OF TABLES


Table page

1-1 Summary of typical skin friction contributions for various vehicles. ........._..... ..............25

1-2 Parameters in the turbulent boundary layer. ............. ...............25.....

3-1 Material properties and geometry parameters used for model validation. .......................79

3-2 Resonant frequency and effective mass predicted by LEM and FEA. ............. ................79

3-3 First 6 modes and effective mass predicted by FEA for the representative structure........79

3-4 Piezoresistive coefficients for n-type and p-type silicon. ............. .....................7

3-5 Piezoresistive coefficients for n-type and p-type silicon in the <110> direction. .............80

3-6 Space parameter dimensions for junction isolation. ............. ...............80.....

4-1 The candidate shear stress sensor specifications. ............. ...............102....

4-2 Upper and lower bounds associated with the specifications in Table 4-1. ......................102

4-3 Optimization results for the cases specified in Table 4-1. ............... ..................10

6-1 LabVIEW settings for noise PSD measurement ................. ............_ ..... 128.__...

6-2 The optimal geometry of the shear stress sensor that was characterized. ................... .....128

6-3 Sensitivity at different bias voltage for the tested sensor. ............. ....................12

6-4 A comparison of the predicted versus realized performance of the sensor under test
for a bias voltage of 1.5V. ................. ...............129......... .

E-1 Input parameters in the ASE on STS DRIE systems. ................... ............... 16

E-2 Anisotropic oxide/nitride etch recipe on the Unaxis ICP Etcher system. ................... .....169

E-3 Anisotropic aluminum etch recipe on the Unaxis ICP Etcher system. ............................169










LIST OF FIGURES


Figure page

1-1 Schematic of wall shear stress in a laminar boundary layer on an airfoil section. ............26

1-2 Schematic representation of the boundary layer transition process for a flat-plate
flow at a ZPG ............. ...............26.....

1-3. Schematic of typical velocity profile for low-speed laminar and turbulent boundary
layers [ 9]. ............. ...............27.....

1-4 The structure of a typical turbulent boundary layer ................. ................ ........ .27

1-5 Estimates of Kolmogorov microscales of length and time as a function of Reynolds
number based on a 1/7th power-law profile. ............. ...............28.....

2-1 Schematic cross-sectional view of the floating element based sensor. ................... .........46

2-2 Schematic plan view and cross-section of a typical floating element sensor ..................46

2-3 Integrated shear force variation as a function of sensor resolution for different
elem ent areas. ................. ...............47......... .....

2-4 Schematic illustrating pressure gradient effects on the force balance of a floating
elem ent. .............. ...............47....

2-5 Schematic cross-sectional view of the capacitive floating element sensor ..........._...........48

2-6 Plan-view of a horizontal-electrode capacitive floating element sensor .........................48

2-7 Schematic top-view of a differential capacitive shear stress sensor ............... ...............49

2-8 A schematic cross-sectional view of an optical differential shutter-based floating
element shear stress sensor ............ ...............49.....

2-9 Schematic top and cross-sectional view of a Febry-Perot shear stress sensor ................50

2-10 Top and cross-sectional view of Moire optical shear stress sensor ............ ..................50

2-11 A schematic top view of an axial piezoresistive floating element sensor .........................5 1

2-12 A schematic top view of a laterally-implanted piezoresistive shear stress sensor ............51

2-13 A schematic 3D view of the side-implanted piezoresistive floating element sensor.........52

3-1 Schematic top view of the structure of a piezoresistive floating element sensor. .............81

3-2 The simplified clamped-clamped beam model of the floating element structure. .............81










3-3 Lumped element model of a floating element sensor: (a) spring-mass-dashpot system
(mechanical) and (b) equivalent electrical LCR circuit. .................. ................8

3-4 Representative results of displacement of tethers for the representative structure ............82

3-5 Representative load-deflection characteristics of analytical models and FEA for the
representative structure. ............. ...............82.....

3-6 Verifieation of the analytically predicted stress profie with FEA results for the
representative structure. ............. ...............83.....

3-7 The mode shape for the representative structure. ............. ...............83.....

3-8 Geometry used in computation of Euler' s angles. ................ ...............84........... .

3-9 Polar dependence of piezoresistive coefficients for p-type silicon in the (100) plane. .....84

3-10 Polar dependence of piezoresistive coefficients for n-type silicon in the (100) plane. .....85

3-11 Piezoresistive factor as a function of impurity concentration for p- type silicon at
300K ............ ...............85.....

3-12 Schematic illustrating the relevant geometric parameters for piezoresistor sensitivity
calculations. ............. ...............86.....

3-13 Schematic representative of a deflected side-implanted piezoresistive shear stress
sensor and corresponding resistance changes in Wheatstone bridge. .............. .... ........._..86

3-14 Wheatstone bridge subj ected to cross-axis acceleration (a) and pressure (b). ................... 87

3-15 Schematic of the double-bridge temperature compensation configuration. ........._.._.........87

3-16 Top view schematic of the side-implanted piezoresistor and p++ interconnect in an
n-well (a) and equivalent electric circuit indicating that the sensor and leads are
junction isolated (b). ............. ...............88.....

3-17 Doping profie of n-well, p++ interconnect, and piezoresistor using FLOOPS
simulation ................. ...............88.................

3-18 Cross view of isolation width between p++ interconnects. ............. .....................8

3-19 Cross view of isolation width between p++ interconnect and piezoresistor. ................... ..89

3-20 Top view of the isolation widths on a sensor tether ................. ............... 90...........

3-21 Top view schematic of the side-implanted piezoresistor with a metal line contact. ..........90

4-1 Flow chart of design optimization of the piezoresistive shear stress sensor. ................... 104










4-2 Logarithmic derivative of obj ective function rmn with respect to parameters. ...............104

5-1 Process flow of the side-implanted piezoresistive shear stress sensor. ................... ........ 112

5-2 SEM side view of side wall trench after DRIE Si. ........... ..... ._ ........_ ....13

5-3 SEM side view of the notch at the interface of oxide and Si after DRIE. ....................1 13

5-4 SEM top view of the trench after DRIE oxide and Si. ......___ ..... ..._ ................1 14

5-5 SEM top views of the trench after DRIE oxide and Si with oxide overetch. ..................1 14

5-6 SEM top views of the trench with silicon grass through a micromasking effect due to
oxide underetch. ................. ...............115.....__ ......

5-7 SEM side view of the trench after DRIE oxide and Si. .......___......... ._. .............1 15

5-8 Photograph of the fabricated device. ....._.._................ ...............116 ...

5-9 A photograph of the device with a close up view of the side-implanted piezoresistor. ..1 16

5-10 Photograph of the PCB embedded in Lucite package. ................ .........................1 17

5-11 Interface circuit board for offset compensation ................. ...............117........... ..

6-1 The bridge dc offset voltage as a function of bias voltages for the tested sensor............ 130

6-2 An electrical schematic of the interface circuit for offset compensation. ................... .....130

6-3 A schematic of the experimental setup for the dynamic calibration experiments. ........13 1

6-4 Forward and reverse bias characteristics of the p/n junction............._._ .........._._ ....13 1

6-5 Reverse bias breakdown voltage of the P/N junction. ......... ................ ...............132

6-7 The nonlinearity of the I-V curve in Figure 6-6 at different sweeping voltages. ...........133

6-8 The output voltage as a function of shear stress magnitude of the sensor at a forcing
frequency of 2.088 k
6-9 The normalized output voltage as a function of shear stress magnitude of the sensor
at a forcing frequency of 2.088 k
6-10 Gain and phase factors of the frequency response function. ...........__.. .........__......134

6-11 The magnitude and phase angle of the reflection coefficient of the plane wave tube.....13 5

6-12 Output-referred noise floor of the measurement system at a bias voltage of 1.5V.........136










7-1 Pressure drops versus length between taps in the flow cell. .............. .....................4

7-2 Experimental setup of static calibration ................. ...............144..............

A-1 The clamped beam and free body diagram. a) Clamped-clamped beam. b) Free body
diagram of the beam. c) Free body diagram of part of the beam. ................. .................156

A-2 Clamped-clamped beam in large deflection. ............. ...............156....

A-3 Clamped-clamped beam in small deflection (a) and free body diagram of the
clamped beam (b)............... ...............156..

B-1 The Wheatstone brid ge. ............. ...............159....

B-2 The thermal noise model of the Wheatstone bridge. ........._._. ........... .................159

B-3 The 1/ f noise model of the Wheatstone bridge. ................. ....._.._............... ..15

E-1 The drawing illustrating the Lucite packaging. ............. ...............170....

E-2 The aluminum plate for the plane wave tube interface connection. ............. .................171

E-3 Aluminum packaging for pressure sensitivity testing. ................ ...._.._ ...............172









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

SIDE-IMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT
BOUNDARY LAYER MEASUREMENT

By

Yawei Li

August 2008

Chair: Mark Sheplak
Major: Aerospace Engineering

In this dissertation, I discuss the device modeling, design optimization, fabrication,

packaging and characterization of a micromachined floating element piezoresistive shear stress

sensor for the time-resolved, direct measurement of fluctuating wall shear stress in a turbulent

flow. This device impacts a broad range of applications from fundamental scientific research to

industrial flow control and biomedical applications.

The sensor structure integrates side-implanted, diffused resistors into the silicon tethers for

piezoresistive detection. Temperature compensation is enabled by integrating a fixed, dummy

Wheatstone bridge adjacent to the active shear-stress sensor. A theoretical nonlinear mechanical

model is combined with a piezoresistive sensing model to determine the electromechanical

sensitivity. Lumped element modeling (LEM) is used to estimate the resonant frequency. Finite

element modeling is employed to verify the quasi-static and dynamic models. Two dominant

electrical noise sources in the piezoresistive shear stress sensor, 1/ f noise and thermal noise,

and amplifier noise were considered to determine the noise floor. These models were then

leveraged to obtain optimal sensor designs for several sets of specifications. The cost function,

minimum detectable shear stress (MDS) formulated in terms of sensitivity and noise floor, is









minimized subj ect to nonlinear constraints of geometry, linearity, bandwidth, power, resistance,

and manufacturing limitations. The optimization results indicate a predicted optimal device

performance with a MDS of O(0.1 mPa) and a dynamic range greater than 75 dB. A sensitivity

analysis indicates that the device performance is most responsive to variations in tether width.

The sensors are fabricated using an 8-mask, bulk micromachining process on a silicon

wafer. An n-well layer is formed to control the space-charge layer thickness of reverse-biased

p/n junction-isolated piezoresistors. The sensor geometry is realized using reactive ion etch

(RIE) and deep reactive ion etch (DRIE). Hydrogen annealing is employed to smooth the

sidewall scalloping caused by DRIE. The piezoresistors are achieved by side-wall boron

implantation. The structure is finally released from the backside using the combination of DRIE

and RIE.

Electrical characterization indicates linear junction-isolated resistors, and a negligible

leakage current (< 0. 12 CLA) for the junction-isolated diffused piezoresistors up to a reverse bias

voltage of -10 V. Using a known acoustically-excited wall shear stress for calibration, the sensor

exhibited a sensitivity of 4.24 pIV/Pa, a noise floor of 11.4 mPa/JA at 1 kHz, a linear

response up to the maximum testing range of 2 Pa, and a flat dynamic response up to the testing

limit of 6.7 k
transducer for turbulence measurements in low-speed flows, a first for piezoresistive MEMS-

based direct shear stress sensors.









CHAPTER 1
INTTRODUCTION

This chapter provides an introduction to wall shear stress and motivation for its

measurement. Then the scaling turbulent boundary layer is reviewed as it applies to dictating the

requirements for wall shear stress sensors. The research objectives and contributions are

presented. This chapter ends with the dissertation overview.

Motivation for Wall Shear Stress Measurement

The quantification of wall shear stress is important in a variety of engineering applications,

specifically in the development of aerospace and naval vehicles. These vehicles span a wide

range of Reynolds numbers (Re) from low Re (unmanned air vehicles for homeland security

surveillance and detection) to a very high Re (hypersonic vehicles for rapid global and space

access). Across the Re range, unsteady, complex flow phenomena associated with transitional,

turbulent, and separating boundary layers play an important role in aerodynamics and propulsion

efficiency of these vehicles [1, 2]. Furthermore, since shear stress is a vector field, it may

provide advantages over pressure sensing in active flow control applications involving separated

flows [3].

The accurate measurement of the wall shear stress is of vital importance for understanding

the critical vehicle characteristics, such as lift, drag, and propulsion efficiency. Therefore, the

ability to obtain quantitative, time-resolved shear stress measurements may elucidate complex

physics and ultimately help engineers improve the performance of these vehicles [4]. Viscous

drag or skin friction drag is formed due to shear stress in the boundary layer. The viscous loss is

highly dependent on the physical aerodynamic/hydrodynamic system; typical viscous losses for

different systems are listed in Table 1-1 [5]. For aircraft, reducing skin friction by 20% results in

a 10% annual fuel savings, and for underwater vehicles, a reduction of skin friction drag of 20%









would result in a 6.8% increase in speed [5]. Therefore, shear stress measurement attracts

attention in sensor-actuator systems for use in active control of the turbulent boundary layer with

an aim of minimizing the skin friction [6].

Wall Shear Stress

When a continuum viscous fluid flows over an obj ect, the no slip boundary condition at the

surface results in a velocity gradient within a very thin boundary layer [7]; the streamwise

velocity increases from zero at the wall to its free-stream value at the edge of the boundary layer.

The velocity profile is shown in Figure 1-1. The viscous effects are confined to the boundary

layer, while outside of the boundary layer the flow is essentially inviscid [7]. Two classes of

surface forces act on the aerodynamic body: the normal force per unit area (pressure) P and the

tangential force per unit area (shear stress) zw For a Newtonian flow, the wall shear stress is

proportional to the velocity gradient at the wall.

The boundary layer is classified as laminar or turbulent depending on Reynolds number or

flow structure [7]. A laminar boundary layer forms at low Reynolds numbers and is

characterized by its smooth and orderly motion, where microscopic mixing of mass, momentum

and energy occurs only between adj acent vertical fluid layers. A turbulent boundary layer forms

at high Reynolds numbers and is characterized by random and chaotic motion [8]. The

macroscopic mixing traverses several regions within the boundary layer. There is a transition

range between laminar and turbulent boundary layers, partially laminar and partially turbulent, as

shown in Figure 1-2. In the transition range, the flow is very sensitive to small disturbances [8].

Typical velocity profiles for low speed laminar and turbulent boundary layer are shown in

Figure 1-3. Due to the intense mixing, the turbulent boundary layer has a fuller velocity profile;

thus, the shear stress in the turbulent boundary layer is larger than in a laminar boundary layer.









The boundary layer thickness, 6(x), is defined as the distance from the wall to the point at

which the velocity is 99% of the free-stream velocity [7]. The laminar boundary layer thickness

in a zero pressure gradient flat-plate flow is given by Blasius as [7]

3 5.0
(1-1)


where Rex is the free stream Reynolds number and given by U x/v, x is the streamwise

distance, Um is the free stream velocity, and v is the kinematic viscosity of the fluid. For

turbulent flow, the boundary layer thickness is estimated by the 1/7th pOWeT laW VeoTcity profile

is [7]

3 0.16
x Re (1-2)


The shear stress is related to skin friction by the skin-friction coefficient

C, = (1-3)
pU 2


The wall shear stress z_ for a one dimensional laminar flow is given by Newton's law of

viscosity [7],

du
zw = p ,- (1-4)
dy I,=0

where pu is the dynamic viscosity of the fluid and u is the local streamwise velocity in the

boundary layer. For turbulent flow, the shear stress is decomposed into mean shear stress r,


and fluctuating shear stress r7, in terms of the Reynolds decomposition,


zw = r, + r,~ (1-5)

The mean skin friction for laminar and turbulent flow are given by [7]









27, 0.664
C (1-6)
f,1la~te pU ~2 JK'_

0.027
and C,,,, (1-7)


respectively. Equation (1-2) and (1-7) are based on the assumption of the 1/7th pOWeT laW fOrm

of the velocity profile proposed by Prandtl [7],


-i~ (1-8)


These formulas are in reasonable agreement with turbulent flat-plate data and are appropriate for

a general scaling analysis [7].

Turbulent Boundary Layer

To understand the temporal and spatial resolution requirements for the shear stress sensor,

we need to understand the relevant time and length scales associated with a turbulent boundary

layer. There are two regions in a turbulent boundary layer: the inner layer and outer layer [9]

The semi-log plot of the structure of a typical turbulent boundary layer is shown in Figure 1-4.

The outer layer (wake region), is turbulent (eddy) shear-dominated and the effect of the wall is

communicated via shear stress. The inner 20% of the boundary layer is defined as the inner

layer, where viscous shear dominates. The overlap layer smoothly connects the inner and outer

layer. There are three regions within the inner layer:

0 < y' < 5 viscous sublayer (or linear) region ut = y
5
45 < y' < 0.23' log region u' = In y' + B

where k is the Karman constant and B is the intercept. They are universal constants with

k = 0.41 and B = 5.0 [7]. The non-dimensional velocity u' is defined as









u = u/u ,


(1-9)


where ul is given by

u = JZS, (1-10)

if is the mean velocity, and p is the density of the fluid. The non-dimensional distance y' is

defined as

y' = y/ll =yu'v, (1-11)

where l' = v/u* is the characteristic viscous length scale. A turbulent flow possesses different

length scales. The largest eddies are on the order of the boundary layer thickness, while the

smallest eddies can approach the Kolmogorov length scales [8]. Kolmogorov's universal

equilibrium theory states that the small scale motions are statistically independent of the slower

large-scale turbulent structures, but depend on the rate at which the energy is supplied by large-

scale motions and on the kinematic viscosity [8]. In addition, the rate at which energy is

supplied is assumed to be equal to the rate of dissipation. Thus, the small eddies must have a

smaller time scale and are assumed to be locally isotropic. Therefore, the dissipation rate and

kinetic viscosity are parameters governing small scale motions. The scaling relationships

between the small and large scale structures in a boundary layer flow are [4, 8, 10]

r-3/4
77 u, : = ( R es) -3 (1-12)


Tu fu63 1/2 -/
andv = (Re,> (1-13)









where r and T are the Kolmogorov length and time scales respectively, ue is the eddy velocity

(typically u, ~ O(0.01U,~) [4]. Substitution of Equation (1 -2) into Equation (1 12) and Equation

(1-13) leads to estimates of the Kolmogorov microscales in terms of Re ,,

r ~ 20x(Rex)-11/14 (1-14)

400"x,) 4/71
and T ~ (e)(-5


The relationship between the Kolmogorov microscales and Reynolds number is given in Figure

1-5 for a zero pressure gradient turbulent boundary layer with Um = 50 m/s, and at a distance

x = 1 m downstream of the leading edge assuming a 1/7th pOwer-law velocity profile.

In order to detect the wall shear stress generated by the smallest eddies in a turbulent

boundary layer, the sensor size must be of the same order of magnitude as the Kolmogorov

length scale [10], and have a flat frequency range greater than the reciprocal of the Kolmogorov

time scale [4]. These microscales are rough estimates, so some researchers used the viscous

length scale l' and time scale, t* = v/u*2 to estimate the required sensor size and bandwidth [11,

12]. For example, Padmanabahn et al. [l l] used 41* in their sensor design, and Alfredsson et

al.[12] used 101*, 81* and 21* in their experiments. Gad-el-Hak and Bandyopadhyay [13]

reported these viscous scales are on the same order of the Kolmogorov scales.

If the sensor size is larger than the Kolmogorov length scale, the fluctuating component

will be spatially averaged, which results in spectral attenuation and a corresponding

underestimation of the turbulent parameters [14, 15]. It has been reported that the sensor smaller

than 20 wall units were free from spatial averaging effects [16] while the sensor lager than 30

wall units suffered shear stress underestimation [17]. Equation (1-12) and (1-13) indicate that as









the Reynolds number increases, the sensor size should decrease and the bandwidth of the sensor

should increase. For example, at Rex = 107, the Kolmogorov length scale is 65 Cpm and the

characteristic frequency is 3.7 k
Lofdahl and Gad-el-Hak stated that a sensor size of 3-5 times of Kolmogorov length is reliable

for accurate turbulence measurement [10]. A summary of parameters and their analytical

expressions for a zero pressure gradient turbulent boundary layer are listed in Table 1-2 [7, 8].

In addition, roughness is another factor that may disturb the turbulent boundary layer. The

roughness height due to the flatness of the device die in the package, misalignment in tunnel

installation, and gap size is denoted by ks, and the characterized roughness is given by


k = k ~(1-16)


In turbulent flow if k' > 5 the roughness protrudes above the thin viscous layer, causing wall

friction to increase significantly [7]. If k' < 4, the wall surface is deemed hydraulically smooth

and the roughness does not significantly disturb the turbulent boundary layer [7].

Research Objectives

The goal of this dissertation is to develop a robust, high resolution, and high bandwidth

silicon micromachined piezoresistive floating element shear stress sensor for turbulent boundary

layer measurement. The shear stress sensor should possess high spatial and temporal resolution

and a low minimum detectable signal (MDS). To date, the quantitative, time-resolved,

continuous, direct measurement of fluctuating shear stress has not yet been realized [4]. Further

effort is required to developed standard, reliable MEMS shear-stress sensors with quantifiable

uncertainties. The detailed description of the choice of the piezoresistive sensing scheme is

discussed in Chapter 2.









Depending on the application, there are several challenges in the development of this

device. An ideal shear stress sensor should have a large dynamic range (O(80 dB) ), large


bandwidth (O(10 kctz)), and a spatial resolution of O(100 pLm) to capture the spectra of the

fluctuating shear stress without spatial averaging. The resolvable shear stress would to be on the

order of O(0.1 mPa), resulting in force resolution of O(10 pN) for the desired spatial resolution


of O(100 ym) In addition, an ideal sensor should be packaged to allow for flush-mounting on

the measurement wall surface to avoid flow disturbances.

Traditional intrusive instruments suffer from insufficient spatial and temporal resolution.

Microelectromechanical systems (MEMS) technology offers the potential to meet these

requirements by extending silicon-based integrated circuit manufacturing approaches to

microfabrication of miniature structures [4]. From the perspective of measurement

instrumentation, the small physical size and reduced inertia of microsensors vastly improves both

the temporal and spatial measurement resolution relative to conventional macroscale sensors.

Thus, MEMS shear stress sensors offer the possibility of satisfying transduction challenges

associated with measuring very small forces while maintaining a large dynamic range and high

bandwidth.

The previous research in MEMS shear stress sensors [18-25] is discussed in detail in

Chapter 2. Three transduction schemes have been developed for direct measurement of shear

stress: capacitive [18, 21, 24], optical [20, 22, 23] and piezoresistive [19, 25]. These previously

developed sensors possess performance limitations and cannot be used for quantitative shear

stress measurements.










This research effort is the combination of multidisciplinary design and optimization,

fabrication, packaging and calibration, which results in a truly flush-mounted, MEMS direct wall

shear stress sensor. The contributions to the above efforts are:

Development of electromechanical modeling and nonlinear constrained design
optimization to achieve good sensor performance for aerospace applications.

Development and execution of a novel micro-fabrication process accounting for p/n
junction isolation and high-quality electrical and moisture passivation.

Development of a sensor package that can be flush-mounted on the wall surface.

Realization and preliminary characterization of a functioning device.

Dissertation Overview

This dissertation is organized into seven chapters and Hyve appendices. Chapter 1 provides

the motivation for the topic of this dissertation. Background information regarding previous

shear stress measurement technology is discussed in Chapter 2. Sensor modeling is discussed in

Chapter 3. This includes the electromechanical modeling, finite element analysis for model

verification as well as specific design issues. Chapter 4 discusses device optimization subjected

to manufacturing constraints and specifications. Chapter 5 describes the detailed fabrication

process and device packaging. Experimental characterization setups and results are presented in

Chapter 6. The conclusion and future work are presented in Chapter 7.

Information supporting this dissertation is given in appendices. Appendix A provides

detailed derivations of the quasi-static beam models and dynamic models. The detailed

modeling of the noise floor of the fully active Wheatstone bridge is discussed in Appendix B. A

fabrication process flow is presented in Appendix C. The process simulation using FLOOPS

[26] is given in Appendix D. The recipes for plasma etching are given in Appendix E. Finally,

packaging details, vendors, and engineering drawings are provided in Appendix F.









Table 1-1. Summary of typical skin friction contributions for various vehicles [5].
Vehicles Typical viscous loss
Supersonic fighter 25-30 %
Large transport aircraft 40 %
Executive aircraft 50 %
Underwater bodies 70 %
Ships at low/high speed 90-30 %


Table 1-2. Parameters in the turbulent boundary layer.
Parameters
Free stream velocity U.n (m/s)
Typical eddy velocity u, (m/s)
Streamwise distance x (m)
Kinematic viscosity
Reynolds number based on
streamwise distance
Boundary layer thickness S(m)

Momentum thickness B(m)

Reynolds number based on
momentum thickness Re,
Reynolds number based on boundary
layer thickness
Skin friction coefficient C,

Wall shear stress ir(Pa)

Kolmogorov length scale 1 (m)

Kolmogorov time scale T (s)


Analytical expression


ue ~ 0.01U.



U~x
Re

6= 0.16x(Rex~)'
B 7
3 72
U.0B
Re, =

Re =u

C, =0.027(Rexi

r, = C, 1pU 2

9 ~ 3(Res)-3/
3 (Re, )0
T ~























u, i' __~---~-No-Slip Boundary Condition

-....Boundary Layer

t' Airfoil




Figure 1-1. Schematic of wall shear stress in a laminar boundary layer on an airfoil section.









Lamina I: Trasio I Trblt
Rev

Fiur -2 chmai rpesnttono teondr lae trasto proesfraft-le
flow~~n ata P []























Laminar


/ Turbulent


Velocity
Figure 1-3. Schematic of typical velocity profile for low-speed laminar and turbulent boundary
layers [9].


u'


Inner
Region


Outer
Region



Wake
Region


~2



10


Buffer
Region


Viscous
Sublayer
Region


Log
Region


10 5 30 104
Non-dimensional Distance

Figure 1-4. The structure of a typical turbulent boundary layer [8].













3 '10
E 10~ '"F




2~' 10\ 3 9




S -$~10 C





Reynolds N~umber Rex

Figure 1-5. Estimates of Kolmogorov microscales of length and time as a function of Reynolds
number based on a 1/7th power-law profile.









CHAPTER 2
BACKGROUND

This chapter provides an overview of the techniques for shear stress sensor measurement

with a focus on floating element sensors. Previous MEMS shear stress sensors are reviewed and

their merits and limitations discussed. A side-implanted piezoresistive shear stress sensor is then

proposed to achieve high spatial and temporal resolution and quantifiable uncertainties.

Techniques for Shear Stress Measurement

The current techniques employed in shear stress measurement are grouped into two

categories: direct and indirect [27]. Indirect techniques infer the shear stress from other

measured flow parameters, such as Joulean heating rate for thermal sensors, velocity profile for

curve-fitting techniques or Doppler shift for optical sensors [27]. The uncertainty in these

measurements is dominated by the validity of the model relating the flow parameter to wall shear

stress [27]. The direct technique measures the integrated shear force generated by wall shear

stress on surface [4]. This technique includes three areas: floating-element skin friction balance

techniques, thin-oil-film techniques and liquid crystal techniques. The floating-element skin

friction balance techniques are addressed in this dissertation. A floating element sensor directly

measures the integrated shear force produced by shear stress on a flush-mounted movable

"floating" element [27]. Direct measurement techniques are more attractive since no

assumptions must be made about the relationship between the wall shear stress and the measured

quantity and/or fluid properties. In addition, direct sensors can be used to calibrate indirect

devices.

Conventional shear stress sensors and MEMS-based shear stress sensors are described in

the following sections, with specific focus on the MEMS floating element technique.









Conventional Techniques

Many conventional techniques have been developed to measure the wall shear stress [28],

including indirect measurement techniques such as surface obstacle devices and heat

transfer/mass transfer-based devices, and direct measurement techniques such as a floating-

element skin friction balance. Several review papers [27-29] catalog the merits and drawbacks

of these devices in various flow situations and a wide range of applications. The indirect

conventional techniques are summarized in the following paragraph.

Surface obstacle devices include the Preston tube, Stanton tube/razor blade and sub-layer

fence. These devices are easy to fabricate and favorable in thick turbulent boundary layers.

However, they are sensitive to the size and geometry of the obstacle in the turbulent boundary

layer. The device can only measure mean shear stress, and unable to measure the time-resolved

fluctuating shear stress. In addition, they rely on an empirical correlation between a 2-D

turbulent boundary layer profile and property measured.

Heat transfer/mass transfer-based devices include hot films and hot wires. They have

advantages of fast response, high sensitivity and simple structure. However, they are sensitive to

temperature drift, have tedious calibration procedures, and suffer calibration repeatability

problems due to heat loss to the substrate/air. In general, these devices are considered to be

qualitative measurement tools [4].

The direct measurement techniques, known as "skin friction balance" or "floating element

balance", have been widely used in wind tunnel measurements since the early 1950's [28].

These techniques measure the integrated shear force produced by the wall shear stress on a flush-

mounted laterally-movable floating element [29]. The typical device is shown in Figure 2-1.

The floating element is attached to either a displacement transducer or to part of a feedback









force-rebalance configuration. Winter [28] cataloged the limitations of this technique, which are

summarized as follows:

* Compromise between sensor spatial resolution and detectable shear force.
* Measurement errors associated with misalignment, necessary gap and pressure gradient.
* Cross-axis sensitivity to acceleration, pressure, thermal expansion and vibration.

Some of these limitations can be significantly mitigated if the dimension of the device is

reduced, which is a motivation for the development of MEMS floating element sensors.

MEMS-Based Techniques

MEMS is a revolutionary new Hield that extends silicon integrated circuit (IC)

micromachining technology for fabrication of miniature systems. The MEMS-based sensors

possess small physical size and large usable bandwidth. The utilization of these devices

broadens the spectrum of applications, which range from fundamental scientific research to

industrial flow control [6] and biomedical applications [30].

From the fluid dynamics perspective, MEMS-based sensors provide a means of measuring

fluctuating pressure and wall shear stress in turbulent boundary layers because the

micromachined sensors can be fabricated on the same order of magnitude of the Kolmogorov

microscale [10]. Lofdahl and Gad-el-Hak reviewed MEMS-based pressure sensors for turbulent

flow diagnosis [10] including background, design criteria, and calibration procedures. Recently,

Naughton and Sheplak reviewed modern skin-friction measurement techniques, such as MEMS-

based sensors, thin-oil film interferometry and liquid crystal coatings. They summarized the

theory, development, limitations, uncertainties and misconceptions surrounding these techniques

[4].

Several microfabricated shear stress sensors of both direct and indirect types have been

reported. The indirect MEMS wall shear-stress sensors include thermal devices [31-34], laser-









based sensors [35], micro-pillars [36, 37] and micro-fences [38]. Thermal shear stress sensors

operate on heat transfer principles. Laser Doppler sensors operate on the measurement of

Doppler shift of light scattered by particles passing through a diverging fringe pattern in the

viscous sublayer of a turbulent boundary layer to yield the velocity gradient. Micro-pillars are

based on a sensor film with micropillars arrays that are essentially vertical cantilever arrays

within the viscous sublayer. These sensors employ optical techniques to detect the wall shear

stress in the viscous sublayer via pillar tip deflection. Micro-fences employ a cantilever structure

to detect the shear stress via piezoresistive transduction.

Direct shear stress sensors include floating-element devices [18-25]. Three transduction

schemes have been used in floating element sensors: capacitive [18, 21, 24], piezoresistive [19,

25] and optical [20, 22, 23].

Floating Element Sensors

Sensor Modeling and Scaling

The typical MEMS floating element shear stress sensor is shown in Figure 2-2. The

floating element, with a length of Le, width of Weand thickness of 7(, is suspended over a

recessed gap by four silicon tethers. These tethers act as restoring springs. The shear force

induced displacement A of the floating element is determined by Euler-Bernoulli beam theory to

be [l l] (the detailed derivation is given in Appendix A)

r LR L~~ 2L,W 21
A = 1 21
4ET LW

where L,, W, and 7( are tether length, width and thickness respectively, and E is the elastic

modulus of tether material. The mechanical sensitivity of the sensor with respect to the applied









shear force, F = r, eLe, is directly proportional to the mechanical compliance of the tethers 1/k

[18]

1 A 1 L,2L,~
k F 4E7( i(i LW 22

The trade-off associated with spatial resolution versus decreasing shear stress sensitivity is

illustrated in Equation (2-1) and Figure 2-3. For example, a sensor with floating element area of

100 ym x100 Ctm, the integrated shear fore is O(10 pN) for a shear stress of O(1 mPa), which

requires the tethers to have a high compliance to get an appreciable element detection. The

compliance is limited by the maximum shear stress achievable before failure occurs or before

nonlinearity in the force-displacement relationship [4] becomes substantial. The minimum

detectable shear stress is determined by the sensitivity and the total sensor noise [39].

Assuming a perfectly damped or under-damped system, the bandwidth is proportional to

the first resonant frequency, Jkhl, where M is the effective mass,

M~ = pL,WE,7 (2-3)

where p is the density of the floating element material and it is assumed that L e, >> L, .

Therefore, the shear stress sensitivity-bandwidth product is obtained as


1 1 L
Jk2 4E pL,W,7' 24

The sensitivity-bandwidth product is a parameter useful in investigations of the scaling of

mechanical sensors. MEMS technology enables the fabrication of sensors with small thickness

and low mass, in addition to large compliance and a superior sensitivity-bandwidth product

comparable to conventional techniques [4]. A MEMS floating element has lengths of










L, = W = O(1000 pm) and 7J= O(10 ym), whereas conventional floating element lengths are

L, = W = O(1 cm) Therefore, with the scaling of mass alone, MEMS-based sensors have a

sensitivity-bandwidth product at least three-orders of magnitude larger than conventional

sensors. MEMS-based sensors also possess spatial resolution at least one-order of magnitude

higher than conventional sensors, which is vital for turbulence measurements to avoid spatial

averaging [4].

Error Analysis and Challenges

Compared to conventional techniques, MEMS shear stress sensors have a negligible

misalignment error. This error is limited by the flatness of the device die [18] because the

floating element, tethers and substrate are fabricated monolithically in the same wafer. Other

sources of misalignment include packaging and tunnel installation, with packaging the dominant

source [4]. Packaging-induced compressive or tensile force may drastically alter the device

sensitivity [18]. The necessary gap between the wall and floating element is also reduced, with a

typical gap size smaller than 5 Cpm [4].

Effect of misalignment

Misalignment of the floating element results in the element not being perfectly flush-

mounted with the wall surface, which disturbs the flow field around the sensor. The effective

shear stress is estimated by integrating the "stagnation pressure (pu?) over the floating

element surface and dividing by the element area [39] to get


TA 0r (2-5)









where k~ is the height of protrusion or recession above or below the wall. Streamwise velocity

u,~ is obtained via relationship between shear stress and velocity gradient in the sublayer,





where p and pu are the density and dynamic viscosity of the fluid, respectively, and z is the

distance from the wall. Substituting Equation (2-6) into Equation (2-5) to obtain the effective

shear stress yields

1 pk 3z
r~ (2-7)
S3 pUL

For a sensor with Le = 1000 Cpm, ks = 10 Cpm under the surface, and r, = 5 Pa in air, the

misalignment error is about 0. 12% Therefore it may be neglected.

Effect of pressure gradient

Error due to a pressure gradient is also greatly decreased for MEMS sensors. As illustrated

in Figure 2-4, there are two sources which introduce pressure gradient errors; one is the recessed

gap beneath the floating element and the other is the net pressure force acting on the lip of the

floating element [26]. The net force acting on the lip of the floating element is given as

dP
FU = (W AP = 7tW, L .(2-8)
Sdy "

The associated effective shear stress is obtained by dividing by the sensor area, W~L,

dP
r T (2-9)
Sdy

The pressure gradient also introduces a shear stress underneath the floating element that can be

estimated to first-order by assuming fully-developed Poiseuille flow,









g dP
r = (2-10)
S2 dy '

where g is the height of the recessed gap beneath the floating element. The total effective shear

stress acting on the floating element is


zef/ = Zw + dP/ + =;.~( T 1+ + (2-11)


3' dP
where p = --is called Clauser's equilibrium parameter, which is employed to compare the
r, dy

external pressure gradient to wall friction in a turbulent boundary layer [7]. The displacement

thickness 3' is a parameter quantifying the mass flux deficit due to viscous effects. As indicated

in Equation (2-11i), the error is dependent on the gap size and thickness of the floating element

and independent of the size of the floating element. The smaller gap and thickness of the

MEMS sensors result in smaller errors compared to conventional floating element sensors; the

MEMS sensors provide approximately a two-order of magnitude improvement in lip force

induced error. To get a more accurate estimate of these errors, direct numerical simulation of the

flow around the sensor is required.

Effect of cross-axis vibration and pressure fluctuations

Errors due to stream-wise acceleration scale favorably for low mass MEMS sensors [28].

The equivalent shear stress due to acceleration is approximated as

F; Ma p L, La
r, = -== p~ta, (2-12)
A, A, WL

where a is the acceleration and A, is the surface area of the floating element, respectively.

Equation (2-12) indicates that the effective shear stress due to stream-wise acceleration is

proportional to the tether thickness. Assuming the stream-wise acceleration is 1 g for a









proposed optimum sensor design with element dimensions of 1000 Cpm x 1000 Cpm x 50 pm and

the tethers dimension of 1000 Cpm x 30 Cpm x 50 pm, the effective stress is found to be 1.14 Pa in

the y -direction. Depending on the aerodynamic body acceleration levels, local acceleration

measurements in conjunction with coherent power data analysis may be used to mitigate

acceleration effects [40]. The stream-wise deflection is obtained from


3 ~MaC, (2-13)


where ke and Cy are the stream-wise stiffness and compliance of the tethers, respectively.

Therefore, the stream-wise acceleration sensitivity is proportional to Cy Assuming flow over

the floating element in the y -direction (Figure 2-4), the cross-axis compliances according to

small-deflection beam theory are


C = (2-14)
S4E~7


and C = (2-15)


The ratios of transverse compliances to compliance in the flow direction are


-` (2-16)



and (2-17)


If T, W, ~ O(50 ym) and L, ~ O(1 mm), the compliance in the x -direction is four orders of

magnitude less than the compliance in the flow direction ( y -direction). Since the deflection is

proportional to the compliance in the associated direction, the transverse deflection (x -direction)










is four-orders of magnitude smaller than in the flow direction ( y -direction). Therefore, the

transverse acceleration effect in x -direction is negligible. However, the compliances in the z -

and y -directions are of the same order, and thus transverse acceleration effects in the z direction

must be taken into account. This can be mitigated by using piezoresistive transduction scheme

via a fully-active Wheatstone bridge configuration. The transverse acceleration and pressure in

the z -direction supplies a common mode signal to the Wheatstone bridge, which can be rej ected

by the differential voltage output. It is critical to minimize the pressure sensitivity as pressure

fluctuations in wall-bounded turbulent flows are much larger in magnitude than wall shear stress

fluctuations [41]. Hu et al. [41] found that the wall pressure fluctuations is 7 20 dB

(depending on frequency) higher than the fluctuations for the streamwise wall shear stress, and

15 20 dB higher than that for spanwise component. The detailed discussion is given in

Chapter 3.

Previous MEMS Floating Element Shear Stress Sensors

Previous research in the floating element shear stress sensor is reviewed in this section.

This review is divided into capacitive, optical and piezoresistive sensing in terms of transduction

schemes. Their respective performance merits and drawbacks are discussed.

Capacitive Shear Stress Sensors

Realizing the merits of scaling shear stress sensors to the microscale, Schmidt et al. [18,

39] first reported the development of a micromachined floating element shear stress sensor with

an integrated readout for applications in low speed turbulent boundary layers, As shown in

Figure 2-5, the sensor was comprised a square floating element (500 Cpm x 500 Cpm x 32 Cpm)

suspended by four tethers (1000 Cpm x 5 Cpm x 32 Cpm) and fabricated using polyimide/aluminum

surface micromachining techniques. A differential capacitive scheme was employed to sense the









deflection of the floating element. This differential capacitive scheme is insensitive to the

transverse movement to first order. The sensor was calibrated in a laminar flow using dry

compressed air up to a shear stress of 1 Pa The achieved minimum detectable shear stress was

0. 1 Pa with a bandwidth of 10 k
model. However, the sensor was sensitive to electromagnetic interference (EMI) due to the high

input impedance, and suffered from the sensitivity drift due to moisture-induced polyimide

property variation. In addition, the capacitive sensing scheme was limited to nonconductive

fluids.

Pan et al. [21, 42] presented a force-feedback capacitive design that monolithically

integrated sensing, actuation and electronics control on a single chip using polysilicon-surface-

micromachining technology. The sensor has a comb finger structure with folded beam

suspension. The folded beam provided higher sensitivity and internal stress relief. The floating

element motion was measured by a differential capacitive sensing scheme while the folded beam

served as mechanical springs (Figure 2-6). A linear measurement sensitivity of 1.02 V/Pa over

a pressure range of 0.5 to 3.7 Pa was achieved in a 2-D continuum laminar flow channel. No

dynamic response, linearity and noise floor results were reported. In addition, the front wire

bonds may disturb the flow in turbulent flow measurements.

Zhe et al. [24] developed a floating element shear stress sensor using a differential

capacitive sensing technique, with an optical technique as a self-test. The sensor was fabricated

on an ultra-thin (50 pm ) silicon wafer using wafer bonding and DRIE techniques. As shown in

Figure 2-7, the sensor consisted of two sensor electrodes, two actuation electrodes, a floating

element (200 Cpm in width and 500 Cpm in length) and a cantilever beam (3 mm in length). The

shear stress was detected by a cantilever beam deflection, with a mechanical sensitivity of










1 Cpm/Pa This sensor was capable of measuring a shear force as small as 5 nN that

corresponded to a shear stress of 50 mPa The static calibration in a rectangular channel shows

a minimum detectable shear stress of 0.04 Pa with 8% uncertainty up to 0.2 Pa, which is the

limit of the calibration technique. No frequency response results were reported.

Optical Shear Stress Sensors

Padmanabhan et al. [20] developed two generations of differential optical shutter-based

floating element sensors for turbulent flow measurement. As shown in Figure 2-8, the floating

element (120 Cpm x 120 Cpm x 7 Cpm and 500 Cpm x 500 Cpm x 7 Cpm ) is suspended 1.0 Cpm above the

silicon substrate by four tethers. Two photodiodes were integrated into the substrate under the

leading and trailing edges of the opaque floating element. The floating element motion induced

by shear force causes the photodiodes shuttering. Under uniform illumination from above, the

normalized differential photocurrent is proportional to the lateral displacement of the element

and the wall shear stress. The sensor could measure a wall shear stress from 3 mPa up to 10 Pa,

with a sensitivity of 0.4 V/mPa (without integration of detection electronics ). The dynamic

response of the sensor was quantified up to the characterization limit of 4 kHz [43]. The

measured shear stress was consistent with predicted theoretical values. The sensor showed very

good repeatability, long-term stability, minimal drift, and EMI immunity. The main drawback to

this sensor was that vibrations of the light source relative to the sensor resulted in erroneous

signals.

Tseng et al. [22] developed a novel Febry-Perot shear stress sensor that employed optical

fibers and a polymer MEMS-based structure. The sensor was micromachined using

micromolding, UV lithography and RIE processes. As shown in Figure 2-9, a membrane was

used to protect the inner sensing parts and support the floating element displacement









measurement. The displacement of the floating element (400 Cpm high, 200 Cpm wide) induced

by the wall shear stress on the membrane (1.5 mm x1.5 mm x 20 Cpm) was detected via an optical

fiber using Fabry-Perot interferometer. The sensor was tested in a steady laminar flow between

parallel plates and the results demonstrated a shear stress resolution of 0.65 Pa/nm The

minimum detectable shear stress was 0.065 Pa. The fragile sensing parts were not exposed to

the testing environment, making the sensor suitable for applications in harsh environments. This

sensor was not tested in flows. The dynamic response and linearity of this sensor are

questionable due to the potential buckling of diaphragm. Furthermore, cross-axis sensitivity due

to vibration and pressure may be significant given the geometry of the sensing element.

Horowitz et al. [23] developed a floating-element shear stress sensor based on geometric

Moire interferometer (Figure 2-10). The device structure consisted of a silicon floating element

(1280 Cpm x 400 Cpm x10 pm ) suspended 2.0 Cpm above a Pyrex wafer by four tethers

(545 Cpm x 6 Cpm x 10 Cpm). The sensor was fabricated via DRIE and a wafer bonding/thin back

process. When the device was illuminated through the Pyrex, light was reflected by the top and

bottom gratings, creating a translation-dependent Moire fringe pattern. The shift of the Moire

fringe was amplified with respect to the element displacement by the ratio of fringe pitch G to

the movable grating pitch g2 The sensor die was flush-mounted on a Lucite plug front side, and

the imaging optics and a CCD camera was installed on the backside for the displacement

measurement. Experimental characterization indicated a static sensitivity of 0.26 Cpm/Pa, a

resonant frequency of 1.7 kHz, and a noise floor of 6.2 mPa/J Drawbacks to this sensor

included an optical packaging scheme not feasible for wind tunnel measurement and limited

bandwidth.









Piezoresistive Shear Stress Sensors

Shajii et al. [19] and Goldberg et al. [44] extended Schmidt's work to develop a

piezoresistive based floating element sensor for polymer extrusion feedback control (Figure 2-

11). The polyimide/aluminum composite floating element was replaced by single crystal silicon.

These sensors were designed for operation in high shear stress 1 kPa -100 kPa), high static

pressure (up to 40 1VPa) and high temperature (up to 300 OC) flow conditions. The floating

element size was 120 Cpm x 140 Cpm in Ng' s design, and 500 Cpm x 500 Cpm in Goldberg' s design.

The element motion was sensed by axial surface piezoresistors in the tethers via configuration

these piezoresistors to a half Whitestone bridge. This sensor was not suitable for turbulent flow

measurement due to low sensitivity as it was designed for maximum shear-stress levels 5 orders-

of-magnitude larger than those in a typical turbulent flow. However, Goldberg et al. [44]

developed a backside contact structure to protect the wire-bonds from the harsh external

environment, which reduced the flow disturbance and associated measurement uncertainty for

turbulence measurement.

Barlian et al [25] developed a piezoresistive shear stress sensor for direct measurement of

shear stress underwater. The sidewall-implanted piezoresistors measured the integrated shear

force, and the top-implanted piezoresistors detected the pressure (Figure 2-12). The

displacement of the floating element was detected using a Wheatstone bridge. The experimental

measurements indicated the in-plane force sensitivity ranged from 0.041- 0.063 mV/Pa, while

the predicted sensitivity was 0.068 mV/Pa The transverse sensitivity was 0.04 mV/Pa with a

corresponding transverse resonant frequency of 18.4 k
cantilever as an input. The dynamic analysis was performed using a laser Doppler vibrometer

with a piezoelectric shaker to drive the in-plane or out-of-plane motion. The in-plane resonant









frequency was experimentally found to be 19 k
The integrated noise floor was 0. 16 CLV over bandwidth of 1 Hz -100 k
the piezoresistors to changes in temperature was investigated in a de-ionized (DI) water bath, and

the temperature coefficient of sensitivity was found to be 0.0081 kOZ/ C No electrical

characteristics of p/n junction isolation and flow characterization are reported and no fluid

mechanics characterization was performed.

A Full-Bridge Side-Implanted Piezoresistive Shear Stress Sensor

According the above discussion, the most successful 1VEMS floating element sensor to

date used integrated photodiodes to detect the lateral displacement via a differential optical

shutter [20]. This sensor can detect the shear stress as low as 1.4 mPa However, it is not

suitable for wind tunnel testing because the sensing system is sensitive to tunnel shock and

vibration. The capacitive transduction technique integrated the mechanical sensor and

electronics on one chip to eliminate the parasitic capacitance [45], and has the capability to

measure small signals. Unfortunately, the sensitivity drifted due to the charge accumulation in

the electrodes [18], which can be mitigated by hermetic sealing [46] or by employing metal

electrodes. However, the shear stress sensor must be exposed to the flow for shear stress

measurement and wind tunnels are typically not humidity controlled environments.

The piezoresistive transduction scheme is widely used in commercial pressure sensors and

microphones due to its low cost, simple fabrication, and higher reliability than capacitive

transduction. In addition, piezoresistive technology can resolve sufficiently small forces up to

O(10 "N) [47]. Shajii et al. [19] proposed a backside-contact, piezoresistive sensor to measure

very high shear stress in a polymer extruder. Axial mode piezoresistive transducers [19, 25] for

high-shear industrial applications have been fabricated using standard ion-implantation









techniques, but more sensitive bending-mode transducers require that the piezoresistors be

located on the tether sidewall. This concept has been proposed by Sheplak et al.[48] and applied

by Barlian et al. who presented an integrated pressure/shear stress sensors for underwater

applications [25]. The authors did not present a comprehensive fluid-induced shear stress

characterization of their sensor. Rather, the sensor was statically characterized using a

mechanical cantilever and dynamically characterized using an acceleration input. In a

conference paper, the authors presented some water flow results possessing a large uncertainty

and an unexplained sensitivity that was larger than the value predicted by beam mechanics [49].

None of these devices have successfully transitioned to wind tunnel measurement tools

because of performance limitations and/or packaging impracticalities [2]. For use in a wind

tunnel, the sensor package must be flush mounted in an aerodynamic model, robust enough to

tolerate humidity variations and immune to electromagnetic interference (EMI). We have

attempted to address these limitations via the development of a fully-active Wheatstone bridge

side-implanted piezoresistive sensor. This approach was motivated by the following two side-

implanted piezoresistive transducer concepts. Chui et al. [50] first presented a dual-axis

piezoresistive cantilever using a novel oblique ion implantation technique. Later, Partridge et al.

[51] leveraged the side-implant process to fabricate a high performance lateral accelerometer.

The device structure developed in this dissertation is illustrated in Figure 2-13 which

shows an isometric view of the floating element, sidewall implanted p-type silicon piezoresistors,

heavily doped end-cap region, and bond pads. In this transduction scheme, the integrated force

produced by the wall shear stress on the floating element causes the tethers to deform and thus

induces a mechanical stress field. The piezoresistors respond to the stress field with a change in

resistance from its nominal, unstressed value due to a change in the mobility (or number of










charge carriers) within the piezoresistor [52]. The conversion of the shear stress induced

resistance change into an electrical voltage is accomplished via configuration of the

piezoresistors into a fully-active Wheatstone bridge to increase the sensitivity of the circuit

compared to half bridge configuration. This bridge requires the presence of a bias current

through the piezoresistors, typically, it is driven by constant voltage excitation. This sensor is

designed to measure shear stress only and to mitigate pressure sensitivity. An on-chip dummy

bridge located next to the sensor is used for temperature corrections.

Ideally, common mode disturbances do not have any effect while differential disturbances

are linearly converted into the bridge output. To achieve a differential signal, the piezoresistors

are oriented such that the resistance modulation in each resistor of a given leg is equal in

magnitude but opposite in sign. These conditions are achieved by placing the side implanted

resistors facing one another such that when one resistor is in tension, the other is in compression.

This results in equal mean resistance but opposite perturbation.

Once the transduction scheme is selected, the mechanical models and transduction sensing

models need to be developed to get sensor performance, such as sensitivity, linearity, bandwidth,

noise floor, dynamic range, MDS. The detailed discussion of the electromechanical modeling is

given in Chapter 3.













u(z)


Floating Element


Restoring Springs

Figure 2-1. Schematic cross-sectional view of the floating element based sensor.


Tether AFloating Element


Flow


Figure 2-2. Schematic plan view and cross-section of a typical floating element sensor [4].


Flow


u(z)











10


10


- l6
10


10
-03 -2 0 2 13
10 10 10 10 1
Shear Stress w (Pa)

Figure 2-3. Integrated shear force variation as a function of sensor resolution for different
element areas.

U.0

u~) 1 We zY
3/ P1 Z P2x y

Wall


Floating Element


Figure 2-4. Schematic illustrating pressure gradient effects on the force balance of a floating
element.









Embeded


Floating Element







Sense Capacitor


Dnive Capacitor


Sense Capacitor


on chip
off chip


Figure 2-5. Schematic cross-sectional view of the capacitive floating element sensor developed
by Schmidt et al. [18].

Tether Floating Element


Release Holes


Expanded View of Comb Finger Structures

Cl

V+ C2

Figure 2-6. Plan-view of a horizontal-electrode capacitive floating element sensor [21].













































Photodiodes


Sense
Electrode




Actuation
Electrode



Pads


r


Figure 2-7. Schematic top-view of a differential capacitive shear stress sensor [24].



Incident Light from a Laser Source

Flow 1 1 ,, ,, Floating 1Element~ute


-I I n-type Si
Oxide Passivation


p-type Si


Figure 2-8. A schematic cross-sectional view of an optical differential shutter-based floating
element shear stress sensor [l l].


F tn Flow

n2 t~I





Tethers -


II


Incoherent Light )l Frinee

Pyrex


_XXI


Reflection Mirror
(Floating Element)


A-A' Cross-Section

Input(Output) Fiber- d


R1 R-


MRTV1 Membrane


Air or Liquid Flow


Figure 2-9. Schematic top and cross-sectional view of a Febry-Perot shear stress sensor [22].


Aluminum Gratings
(Floating Element &
Base Gratmngs)


Incident


Reflected Moire


Laminar Flow Cell


Ti
L-r


Floating. Element


Figure 2-10. Top and cross-sectional view of Moire optical shear stress sensor [23].


"I I



Floating Element



























Figure 2-11. A schematic top view of an axial piezoresistive floating element sensor [19].


Top-Implanted Piezoresistor for
Pressure Measurement


Tether


Floating Element


Side-Implanted P~iezoresistor for
Shear-Stress Measurement


Figure 2-12. A schematic top view of a laterally-implanted piezoresistive shear stress sensor
[25].












R+M~


Sidewall Implanted
Plezoresistor ,n a


Cr ~R+M\ ~ R-M



Bond Pads Silicon Tether

n-well



Figure 2-13. A schematic 3D view of the side-implanted piezoresistive floating element sensor.









CHAPTER 3
SHEAR STRESS SENSOR MODELING

This chapter presents the electromechanical modeling of the MEMS side-implanted

piezoresistive shear stress sensor. These models are leveraged for use in finding an optimal

sensor design (detailed discussion in Chapter 4). Formulation of the objective function for

performance optimization begins with structural and electronic device models of the shear stress

sensors. The structural response directly determines the mechanical sensitivity, bandwidth, and

linearity of the dynamic response. The piezoresistor design determines the overall sensitivity

and contributes to the electronic noise floor of the device. The organization of this chapter is as

follows.

First, the mechanical modeling is discussed, including quasi-static modeling and dynamic

response analysis. Linear and non-linear quasi-static behaviors are presented. Lumped element

modeling is employed to find the dynamic behavior of the sensor. These analytical models were

verified using finite element analysis (FEA) in CoventorWare".

Second, the piezoresistive sensing electromechanical model is developed, where the

resistance and piezoresistive sensitivity for non-uniform doping are derived via stress averaging

and a conductance-weighted piezoresistance coefficient. Two dominant electrical noise sources

in the piezoresistive shear stress sensor, 1/ f noise and thermal noise, as well as amplifier noise

are considered to determine the noise floor.

Finally, some device specific issues are addressed, including transverse sensitivity,

acceleration sensitivity, pressure sensitivity, junction isolation issues and temperature

compensation via a dummy bridge.










Quasi-Static Modeling

In this section, the sensor structure is discussed and modeled. Quasi-static models for

small and large floating element deflections that make use of Euler-Bernoulli beam theory and

the von Karman stain assumption, respectively, are presented. Two methods are used in large

deflection analysis, an energy method and an exact analytical method.

Structural Modeling

Floating element sensors are composed of four tethers and a square floating element. A

schematic of the piezoresistive shear stress sensor is shown in Figure 3-1. The floating element

is suspended above the surface of the silicon wafer by tethers, each of which is attached at its end

to the substrate. Side-implanted boron in the sidewalls of the tethers forms the four

piezoresistors. These resistors are aligned in the <110> direction and located near the edge zone

of the tethers to achieve the maximum sensitivity. Two resistors are oriented along opposite

sides of each tether. When the fluid flows over the floating element, the integrated shear force

causes the tethers to deform and induces a bending stress.

For the mechanical analysis, the floating elements and tethers are assumed to be

homogeneous, linearly elastic, and symmetric. In practice, this is not strictly valid as the beam is

partially covered by thin silicon dioxide and silicon nitride layers. The floating element is

assumed to move rigidly under the applied shear stress, and the motion is permitted in-plane

only. The tethers are assumed to be perfectly clamped on the edge. The effects of pressure

gradient and gap errors are ignored. Furthermore, the Young's modulus and Poisson ratio are

assumed to be constant and do not change with processing.









Small Deflection Theory

Assuming that L, >> W,, T,, the tethers can be modeled as a pair of clamped-clamped

beams with a length of 2L,, subj ected to a uniform distributed load Q (per unit length) and a

central point load P [39], as shown in Figure 3-2. The distributed load is due to the shear stress

acting on the tethers and is given as

Q = r,W,. (3-1)

The point load, P is the effect of the resultant shear force on the floating element and is given

by

P = r,W,Le/2, (3 -2)

where the factor of 1/2 comes from the symmetry of the problem. The maximum deflection and

bending stress distribution is obtained using Euler Bernoulli beam theory. The detailed

derivation is given in Appendix A. The lateral displacement of the beam is given by


w~x) [ (IYL,L, +8(~L, x -(2WY,L, +8WL,)x' +2(xy (0<;x 4EW,7

where E = 168 GPa is the Young's modulus of silicon in the (110) direction [53]. The

maximum deflection occurs at the center of the beam and is obtained by substituting x = L, into

Equation (3-3) to get

r,W,LBI L,r ]II+2WL, 34
A-12 34
4E7E W W,L,

This corresponds to the floating element displacement. The second term in the brackets of

Equation (3-4) is a correction for the distributed wall shear stress on the tethers. Equation (3-4)

indicates that the important parameters affecting the scaling of the device are the area of the

floating element, W,L,, ratio of the tether length to the tether width, L,/R,, and ratio of the area










of a tether to that of the floating element, WL,/RL, If the tether surface area WL, << WL,, the

stiffness is approximated as

1 A 1 L
k w~~e.Et (3-5)


This indicates that the stiffness is proportional to the tether thickness and ratio of the tether width

and length. The bending stress distribution through the width and length of the tether is given by


7,e~~e 2y 3 2WL, W~ x 3WL, x 0xL
0-2(x, y)= 1 ~ + + ~ + (36
W, Te W 4 WeLe 2 WeL L, WeL L, 0
where x = 0 is at the end of the beam, and y = 0 is on the side wall surface. Equation (3-6)

indicates that the maximum shear stress is located at the end of the beam and on the side wall

surface ( x, y = 0 in Figure 3-2).

Linear Euler-Bernoulli beam theory [54] fails for sufficiently large wall shear stresses

because the mid-plane of the beam is strained [46]. The beam grows stiffer as the deflection

becomes large. Furthermore, the nonlinear motion generates undesired harmonic distortion in

the frequency domain. The sensor is required to maintain a linear relationship between shear

stress and displacement in order to preserve spectral fidelity for time resolved measurement.

This requirement places a nonlinear constraint in the sensor design optimization (discussed in

Chapter 4). A large deflection mechanical model was therefore developed for use in determining

this constraint.

Large Deflection Theory

Large deflection theory provides a measure of the maximum shear stress that may be

measured while maintaining mechanical linearity. Two analysis techniques are pursued to









determine the nonlinear mechanical behavior of the sensor: the strain energy method [46] and an

exact analytical method. The detailed derivations are given in Appendix A.

Energy method

The deflection predicted by the strain energy method [46] is obtained by assuming a trial

function which meets both the clamped boundary condition and symmetry condition of the beam,


w(x) = ^1+ cos (37
82 iL, ) : 37

where A, is the floating element deflection. The trial function is substituted into the expression

for strain energy in the beam and the principle of minimum potential energy is applied. The

result is


3 z w,~ L, WL
Az :1+ Ltr = -, 1+2 .:L (3-8)


Comparing this result to Equation (3-4), one can see that cubic nonlinearity term has been added.

The mechanical response of the floating element sensor will be linear provided that the non-

linear term is small with respect to unity; that is, if the displacement of the sensor is small in

comparison to the tether width, (Az /W,) << 1. The nonlinear term is cubic and therefore

represents a Duffing spring behavior, or stiffening of the beam as deflections become large. This

means that the nonlinear deflection is smaller than the ideal linear deflection for large shear

stresses.

Exact analytical model

In the large deflection model, the neutral axis tension force Fa is taken into account. The

average axial tension force is obtained by integrating the neutral axis strain along the length of









the beam. It then serves as a constitutive equation between axial force and strain. The detailed

model development procedure is given in Appendix A. The maximum deflection predicted by

the exact analytical method is obtained using von Karman strain assumption,

P .cosh(ALl,)-1 n +P oP QL PL
2AFE F A sinh(AL, ) ~~Y 2 2 2Fa 2F;

where the axial force Fa is given by



F = dxay(( (3-10)


and Ai is given by

A= 12,/EW (3-11)

There are five variables, four boundary conditions and one constitutive equation. But the

equation is indeterminate, so the final solution is obtained using an iterative technique to find Ai,

and therefore obtain the maximum deflection.

Lumped Element Modeling

Lumped element modeling is used to represent the fluidic to mechanical transduction of

the shear stress sensor and facilitates the prediction of the dynamic response. The main

assumption of LEM is that the length scale of the physical phenomena of interest is be much

larger than the characteristic length scale of the device [55]. For the shear stress sensor, this

means that the bending wavelength of the beam must be much larger than the length of the

tethers. The LEM provides a simple way to estimate the dynamic response of a system for low

frequencies, up to just beyond the first resonant frequency, which is appropriate for design

purposes [56].









There are several types of elements in the lumped element model. For example, in a

lumped mechanical system, mass represents the storage of kinetic energy, compliance of a spring

(inverse of stiffness) represents the storage of potential energy, and a damper represents the loss

of energy through dissipation. Similarly, in lumped electrical systems, generalized potential

energy is stored in a capacitor, generalized kinetic energy is stored in an inductor, and energy is

dissipated via a resistor.

From a LEM perspective, the two sets of tethers are modeled as a spring possessing an

effective compliance C_,, In an impedance analogy, this compliance shares a common

displacement with the effective mass IM,,, of the tethers and floating element as well as the

damper, R,, of the system. The main source of damping is the viscous damping underneath the

element, and thermoelastic damping, compliant boundaries and vibration radiation to the

structure boundaries are neglected in this research. Therefore, the sensor is modeled as a spring-

mass-dashpot system, as schematically shown in Figure 3-3. In the equivalent circuit, the

voltage and current are analogous to force and velocity, respectively. The motion of the mass-

spring-dashpot system is described by the classic second-order differential equation,


F (t) = M,,, + R, + 1/C,,, A (3 -12)
medt2 dt

Therefore, the frequency response function of the device is found to be

A (jei) 1
H( je) =(3-13)
F( jm) ( jeS)2 M,,l,, + jC(R, + 1 C,,,e

where the angular frequency m = 27r f f. is the cyclic frequency, and j = J-l. Assuming a

lightly damped system, the first resonant frequency f, is










f = (3-14)


The detailed derivation of the lumped elements is given in Appendix A. The effective

mechanical compliance is determined by equating the potential energy stored in the beam to that

of an equivalent lumped system and is


C = 1+2 1+4 + (3-15)
2E7E ( W,L, 1 L, 15 ,L


The effective mass is obtained by equating the kinetic energy of the sensor to that of a lumped

system and is


1494 ,L, 223 8 W,, 1024 (,(
M = psWL,( 1+ '+ ~ + 12 (-16
;se315 WL 315 L 315 WL WL,


where p,, = 2331 kg/m3 is the density of silicon [53].

Finite Element Analysis

To verify the analytical models, a finite element analysis with a clamped boundary

condition on the edge of the tethers is performed. The material properties of silicon and the

geometry of a representative structure are given in Table 3-1.

Finite element analysis is performed in CoventorWare" using the multi-mesh model by

partitioning the continuum solid model into plate and tether volumes. A fine mesh is used in the

tethers because of the large stress gradients with respect to those found in the plate. These

volumes are j oined to form one volume via RigidLink after meshing. The mesh is composed of

parabolic Manhattan brick elements. A mesh refinement study revealed sufficient elements

dimensions are 3 Cpm,0.5 Cpm and 1 Cpm in length, width and thickness within the tethers,










respectively, and 10 Cpm,10 Cpm,1 Cm within the plate. Since the device is symmetric, only half

of the structure is analyzed in the model, with 6600 elements in the analysis.

A representative displacement field of the tethers at r, = 5 Pa is shown in Figure 3-4. The

comparison in Figure 3-4 indicates that the nonlinear analytical model is in agreement with FEA

simulation results. Figure 3-5 shows the maximum displacement of the floating element as a

function of applied shear stress for analytical linear and nonlinear models, nonlinear energy

method model and FEA model. This comparison in Figure 3-5 indicates that all results are in

agreement in the linear range (50 Pa approximately), while the nonlinear analytical model,

nonlinear energy method model and FEA models agree in this nonlinear deflection region.

Figure 3-6 shows the stress distribution using analytical linear model (Equation (3-6)) and FEA

results along the tether length on the sidewall surface ( y = 0) for the representative structure.

Figure 3-6 demonstrates that the analytical model is in agreement with the FEA model. The

bending stress varies from tensile to compressive in a parabolic distribution along the tether

length. Figure 3-6 shows that the maximum stress occurs on the edge zone ( x, y = 0 ) of the

tether.

The resonant frequency obtained from LEM (12.44 k
well, as shown in Table 3-2. The next 5 modes were also found using FEA and are given in

Table 3-3. The first six mode shapes are shown in Figure 3-7. The in-plane resonant frequency

(second mode) is 17.08 k
because the tether width is greater than the tether thickness for the verification studies (Table 3-

1). Clearly, the representative dimensions used for model verification are not a preferred design,

let alone an optimized design.









Piezoresistive Transduction

In 1954, Smith [52] discovered the piezoresistance effect in silicon and germanium. The

piezoresistance effect is defined as the change of semiconductor resistivity due to a change in

carrier mobility that results from an applied mechanical stress. In piezoresistive transduction, the

resistance modulation is a function of the applied stress and piezoresistive coefficients (xjz [57].

For the cubic crystal structure of silicon under small strain, the correlation of normalized

piezoresistivity (Ap/ p) and stress for reduced tensor notation reduces to






-< > =3 (3-17)
pI~2 A 0 0 0 O4
Ap 0 0 O r4 0 9
Ap1 0 0 0 0 0 z4 1,,

where Ap is the change in resistivity, a, are normal stresses along the cubic crystal < 100 >

axes, and 5, are shear stresses.

For a given resistor geometry, there are two piezoresistive coefficients used for

piezoresistive sensing analysis in terms of stress orientation with respect to the current. The

longitudinal piezoresistive coefficient captures the effect of an applied stress in the same

direction as the current, and the transverse piezoresistance coefficient captures the effect of an

applied stress in the direction perpendicular to the current. The longitudinal and transverse

piezoresistive coefficients in terms of the fundamental piezoresistive coefficients and direction

cosines are given by, respectively [58],

a =x, +2 %4 2 1 2 12 1Z2 l2 12\l (3-18)


and 4 = n,2 (%4 + 2 1~)(l 1 2 12n1 nZ13Z) (3-19)









where (ly,ng,n ) is the set of direction cosines between the longitudinal direction and the crystal


axis, and 13,,m, n,n is the set of direction cosines between the transverse direction and the

crystal axis. The direction cosines are given in terms of Euler' s angles [59]

1, m, n, c~c~cry s~sry s~c~cry + c~sy -s~cry
1, m, n, = c~c~sry s~cry -s~c~sy + c~cy -s~sry ,(3-20)
13m, n, c~s8 s~s8 cB

where c# = cos (#), sf = sin (#), and etc. The geometry of the Euler' s angle i s shown in Figure

3-8. In this research, a (100) wafer is used, thus B = 0, y/ = 0 and # sweeps from 0 to 180

degree in Figure 3-8. Therefore, the matrix (3-20) reduces to,

1, m, n, c# s# 0
1, m, n, I= -s# c# 0 (3-21)
13 m, n, O 0 1

The piezoresistive coefficients, 4z;, 4i, and try are given in Table 3-4 for both p-type and n-type

piezoresistors at room temperature for low doping concentrations.

For this piezoresistive device, the floating element sensor features integrated side-

implanted diffused resistors [25, 50, 51] in the element tethers for piezoresistive detection. In

this transduction scheme, the integrated force produced by the wall shear stress on the floating

element causes the tethers to deform and thus creates a mechanical stress field in the tethers. The

piezoresistors respond to the mechanical stress field with a change in resistance from its nominal

unstressed value [46] as indicated by

AR Ap
= gr + 4r, ,(3 -22)
R p









where p and R are the resistivity and resistance of the piezoresistor, respectively, A signifies

the perturbation in the resistance and resistivity due to the piezoresistive effect, a, is the bending

stress along the beam, and o, is the transverse stress. For a beam subjected to pure bending,

Equation (3-22) simplifies to


S= zzG:,. (3-23)

Piezoresistive Coefficients

The piezoresistive coefficients depend on crystal orientation, doping type and level, and

temperature. This dependence is typically expressed as a product of the coefficient' s low-doped

room temperature value so~ and a piezoresistive factor P(N, T) [59]


~z(N, T) = ~zoP(N, T), (3-24)

where Ni is the doping concentration and T is the temperature. For a (100) wafer, the

dependence of the piezoresistive coefficient on the crystal direction is given in Figure 3-9 and

Figure 3-10 for p-type and n-type piezoresistors, respectively. This indicates that the maximum

piezoresistive coefficient for p-type silicon is in the (110) direction, while for n-type silicon the

maximum is in the (100) direction. Also note that n-type silicon has a larger achievable

piezoresistive coefficient than p-type silicon. The longitudinal and transverse piezoresistive

coefficients zz, and z, in the (110) direction for n-type and p-type silicon are given in Table 3-5

[52]. As shown in Table 3-5, piezoresistors in p-type silicon are more sensitive than for n-type

in the (110) direction, which is parallel or perpendicular to the flat of a (100) wafer. In this

design, the p-type piezoresistors are chosen due to its high sensitivity in the (110) direction and









because of the lower temperature sensitivity at higher doping concentrations compared to n-type

piezoresistors [60].

Many theoretical [59] and experimental [61-63] studies have reported the dependence of

the piezoresistive factor P(N, T) on doping concentration at room temperature. Kanda' s model

[59] is most popular and is accurate for low concentrations. However, when compared to

experimental data [61-63], Kanda' s model under predicts the roll-off of P(N, T) for

concentrations above 10'7 cm For doping concentration above 10 cm the fundamental

piezoresistive coefficient is expressed as a product of its lightly-doped room temperature value

4,~ and the experimentally fitted piezoresistive factor P(N, T) [47],


Fr (N, T) = 4P(N, T) = 4, log .312 1-004 (3-25)


The piezoresistive factor is plotted in Figure 3-11 versus concentration at room temperature. The

piezoresistive coefficient is also temperature dependent. At higher doping concentrations, there

will be a reduction in both thermal noise and 1/ f noise compared to lower doping concentrations

[47]. In addition, the temperature dependence of the piezoresistance coefficient is reduced

significantly as the concentration increases at low doping concentration. For doping

concentrations above 10" cm3, the piezoresistance coefficient is almost independent of

temperature variation [61]. However, the sensitivity degrades due to the reduced piezoresistive

coefficient at a high doping level [62]. Thus, there is a tradeoff between sensitivity and noise

floor. This tradeoff suggests optimization is necessary to obtain the best performance, as will be

discussed in chapter 4.









Piezoresistive Sensitivity

For the structure shown in Figure 3-12, the side-implanted piezoresistors are fabricated by

first implanting p-type impurities (boron) into the sidewall, followed by a diffusion step to drive-

in and to electronically activate the impurities. The impurities diffuse laterally, and the resulting

impurity concentration profie decreases from the surface of the side wall to the junction depth.

If the unstrained impurity profile as a function of depth, N:(y), is known, the piezoresistive

coefficient profie tr(y) can be determined. As shown in Equation (3-6), the stress varies along

the beam, and varies across the junction depth, y, as well. Therefore, the product of the stress

and the piezoresistive coefficient distributions need to be integrated in the electromechanical

model .

Several models have been developed for piezoresistive sensitivity. Tortonese [64] and

Harley [65] built a two-step model for non-uniform doping concentration and formulated an

efficiency factor to be inserted into the numerator of the surface sensitivity equation. In

integrating across the beam, their model does not account for the junction isolation of diffused

resi stores. Senturia [46] presents the piezoresistive coefficient dependence of the doping

concentration, but does not account for stress variation as a function of depth. Sze's model [57]

addresses stress variations across the resistors (y -direction) and incorporates a conductance-

weighted piezoresistance coefficient. Sze, however, did not account for the stress variation along

the piezoresistor (x -direction). Based on Harley's work, a new model was developed by

involving stress averaging along the tether length and across the depth of piezoresistor, and using

a conductance-weighted piezoresistive coefficient.

Two issues need to be considered in calculating the piezoresistive response. One is that

the piezoresistors are typically formed by diffusion, thus have a non-uniform doping profile with









respect to junction depth. The second issue is that piezoresistors also span a finite area on the

device, and hence have non-uniform stress with respect to length and depth. The derivation of

the resistance of the piezoresistor begins with the non-uniform doping concentration that varies

from the sidewall surface to the junction depth ( y -direction). The stress varies in this direction

as well. As shown in Figure 3-12, the resistor can be considered as a stack of slices, where each

slice has a slightly different doping concentration and stress. The current flow is in x direction,

so the slices ( dy ) are connected electrically in parallel because they share the same potential.

The stress also varies along the length of the resistor (x direction). Thus, the resistor is also

segmented along its length. These segments (dx) are connected in series due to the same current

flow. The mechanical model assumes that L, >> W and 72, thus the differential resistance of a

unit cell for a small segment dx and a small slice dy with width of W, is given by

1 p, ( x, y) dx
dRunlt, (x, y) (3 -26)
dG,,,,,, (x, y) W dy

where it is assumed that y = 0 at the surface and y = W,/2 at the neutral axis. In Equation

(3-26), o, (x, y) is the stressed resistivity determined by [46]

Pe~x y)= Po~y)1+7z (~o-2x, )),(3 -27)

where peo (y) is the unstressed resistivity and 0-t(x, y) is given in Equation (3-6). For non-

uniform doping, peo(y) is given by [66]


peo (y) = ,(3 -28)
p, (y)qN, (y)

where q = 1.602 x 10-1 C is the electronic charge of an electron and up (y) is the boron

mobility. In this research, the mobility is obtained from [67]. To simply the calculation process,









we use conductance G = 1/R rather than resistance in the derivation. The total conductance for

segment dx is obtained by summing the conductance of each unit


dG,I, = CdG 1Wd .(329
aceL~ "" d Peo(y) (1+ zzl(y)01 (x, y))

The total resistance is determined by summing the resistance of the small dx segments,

LR +L,. LR +L,
R +AR / dGstice = 1 dx ,v (3-30)
LR LR W dy
a, Pe(y)(1+ ;z,(y)o, (x, y))

where LR = 10 Cpm is the overlap end cap and it does not change the resistance value. The total

unstressed resistance is similarly found by integrating along the length of the resistor using the

unstressed resistivity,

LR +L,. LR +L,
R = [1/d~ticedx .(3-3 1)
LR R W dy


Then the resistance modulation is obtained by arranging Equation (3-30) and (3-31),



AR R+AR -R peo(F LR+L
R R o dx-yL R+ ,1. (3-32)
R R L LR Tdy



Electromechanical Sensitivity

The four side-wall implanted piezoresistors form a full Wheatstone bridge circuit that

provides sensitivity enhancement for a small change in resistance. As illustrated in Figure 3-13,

when the tether deflects in the y direction, piezoresistors 1 and 3 experience a compressive

stress while 2 and 4 experience a tensile stress. These resistors experience a change in resistance









of -MR and MR, respectively. For an ideal bridge, R, = R, = R MR and R, = R4 = R + MR, so

that the output voltage, Vo, for a given bias voltage V,, is


V R4 R' V,= (3-33)
ii : R,+R4 R,+R, R

The sensitivity of the piezoresistive sensor is defined as the change of output voltage per unit of

applied shear stress and for a linear sensor is expressed as

aV, V
Sm<= (3-34)


Substituting in Equation (3-33), the electromechanical sensitivity is rewritten as


Sm, = (3 -3 5)
RT,

Noise Model

The key sources of the electrical noise in piezoresistive sensors are thermal noise, low

frequency 1/ f noise, and amplifier noise [65]. Physical fluctuations of the floating element at

an equilibrium temperature, T, can result in random motion of the device; however, the

contribution of thermomechanical displacement noise has been found to be much smaller than

the electronic noise sources except at mechanical resonance [47]. For an ideally balanced

Wheatstone bridge, the bias source noise will be common mode rej ected.

Thermal Noise

Thermal noise, also known as "Nyquist" or "Johnson noise", is produced when electrons

are scattered by thermal vibration of the lattice structure [68]. Since higher temperatures lead to

increased vibrational motion, thermal noise power spectral density (PSD) is directly proportional

to temperature. Moreover, thermal noise is present in thermodynamic equilibrium, and its PSD

is independent of frequency since random thermal vibrations are not characterized by discrete









time constants. The thermal noise PSD (S,, ) is modeled by Nyquist [68], which was

experimentally verified by Johnson [69], as

S,, = 4kTR (3 -3 6)

where kg = 1.38e-23 J/K is the Boltzmann constant, R is the total resistance in the resistor, and

T is the temperature in Kelvin. In a piezoresistor, the rms noise voltage, V,, due to thermal

noise is obtained by taking the square root of the thermal noise PSD integrated over the bin

width of interest Af = f2 J; [68],



Vm S, Vdf = J4kg TR f ,(3-37


1/J Noise

The dominant noise source for most ion-implanted piezoresistors is 1/ f noise. Hooge

[70] first reported that the 1/ f noise PSD of a piezoresistor is inversely proportional to the total

number of carriers in the resistor when an external dc bias voltage is applied, and is given by


S,/ HV2,f (3-38)


where VR is the voltage across the resistor, N, is the total number of ionized carriers in the

resistor, f is frequency, and aH is Hooge parameter, with the experimental values ranging from

5 x10-6 to 2x10-3 [71]. Hooge' s parameter is sensitive to bulk crystalline silicon imperfections

and the interface quality. Low frequency noise occurs under non-equilibrium conditions and its

spectra is proportional to the square of the applied voltage. Two physical mechanisms have been

proposed to account for the low frequency noise: random trapping/detrapping of carriers at the









surface and bulk electronic traps, and random mobility fluctuations [72]. The noise power of

1/ f noise is obtained by integrating Equation (3-3 8) over a frequency range of operation


aR =In (3-39)


The total number of ionized carriers in the resistors for the piezoresistor geometry in Figure 3-12

is given as


No = Lj,i*.W N(dy (3-40)


where N, (y) is the p -type doping concentration. As indicated in Equation (3-39), 1/ f noise

increases for small volumes and highly resistive piezoresistors.

In this dissertation, the typical input noise of a low noise amplifier at 1 kHz ,

4 nV/JA [73], is used in the noise floor model. For an ideally balanced Wheatstone bridge

assuming a unity gain amplifier, the total rms output noise voltage I is


I =1 aH B2N 4.~, 7 4,TR, f (4e-9 Af (3-41)


where the first, second and third terms in Equation (3-41) are the contribution of 1/ f noise,

thermal noise, and the amplifier noise, respectively. The detailed derivation of Equation (3-41)

is given in Appendix B. Since narrow bin turbulence spectra are desired, a figure of merit bin

width of Af = 1 Hz centered at 1 kHz is used in this dissertation; therefore, J = 999.5 Hz and

f2 =1000.5 Hz.

The minimum detectable shear stress (MDS) or input noise, Zminn is the minimum shear

stress that the shear stress sensor can resolve in the presence of noise, and is defined as










r =" (3 -42)
mm, S

The dynamic range (DR) is then given by


DR = 201og zmax (3-43)


Device Specific Issues

In this section, a few specific design issues are addressed, including transverse sensitivity,

acceleration sensitivity, pressure sensitivity, temperature compensation and device junction

isolation issues.

Transverse Sensitivity

Transverse sensitivity was discussed in Chapter 2 (Equation (2-16)), and restated here

briefly. Recall that the transverse mechanical sensitivity in the x -direction can be neglected due

to the large differences in bending versus axial stiffness, while transverse mechanical sensitivity

in the z direction is of the same order as in the flow direction. The x -direction also possesses

electromechanical rej section for an ideally balanced bridge.

Assuming the flow is in the y direction, when the sensor is subj ected to an x-axis

acceleration, piezoresistors 1 and 2 experience a tensile stress while 3 and 4 experience a

compressive stress. These resistors experience a change in resistance of MR (piezoresistors 1

and 2 and -MR (piezoresistors 3 and 4), respectively (Figure 3-14 (a)). The resistances in the

bridge become R, = R, = R + MR, R, = R4 = R MR The output voltage, Vo, for a given bias

voltage V,, is given by

R, R R+MR R-MR
V =0 (3 -44)
oR, +R, R, + R4 2R +2MR 2R 2M









When the fluctuating pressure load acts in the z direction, the stress distribution in all four

tethers is the same, leading to equal resistance perturbations (AR) in all four piezoresistors. The

reaction of the Wheatstone bridge due to pressure is shown in Figure 3-14 (b). The total pressure

effect is to supply a common mode signal into this differential sensing scheme, which does not

affect the voltage output. Therefore, the ideal electromechanical sensitivity due to the x-axis load

and pressure disturbance is ideally equal to zero. In reality, there will still be transverse

sensitivity due to bridge mismatch.

Temperature Compensation

The output voltage of a piezoresistive sensor is dependent on temperature due to the

thermal sensitivity of the resistance, strain and piezoresistive coefficient [46]. In this

dissertation, it is assumed that the thermal coefficient of resistance will dominate over thermal

strain effects and changes in the piezoresistive coefficient. The typical temperature coefficient of

resistance for a laterally implanted sensor is reported to be 0.0081 kOZ/oC, which is much larger

than the shear stress sensitivity [25]. Since it is impossible in practice to have absolute

temperature control in a wind tunnel, temperature compensation of the output signal must be

employed. In it important that the temperature is measure as close as possible to the sensing

element to avoid compensation errors due to temperature gradients in the flow. In this thesis, the

temperature compensation of the resistors are achieved using a double bridge configuration [74].

As shown in Figure 3-15, two Wheatstone bridges are used on one chip; one is the active

Wheatstone bridge with output that is a function of shear stress and temperature, while the other

is a dummy compensation Wheatstone bridge with output that acts as a thermometer and only

depends on temperature. The dimension of the compensation bridge resistors is identical to the

active bridge and is kept as close as possible to the active bridge (safe distance of 100 Cpm










suggested for the peripheral circuits [75] ). The detailed temperature compensation procedure

for the non-ideal case of a statically unbalanced bridge is discussed in Chapter 6.

For ideally balanced Wheatstone bridge, the power supply noise is just a common mode

signal to the bridge and would not affect the bridge voltage output. In most physically realized

devices, the bridge is not exactly balanced. Therefore, the power supply noise contribution to the

noise scales with the bridge offset voltage output normalized by the bias voltage.

Device Junction Isolation

One design issue is the difficulty of realizing a junction-isolated, laterally diffused resistor

in the sidewall of a tether. As shown in Figure 3-16, the p-type piezoresistor (with resistance

Rs), the p++ interconnects (with resistance R,) and the n-type substrate form a p/n diode. For

an ideal p/n diode, the leakage current is negligible in the reverse bias region [76]. When the

reverse voltage exceeds a certain value, the reverse current will increase rapidly and the diode

will breakdown. To ensure the current flows exclusively through the p-type regions, the p/n

junction must be reverse-biased for all possible bias voltages along the entire length of the

piezoresistor and interconnect. This section addressed design issues associated with this design

constramnt.

Two issues must be taken into account in the design: (1) maintaining junction isolation and

(2) avoiding p/n junction breakdown while achieving the desired piezoresistor sensitivity. When

a voltage is applied between the two p++ interconnects, the p/n junction voltage varies linearly

with position due to a linear voltage drop across a distributed resistance. For junction isolation,

the p/n junction must be reverse-biased at all spatial locations.

Under reverse bias, a p/n junction develops a space charge layer due to the depletion of

carriers [76]. In order to maintain electrical isolation, it is necessary to ensure that the space









charge layers for adjacent p-type regions extending into the n-type substrate do not overlap or

'punch-through'. The space charge layers punch-through will cause the corresponding p regions

to become shorted, resulting in a non-functional device. Assuming uniform doping, the acceptor

concentration in the p region is assumed to be N and the donor concentration in the n region is

assumed to be ND The space charge layer widths on the p-side (x,) and n-side (x,,) are given

as a function of the junction voltage V~ [76],


xE, ((() = t i, ) (3 -45)
ql N (N +ND)


and x, (P)= St, A Fi, -), (3-46)
ql ND 4+ND )

where E,1 = 1.045 x 10' F/cm is the silicon permittivity, and the intrinsic number of electrons is

n, = 10'0 /cm3 in Silicon at room temperature. The built-in voltage is given as


k In N~N(3-47)

In order to electrically isolate the p++ regions, the entire length of the p/n junction must be

reverse-biased (~ < 0) The space charge layer width in the p and n region, x, and x~,,

respectively, increases with reverse bias. The total space charge width on the n side is given by

W(y) = x, (()+ x, (-(? +? )) (3-48)

If the total space charge layer width on the n side, W (V increases to the width between the

piezoresistor and the p++ interconnect, L,, or to the width between the p++ interconnects, L, ,

the space charge layers will punch-through, causing the corresponding p regions to be shorted.









To avoid punch-through, W V ) <
Additionally, lateral diffusion that occurs during high temperature process steps, leading to an

increase in the actual width of the p-type region compared to the designed width, must be taken

into account. Therefore, the total isolation width is approximated by

V1-2L=z,+x V1)+x -(r V+V1 (3-49)

where Ld is the lateral diffusion width estimated from the net effect of high temperature process

time on the diffusion length (thermal budget) [77]. The total thermal budget (Dt)mt is equal to

the sum of the diffusion x time, Dt products for all high temperature cycles affecting the lateral

diffusion, (Dt),, = D~t where D, and t, are the diffusion coefficient and time associated

with each processing step.

In this design, the doping profie is non-uniform, and the acceptor concentration in the p

region N ,(y) and the donor concentration in the n region ND f) Vary with depth, as shown in

Figure 3-17. The non-uniform doping profies are obtained by FLOOPS" simulation [78], where

sidewall boron implantation in amorphosized silicon is simulated by SRIM [79] and then

imported to FLOOPS ". The cross-sectional view of the isolation width for a doping profile at a

bias voltage of 10 V is shown in Figure 3-18 and Figure 3-19, which are associated with the A-A

and B-B cuts shown in Figure 3-20. The dimensions of the tether width W the sidewall

implanted piezoresistor depth L4, the p++ interconnect width L3, and the space parameters, L,,

L2 and L, are listed in Table 3-6 for the actual device.

There is a tradeoff between the p++ interconnect widths, L3 and L4 and the punch-

through width L,. A large value of L3 and L4 is desired to reduce the lead resistance. The










resulting narrow gap, L,, may cause p/n junction punch-through. On the edge of the tethers, the

p++ interconnects are tilted 24 degrees from the tether centerline to increase the isolation gap

spacing. For the worst case, V, = -10 V at left and 0 V on the right, as shown in Figure 3-20,

there is about 9 Cpm between adjacent p++ interconnects assuming a lateral diffusion of

~ 1.1 pm Meanwhile, a crossover between the piezoresistor and p++ interconnects must be

avoided. As shown in Figure 3-19, the space charge layer of the piezoresistor in the n-well

increases as the depth increases. If the space between the piezoresistor and the p++ interconnect

is too close, there will be crossover and the p-region will punch through. A top view of the

isolation width is shown in Figure 3-20. The blue region is the tether, the cyan region is the p++

interconnects, the green region is the piezoresistor, and the pink line is the final isolation width

considering lateral diffusion and space charge diffusion to the n-well at V, = -10 V (worst case).

In order to minimize the space charge width in the n-well, one can increase the doping

concentration of the n-well, ND There is, however, a tradeoff between increased n-well doping

concentration and reduced reverse breakdown voltage. With increasing doping, the internal

electric field increases and the reverse junction breakdown voltage decreases [80, 81]. The

breakdown voltage decreases from ~ 50 V to ~ 10 V when the impurity concentration increases

from 1.0 x1016 -3" to 1.0 x10 cm-3

The curvature of the tether corner and the curvature of the junction regions must also be

considered. A sharp corner dramatically increases the mechanical stress, which could lead to

possible failure of the materials [82]. Additionally, a sharp corner in the p/n junction may

increase the local electric field and decrease the breakdown voltage [83]. Thus, the corner is

rounded. The stress concentration factor, K, depends on the fillet radius for a given thickness

[82] and is relatively high when the ratio of the fillet radius and tether width is less than 0.5. In









this design, K is chosen as 0.9. In addition, 4 slots in the substrate near the edge of each tether

are designed to relieve stress concentrations that arise during fabrication [51].

In order to avoid these issues, a metal contact design is employed, where the metal lines

run on the top of the tethers to connect either side of the laterally implanted piezoresistors, as

shown in Figure 3-21. Because there are two 50 Cpm deep trenches on both sides of the tether

for tether release, the fabrication process of this design is very challenging and is discussed in

detail in Chapter 5.

Summary

Electromechanical modeling of a side-implanted piezoresistive floating element shear

stress sensor has been developed for aerospace applications. Two Wheatstone bridges are

employed, an active bridge for shear stress sensing and a dummy bridge for temperature

compensation. The predicted sensitivity, noise floor, dynamic range and MDS have been

modeled and verified by FEA.

To accurately resolve the fluctuating shear stress in a turbulent boundary layer, the shear

stress sensor is desired to possess a small size, large usable bandwidth and a low MDS. MDS

depends on the geometry of sensors and piezoresistors, dopant profile, process parameters, and

sensor excitation. To achieve a low MDS, it is favorable to maximize sensitivity and minimize

noise. However, there are tradeoffs between sensitivity and noise floor. It is necessary to

perform design optimization to balance these conflicting requirements. Additionally, the sensor

design is constrained by temporal and spatial resolution requirements as well as structural limits.

The detailed optimization is discussed in Chapter 4.









Table 3-1. Material properties [53] and geometry parameters used for model validation.
Density of silicon ps dkg/m3) 2330
Young's modulus in [110] orientation E(GPa) 168
Poisson ratio v 0.27

Lemooungth of ehesLm 400
Thickness of the tethers 7(Clm) 3
Width of the tethers W (pmn) 4
Length of the square floating element Le (pm) 150


Table 3-2. Resonant frequency and effective mass predicted by LEM and FEA for the
representative structure given in Table 3-1.
Frequency (k LEM 12.44 1.66e-10
FEA 12.47 1.72e-10



Table 3-3. First 6 modes and effective mass predicted by FEA for the representative structure
given in Table 3-1.
Mode Domain Frequency~ (kd~z) Effective Mass (kg)
1 12.47 translationall in z -direction) 1.72e-10
2 17.08 translationall in y -direction) 1.74e-10
3 34.95 (rocking mode about x -axis) 6.82e-10
4 162.33 (rocking mode about y -axis) 18e1
5 170.11 (rocking mode about z -axis) 1.84e-11
6 219.50 translationall in x -direction) 1.70e-11



Table 3-4. Piezoresistive coefficients for n-type and p-type silicon [53].
4i, (10-"Pa ') 42~ (10-"Pa ') F4 1-P
n-type -102.2 53.4 -13.6
p-type 6.6 -1.1 138.1












Table 3-5. Piezoresistive coefficients for n-type and p-type silicon in the <110> direction [53].
gil(* 10-"Pa') (0-P)
n-type -31.2 -17.6
p-type 71.8 -66.3



Table 3-6. Space parameter dimensions for junction isolation.
W L, L2 L3 L4 L,
30 Cpm 9 Cpm 13.6 Cpm 15 Cpm 1 Cpm 33 Cpm






















Figure 3-1. Schematic top view of the structure of a piezoresistive floating element sensor.


,i Lt C Le Lt

Tether Floating Element

y~ PQ
0 xWt ~Tt
a 2Lt

Figure 3-2. The simplified clamped-clamped beam model of the floating element structure.



k=1/Cme Mme Rd Cme

F U rF




(a) (b)
Figure 3-3. Lumped element model of a floating element sensor: (a) spring-mass-dashpot system
(mechanical) and (b) equivalent electrical LCR circuit.











0.07


0.0

0.5




0.03

0.02

0.01


-9 FEA
No~riiear Ar-alytical


O.4 0.6
I~Nortlized Tethe~r Lengthx/Lt


Figure 3-4. Representative results of displacement of tethers for the representative structure
given in Table 3-1 at r, = 5 Pa .


40 60
Wall Shear~ Stress w (Pa)


Figure 3-5. Representative load-deflection characteristics of analytical models and FEA for the
representative structure given in Table 3-1 and r = 5 Pa .














-El- FEA

0.5 ---'--- Linear Analytical




-0.5




-1




0 0.2 0.4 0.6 0.8 1
Normaolized Tether Isngth x/Lt


Figure 3-6. Verification of the analytically predicted stress profile (Equation (3-6)) with FEA
results for the representative structure of Table 3-1 and r, = 5 Pa .












Translational in z -direction Translational in y -direction Rocking mode about x -axis











Rocking mode about y -axis Rocking mode about z -axis Translational in x -direction


Figure 3-7. The mode shape for the representative structure of Table 3-1 and r, = 5 Pa .


































Figure 3-8. Geometry used in computation of Euler' s angles [59].


88010


<110>


1


240 300
270



Figure 3-9. Polar dependence of piezoresistive coefficients for p-type silicon in the (100) plane.













S1.58009
60


0


300


Figure 3-10. Polar dependence of piezoresistive coefficients for n-type silicon in the (100) plane.


- Ian~da
--- fHnrley


0.9



0.8

0 0.75


0.65


17 18
10 10
Boron Cbnlcentation (cm 3)


20
10


Figure 3-11. Piezoresistive factor as
300K [47].


a function of impurity concentration for p- type silicon at













996


Tether


iezoresistor End Cap


Td dxj


Wt


Figure 3-12. Schematic illustrating the relevant geometric parameters for piezoresistor
sensitivity calculations.


Flow


Tether


Floating Element


J R4


Compression

Tension

R2~~-- -


Tension


Compression


Figure 3-13. Schematic representative of a deflected side-implanted piezoresistive shear stress
sensor and corresponding resistance changes in Wheatstone bridge.


/I,




























(a) (b)

Figure 3-14. Wheatstone bridge subjected to cross-axis acceleration (a) and pressure (b).

~Circuit for
Offset Comp. SR560
Pre Amp
Piezoresistive Iv tIH~O
Bridge VBH390





Circuit for
Offset Comp. SR560
Compensation Pre Amp
Bridge 1V8 ;,- HP34970ADM





Figure 3-15. Schematic of the double-bridge temperature compensation configuration.










End Cap


Piezoresistor (p )


Figure 3-16. Top view schematic of the side-implanted piezoresistor and p++ interconnect in an
n-well (a) and equivalent electric circuit indicating that the sensor and leads are
junction isolated (b).



25

--*-- Pf interconnect
-- piezoresistor


,c~ t1

15,,
10 -


10t
10l


0.5 1 1.5 2
Deptl~um)


Figure 3-17. Doping profile ofn-well,
simulation.


p++ interconnect, and piezoresistor using FLOOPS































0.8









1.6



O 5 10 15 20
Isolation Width (Cun)


Figure 3-18. Cross view of isolation width between p++ interconnects (A-A cutinFeiguore 3-20).

in igre3-O )
























Figure 3-20. Top view of the isolation widths on a sensor tether.




p++\

Piezotirei stor 4 Tether













n-well

Bond Pads
Al-Si( 1%)


Figure 3-21. Top view schematic of the side-implanted piezoresistor with a metal line contact.









CHAPTER 4
DEVICE OPTIMIZATION

This chapter presents the nonlinearly constrained design optimization of a micromachined

floating element piezoresistive shear stress sensor. First, the problem formulation is discussed,

including the objective function and constraints based on flow conditions. Next, the

optimization methodology is outlined. The optimization results are then presented and

discussed. Finally, a post-optimization sensitivity analysis of the objective function is

performed.

Problem Formulation

The objective function is selected based on tradeoffs identified between the sensitivity and

noise floor of the shear stress sensor. The constraints are formed due to physical bounds,

manufacturing limits and operational requirements [84], and are dependent on the flow

conditions of the desired applications.

The obj ective function and constraints are functions of the design variables, including the

geometry of the floating element structure and the piezoresistors, the surface doping

concentration, and sensor excitation. The detailed discussion of the design variables chosen is

presented in next subsection.

Design Variables

The obj ective function and constraints depend on geometry of sensors structures and

piezoresistors, process related parameters, and sensor operational parameters. The geometry

parameters include tether length L,, tether width W, tether thickness, 7(, floating element length

Le, and piezoresistor lengthLr, piezoresistor width W The process related parameters include

piezoresistor surface concentration Ns and junction depth yJ (assuming a uniform doping

profile). The sensor operational parameter is the supplied bias voltage.









The geometry parameters of the sensor structure determine the mechanical characteristics

of the sensor, such as sensitivity, linearity and bandwidth. Design issues related to the tether

width ( and tether thickness 7( are addressed here. As discussed in Chapter 3, the minimum

tether width W, is set to 30 Cpm to avoid p/n junction punch through. The tether thickness must

be larger than the tether width to ensure that the cross-axis resonant frequency is larger than the

in-plane resonant frequency. As shown in the representative structure in Table 3-1, the first

mode is out of plane due to the tether thickness larger than the tether width. The increases in

tether thickness results in bending stress decreases (Equation (3-6)), and thus sensitivity

decreases (Equation (3-23)). On the other hand, the piezoresistor related parameters, such as

piezoresistor length Ly piezoresistor width W,, and p/n junction depth y, and surface

concentration Ns, are related to noise floor and sensitivity.

For each design optimization, different tether thickness, junction depth and tether width

may be achieved, but all designs are fabricated in one wafer due to economic constraints. Thus

these parameters for each design must be set to the same value. In this research, the tether

thickness is set to 50 Cpm considering the sensitivity of the shear stress sensor and SOI wafer

availability. Due to the rough sidewall surface near the buried oxide layer after DRIE process

and no passivation on the bottom of the tethers after final release, the high 1/ f noise and current

leakage became issues in the piezoresistor design [85]. Partridge et al.[51] investigated the

accelerators with piezoresistors implanted in the top 15 Cpm (total thickness), 5 Cpm, 3 Cpm of the

flexures, and found that 3 Cpm case has large sensitivity and low 1/ f noise. In this research,

piezoresistor width W,= 5 Cpm is chosen to avoid current leakage while maintaining high










performance. A junction depth of y, = 1 Cpm is chosen taking account the piezoresistor and p++

interconnection and the manufacturing constraint.

In summary, six design variables are included in the optimization design, and they are

tether length L,, tether width W, floating element length Le, and piezoresistor length L ,

piezoresistor surface doping concentration Ns and bias voltage V, .

Objective Function

As stated in Chapter 1, to accurately recognize the fluctuating wall shear stress in the

turbulent boundary layer, the measurement device must possess sufficiently high spatial and

temporal resolution as well as a low MDS, which is defined as the ratio of noise floor to the

sensitivity. Therefore, lowering the noise floor and increasing sensitivity are favorable in shear

stress sensor design to achieve a low MDS [84]. Some parameters, such as junction depth,

surface doping concentration and bias voltage, affect both sensitivity and noise floor creating

tradeoffs between these performance parameters. The following discusses the tradeoffs in

sensitivity and noise floor and the arrival at the MDS as the obj ective function of the

optimization.

Junction depth, y, and surface doping concentration, Ns, are two major factors involved

in processing that affect sensitivity and noise floor. As discussed in chapter 3, changes in Ns

while keeping y, constant invoke tradeoffs between noise and sensitivity. If Ns increases, the

resistivity of the piezoresistor decreases and the total carrier number increases. This leads to the

reduction of thermal noise and 1/ f noise. Conversely, sensitivity decreases due to the reduction

of the piezoresistive coefficient Fr, from high doping concentration (Equation (3-23)).









The bias voltage V, also affects both sensitivity and noise floor. As V, increases, the

sensitivity increases (Equation (3-35)) because the output voltage is directly proportional to the

bias voltage. The voltage noise contribution from 1/ f noise also increases squarely as indicated

by Equation (3-3 8).

By establishing the MDS as the obj ective function, a balance between noise floor and

sensitivity is achieved. Previous researchers have investigated the potential and methods in

piezoresistive sensor optimization. Harley and Kenny [47] presented an informal graphical

design optimization guidelines in the form of design charts by varying the dimensions of the

cantilever, the geometry of the piezoresistor, doping level, and process issues related to

sensitivity and noise floor. Papila et al. [84] performed a piezoresistive microphone Pareto

design optimization, in which the tradeoff between pressure sensitivity and electronic noise is

investigated. The Pareto curve indicated that the MDS in units of pressure is the appropriate

parameter for performance optimization.

Constraints

The constraints are determined by physical bounds, fabrication limits and performance

requirements [84]. The constraints used in this optimization and their associated physical

explanations are listed below:

* Piezoresistor geometry: Ly /Lt <0.4, as discussed in Chapter 3, stress changes sign at the
longitudinal center of the tether (shown in Figure 3-6). Thus, the sensitivity will be
reduced if the length of the piezoresistor is larger than L,/2. As a result, the maximum
piezoresistor length is limited to 40% of the tether length

* Resistance: R,/4 > 3, represents a balance between the sensor resistance R, being 3
times larger than the interconnect resistance R, but small enough to minimize
electromagnetic interference (EMI).

* Frequency: f, > f ,, puts a bandwidth constraint in the design. The constraint changes
with flow conditions.










* Power consumption: Pgh <; 0.1, where P,. = V/2/(Rs + RL ) When P,.M increases to a large
value, the temperature of the piezoresistor will increase due to Joule heating resulting in
voltage drift and eventually electromigration.

* Nonlinearity: A, -AL /A, <3%, device linearity is required to keep spectral fidelity for
time-resolved measurements.

* In-plane resonant frequency: 7( > W To avoid disturbing the flow at the sensor resonance,
the tether thickness T, is required to be larger than tether width W, to ensure the onset of
the in-plane resonant frequency occurs before the out of plane. In this dissertation, the
minimum tether width is 30 p~m and its upper bound is set to 40 p~m ,thus the tether
thickness is set to 50 p~m.

* Lower bounds (LB) and upper bounds (UB): LBR t (L,,, W W ;, LN, V,~) I UB, present the
limitation of the design variables. LB and UB are given in Table 4-2 based on the
candidate shear stress design specifications and design issues related to fabrication.

In summary, both the obj ective function and constraints are nonlinear. Therefore, the

optimal performance design deals with solving the constrained nonlinear optimization problem.

Candidate Flows

Several sensor specifications associated with various flow phenomena, ranging from low

speed flow to supersonic and hypersonic flow, are listed in Table 4-1. Here rmax is the maximum

shear stress to be measured and constrained by non-linearity, fmin is the minimum resonant

frequency to provide adequate temporal resolution and Lemax is the maximum floating element

size that determines the lowest tolerable spatial resolution, Wmin is the minimum tether width

that is limited by the junction isolation, and 7( is the minimum thickness that is constrained by

the in-plane resonant frequency. The temporal and spatial resolution fmm, and Lemax are chosen

to approach the Kolmogorov time and length scales, but are sufficiently conservative to yield a

proof of concept device.









Methodology

The design problem is formulated to find the optimum dimensions of the floating element

and tethers, geometry and surface doping concentration of piezoresistors, and bias voltage for

each candidate flow. Mathematically, the optimization seeks to minimize the MDS subj ect to

constraints. The key points regarding the optimization of the minimum detectable shear stress,

rmn, are summarized below:

Design variables: L,, Wt, We, Lr, V, and Ns-

Objective function: minimize F(X)= Zrmn, where X is the design variable vector.

Constraints :

g, = L,/(0.4L,)-1<0 O; g2 nu r~f -1<; 0; g3 = 1-Rs,/3RL~ <;

g4 =10V,2/(R + RL) 1<0; g, = 16, 6L/0.036, -1<~0;

g = LB /x, -1<0, i =6,8,...,11; g =x,/ UB -1< 0,j= 12, 13...17.

where xl = L,, W,, W, L,, Ns and V, Since the magnitudes of design variables differ by several

order of magnitude (Table 4-2), all variables are non-dimensionalized to avoid singularities in

the program. This nonlinear constrained optimization is implemented using the function fmincon

in MATLAB" (2006b) [86] optimization Toolbox, which employs sequential quadratic

programming (SQP) for nonlinear constrained problems and calculates the gradients by finite

difference method. The optimum value of Ns for different designs might be different. All

designs, however, are fabricated on one wafer. Therefore, surface concentration, Ns, for all

designs must be set to the same value. In this dissertation, the optimal Ns for first three cases

were the same and is Ns=7.7 x1019 -3". This value was chosen as the surface concentration for









all designs. The optimization was re-implemented using this fixed concentration following the

same steps described above.

The SQP method is a local optimizer and is highly dependent on the initial value. The

initial designs are selected randomly, and a number of local optimum solutions from different

initial designs were obtained. The solution identifies one best design points as the optimal

solution. A global optimization algorithm using particle swarms [87] is also employed to

investigate the possibility of improving the optimum solutions. It is found that global

optimization solution is very similar to the optimization results obtained by fmincon function.

The global optimization results have a large computational cost.

Optimization Results and Discussion

In the optimization, the doping profile is assumed to be uniform to simplify the modeling.

The Gaussian profile is more accurate than a uniform profile, but it is not employed in this

research to avoid computational cost. The doping concentration for p++ interconnect is achieved

as 2.0x1020 -3, With a junction depth of 1 Cpm for all designs. In this research, the material

properties of silicon is fixed.

The resulting optimization design is shown in Table 4-3. The highlights are active

constraints. Since the low resistance results in low thermal noise, but the power dissipation

increases. Therefore, the power constraint is always active (close for case 9). For each device,

the dynamic range from the optimum design is in excess of 75 dB. Kuhn-Tucker conditions

[88] are conducted to check the optimality and active constraints, which are stated as follows:

*Lagrange multipliers 1, are nonnegative, and satisfy equation (4-1)


dF n = i=1,2...m, (4-1)










where ng is the total number of constraints, and m is the total number of design variables.


Lagrange multipliers S are obtained by the fmincon M~ATLAB function.

* The corresponding 1, is zero if a constraint is not active. The active constraints for each
case are indicated in bold font in Table 4-3.

Once the optimum design for uniform doping is obtained, non-uniform doping profies are

applied to achieve the Einal performance of the sensor. The optimization flow chart is shown in

Figure 4-1. The non-uniform doping profies are obtained by FLOOPS simulation [26], where

sidewall boron implantation to amorphous silicon is simulated by SRIM simulation [79] and

imported to FLOOPS. The surface concentration of the piezoresistor, the piezoresistive

interconnection, and n-well are achieved to 7.7 x1019 -3 2.0 x1020 cm and 7 x1016 -3"

respectively, as shown in Figure 3-17. The results indicate that non-uniform doping profies

yield approximately a 5 dB decrease in dynamic range. Therefore, implementing a Gaussian

profile as part of the optimization would result in a more accurate model and thus optimal

design.

Sensitivity Analysis

Due to parameter uncertainty caused by process, ra~n may achieve different values than

theoretical optimization. The sensitivity analysis is implemented to understand sensitivity of

MDS to the variations of the design variables, constraints, and Eixed parameters at the optimum

design. Therefore, sensitivity analysis is a post-optimization step, which involves two parts:

* Sensitivity of the obj ective function to design variables at the optimum design.

* Sensitivity of the obj ective functions to the Eixed parameters at the optimum design, where
the effect of a change in the active constraints on the obj ective function is taken into
account.









For the sensitivity analysis with respect to the design variables, logarithmic derivative [88]

is employed to measure the sensitivity of MDS to uncertainty of design parameters at the

optimum design,

8 log (zrs., r,, x
(4-2)
dlog(xl) Dx~ Zrm

where x = L,,W, We,L,, and N, .

For the sensitivity analysis with respect to the fixed parameters, equation (4-2) is invalid if

the nonlinear inequality constraints are active. Lagrange multipliers based on the Kuhn-Tucker

conditions [88] is employed to calculate the sensitivity of the optimal solution to the fixed

parameters. Assuming that the objective function and the constraints depend on a fixed

parameter p, so that the optimization problem is defines as,

minimize F (X, p)
(4-3)
such that g, (X, p?) > 0 j=1,2... 17.

The gradient of F with respect to p is given as [88],

dF F; dg,
Ar a (4-4)
dp dp dp

where go denotes the active constraint functions and go = 0 from Kuhn-Tucker conditions. The

equation (4-4) indicates that the Lagrange multipliers are a measure of the effect of a change of

the constraints to the objective function. Lagrange multipliers Ai = 0 for active constraints,

otherwise it is obtained by

A = N'N IN' VF (4-5)

where N and VF are defined as
dg~
N= ,j=1,2...17, i=1,2...6 (4-6)
drx'









8F
and VF- i=1,2...6 (4-7)


The sensitivity of rmin to uncertainty of the fixed parameters is given as

8% in % ril P (4-8)
dp/ p dp dp rm

ii can be obtained from the output of fmnincon function directly. The fixed parameters are

p = yJ,Wr,T,, Ns

For case 1, power is the active inequality constraint, and the associated Lagrange

multiplier, Ai = 0.0026179, is obtained from MATLAB calculation. Therefore, Equation (4-2) is

employed to calculate the sensitivity of MDS to uncertainty of design parameters (L,, W,, We,

Lr and V,) at the optimum design. Equation (4-8) is employed for the fixed parameters (y ,,

Wr, 7( and Ns). Figure 4-1 shows the sensitivity of ran to uncertainty of the design variables

and fixed parameters for case 1, i.e., 10% change of the tether width causes 19% change of the

minimum detectable shear stress. It is illustrated that r, is sensitive to variation of tether

width, W,, tether length, L,, floating element width, We, and junction depth, yJ The MDS is

less sensitive to variation of piezoresistor length Lr. In summary, rmin is very sensitive to

uncertainties of tether and element dimensions, junction depth and width of the piezoresistors,

and less sensitive to uncertainties of piezoresistor length.

Summary

This section described the choice of objective function and associated constraints. The

optimization has been implemented for nine designs, from low Reynolds number flow to

supersonic and hypersonic flow. The optimization results indicate that the dynamic range

exceeds 75 dB for all designs based on a uniform doping profile. Accounting for non-uniform









doping profile results in a 5 dB decrease in dynamic range. The sensitivity analysis indicates

that the MDS is very sensitive to uncertainties of tether and element dimensions, junction depth

and width of the piezoresistors, and less sensitivity to uncertainties of piezoresistor length.









Table 4-1. The candidate shear stress sensor specifications.
Low Speed Supersonic, High Re Hypersonic, Underwater
Deic 1 2 3 4 5 6 7 8 9

tmax (Pa) 5 5 5 50 50 100 100 500 500

.fmn (k~Hz) 5 5 10 10 50 50 100 100 200

Lema (pLm) 1000 1500 1000 1000 1000 1000 500 500 500

Wan(p) 30 30 30 30 30 30 30 30 30

7;(pm) 50 50 50 50 50 50 50 50 50



Table 4-2. Upper and lower bounds associated with the specifications in Table 4-1.
Design Variables and LB UB Flow Description
L (gmn) W, (gm) L (gmn) L, (gmt) Vi, (V) Ns (cm-3 min (Pa) fmin(kHz)

1100 1000 30- 40 100 1000 50 400 5 10 5e+18 2e+20 5 5
2 100 1000 30- 40 100 1500 50 -400 5 10 5e+18 2e+20 5 5
3 100 1000 30- 40 100 1000 50 400 5 10 5e+18 2e+20 5 10
4 100 1000 30- 40 100 1000 50 400 5 10 5e+18 2e+20 50 10
5 100 1000 30- 40 100 1000 50 400 5 10 5e+18 2e+20 50 50
6 100 1000 30- 40 100 1000 50 400 5 10 5e+18 2e+20 100 50
7 100 1000 30- 40 100 500 50 400 5 10 5e+18 2e+20 100 100
8 100 1000 30- 40 100 500 50 400 5 10 5e+18 2e+20 500 100
9 100 1000 30- 40 100 500 50 400 5 10 5e+18 2e+20 500 200










Table 4-3. Optimization results for the cases specified in Table 4-1 (bold for active constraints).


Parameter Casel1 Case2 Case3 Case4 Case5 Case6 Case7 Case8


Case9


max (Pa)

L, (p~m)

0' (pm)

w' (p~m)

L, (p~m)

VB (V)




f (kHz)

Rs (R)

RL (2)


5

1000

30

1000

228.5

10

0.1

9.8

851

149


5

1000

30

1500

228.5

10

0.1

6.60

851

149


5

1000

30

983.5

228.5

10

0.1

10

851

149


50

991.2

30

996.1

228.5

10

0.1

10

851

149

3.58e-5

21.1

0.33

103.7


50 100 100 500 500

343.6 348.7 308.8 500.4 500

30 30.7 30 30 30

1000 993.3 499.1 250.2 100

98.8 99.9 88.6 126.8 117.7

6.8 6.8 6.5 7.6 6.0

0.1 0.1 0.1 0.1 0.07

50.53 50.01 130.15 104.07 231.11

368 372 330 470 438

94 94 89 105 102

6.64e-6 6.40e-6 1.47e-6 1.13e-6 4.20e-7

11.0 10.97 10.95 11.19 9.54

1.66 1.72 7.44 9.88 2.28e-2

89.6 95.3 82.6 94.1 86.8


S,, (V/Pa) 3.65e-5 7.92e-5 3.54e-5

V, (nV) 21.1 21.1 21.1

rmn (mPa) 0.58 0.27 0.60

DR (dB) 78.7 85.4 78.5



































Figure 4-1. Flow chart of design optimization of the piezoresistive shear stress sensor.


Lt Wt We Tt VB Ns yj Wr Lr


Figure 4-2. Logarithmic derivative of objective function r, with respect to parameters (Casel).


MDS
(Uniform Doping)
FLOOPS Simulation
(non-uniform doping)

Final MDS









CHAPTER 5
FABRICATION AND PACKAGINTG

The fabrication process and packaging of the side-implanted piezoresistive shear stress

sensor are presented in this chapter, with the aid of masks and schematic cross section drawings.

A detailed process flow is given in Appendix C, which lists all the process parameters,

equipment and labs for each step. The detailed packaging approach for wind tunnel testing is

also presented.

Fabrication Overview and Challenges

The first generation of the shear stress sensor is fabricated in an 8-mask, silicon bulk-

micromachining process. All the masks are generated using AutoCAD" 2002 and manufactured

in Photo Sciences, Inc (PSI). It is described in detail in the following sections. Some challenges

in this process are addressed before starting the process flow:

* Side-implanted piezoresistors: boron is side implanted into the silicon tethers to form the
piezoresistors with an oblique angle of 54o normal to the top surface. The traditional
piezoresistor is formed by top implantation. The doping profile for side-implantation is
simulated via FLOOPS, and the accuracy of the profile needs to be judged only after
device testing.

* Trench filling: 50-Cpm-deep trenches were etched on the top surface to define the tethers.
Trench filling is required to obtain good photoresist coverage before subsequent deposition
and patterning of the metallization layer.

* Junction isolation: the space between piezoresistors and p++ interconnects should be larger
than the isolation width to avoid p/n punch through, as discussed in chapter 3.

Fabrication Process

The fabrication process starts with a 100-mm (100) silicon-on-insulator (SOI) wafer with a

50-Cpm-thick 1~5 R-cm n-type silicon device layer above a 1.5-Cpm-thick buried silicon dioxide

(BOX) layer. The corresponding background doping concentration is from 2.5 x10 cm-3 to

5 x 1014 -3" The total wafer thickness is 450 Cpm A brief overview of the process is as

follows. The four side-implanted piezoresistors are first formed by boron oblique implantation.









The structure of the sensor is then defined by DRIE Si etch. Thermal dry oxide is grown for high

quality passivation. Al-Si (1%) is deposited and patterned to form the bond pads. PECVD

nitride is deposited as a moisture barrier layer. Finally, the structure is released from the

backside via DRIE Si and RIE of the oxide and nitride. The process flow is broken down into 8

maj or steps as follows:

a. The n-well formation: the fabrication begins with the formation of the n-well by a

phosphorus blanket implantation (Figure 5-1 (2)). An energy of 150 keV and a dose of

4.0 x10' cm2 are used to achieve a surface concentration of 6.5 x10 cm-3 to control the space-

charge layer thickness of the reverse-biased p/n junction-isolated piezoresistors.

b. Reverse bias contact: a 100 nm thin oxide layer is then deposited via plasma-enhanced

chemical vapor deposition (PECVD) and patterned, then etched via buffered oxide etch (BOE) in

preparation of the reverse-bias contact implant. This step also creates alignment marks on the

top surface. Phosphorus is then implanted with energy of 80 keV and dose of 9.0 x1013 -m2 to

achieve a n++ region with a surface concentration of 1.8 x10 cm-3 (Figure 5-1 (4)). The device

is then annealed at 1000 oC for 450 minutes to drive-in the inpurities.

c. Piezoresistor interconnects: the oxide is selectively removed by BOE. Then, a two-step

Ge preamorphization implant is performed to minimize the effect of random channeling tail

caused by the subsequent high-dose boron implantation [66], which provides a heavily doped

Ohmic body contact. The preamorphization implant energies are 160 keV and 50 keV,

respectively, and a dose of 10 cm 2. This preamorphization is to ensure no more than 2% of the

implanted boron dose penetrates into the substrate [89]. Then boron is implanted into the silicon

with a dose of 1.2 x 10' cm2 and an energy of 50 keV to provide Ohmic contacts (Figure 5-1

(5)). The resulting surface concentration and junction depth, xJ while taking into account the









thermal budget of the entire process, are simulated by FLOOPS to be 1.96 x 1020 -3" and 1 pm ,

respectively. The interconnect region begins from the edge of the tether and distributes

symmetrically along the centerline of the tethers to minimize the sensitivity error, with a larger

width on the end cap to decrease the resistance. The FLOOPS simulation file is given in

Appendix D.

d. "Nested" mask release: a 1 Cpm oxide layer is deposited via PECVD and patterned via

reactive ion etch (RIE) [90] to serve as a nested mask for the deep reactive ion etch (DRIE) [91]

that defines the tethers and floating element (Figure 5-1 (7)). New alignment marks are also

created in this step.

e. Side wall etch and side wall implantation: the wafers are then patterned using the mask

SIM (Figure 5-1 (8)). To ensure good contact between the piezoresistor and the p++

interconnect, the SIM mask has a 4 Cpm overlap with the p++ interconnect on the edge of the

tether, 10 Cpm overlap with the p++ interconnect on the end cap, and 4 Cpm overlap with

sidewall. Prior to DRIE, the native oxide or oxide residues are etched via BOE about one

minute. The Si is then etched vertically to approximately 8 Cpm deep by DRIE to form the

trenches for the sidewall oblique implant, as shown in Figure 5-2 (scanning electron microscope

(SEM) top view). The trench width is set to (5 +1.1 Clm) x tan (54' )=8.5 pm to achieve a 5 pLm

implant, where 54" is the implant tilt angle from the normal axis, and 1.1 Cpm is the thickness of

the oxide layer. The sidewall implantation is restricted on the top 5 Cpm to ensure the silicon

surface on which the boron implanted is smooth and avoid forming the current leakage path on

the bottom [85]. This can reduce the 1/ f noise at low frequency [85]. The basic recipes on STS

DRIE system and Unaxis RIE systems are shown in Appendix E.









The extruded oxide resulting from the DRIE is etched via BOE (6:1) for one minute, as

shown via the scanning electron microscope image in Figure 5-3. This avoids the protruded

oxide blocking the implant dosage to the side wall. Hydrogen annealing (1000"C, 10 mTorr for

5 minutes) [92] is performed to smooth the scallops on the sidewalls that arise from the DRIE

process, which will improve the noise floor [25]. A 0. 1 Cpm oxide layer is thermally grown as a

thin implant oxide layer on the sidewall, which must be accounted for in the thermal budget.

After a two-step Germanium preamorphization implant, boron is then implanted with an

energy of 50 keV, a dose of 2x 1016 -m2 (two times of the simulation dose to compensate the

solubility loss at high dosage) and an oblique angle of 54o to achieve a 5 Cpm shadow side wall

implantation (shown in Figure 5-1 (9)).

f. Tether definition: the oxide on the trench bottom is then etched via DRIE while the

oxide on the sidewall is left to protect the doped sidewall, as shown in Figure 5-4. This is a time-

controlled process: an over-etch will expose silicon on the edge of the sidewall of the tether

(Figure 5-5), while an under-etch will create a "silicon grass" effect [93] after the subsequent

DRIE silicon etch due to the oxide residues that acts as a micromask (Figure 5-6). The

channels/trenches are then etched via DRIE with the BOX as an etch stop, as shown in Figure 5-

7 (note the rough surface is caused by the dicing saw). The tether sidewall oxide is then etched

for two minutes by BOE (6:1). Subsequently, the wafers are annealed at 1000" C for 60 min to

drive in the boron to form the piezoresistors. A 0. 1 Cpm thin dry oxide layer was thermally

grown at 975" C as an electrical passivation layer. The temperature 975" C is selected to avoid

excessive diffusion and excessive compressive stress when the temperature is below 950" C

[94]. Meanwhile, the boron is segregated into the oxide from the silicon.









g. Metallization and nitride passivation: since there are 50-Cpm-deep trenches on the wafer

for tether release, it is necessary to fill the trench to achieve good photoresist coverage before

subsequent wafer patterning. A two-step trench filling process is performed as follows: first, a

thin layer of photoresist AZ 1512 is coated and soft baked, then a thick photoresist AZ9260 is

coated and soft baked; second, the wafer is flood exposed for 300 seconds and developed using

developer AZ400 until the surface is clear. Thus, the trench can be reduced from 50 Cpm to only

5~6 Cpm deep if following the above process once or twice.

After filling the trenches with photoresist, the oxide is patterned and then etched via BOE

(6: 1) to open contact vias for Al sputtering. This step is very critical for the quality of the metal

contact. Since the boron laden silicon dioxide etches much slower than the standard oxide


etching (1000 A min ), an over etch is required to remove all oxide to ensure an Ohmic contact.

Any residual oxide left over will result in Schottky diode effect. A 1-ym-thick layer of Al-Si

(1%) is sputtered and patterned via RIE to form the metal interconnects (Figure 5-1 (12)). A

200-nm-thick, low-stress silicon nitride layer is deposited via PECVD to from a protective

moisture barrier. The bond pads are exposed by patterning and plasma etching the silicon nitride

via RIE.

h. Backside release: to protect the device, the front side of the wafer is coated with a 10-

Cpm-thick photoresist layer. The wafers are then patterned from the backside using front-to-back

alignment. The structure is released from the backside using DRIE up to the BOX layer (Figure

5-1 (14)), along with an oxide and nitride etch using RIE (Figure 5-1 (15)). Finally, a post-

metallization anneal is performed in forming gas (4% H2, 96% N2 ) at 450"C for 1 hour [95].

This annealing allows the aluminum to react with the native oxide to remove the tunneling oxide,

and allow the hydrogen to passivate the interface traps. This improves the contact resistance and









reduces the electrical noise floor [25]. The fabricated device is shown in Figure 5-8 and the

close view of the piezoresistors is shown in Figure 5-9. The trenches between each device were

patterned and created during back side release, thus the die can be easily separated by tweezers.

Sensor Packaging for Wind Tunnel Testing

After fabrication, the individual die (6.2 mmx6.2 mm) were then packaged in a custom

printed circuit board (PCB) (20 mmx20 mm) designed for modularity. The PCB layout was

performed using Protel and was manufactured by a commercial vendor, Sierra Proto Express.

The MEMS device die and PCB were then packaged by Engent Inc. The MEMS die are flush-

mounted into a machined cavity in the PCB and sealed with epoxy at the perimeter. The

aluminum bond pads are then bonded to gold pads on the PCB. Subsequent to the bonding

process, the wire bonds are covered by non-conductive epoxy to protect the wire bonds from the

gas flow in the calibration wind tunnel or flow cell. The roughness of the epoxy is less than

300 Cpm and is located (3.2 mm ) downstream of the sensing element to mitigate flow

disturbances. The PCB package is then flush-mounted into a Lucite package, which in turn is

flush mounted in an aluminum plate to minimize flow disturbance. Figure 5-10 shows the PCB

embedded in the Lucite package. Copper wires (gauge 26) pass from underneath up through the

vias in the PCB and are soldered to PCB via rings. The wire is reinforced by the glue on the

backside of the Lucite package.

An interface circuit board was designed for offset compensation and signal amplification,

as shown in Figure 5-11. This board includes two sets of compensation circuitry: one for active

bridge, another for dummy bridge. Each circuit has two amplifying stages: the first stage is used

to null the amplified offset, and the second stage is to amplify the compensated signal. The

detailed description of the interface circuit for offset compensation is given in Chapter 6. This









board is attached on the backside of the device package and supported by two screws that

connect it to the Lucite packaging. The copper wires for the signal output and voltage supply

from the Lucite plug are soldered to this board. There are eight BNC connectors for the

amplified signal outputs and power supplies.













(1) Starting with SOI wafer with 50um top Si layer
(2) Blanket P implantation to create n-well




n-Si


(3) PECVD oxide (0.1um). Pattern & BOE etch oxide

(4) Reverse bias implantation: P implantation
followed by N2 annealing it++ p






n-Si

(5) Pattern & wet etch oxide followed by "piezo" contact
implantation


Al-Si(l%)(l1pm ) ptt Ohmic Contact (Ilm)





n-Si


(13) PECVD silicon nitride then pattern it to expose the bond pads

(14) Backside Si DRIE etch


A-A




n-Si


(9) Thermal oxidation followed by side wall B implantation

B-B 1 540 Boron





n-Si


(10) Remove top oxide(0.1um) & DRIE Si (50um) to define tethers





n-Si

(11) Wet etch oxide(0.1um), thermal diffusion and thermal oxidation

(1)Trench filling, Wet etch oxide to open contact vias followed by
Al-Si(1%) sputtering and Al etch via RIE
IA- O


(6) PECVD oxide (1um)

(7) Pattern & dry etch oxide


(8) Pattern & DRIE trench ~10um for side wall implantation
followed by H2 annealing


I


Tether Centerline


B B


Figure 5-1. Process flow of the side-implanted piezoresistive shear stress sensor.


A-


1


A


(15) RIE etch oxide and nitride to release the structure







(16) Forming gas anneal at 450 degree for 1 hour



SiO2 P++ I PR Al (%1 SI)
Silicon Nitride Piezoresistor In-well




















Oxide Mask











Figure 5-2. SEM side view of side wall trench after DRIE Si.

Extrude Oxide


Silicon


Figure 5-3. SEM side view of the notch at the interface of oxide and Si after DRIE.















Oxide


Figure 5-4. SEM top view of the trench after DRIE oxide and Si.


Oxide


Exposed Silicon due
to Oxide Overetch


Figure 5-5. SEM top views of the trench after DRIE oxide and Si with oxide overetch.





























Figure 5-6. SEM top views of the trench with silicon grass through a micromasking effect due to
oxide underetch.


Figure 5-7. SEM side view of the trench after DRIE oxide and Si.





Active
Wheatstone
Bridge



Dummy
Wheatstone
Bridge for
Temperature
Compensation



Bonds Pads




Figure 5-8. Photograph of the fabricated device.


Side-Implanted
Piezoresistor


Trench for
Tether Release


Slots for
Stress Release


p++ Interconnect


Figure 5-9. A photograph of the device with a close up view of the side-implanted piezoresistor.










c\ Solder Connections


Holes for


PCB


Epoxy
SCovered
Wirebonds


P)


Lucile
Package



Holes for Offset CompCens
Board Installation


MDEi/S


Figure 5-10. Photograph of the PCB embedded in Lucite package.


AD624


AD711


Figure 5-11. Interface circuit board for offset compensation.


ation









CHAPTER 6
EXPERIMENTAL CHARACTERIZATION

Preliminary electrical and fluidic characterization were performed to determine the

performance of the shear stress sensor and to partially compare to the analytical models

discussed in Chapter 3. The experimental setup for sensor characterization is described and then

the results are presented. The experiments include measurement of characteristics of p/n diode,

system noise, sensor sensitivity and linearity, and frequency response.

Experimental Characterization Issues

There are two complicating issues in characterizing the sensors: the initial offset voltage

output without shear stress applied and the temperature sensitivity of the bridge output. These

two issues directly affect the measurement resolution and static sensitivity. Therefore, offset

compensation and temperature compensation must be employed for the static calibration

experiments. The motivation and methodology for offset compensation is discussed in the

following paragraphs. The temperature compensation was not performed and will be discussed

in Chapter 7.

For a balanced Wheatstone bridge, the differential voltage output of the sensor is directly

proportional to the applied shear stress. In reality, the Wheatstone bridge is not perfectly

balanced due to uncertainty in the fabrication process. As shown in Figure 6-1, the dc offset

exists without applied shear stress, and is directly proportional to the bias voltage. The offset is

typically O(10 mV/V), or even larger in some device die. The optimization results in Chapter 4

indicate that the normalized sensitivity of the sensor designs is O(1 CIV/V/Pa). Such a small

sensitivity requires high gain amplification prior to being sampled by data acquisition board.

However, a dc offset will cause amplifier saturation even at a relatively low gain. Therefore, it is

imperative to minimize or eliminate the offset to maximize the dynamic range of the









measurement system. An approach for the interface circuit readout is discussed as follows for dc

offset compensation.

The interface circuit consists of a precision programmable instrumentation amplifier

AD625 and a high speed precision Op Amp AD 711 from Analog Devices [73], as shown in

Figure 6-2. The gain of the AD625 is set by adjusting external resistors RF and RG and is given

by 4RF /RG +1. The AD711 acts as a unity buffer. The initial offset voltage goes through the

amplifier AD625 with a set gain of 21. Then the amplified offset voltage is precisely controlled

by adjusting the input of the AD71 1, which is provided by a Stanford Research Systems SIM928

isolated voltage source [96]. SIM928 is an ultra low noise voltage source (10 CLVrms at 1 kHz

bandwidth) that provides a stable low-noise voltage reference with mV resolution.

Unfortunately, there was an error in the second amplifier stage of the PCB and a decision was

made to just proceed with AC shear stress calibrations to demonstrate "proof of concept"

functionality.

Experimental Setup

In this section, the experimental setup for the shear stress sensor characterization is

discussed. A probe station is used to measure the current-voltage (I-V) characteristics of the

sensor. A plane wave tube (PWT) is then used to determine the sensor linearity, sensitivity and

frequency response. Then sensor system noise is measured with dynamic calibration setup in the

plane wave tube with speaker amplifier off.

Electrical Characterization

Electrical characterization includes measurement of the bridge impedance and leakage

current of the junction-isolated devices, as well as the breakdown voltage. All measurements









were made using an Agilent 4155C semiconductor parameter analyzer and a wafer level probe

station.

As discussed in Chapter 5, the p/n junctions are formed by the p-type piezoresistor and the

p++ interconnects with the n-well. To ensure that the current flows entirely through the p-type

regions, the p/n junction must be reverse biased and the leakage current should be negligible. In

this experiment, the reverse bias characteristics of the p/n junction were measured to determine

the leakage current from the piezoresistors to the n-type substrate. The resistance is extracted

from the I-V characteristics of the piezoresistors in the p/n forward bias region.

Dynamic Calibration

The frequency response and linearity were deduced using Stokes' layer excitation of shear-

stress in a plane-wave tube (PWT). This technique utilizes acoustic plane waves in a duct to

generate known oscillating wall shear stresses [97]. This technique relies on the fact that the

particle velocity of the acoustic waves is zero at the wall due to the no-slip boundary condition.

This leads to the generation of a frequency-dependent boundary layer thickness and a

corresponding wall shear stress. Therefore, at a given location, the relationship between the

fluctuating shear stress and acoustic pressure is theoretically known. The acoustically-generated

wall shear stress for the frequency range of excitation in this paper is approximated by [97]


r'zze an 9 ) (6-1)


where p' is the amplitude of the acoustic perturbation, j = J-l, v is the kinematic viscosity, m


is the angular frequency, k = /cil is the acoustic wave number, 17 = J is the non-

dimensional Stokes number and b is the half height of the duct.









A conceptual schematic of the dynamical calibration setup is shown in Figure 6-3. The

plane wave is generated by a BMS 4590P compression driver (speaker) that is mounted at one

end of the PWT. The PWT consists of a rigid-wall 1"xl" duct with an anechoic termination (a

30.7" long fiberglass wedge), which is responsible for supporting acoustic plane progressive

waves propagation along the duct [97]. The sensor and a reference microphone (B&K 4138) are

flush-mounted at the same axial position from the driver.

The usable bandwidth for plane waves in the PWT is defined by the cut-on frequency of

the first higher order mode which is 6.7 k
output voltage from the AD625 interface circuit is ac-coupled and amplified 46 dB by the SR560

low noise preamplifier. A B&K PULSE Multi-Analyzer System (Type 3109) is used as the

microphone power supply, data acquisition unit, and signal generator for the source signal in the

plane wave tube.

Noise Measurement

A noise measurement is necessary to determine the minimum detectable signal (MDS).

The sensor is mounted on the sidewall of the plane wave tube and the speaker amplifier is turned

off. This provides a reasonable estimate of the entire sensor system noise floor as installed in a

calibration chamber. The compensated voltage output is amplified by the AD625 and the SR560

low noise preamplifier (ac coupled), and then fed into the SRS785 spectrum analyzer [98]. The

spectrum analyzer measures the noise power spectral density (PSD), using a Hanning window to

minimize PSD leakage. The measured noise PSD includes the sensor noise and the setup noise,

including noise from sources such as EMI, the amplifier, the spectrum analyzer, and the power

supply. LabVIEW is used for data acquisition and manipulation. The noise PSD is measured in

three overlapping frequency spans from 10 Hz to 1024 Hz The settings for three frequency

ranges are listed in Table 6-1.










Experimental Results


Electrical Characterization

As shown in Figure 6-4, I-V characterization results indicate a negligible leakage current

(< 0.12 CLA) up to a reverse bias voltage of -10 V. The reverse bias breakdown voltage for the

P/N junction is around 20 V or greater (Figure 6-5).

I-V measurements of the diffused resistors across the Wheatstone bridge are shown in

Figure 6-6 for a representative design in Table 6-2. One curve is for the resistors across the bias

voltage port and ground, another is for the resistors across the output ports V, and V2 The

nonlinearity of the I-V curve is obtained subtracting the actual voltage in the VB-GND curve (or

V1-V2) from a linear curve fit (fit between -0.5 V to 0.5 V and extended to +10 V ), then

normalizing by the linear curve and multiplying by 100. The nonlinearity is shown in Figure 6-

7. The linear variation of current with voltage below 5 V (3% nonlinearity in Figure 6-7)

indicates Ohmic behavior of the piezoresistors and p++ interconnects. The average resistances

across the bridge are 397 0Z and 411 R respectively, while the predicted value for the

individual resistor is 1 kO The smaller than predicted resistances may due to the high implant

dosage (double of the simulation value to avoid solubility loss). The asymmetry of V1-V2

curve may be due to the Schottky effect. The asymmetry may also be due to residual heating as

the voltage was swept from -10 V to 10 V instead of performing two tests sweeping the voltage

from 0 to 10V and 0 to -10 V. The root cause of this asymmetry requires further study.

Dynamic Calibration Results and Discussion

The dynamic sensitivity and linearity of the sensor were tested with a single tone of

2.088 k
2.088 k








of the static sensitivity. In this measurement, the frequency span was 0.2-6.4 k
frequency resolution of 32 Hz 3000 linear averages with 0% overlap were taken to minimize

the random error. The sensor was operated at bias voltages of 1.0 V, 1.25 V and 1.5 V This is

substantially lower than the optimized bias voltage of 10 V because electronic testing indicated

nonlinearities in the current-voltage relationship at excitation voltages above 4.5 V from resistor

self-heating. Any resistor self-heating will lead to temperature-resistive voltage fluctuations due

to unsteady convective cooling [38]. In other words, the direct sensor will behave somewhat like

an indirect sensor. To avoid this phenomenon, testing was limited to bias voltages of 1.5 V and

below.

The dynamic sensitivity is the ratio of the differential sensor output voltage to the input

wall shear stress. Ideally, the lateral displacement of the floating element will be solely a

function of the acoustically generated wall shear stress. In practice, however, it is known that

there will be an additional displacement due to the local pressure gradient forces generated by

traveling acoustic waves across the floating element [43]. The magnitude of the effective shear

stress including pressure-gradient effects for a purely-traveling acoustic wave in a duct is [43]



r (I)= f b = 1+ + t razz .p: (6-2)

The second and third terms of Equation (6-2) represent the error due to the fluctuating flow

beneath the element and the net fluctuating pressure force acting on the lip (assuming a square

element). Accounting for the fact that the actual shear stress is proportional to JJ, the

magnitude of the error terms is proportional to f The second term of Equation (6-2) assumes

that Le >> g so that the flow underneath the element can be approximated by fully-developed

pressure-driven flow in a slot. For the current sensor, g = 400 Cpm and Le = 1000 pm Clearly,









this approximation is invalid and the flow beneath the element is sufficiently complex and must

be evaluated using computational techniques. Therefore, only an estimate for the pressure

gradient force acting on the thickness can be provided. The maximum error for this term is

7.5 dB (2.4r 7,,) at the highest frequency tested, 6.7 k
phase with the actual shear stress.

By adjusting the SPL from 123 dB to 157 dB, the induced shear stress varies from

0.04 Pa to 2.0 Pa Figure 6-8 shows output voltages response to the shear stress variation at

different bias voltages. The slopes of the plots shown in Figure 6-8 indicate the dynamic

sensitivity of the sensor at different bias voltages. For all bias conditions, the sensors respond

linearly up to 2.0 Pa and the sensitivities are 2.905 CLV/Pa, 3.602CLV/Pa and 4.242CLV/Pa at

bias voltages of 1.0 V, 1.25 V and 1.5 V, respectively.

The normalized sensitivity is defined as the ratio of sensitivity to applied bias voltage. For

a Wheatstone bridge without resistor self-heating, the normalized sensitivity is a constant. If

resistor self-heating is occurring, a power-law dependence on the power dissipation is expected.

The slopes of Figure 6-9 are the normalized sensitivities at bias voltages of 1.0 V, 1.25 V and

1.5 V, respectively, which are 2.905 CLV.V/Pa, 2.882 pV V/Pa and 2.828pV. V/Pa The

predicted normalized sensitivity is 3.65 CLV V/Pa Note that for Figure 6-9, the initial offset

voltages were subtracted for normalized slope comparison purposes. The close match in

normalized sensitivities (<3% variation) indicates that the sensor is responding solely to the

piezoresistive effects and not unsteady convective cooling. This piezoresistive effect is a

combination of shear stress sensitivity, pressure gradient sensitivity and normal pressure

sensitivity .









The frequency response at a bias voltage of 1.5 V was also investigated in this experiment.

For this test, the generator is set to a random signal with a span of 6.4 k
frequency of 3.4 kHz to ensure that all harmonics up to 6 kHz are captured. A 200 line FFT is

used corresponding to frequency resolution of 32 Hz At each measurement frequency, 2000

linear averages are taken with 0% overlap. The input shear stress is desired to be 0.3 Pa The

theoretical SPL for each measurement frequency obtained via Equation (6-1). By adjusting the

SPL at specific frequency, the target shear stress is then achieved. The normalized frequency res

ponse function of the shear stress sensor is given as [43]


H ( f )= "' ,(6-3)
TwZlll( f ) dV

where Vou, ( f ) is the sensor output with a known input, Twazz ( f) is obtained via Eqluation (6-1),

and Br/BV is the flat band sensitivity. For this experiment, the sensitivity at 2.088 k
the linearity test was used for normalization. Figure 6-10 demonstrates the magnitude and phase

of the actual frequency response function of the shear stress sensor for a nominal input shear-

stress magnitude of 0.3 Pa. The gain factor is flat and is between -3.01 dB to 0.09 dB for this

test. The phase is flat up to 4.552 kHz. It is noted that the gain factor at frequency of

2.088 k
measurements. These results are not corrected for non-idealities in the anechoic termination

which results in a finite reflected wave [97]. In addition, there is some suspicion that the results

above 4.552 k
Regardless, there is no apparent resonance in this sensor up to 6.7 k
To check the wave reflection effect on the measurement, the two-microphone method [99]

is used to measure the reflection coefficient, as shown in Figure 6-11. The frequency spans from









0.2 Hz to 6.4 k
linear averages with 0% overlap are taken. The results indicated that the magnitude of the

reflection coefficient is comparatively large when the frequency is below 1 kHz Therefore, the

frequency in the measurement for both linearity and frequency response are above 1 kHz to

minimize the uncertainty.

The lower end of the dynamic range of the sensor is ultimately limited by the device noise

floor. The output-referred noise floor of the sensor and measurement system is shown in Figure

6-12 for a bias voltage of 1.5 V As expected, the noise spectrum is dominated by 1/ f noise

indicating that the signal-to-noise ratio for this sensor is a strong function of frequency. At

1 kHz (with 1 Hz bin) the output-referred noise floor of the sensor and measurement system is

48.2 nV/JH which corresponds to the minimum detectable shear stress of 11.4 mPa.

Summary

Preliminary electrical and dynamic characterization and the noise determination are

presented to demonstrate device functionality. At a bias voltage of 1.5 V, the dynamic

characterization of the device revealed a linear response up to at least 2.0 Pa and a flat response

up to the frequency testing limit of 6. 7 kHz The theoretically predicted resonant frequency is

9.8 k
detectable shear stress at 1 kHz is 11.4 mPa Therefore, the experimentally verified dynamic

range is 11 mPa-2 Pa The theoretically predicted upper end of the dynamic range at 3% static

non-linearity is 5 Pa. The upper ends of the dynamic range and bandwidth, however, could not

be verified due to constraints in the calibration apparatus. A summary of the experimental

results compared to the predicted results for a bias voltage of 1.5 V are listed in Table 6-4. The

normalized sensitivity is close to the predicted design value, but resistor heating precluded using









higher bias voltages, thus lowering the maximum allowable sensitivity by 16.5 dB.

Furthermore, the noise floor is roughly a factor of 7 higher than predicted. This may be due to

the noise floor measured is the total system noise, which includes setup noise and sensor noise,

whereas the predicted value is just due to the sensor and the AD 625 circuit. There are also

substantial differences in the predicted versus realized bridge impedance which means that the

voltage noise of the resistors may also be higher than predicted.









Table 6-1. LabVIEW settings for noise PSD measurement
Frequency Range (Hz) Bin Width (Hz ) Number of Averages
10-200 0.25 2300
200-1600 2 4000
1600-102400 128 30000



Table 6-2. The optimal geometry of the shear stress sensor that was characterized.
Parameters Design Values
Target Shear Stress r t(Pa) 5
Tether Length L, (pm) 1000
Tether Width W, (ym) 30
Tether Thickness 7((pm) 50
Floating Element Width W (pm) 1000
Piezoresistor Length L, ~(Cm) 228.5
Piezoresistor Width W (ym) 5
Piezoresistor Depth y,; (ym) 1


Table 6-3. Sensitivity at different bias voltage for the tested sensor.
Bias Voltage (V) Sensitivity (mV/Pa)
1.5 0.27
2.95 0.71
3.1 0.93
4.8 3.0








Table 6-4. A comparison of the predicted versus realized performance of the sensor under test
for a bias voltage of 1.5V.
Parameters Theoretical Value Experimental Result
Normalized Sensitivity (CIV/V/Pa) 3.65 2.83
Noise Floor (nV) 6.5 48.2
MI/DS (mPa) 1.2 11.4
Bandwidth (kH~z) 9.8 >6.7
Resistance (02) 1000 397

rmax (Pa) 5 >2

















)- -.02 -- -


-0.03 -- - -*


O -.04 -





-0.06
O 1 2 3 4 s
Bias Voltage( V)


Figure 6-1. The bridge dc offset voltage as a function of bias voltages for the tested sensor.




V1 1


RF I 10 ~Output
CVA RG ~i 5AD625
Rv 7

S16-

WheatstoneVBig AD7111


Offset Null SIM 928


Figure 6-2. An electrical schematic of the interface circuit for offset compensation.









































4

2

n


-I

10 -8 -6 -4 -2 O 2
Bias Voltage ( V)


PC

Techron 7540 Power B&K Pulse
Supply Amplifier Analyzer System
Anechoic
Acoustic Plane Wave Mirpoe Termination


Speaker


Shear Stress Sensor


Offset Null &
Amplification Circuit


Figure 6-3. A schematic of the experimental setup for the dynamic calibration experiments.


Bias


Forward
Bias


Figure 6-4. Forward and reverse bias characteristics of the p/n junction.


)))ii





























-10
-20 -15 -10 -5
Bias Voltage ( V)

Figure 6-5. Reverse bias breakdown voltage of the P/N junction.


30


20 - -


10~ -~ --V2~C-'Fti

y = 2.43*x +~ 0.273




-10 -


- V -GND


-Linear FittingI


V GhD Linear FittingI


y= 2.52*x- 0.01
R2= 0.9992


Bias Voltage( V)


Figure 6-6. I-V characteristics of the input and output terminals of the Wheatstone bridge.


























2-


0-


-2
-10


0
Voltage (Volts)


Figure 6-7. The nonlinearity of the I-V curve in Figure 6-6 at different sweeping voltages.


O


8

7






4



2

1

0


y = 3.6Q2*x +0.01884

y = 2.9b5*x + 0.004148j


a V =1 V

o V =1.25 V
V =1.5 V


0.5 1
Shear Stress (Pa)


Figure 6-8. The output voltage as a function of shear stress magnitude of the sensor at a forcing
frequency of 2.088 k













y= 2.905*xt 0.3113 for V 1.OV
5 --

Sy= 2.882* -0.2964 for 1.V 1.25

Sy= 2.828*x- 0.2914 for B.V 15




~2 V =1.0 V
I./.o V =1.25 V
o4 V-B=1 .5 V
Z 1 - -
Linear Fittin~g

O 'F
O 0.5 1 1.5 2
Shear Stres (Pa)


Figure 6-9. The normalized output voltage as a function of shear stress magnitude of the sensor
at a forcing frequency of 2.088 k


10




-10

1 2 3 4 5 6
Frequency (k~z




50 -0



1 2 3 4 5 6
Frequency (k~z


Figure 6-10. Gain and phase factors of the frequency response function.












0.8

0.6

S0.4

0.2

O



200

100

0

.c-100


1 2 3 4 5 6
Freq [kH|


1 2 3 4 5 6
Freq [kH|


Figure 6-11i. The magnitude and phase angle of the reflection coefficient of the plane wave tube.

















S10
System Noisp



S1 Systemn"hemrmal Noise"






1 2 3 4 5
10 10 10 10 10
Frequency (Hi

Figure 6-12. Output-referred noise floor of the measurement system at a bias voltage of 1.5V.









CHAPTER 7
CONCLUSION AND FUTURE WORK

Summary and Conclusions

A proof-of-concept micromachined, floating element shear-stress sensor was developed

that employs laterally-implanted piezoresistors for the direct measurement of fluctuating wall

shear stress. The shear force on the element induces a mechanical stress field in the tethers and

thus a resistance change. The piezoresistors are arranged in a fully-active Wheatstone bridge to

provide rej section to common mode disturbances, such as pressure fluctuations. A dummy bridge

located next to the sensor is used for temperature corrections. The device modeling, optimal

design, fabrication process, packaging and comprehensive calibration were presented.

Mechanical models for small and large deflection of the floating element have been

developed. These models are combined with a piezoresistive model to determine the sensitivity.

The dynamic response of the shear stress sensor was explored by combining the above

fundamental mechanical analysis with a lumped-element model. Finite element analysis is

employed to verify the mechanical models and lumped-element model results. Dominant

electrical noise sources in the piezoresistive shear stress sensor, 1/ f noise and thermal noise,

together with amplifier noise, are considered to determine the noise floor. These models are then

leveraged to obtain optimal sensor designs for measuring shear stress in several flow regimes.

The cost function, minimum detectable signal (MDS) formulated in terms of sensitivity

and noise floor, is minimized subj ect to nonlinear constraints on geometric dimensions, linearity,

bandwidth, power, resistance, and manufacturing constraints. The optimization results indicate

that the predicted optimal device performance is improved with respect to existing shear stress

sensors, with a MDS of O(0.1 mPa) and dynamic range greater than 75 dB. A sensitivity









analysis indicates that the device performance is most responsive to variations in tether

geometry.

The process flow used an 8-mask bulk micromachining process, involving PECVD,

thermal oxidation, wet etch, sputtering, DRIE and RIE fabrication techniques. After fabrication,

the die was packaged for wind tunnel testing in a custom printed circuit board for modularity.

An interface circuit board was designed for amplification and offset compensation.

Then the sensor was calibrated electrically and dynamically. Electrical characterization

indicates linear junction-isolated resistors, and a negligible leakage current (<0.12 CLA) for the

junction-isolated diffused piezoresistors up to a reverse bias voltage of -10 V. Using a known

acoustically-excited wall shear stress for calibration at a bias voltage of 1.5 V, the sensor

exhibited a sensitivity of 4.24 pV/Pa, a noise floor of 11.4 mPa/A~ at 1 kHz a linear

response up to the maximum testing range of 2 Pa, and a flat dynamic response up to the testing

limit of6.7 kHz These results coupled with a wind-htnnel suitable package are a significant

first step towards the development of an instrument for turbulence measurements in low-speed

flows. The system noise is 48.2 nV/JH at 1 kHz (with 1 Hz bin), and is roughly 7 times

higher than predicted. Static heating limitations limited the maximum bias voltage to 1.5 V

instead of 10 V .

Suggestions for Future Work

Future work should focus on the comprehensive characterization of the sensor to determine

absolute performance and to compare against all of the theoretical predictions. An uncertainty

analysis of all experiments and accurate measurement of the sensor geometry are required to

enable this comparison. Specifically, a temperature compensation approach must be realized that

will enable the static calibration of the sensor as well as any dc measurement application. The









resonant frequency of the sensors must be determined. Sensitivity to vibration and pressure

fluctuations must also be determined. Detailed noise measurements that isolate the contribution

from the piezoresistor should be carried out. Finally, the flow around the floating element will

be investigated via numerical simulations to provide an improved estimate of pressure gradient

induced errors. In the following subsection, several suggestions for carrying out these

measurements are discussed below.

Temperature Compensation

The sensitivity of the shear stress sensor changes with temperature due to the variation of

the piezoresistive coefficient with temperature, as indicated in Equation (3-23) and (3-24). In

sensor static calibration in a 2-D laminar cell, the sensitivity is defined as the slope of the curve

of voltage output versus shear stress. However, due to the temperature effect, the output voltage

is a function of shear stress and temperature. Thus the temperature induced voltage output

should be subtracted from the active bridge voltage output. For the identical active and dummy

Wheatstone bridge, the temperature effect on them should be same. Therefore, the temperature

effect on the active bridge in the static calibration can be removed by subtracting the voltage

output of the dummy bridge.

Unfortunately, the active bridge and dummy bridge are not identical due to Wheatstone

mismatch. So the voltage output dependence of the temperature need to be measured for both

active bridge and dummy bridge. The output voltage of the active bridge is a function of shear

stress and temperature variations, while the dummy bridge depends on temperature variation

only. The measured output voltages in the laminar flow are I-in (r~,,T) for the active bridge and


I-, (T) for the dummy bridge, respectively. The slope of the voltage vs. temperature curve is S,,









for active bridge and S~d for dummy bridge. In the static calibration, the output voltage

dependence of shear stress is given as

l(w>= l (4wT)-~ (T) (7-1)

Assuming that the slope of the Vo vs. T curve remains constant and they are given as,


(7 -2)
Vid(T) d TO S~d

Substituting V (T) from Equation (7-1) into (7-2) and rearranging it, the shear stress dependent

output voltage is obtained as


V,(r)= V,(rT)V (o))- (Vd(T)-d T)),(7-3)
T~d

where V~ (To) is the initial voltage value at room temperature. The Equation (7-3) indicates that


S,, and S~d must be obtained in order to get V (r.). Preliminary experiments prior to

employing dc offset nulling were performed to determine the temperature sensitivity.

Unfortunately, the large dc offset limited the quality of the results. The experimental set up is as

follows.

The voltage output dependence of temperature variation is conducted in two bath settings.

Both bathes are filled with DI water. The outer bath is the chamber of Isotemp refrigerated

circulator, and the inner bath is glass beaker. The packaged sensor is sitting on the top of the

beaker. The beaker is used to protect the sensor from flow circulation disturbance. The

compensated voltage output is connected to a HP34970A data acquisition unit and DAQ card. A

HP34970A digital voltage meter is used to minimize the 60 Hz noise. LabVIEW is used for

data acquisition.









Static Characterization

Initially, we attempted to statically characterize the sensor, but the temperature sensitivity

and dc offset issues prevented any meaningful results. The goal of the static characterization is

to verify the sensor design and characterize the sensitivity and linearity. After temperature

compensation and dc nulling have been achieved, a static calibration can be performed. The

flow cell design is such that an ideal one-dimensional fully developed incompressible laminar

flow exists between two semi-infinite parallel plates (Poiseuille flow between two parallel

plates). For this case, the pressure drop is constant and the wall shear stress is given by the

theoretical relation [7]

h dP
r (7-4)
S2 dxC

where h is the height of the channel in meters and P is pressure in Pascals. Detailed setup

information can be found in [34].

The incompressible flow is first verified before the sensor static calibration. The

incompressible flow exhibits a linear pressure drop versus length for wall shear stress up to

2 Pa, which is a necessary assumption for Equation (7-4). The pressure measurements are

carried out using the Scannivalve pressure measurement system. This multiplexing valve system

allows the pressure taps to be reached sequentially to measure pressure drop between the first

pressure tap and other taps downstream. The inlet flow rate is regulated using a mass flow

controller (GFC4715). A linear pressure drop versus length is displayed in Figure 7-1.

Figure 7-2 shows the experimental setup for the static calibration of the wall shear stress

sensor. The sensor is flush-mounted on one wall of the laminar flow cell and oriented for

measuring wall shear stress in the flow direction. The corresponding pressure drops across two

pressure taps 1F and P, is measured using a differential pressure gauge, Heise pressure meter.










The voltage output is first fed into the compensation circuit. The compensated signal is then

supplied to a HP34970A precision digital voltage meter to eliminate 60Hz noise from the power

supply by averaging. The mass flow rates are controlled automatically by LabVIEW to obtain

different pressure drops and correspondingly wall shear stress. LabVIEW is also used for data

acquisition and manipulation.

Noise Measurement

In order to determine the isolated resistor noise characteristics, the sensor is placed in a

double-nested Faraday Cages to improve the electromagnetic interference (EMI) reduction [98].

The compensated voltage output is amplified by a SR560 preamplifier, and then fed into the

spectrum analyzer (SRS785). The spectrum analyzer (ac coupled) measures the noise power

spectral density (PSD), using a Hanning window to avoid PSD leakage. The noise PSD of the

sensor is obtained by subtracting the setup noise PSD from the total measurement noise PSD.

The setup noise sources include EMI and noise from the amplifier, spectra analyzer, and power

source.

Recommendations for Future Sensor Designs

Based on lessons learned during the first generation shear stress sensor fabrication and

characterization, there are several issues that need to be addressed in future designs.

Specifically, issues regarding resistor self-heating and pressure sensitivity need to be addressed.

In the sensor calibration, piezoresistor self-heating was clearly present when the dissipated

power was greater than 10 mW A study of the normalized sensitivities indicated that self-

heating could be avoided all together for a power dissipation limit of 5.7 mW Therefore, the

power dissipation limit in the design optimization should be decreased from 100 mW down to

10 mW to avoid resistor self heating. The power limit will be a function of the tether geometry,

but the order of magnitude in power reduction will provide a better estimate of appropriate









biasing conditions for design purposes. A detailed numerical study of the resistor heating may

also provide insight into this phenomenon, but this may be challenging due to the complexity of

the convective boundary conditions at the tether surface.

For a balanced Wheatstone bridge, pressure fluctuations should not affect the voltage

output. Preliminary pressure calibrations, however, indicate that the pressure sensitivity is only

O(10 dB) lower than the shear stress sensitivity. In addition to achieving better control of the

resistor implant process to balance the bridge, this can be mitigated by extending the side-

implanted resistor all the way down tether thickness. The fabrication process should change

correspondingly to protect the bottom of the piezoresistor with a high quality passivation. In

current sensor design, the piezoresistor is implanted on the top 5 Cpm of the tether thickness to

avoid resistor current leakage. So in the final backside release step, the BOX layer was removed

to release the str-ucture and the tether bottom is exposed to the flow without any protection. This

will cause sensitivity drifting if the piezoresistor is implanted on the whole tether thickness. A

process flow must be designed to realize an electrically passivated resistor that extends to the

bottom of the resistor thickness.

In general, improved test structures are needed to provide additional information about the

side-planted resistors. Specifically, a test structure must be added into the mask design to enable

the measurement resistor doping profile via secondary ion mass spectroscopy (SIMS). In

addition, providing additional bond pads for each resistor will permit a resistor trim based

approach to bridge balancing and temperature compensation [60].













*Testing Data
-linear Fitting~


S100





60


1 2 3 4 5 6 7
Length (Inch)


Figure 7-1. Pressure drops versus length between taps in the flow cell.


Figure 7-2. Experimental setup of static calibration.









APPENDIX A
MECHANICAL ANALYSIS

A clamped-clamped beam with a central point force and a distributed pressure load is

shown in Figure A-1 (a). This is a second order statically indeterminate problem. Euler

Bernoulli beam theory is used to predict the linear, small deflection behavior and Von Karman

strain is included in the nonlinear, large deflection models. Two methods, an energy method and

an exact analytical method, are used to solve the large deflection problem. Using Euler-

Bernoulli beam theory, the stress distribution is also derived.

Small Deflection

Equilibrium equations may be written based on the free body diagram of the symmetric

str-ucture, Figure A-1(b). The relationships between the resultant forces, RA and R,, point load

P, and distributed load Q are thus

RA = R, = P/2 + QL,, (A-1)

where P = zw Le, 2 = zW, and z is the wall shear stress. The nonlinear differential

equation governing the beam deflection caused by bending is given as [82]

d2 (~~~2
El = M~ (A-2)
1+ (dw/dxh)iU

where w(x) is the deflection in the z direction, E is the Young's Modulus, I is the area

moment of inertia given as I = (T43/12, and Mx is the resisting moment in cross of x Writing

the equation for moment equilibrium, C1MD = 0, yields

Mx = -M~A RAX e2/2 (A-3)









where M~ is the resisting moment, and M~ = M, due to the symmetry of the structure.

Assuming the rotation d~w/dx is very small, Equation (A-2) is simplified to

d2w(x) Ml
(A-4)
dx~C El

Integrating Equation (A-4) yields the rotation and deflection of the beam along its length,


Av(x)LC E1 (Mx 1 1
-~X +-Mx + Rx4 Ox 1, (A-5)

and w(x)= +- 3 Ox A6
El 2 6 24

where c, and c, are constants. There are three unknown quantities in Equations (A-5) and (A-6)

n~, M1 ,nd c, Therefore, three boundary conditions should be employed,

w ,(0) = (clamped), (A-7)


= 0 (clamped), (A-8)


and = 0 (symmety) (A-9)


Substituting the above boundary conditions and R, from (A-1) into (A-6), one obtains

c1 = c, = 0, (A-10)

1 1
and M=4PL, + 3 L, (A-11)


The displacement wu(x) is then obtained by substituting Eqluation(A-10)-(A- 11) and

momentum of inertia I = (7~3 /12 into (A-6)


w(x) = [3 L;5WL,+8(L,) -(2 L,+8WL,)x3+ 2Wx4 ], (0 4E'TV3









The maximum deflection at the center of the beam is given as

7w W L L 2W L
AL = -w(L,)= 1+7 .I W (A-13)


Large Deflection-Energy Method

In a large lateral deflection, the beam experiences bending and stretching. The total strain

is composed of bending and stretching strain [42]

t beding strnchig ,(A-14)

d2W
where sbending 2 y is the position upward. The axial strain at y = W/2 is given as [100]


du 1 dwY\
E --+- -l (A-15)
dx 2 dx~C

The total change in beam length is given by

/dL =\~I f eS dx + (A-16)
J 0 a dx 2 dx(

The integration of the first term is zero due to the clamped-clamped boundary condition. The

axial stain is the total change in beam length divided by the total length of the beam


strentchin 2L, 4L, dxS~ rI~) ~ il

The total strain is obtained as


E = y + W--c4 JO -~\a~l d (A-1 8)


For large deflection, a trial function in the form of a cosine is assumed, as it automatically

satisfies the doubly clamped boundary condition and is a maximum at the center of the beam.

The trial function is thus











w 8x=^ 1+ cos '(1 ,1 (A-19)


where A, is the maximum deflection at the center of the beam. Substituting this model into

(A-18) yields

dw~ Awarsi z(L, x) (-0

d2 8 sm2~ ~ 1 (A-20)
dx~C 2 L, L,







E = y co z(A-22)
'2 L,2 L, 1 6L,2

The strain energy density is given as


U = rds= Ee E y cos ^z(A-23)
o a2 2 2L, L, 16L,


The strain energy is then obtained


U = UodV= 00L dxy (A-24)

The total strain energy is obtained by integrating Equation (A-24) to yield


U = E7( ^z6L3 4rrr .~ (A-25)


Based on the principle of virtual work, the total potential energy W is equal to the stored strain

energy minus the work done by the external forceK ,

W= U-K, (A-26)

where K is given by











K= P3+Q "L 1+ cos =(~ A,(+QL) (A-27)


The equilibrium configuration is that in which the potential energy is minimized. The minimum

is obtained when

dW Ag43
-- = E;7t +~~~4: a'i"w r WL -r WL, =0. (A-28)
d6 48L 3 64L,3 2 "

Rearranging Equation (A-28) yields
x 4 4 rW L 2 ,L, L
As-+- =-- -1+ (A-29)
96 128W 4E(t WL,


Simplifying the above equation, ~21 and-~ -, yields an approximate large deflection
96 128 4~

solution,


3( A L 2 WL, L
A,~E7 1+ 1 (A-30)


Large Deflection-Analytical Method

For large deflection, axial force in the beam is not zero as in the small deflection model,

and serves as a constitutive equation in the modeling analysis. Since the beam is symmetric,

only half of the beam is analyzed, as shown in Figure A-3. For large deflections, taking axial

force Fb into account, the differential equation governing the beam deflection caused by bending

is given as

d2WX
El = M~(x), (A-31)
dx~C

where the slope of beam caused by large deflection is assumed d~w/dx <<1i, and therefore


(dw/~dx)2 is negligible. The moment M(x) is given by









1 P
M~(x) = Q x2 +- x -Mo0 Fa (w(0)- w(x)) (A-32)
2 2

where w(0) is an unknown constant. Substituting Eqluation (A-32) into Eqluation (A-31) yields

d2w(x) 1 P
El 2 Fw(x)-=- Qx2 + -x-Mo-F,w(0). (A-33)
dx~C 2 2

The above equation can be solved as a superposition of one general solution wn and a particular
solution ws
w(x) = wn (x) + ws(x), (A-34)

where w, (xC) = C, sinh(ilx) + C2 COsh(ilx) and w, (x) = axc2 + bx + c, assuming ii=l .

Substituting ws into Equation (A-33), a, b, and c are obtained as

Q P MQ
a- b= and c = w(0)+
2F a F Fi A2


Equation (A-34) can be rewritten as

Q! P MQ
w(x) = C, sinh(ilx) +C2 COsh(ilx) x2 --~x +w(0)+ o,
2F; 2F; F F122


(A-35)


for which the boundary conditions are:


dwY (0)
=0,


dw (L,)


w,(L,)= 0.

- W/2 is nonlinear and is given as


2d oE EA'F


(A-36)


(A-37)


(A-38)


and

For large deflection, the axial strain at y I

du
E 0


(A-39)









where A = 7(W Integrating the above equation yields


EA du d
F = l oN, ~1 +- (A-40)
"L dx 2 dx~C

The first term in the integration is zero due to the doubly clamped boundary condition. Axial

force Fa in the neutral axis y = W/2 is then obtained as

F:~EA dw ~\2LC
FI = dx (A-41)


There are five unknown variables: C,, C2, F ,Mo, and w(0), thus five boundary conditions are

needed to solve for these unknown variables. However, only three boundary conditions (A-36)-

(A-38) and one constitutive equation (A-41) are available. Another condition is w1(0) = wI(0).

The problem is indeterminate and an iterative technique must be used to find the final result.

First, we applied boundary conditions (A-36)-(A-3 8) and the constitutive equation (A-41)

into Equation (A-3 5) and solve it to get the maximum deflection as a function of the axial force

in the neutral axis, F~ The detailed procedure for solving this problem is given in the following.

Substituting (A-35) into boundary conditions (A-36) and (A-37) yields

P 1 PP
C,=E an C2 Q+- coh(L,) (A-42)


Substituting C, and C2 into (A-35) and setting x = 0 yields

Q! 1 PP
Mo QL +---cosh(L).(-3
22 2 Sinh(AL, 2 243

Substituting Mo from (A-43) and C, and C2 fTOm (A-42) into (A-35) yields

P cosh(ilx) -1
w~x)= -sn(A) QL +-cosh( AL. ) I -x2 --~x +w(0) (A-44)
2ilF FAsn(L) 2 2 2F 2F









Substituting (A-3 8) into (A-44) yields deflection at the center,

P cosh(3L, )-1/, P _P Q~li~T j+tL'2 PL,
w(0) = --sinh(ALl,) QL,`""' +F ohAL)+ + '
2ilF FA lsinh(AlL ) 2 2 2

Derivative Equation (A-44) to obtain

dw (x) 1c P ohix sinh(Ax) /1~ P P~o \ ) P
dx F 2sinh(AL, )\Y 2 22.


(A-45)





(A-46)


Secondly, we solve the maximum deflection equation (A-45) by iterating Fa An initial

value Fa =10-4 Pa is selected randomly and the following steps are performed to obtain the

maximum deflection, w (0) .

dwy a
1) Substitute Fb into (A-46) to get where ii = .-
dre El


2) Substitute -into (A-41) to obtain new F .


3) Repeat 1), 2) until the relative error IFa"' Fa" /Fa"' < le 6 .

4) Substitute F into (A-45) to find the maximum deflection w,(0).


Stress Analysis

The bending stress along a beam (shown in (A-3)) is given as [82]

F; 2f y
cr =-+ =,
A I


(A-47)


where IZ is the moments of inertia for the z axis, and IZ = 7,'W3/12. In small deflection, the

axial force Fb = 0 A free body diagram of the clamped beam is shown based on the discussion









in the small deflections section, where R, and MA are obtained from Equation (A-1) and (A-11i),

respectively. The moment for a certain length from the edge of the beam is obtained as,

11 1 1
M= PL, QL2 PQ x--x2. (A-48)
4 322

Substituting Equation (A-48) into (A-47) and simplifying the equation to obtain the bending

stress along the beam (0 <; x < L,) at y = 0,

3 2~L2
r, LL, 3 2(L, 3 6(L, x 3(L, x
~27t 4 WL, 2 LL, WL L

Effective Mechanical Mass and Compliance

In this section, the mechanical lumped parameters for a clamped-clamped beam are found.

These parameters include lumped compliance obtained via the storage of potential energy and

lumped mass obtained via the storage of kinetic energy. These results are used in Chapter 3 to

develop the lumped element model of a laterally diffused piezoresistive shear stress sensor.

Recall that the lateral displacement and maximum displacement of the clamped-clamped

beam in small deflection given in Chapter 2,


w(x) = [ 3 LL, + 8(Lt2 2 (2 L + 8 L,)x 3 + 2 (x4 (0 <;x 4E 37


Tw LL [~;12L, A-
and w(L,)= 2 .(-1


The kinetic co-energy W, of a rectilinear system with a total effective mass m moving

with velocity u is given as,

1
W, = -mu2 (A-52)


For a simple harmonic motion, the velocity and displacement of the beam are related by









u(x)= jcuw(x), (A-53)

where m is the frequency and uI (L,) = jew l(L,) uI (x) is then expressed as

w (x)
u(x)= u (L,) (A-54)


For an infinitesimal element on the beam with a mass of psW~dx, the kinetic co-energy

dW,' is calculated using Equations (A-52) and (A-54) to be

S1 p,,W7tu2 (L,)
dW, psI,7,W'(u2 __2 (x)dx ~ (A-55)
2 2w2 (L,)

where psl is the density of silicon. Integrating Equation (A-55) over the beam gives the total

kinetic co-energy of the system,

r s t (L,)T( 1 2 Ly
W, = 2 dW, w2(x~dx (A-56)
o W2(L,) o

The reference point is x = Lt, which corresponds to the maximum deflection of the beam wi(Lt).

The distributed deflection of the beam can be lumped into a rectilinear piston by equating the

kinetic energy obtained in Equation (A-56) to the kinetic energy of the rectilinear piston of mass




W = (A-57)


Equating Equation (A-57) and (A-56) yields effective mechanical mass as


M,,, =2 I" w2(x)dx (A-.58)


Since the velocity of the plate is u = ~jmw(L,) the effective mechanical mass of the device

is the sum of the mass of the plate and the effective mechanical mass of the beam,









M2, M Z~ + MZh = p,,L WT, + M .


(A-59)


The strain energy stored in the beam due to its deflection can be expressed as





The strain energy of an equivalent spring is given by

WE=1 -1 w(2,(
2 C,

where C,,, is the mechanical compliance of the beam. Equating Equation (A-61) and (A-60)

yields

w(L,)2

Ziod2W()LC


Substituting wu(x) and w(Lt) in Equation (A-50) and (A-51) into (A-_59) and(A-62) yields


L-60)


L-61)


L-62)


1+1494 WL,
315 WL


nM,,, pW,WL,7t


(A-63)


(A-64)


1+4
WL


2238WL,1024 W L,
315 WL, 315 WL


+2tVL,
W liiL)


1 L,
C = 7\~


641 WL, 2L











P W



2Le


Rx
x=0





Ax=0l


M, f


"'B


/I


Figure A-1. The clamped beam and free body diagram. a) Clamped-clamped beam. b) Free body
diagram of the beam. c) Free body diagram of part of the beam.


x


Figure A-2. Clamped-clamped beam in large deflection.


VM


R" x


Figure A-3. Clamped-clamped beam in small deflection (a)
clamped beam (b).


and free body diagram of the


?~ :









APPENDIX B
NOISE FLOOR OF THE WHEATSTONE BRIDGE

For a Wheatstone bridge shown in Figure B-1, assuming R, = R, = R, = R, = R we get

I, = V,/2, therefore the voltage across each resistor is

VR B B/2Yla= V,/2 (B-1)

The current through the resistor is


IR B (B-2)
2R

Assuming the noise sources are uncorrelated, the mean square noise can be solved as a

superposition of the mean square thermal noise, the 1/ f noise, and the amplifier noise. For

thermal noise, the equivalent noise model is given in Figure B-2. The rms thermal voltage is

given as


;aen,a, E + ==ii~ 4k~,iiiT (RR Af +kT ( R ) A = 4k,TRAf (B-3)

For 1/ f noise, the equivalent noise model is given in Figure B-3. The mean square

current noise is


I = RIn .(B-4)


The mean square voltage noise E, is obtained as




Substituting Equation (B-4) and (B-2) into (B-5) to obtain

E,=aHR 2 HR2 7 R

(B-6)

Nc4R / Nc4R /41(

157









Rearrange the above equation to get


(B -7)




(B-8)


The rms 1/ f voltage is obtained as


The total noise floor is obtained via the superposition of the mean square noises


2~ +4khTRAf +(e-/p9)2 ,


(B-9)


where the last term in the above equation is the low amplifier noise.


E 2 H ," 2~ 2 .
8No 4N


V = HV,2

























Figure B-1. The Wheatstone bridge.

R,

V,

R2 R



E Rf, E2
VI ~ cx V2


Figure B-2. The thermal noise model of the Wheatstone bridge.

R,

V, R R


R2 R3

E' R //R, R 4//R3 E,
VI--tx V,


Figure B-3. The 1/ f noise model of the Wheatstone bridge.










APPENDIX C
PROCESS TRAVELER

Wafer: n-type <100> 1-5 ohm-cm, SOI wafer

Start with SOI wafer (n-Si (100) 1-5 O2-cm) with 50Clm silicon on 1.5um buried oxide (BOX).

DI rinse

Masks

Reversed biased mask-------RBM

Piezo contact mask-------PCM

Nested mask-------NM

Side implant mask-------SIM

Bond pad cuts mask-------BPCM

Metal mask-------MM

Bond pad mask-------BPM

Process Steps

1. n-well Implant

* Ion implant- dopant = phosphorus, energy = 150 keV, dose = 4el2 cm-2. 7 degree tilt,
blanket implantation. This forms the n-well. This needs to be simulated first.

* Piranha clean

2. PECVD oxide: deposit oxide 0.1pum via PECVD

3. Reverse Bias Contact

* Coat and pattern photoresist/oxide on front side

0 HMDS evaporation for 5min
0 Spin AZ 1529 at 4000rpm for 50sec & softbake at 90"C oven for 30min
0 Pattern by mask RBM
Exposure 60sec at 8.8mJ/cm2
Develop at AZ300MIF for 50sec
Hard bake at 90"C oven for 60min










* BOE(7:1) : ~80sec to etch 0.1um oxide. This step puts alignment marks on the wafer

* Ion implant- dopant -phosphorus, energy = 80 keV, dose = 9el3 cm-2. 7 degree tilt

* Ash strip photoresist

* RCA clean

* Thermal annealing at T = 10000 C, time=420sec in nitrogen

4. Inplant Interconnection Contact

* Coat and pattern photoresist/oxide on front side

0 HMDS evaporation for 5min
0 Spin AZ 1529 at 4000rpm for 50sec & softbake at 90"C oven for 30min
0 Pattern by mask PCM, align to the alignment marks created via RBM
Exposure 60sec at 8.8mJ/cm2
Develop at AZ300MIF for 50sec
Hard bake at 90" C oven for 60min
* BOE(7:1) : 90sec to etch 0.1um oxide. This step puts alignment marks on the wafer

* Preamorphization Implant

lon implant- dopant = Ge, energy = 160 keV, dose = lel5 cm-2 .7 degree tilt
lon implant- dopant = Ge, energy = 50 keV, dose = lel5 cm-2 .7 degree tilt
* Ion implant- dopant = boron, energy = 50 keV, dose = 1.2el6 cm-2 7 degree tilt

* Ash strip photoresist

* Piranha clean

5. Nested Mask Release

* Deposit PECVD oxide l Cym

* Coat and pattern photoresist on front side

0 HMDS evaporation for 5min
0 Spin AZ 1529 at 2000rpm for 50sec & softbake at 95"C convection oven for
25min
0 Pattern by mask NM, align to the alignment marks created via PCM
Exposure 85sec at 7.9 mJ/cm2
Develop at AZ300MIF for 60sec
Hard bake at 90"C oven for 60min
* Plasma dry oxide etch. This step puts new alignment marks on the wafer










* BOE(6:1) oxide etch to remove the oxide residues

6. Etch Sidewalls

* Coat and pattern photoresist on front side

0 HMDS evaporation for 5min
0 Spin AZ 1512 at 2000rpm for 40sec & softbake at 95"C hotplate for 50sec
o Pattern by side implantion mask(SIM), align to the alignment marks created via
NM
Exposure 19sec at 4.5mJ/cm2
Develop at AZ300MIF for 70sec
Hard bake at 90"C oven for 60min
* BOE(6:1) oxide for 2min

* DRIE silicon to ~8Cpm deep

* BOE(6:1) oxide for 60sec to avoid Piezoresistor and Piezo contact disconnection due to
DRIE undercut

* Ash strip photoresist

* Piranha clean

7. Hydrogen Annealing

* T = 10000C P=5mTorr for 5min in pure hydrogen for surface roughness reduction

8. Oxidation: thermal grown wet oxide 1000A at T=1 000oC

9. Side Wall Implantation

* Preamorphization implant

lon implant- dopant = Ge, energy = 160 keV, dose = lel5 cm-2 54 degree tilt
lon implant- dopant = Ge, energy = 50 keV, dose = lel5 cm-2 54 degree tilt
* Ion implant- dopant = boron, energy = 50 keV, dose = lel6 cm-2 54 degree tilt

* Piranha clean

10. Beam Definition

* Etch oxide by reactive ion etch via dielectric setting in STS

* DRIE silicon to BOX

* BOE(6:1) 2min to remove oxide (ensure to remove 0.1um oxide on sidewall)

162









11. Oxidation


* Piranha clean

* Annealing at T=1000oC for 60min in nitrogen

* Thermal dry oxide grown at T=975oC: for 235min (0.1Cpm)

12. Bond Pad Cuts

* Trench filling

o Spin AZ 1512 at 800rpm for 40sec & softbake at 95"C hotplate for 50sec
o Spin AZ9260 at 800rpm for 50sec & softbake at 90"C oven for 30min
0 Flood exposure
Exposure 300sec at 7.9mJ/cm2
Develop at AZ400MIF till clear
* Coat and pattern photoresist on front side

0 HMDS evaporation for 5min
0 Spin AZ 1512 at 0.5k/2k for 5/40sec & softbake at 95"C hotplate for 50sec
o Pattern by bond pad cuts mask(BPCM), align to the alignment marks created via
PCM
Exposure 45sec at 4.5mJ/cm2
Develop at AZ300MIF for 60sec
Hard bake at 90"C oven for 60min
* BOE(6:1) oxide for 15min

* Remove photoresist

13. Metalization

* Trench filling

* Desccum in oxygen plasma

* Deposit lum Al-Si(1%) to avoid spiking via sputtering

* Coat and pattern photoresist on front side

0 HMDS evaporation for 5min
0 Spin AZ 1529 at 0.2k rpm and stay for 2min. Then spin at 0.2k/2k rpm for
10/50sec with ramp rate of 100/500 rmp/s
o Softbake at 90"C oven for 30min
0 Pattern by metal mask (MM), align to the alignment marks created via BPCM
Exposure 100sec at 7.9mJ/cm2
Develop at AZ300MIF for 1min 30sec









Hard bake at 90"C oven for 60min
* Etch Al by RIE

* Remove photoresist

14. Nitride Passivation

* Deposit 2000A PECVD silicon nitride

* Trench filling

* Coat and pattern photoresist on front side

0 HMDS evaporation for 5min
0 Spin AZ 1512 at 4000rpm for 40sec & softbake at 95"C hotplate for 50sec
o Pattern by bond pad mask(BPM), align to the alignment marks created via MM
Exposure 18sec at 4.5mJ/cm2
Develop at AZ300MIF for 60sec
Hard bake at 90"C oven for 60min
* Etch nitride by RIE

* Remove photoresist

15. Final Release

(a) Device wafer

* Spin AZ9260 on front side of the device wafer

o Spin speed 200rpm, ramp rate 100rpm/s for 10s, wait for 1min. Run this recipe
twice
0 Spin speed 4000rpm, ramp rate 1000rpm/s for 50s
o Soft bake at 90"C oven for 30min

* HMDS on the backside

* Spin AZ9260 on backside of the device wafer

o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s

o Soft bake in 90"C oven for 30min

* Pattern by back release mask(BRM), align to the alignment marks created via NM

o Exposure 25 sec in EVG520 mask aligner

o Develop at AZ300MIF for 3min 40sec










o Hard bake at 90' C oven for 60min

(b) Carrier wafer

* Spin PR AZ9260 on a carrier wafer

o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s

* Soft bake at 90"C oven for 20-30min

* Put some cool grease on the edge of the carrier wafer

* Bake on hotplate, 60"C for 5min

* Put the device wafer face down on the carrier wafer.

* Put on the hotplate, apply pressure using swab

(c) DRIE

* Run DRIE, stopped until 50um silicon left

* Put the wafer on the hotplate 60"C for 5min, separate from the carrier wafer

* Separate the wafer into individual dies

(d) Process on individual dies
* Spin AZ9260 on a carrier wafer

o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s

o Put the device die on the top of the carrier wafer, apply pressure using swab

o Soft bake in 90"C oven for 30min

* DRIE to BOX layer

* RIE BOX layer for 15min, run BOE 5-10min to remove the residues

* RIE nitride for 6min

* Remove the device die using tweezers

* Put the device die in AZ400 PR stripper

* Plasma clean in Asher for 10min









APPENDIX D
PROCESS SIMULATION

This chapter includes the FLOOPS process simulation of the piezoresistor, p++

interconnects and n-well, as well as the reverser bias connections.

(a). Piezoresistor

This program simulates the doping profile of piezoresistor in the silicon layer after ion

implantation, anneal and thermal oxidation. The boron is implanted into preamorphization Si

layer with oxide as a screen layer. Its initial doping profile is simulated by SRIM, and then

imported to FLOOPS file for subsequent process simulation.

line xloc=-0.1 spa=0.005 tag= SiO2top
line x loc=0 spa=0.005 tag-top
line x loc=1.5 spa=0.01 tag=bot
region oxide xlo=SiO2top xhi=top
region silicon xlo=top xhi=bot
imit
#profile name=B_SRIM
inf-/home/yawei/Floops~new/SRIM B 50keV_0.1umSiO2 Si_only.txt
sel z=B SRIM*5 name=Boron
sel z=log(Boron)
layer
etch oxide time=1 rate=0.1 iso
diffuse temp=1000 time=60
diffuse temp=975 dry time=23 5
puts "### Oxide thickness after thermal oxide is [expr [interface oxide /silicon] [interface gas
/oxide]] um."
sel z=logl0(Boron)
plot.1Id bound !cle label=PZR
set cout [open /home/yawei/Floops~new/pzrdata w] puts $cout [print.1Id] close $cout
sel z=logl0(5.0el4)
plot.1Id !cle label-background
sel z = Boron-5el4
puts "The Junction Depth is [interpolate silicon z=0.0]"
set z=Boron
layer

(b). P++ interconnection and n-well

#p++ surface concentration is ~1e+21 and n-well Ns~1e+16
# generate grid









line x loc=0 spa=0.001 tag-top
line x loc=1.0 spa=0.01
line x loc=2.5 spa=0.01 tag=bot
region silicon xlo=top xhi=bot
imit
sel z=5el4 name=Phosphorus
implant phosph dose=4.0el2 energy=150 tilt=7
#deposit 0.1lum PECVD oxide
deposit time=4 rate =0.030 oxide grid=10 puts "Oxide thickness after PECVD oxide is [expr
[interface oxide /silicon] [interface gas /oxide]] um."
diffuse temp=1000 time=450
strip oxide
implant boron dose=1.2el6 energy=50 tilt=7
#strip oxide
#deposit lum PECVD oxide
deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD
oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um."
diffuse temp=1000 wet time=9.2 # oxide thickness is 1000A
etch oxide time=1 rate=0.1 iso
diffuse temp=1000 time=60
diffuse temp=975 dry time=23 5
sel z=logl0O(Phosphorus+1)
plot.1id bound !cle color-blue label=nwell
set cout [open /home/yawei/Floops~new/nwelldata w] puts $cout [print.1id] close $cout
sel z=logl0(5el4)
plot.1id !cle color-pink label-background
sel z=logl0(Boron+1)
plot.1id bound !cle color-red label=p++
set cout [open /home/yawei/Floops~new/ohmicdata w] puts $cout [print.1id] close $cout
sel z = Boron- Phosphorus
layer
puts "The Junction Depth is [interpolate silicon z=0.0]"

(c). Reverse biased contact

line x loc=0 spa=0.005 tag-top
line x loc=2.5 spa=0.01 tag=bot
region silicon xlo=top xhi=bot
imit
sel z=5.0el4 name=Phosphorus
implant phosph dose=4.0el2 energy=150
#deposit 0.1lum PECVD oxide
deposit time=4. 19 rate =0.0239 oxide grid=10 puts "Oxide thickness after PECVD oxide is [expr
[interface oxide /silicon] [interface gas /oxide]] um."
strip oxide smooth
set t [open temp.P w+]









sel z=Phosphorus
puts $t [print.1id]
close $t
# start with a new grid ... since strip oxide removes the nodes near the surface where the new
phosphorus profile is about to go set former~interface [interface gas /silicon]
line x loc=$former~interface spa=0.0001 tag-top
line x loc=0.1 spa=0.001
line x loc=1.0 spa=0.01
line x loc=2.5 spa=0.01 tag=bot
region silicon xlo=top xhi=bot
imit
profile name=Phosphorus inf-temp.P
# inplant phosphorus for reverse bias contact
implant phosph dose=9.0el3 energy=80 tilt=7
sel z=logl0(Phosphorus)
plot.1id bound !cle color-red label=Profile~ini
#Thermal Annealing 450min at T=1000 deg
diffuse temp=1000 time=450
#deposit lum PECVD oxide
deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD
oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um."
# thermal grown oxide 1000A at T=975 deg
diffuse temp=1000 dry time=9.2
etch oxide time=1 rate=0.1 iso
diffuse temp=1000 time=60
diffuse temp=975 dry time=23 5
puts "### Oxide thickness after thermal oxide is [expr [interface oxide /silicon] [interface gas
/oxide]] um."
sel z=logl0(5.0e+14)
plot.1id bound !cle color-black label-background
sel z=logl0O(Phosphorus+1)
plot.1id bound !cle color-blue label=reverse~bias
set cout [open /home/yawei/Floops~new/reversedata w]
puts $cout [print.1d]
close $cout
layers




























Table E-2. Anisotropic oxide/nitride etch recipe on the Unaxis ICP Etcher system.
Parameters Oxide Nitride
CHF, flow (sccm) 45 -
SF6 flOW (Sccm) -- 15
O, flow (sccm) 3 5
RF2 power (W) 600 300
RF1 power (W) 100 100
Chamber pressure (mTorr) 15 20
Helium flow (sccm) 20 10

Table E-3. Anisotropic aluminum etch recipe on the Unaxis ICP Etcher system.
Parameters Settings
Ar flow (secm) 5
Cl, flow (sccm) 30
BC1, flow (sccm) 15
RF2 power (W) 500
RF1 power (W) 100
Chamber pressure (mTorr) 5
Helium flow (sccm) 20


APPENDIX E
MICROFABRICATION RECIPE FOR RIE AND DRIE PROCESS

.Input parameters in the ASE on STS DRIE systems.
Parameters 50 Cpm Si etch 8 Cpm Si etch SiO, etch
Coil power 600 W 600 W 800 W
Platen power 12 W 12 W 130
APC (mTorr) 28 (fixed) 28 (fixed) 50 (auto)
Etching process 11 6
Passivation process 6.5 4
SF, flow (sccm) 130 130
O, flow (sccm) 13 13
C4F, flow (sccm) 85 85


Table E-1.


Varies
Varies


Varies
Varies


Etching cycle
Passivation cycle


Varies
Varies










APPENDIX F
PACKAGINTG DRAWINTGS



Measurements Units: mm


Material: Lucite


Insert O-ring


SIDE VIEW


Screw A


Using device chip to ensure
it flush-mounted


TOP VIEW


Hole Through the Lucite to
Take Out the PCB Package


R 15


Note: Sharp Corner
Is Required


oo oo
po oo


Holes Through the Lucite-


R 25


Figure E-1. The drawing illustrating the Lucite packaging.

















O1
f I-130


Measurements Units: mm
Material: Aluminum
SIDE VIEW


i
c\i
-f


Threaded A


TOP VIEW


Figure E-2. The aluminum plate for the plane wave tube interface connection.


25
















Is -


r I 1




t,


.111


Lucite Package


SIDE VIEW






TOP VIEW

9.525 (0.375")


TC


109.22 (4"3)


0127.62 (0.3")


Figure E-3. Aluminum packaging for pressure sensitivity testing.










LIST OF REFERENCES

[1] P. J. Johnston, J. Allen H. Whitehead, and G. T. Chapman, "Fitting Aerodynamics and
Propulsion into the Puzzle," Aerospace America, pp. 32-42, 1987.

[2] W. Shyy, M. Berg, and D. Ljungqvist, "Flapping and Flexible Wings for Biological and
Micro Air Vehicles," Prog. Aerosp. Sci., vol. 35, pp. 455-505, 1999.

[3] M. Sheplak, L. Cattafesta, and Y. Tian, "Micromachined Shear Stress Sensors for Flow
Control Applications," IUTAM~Synposiunt on Flow Controla~ndM~EMS, London, England
2007, pp. 67-73.

[4] J. W. Naughton and M. Sheplak, "Modern Development in Shear Stress Measurement,"
Prog. Aerosp. Sci., vol. 38, pp. 515-570, 2002.

[5] M. Gad-el-Hak, Flow Control: Cambridge University Press, 2000, pp. 209-210.

[6] R. Rathnasingham and K. S. Breuer, "Active Control of Turbulent Boundary Layers," J.
Fluid2~ech., vol. 495, pp. 209-233, 2003.

[7] F. M. White, Viscous FluidFlow, 2nd ed.: McGraw Hill, 1991, Ch. 1, 4, 5, 6.

[8] H. Tennekes and J. L. Lumley., A First Course in Turbulence: The MIT Press, 1972, Ch. 1,


[ 9] Y. A. Cengel and J. M. Cimbala, Fluid Mechanics: Fundamentalsd~~~dd~~~ddd~~ andApplications:
McGraw-Hill 2006.

[10] L. Lofdahl and M. Gad-el-Hak, "MEMS-Based Pressure and Shear Stress Sensors for
Turbulent Measurement," M~ea~s. Sci. Tech., vol. 10, pp. 665-686, 1999.

[1l] A. Padmanabhan, "Silicon Micromachined Sensors and Sensor Arrays for Shear-Stress
Measurements in Aerodynamic Flows," Ph.D Dissertation in Department of Mechanical
Engineering, Massachussets Institute of Technology, 1997.

[12] H. Alfredsson, A. V. Johansson, J. H. Haritonidis, and H. Eckelman, "The Fluctuating
Wall-Shear Stress and the Velocity Field in the Viscous Sublayer," Phys. Fluids, vol. 31,
pp. 1026-1033, 1988.

[13] M. Gad-el-Hak and P. R. Bandyopadhyay, "Reynolds Number Effects in Wall-Bounded
Flows," Appl. M~ech. Rev., vol. 47, pp. 307-365, 1994.

[14] J. M. Corcos, "Resolution of Pressure in Turbulence," J Acoust. Soc. Am., vol. 35 (2), pp.
192-200, 1963.

[15] T. A. Brungart, G. C. Lauchle, S. Deutsch, and E. T. Riggs, "Outer-Flow Effects on
Turbulent Boundary Layer Wall Pressure Fluctuations," J. Acoust. Soc. Am., vol. 105, pp.
2097-2106, 1999.










[16] R. F. Blackwelder and J. H. Haritonidis, Scaling of the Bursting Frequency in Turbulent
Boundary Layer," J. Fluid2~ech., vol. 132, pp. 87-103, July 1983.

[17] W. W. Willmarth and L. K. Sharma, "Study of Turbulent Structure with Hot Wires
Smaller than the Viscous Length," J. Fluid2~ech., vol. 142, pp. 121-149, May 1984.

[18] M. A. Schmidt, R. T. Howe, S. D. Senturia, and J. H. Haritonidis, "Design and Calibration
of a Micromachined Floating-Element Shear-Stress Sensor, IEEE Trans. Electron
Devices, vol. 35, pp. 750-757, 1988.

[19] J. Shajii, K.-Y. Ng, and M. A. Schmidt, "A Microfabricated Floating Element Shear Stress
Sensor Using Wafer-bonding Technology," J. M~icroelectromech. Syst., vol. 1 (2), pp. 89-
94, June 1992.

[20] A. Padmanabhan, H. Goldberg, K. D. Breuer, and M. A.Schmidt, "A Wafer-Bonded
Floating-Element Shear Stress Microsensor with Optical Position Sensing by
Photodiodes," J. M~icroelectromech. Syst., vol. 5 (4), pp. 307-315, 1996.

[21] T. Pan, D. Hyman, and M. Mehregany, "Microfabricated Shear Stress Sensors, Part 1:
Design and Fabrication," AIAA J., vol. 37, pp. 66-72, 1999.

[22] F.-G. Tseng and C.-J. Lin, "Polymer MEMS-Based Fabry-Perot Shear Stress Sensor,"
IEEE Sensors 1, vol. 3, pp. 812-817, Dec. 2003.

[23] S. Horowitz, T.-A. Chen, V. Chandrasekaran, K. Tedjojuwono, L. Cattafesta, T. Nishida,
and M. Sheplak, "A Micromachined Geometric Moire Interferometry Floating-Element
Shear Stress Sensor," IEEE Solid'-State Sensor and Actuator Workshop, 2004, pp. 13-18.

[24] J. Zhe, V. Modi, and J. Kenneth. R. Farmer, "A Microfabricated Wall Shear-Stress Sensor
with Capacitative Sensing,"1 M.2icroelectromech. Syst., vol. 14 (1), pp. 167-175, Feb.
2005.

[25] A. A. Barlian, S.-J. Park, V. Mukundan, and B. L. Pruitt, "Design and Characterization of
Microfabricated Piezoresistive Floating Element-Based Shear Stress Sensors," Sensors and'
Actuators A, vol. 134 (1), pp. 77-87 2007.

[26] M. E. Law and S. Cea, "Continuum Based Modeling of Silicon Integrated Circuit
Processing: An Obj ect Oriented Approach," Computational Materials Science, vol. 12, pp.
289-308, August 1998.

[27] J. I. Haritonidis, "The Measurement of Wall Shear Stress," Ad'vances in Fluid Mechanics
Measurements, Springer-Ve'i /a. pp. 229-261, 1989.

[28] K. G. Winter, "An Outline of the Techniques Available for The Measurements of Skin
Friction in Turbulent Boundary Layers," Prog. Aerosp. Sci., vol. 18, pp. 1-57, 1977.

[29] T. J. Hanratty and J. A. Campbell, "Measurements of Wall Shear Stress," Fluid2~ech.
Measurements, 1983, pp. 559-615.










[30] T. K. Hsiai, S. K. Cho, P. K. Wong, M. Ing, A. Salazar, A. Sevanian, M. Navab, L. L.
Demer, and C.-M. Ho, "Monocyte Recruitment to Endothelial Cells in Response to
Oscillatory Shear Stress," FASEB 1, vol. 17(12), pp. 1648-1657, September, 2003.

[3 1] B. Oudheusden and J. Huij sing, "Integrated Flow Friction Sensor, Sensors and Actuators
A, vol. 15, pp. 135-144, 1988.

[32] E. Kalvesten, G. Stemme, C. Vieider, and L. Lofdahl, "An Integrated Pressure-Flow
Sensor for Correlation Measurement in Turbulent Gas Flow," Sensors and Actuators A,
vol. 52, pp. 51-58, 1996.

[33] C. Liu, J.-B. Huang, A. Z. Z, F. Jiang, S. Tung, Y.-C. Tai, and C.-M. Ho, "A
Micromachined Flow Shear-Stress Sensor Based on Thermal Transfer Principles," J.
M~icroelectromech. Syst., vol. 8 (1), pp. 90 -99, March 1999.

[34] M. Sheplak, V. Chandrasekaran, A. Cain, T. Nishida, and L. N. C. III, "Characterization of
a Micromachined Thermal Shear Stress Sensor," AIAA 1., vol. 40, pp. 1099-1104, 2002.

[35] D. Fourguette, D. Modarress, F. Taugwalder, D. Wilson, M. Koochesfahani, and M.
Gharib, "Miniature and MOEMS Flow Sensor," AIAA paper 2001-2982, 2001.

[36] C. Bruicker, D. Bauer, and H. Chaves, "Dynamic Response of Micro-Pillar Sensors
Measuring Fluctuating Wall-Shear-Stress," Exp in Fluids, vol. 42 (5), 2007

[37] C. Bruicker, J. Spatz, and W. Schroider, "Feasability Study of Wall Shear Stress Imaging
Using Microstructured Surfaces with Flexible Micropillars," Exp. in Fluids, vol. 39 (2), pp.
464-474, Aug. 2005.

[38] T. V. Papen, H. Steffes, H. D. Ngo, and E. Obermeier, "A Micro Surface Fence Probe for
the Application in Flow Reverse Area," Sensors andActuators A, vol. 97-98, pp. 264-270,
2002.

[39] M. A. Schmidt, "Microsensors for the Measurement of Shear Forces in Turbulent
Boundary Layers," Ph.D Dissertation in Mechanical Engineering, Massachussets Institute
of Technology, 1988.

[40] B. Carroll, E. Boulos, M. Sytsma, L. Cattafesta, J. P. Hubner, and M. Sheplak, "Aero-Optic
Measurement Facility Characterization," in 42ndAerospace Sciences M~eeting and Exhibit,
AIAA Paper 2004-0936, Reno, NV, 2004.

[41] Z. W. Hu, C. L. Morfey, and N. D. Sandham, "Wall Pressure and Shear Stress Spectra
from Direct Simulations of Channel Flow," AIAA J., vol. 44 (7), July 2006 2006.

[42] T. Pan, D. Hyman, and M. Mehregany, "Microfabricated Shear Stress Sensors, Part 2:
Testing and Calibration," AIAA J., vol. 37, pp. 73-78, 1999.










[43] M. Sheplak, A. Padmanabhan, M. A. Schmidt, and K. S. Breuer, "Dynamic Calibration of
a Shear-Stress Sensor Using Stokes-Layer Excitation," AIAA J., vol. 39 (5), pp. 819-823,
May 2001.

[44] H. D. Goldberg, K. S. Breuer, and M. A. Schmidt, "A Silicon Wafer-Bonding Technology
for Microfabricated Shear-Stress Sensors with Backside Contacts," IEEE Solid-State
Sensor and Actuator Workshop, Hilton Head, SC, 1994, pp. 111-115.

[ 45] N. Maluf, An Introduction to M\~icroelectronzechanical Systems Engineering. Norwood,
MA: Artech House, 2000.

[46] S. D. Senturia, M~icrosystent Design: Kluwer Academic Publishers, 2001, Ch. 10, 17, 18,
19.

[47] J. A. Harley and T. W. Kenny, l/fNoise Considerations for the Design and Process
Optimization of Piezoresistive Cantilevers," J. M~icroelectronzech. Syst., vol. 9 (9), June
2000.

[48] M. Sheplak, L. Cattafesta, and T. Nishida, "Microelectromechanical Floating Element
Flow Sensor," U. S Patent Number: 6966231, Issued on November 22, 2005.

[49] A. A. Barlian, R. Narain, J. T. Li, C. E. Quance, A. C. Ho, V. Mukundan, and B. L. Pruitt,
"Piezoresistive MEMS Underwater Shear Stress Sensors," M~EMS' 06, Istanbul, Turkey,
2006, p. 626.

[50] B. W. Chui, T. W. Kenny, H. J. Mamin, B. D. Terris, and D. Rugar, "Independent
Detection of Vertical and Lateral Forces with a Sidewall-Implanted Dual-Axis
Piezoresistive Cantilever," Appl. Phys. Lett., vol. 72 (11), pp. 1388-1394, 1998.

[51] A. Partridge, J. K. Reynolds, B. W.Chui, E. M.Chow, A. M.Fitzgerald, L. Zhang, N. I.
Maluf, and T. W.Kenny, "A High-Performance Plannar Piezoresistive Accelerometer," J.
M~icroelectronzech. Syst., vol. 9 (1), March 2000.

[52] C. S. Smith, "Piezoresistance Effects in Germanium and Silicon," Physical Review, vol.
94, 1954.

[53] M. Madou, Fundamentalsd~~~dd~~~ddd~~ of2\~icrofabrication: CRC Press, 1997, Ch. 4.

[ 54] A. H. Nayfeh and P. F. Pai, Linear and Nonlinear Structural M\~echanics: John Wiley &
Sons, Inc, 2004, pp. 183.

[55] M. Rossi, Acoustics andElectroacoustic. : Artech House, 1988, pp. 245.

[56] J. Merhaut, Theory ofElectroacoustics: McGraw-Hill Inc., 1981, Ch. 1.

[57] S. M. Sze, Semiconductor Sensors: Wiley-Interscience, 1994, pp. 160.










[58] O. N. Tufte and D. Long, "Recent Development in Semiconductor Piezoresistive Devices,"
Solid State Electronics, vol. 6, pp. 323-338, 1963.

[59] Y. Kanda, "A Graphical Representation of the Piezoresistive Coefficients in Silicon," IEEE
Trans. Electron Devices, vol. 29 (64), pp. 64-70, 1982.

[60] J. Brysek, K. Petersen, J. Joseph R. Mallon, L. Christel, and F. Pourahmadi, Silicon
Sensors and2\~icrostructures: Lucas NovaSensor, 1991, Ch. 4.

[61] O. N. Tufte and E. L. Stelzer, "Piezoresistive Properties of Silicon Diffused Layers," J.
Appl. Phys., vol. 34 (2), pp. 313-318, 1963.

[62] W. P. Mason, J. J. Forst, and L. M. Tornillo, Recent Developments in Semiconductor
Strain Transducers: New York, 1962.

[63] D. R. Kerr and A. G. Milelnes, "Piezoresistance of Diffused Layers in Cubic
Semiconductors," J. Appl. Phys., vol. 34 (4), pp. 727-731, 1963.

[64] M. Tortonese, "Force Sensors for Scanning Probe Microscopy," Ph.D Dissertation in
Department of Mechanical Engineering: Stanford University, 1993.

[65] J. A. Harley, "Advances in Piezoresistive Probes for Atomic Force Microscopy," Ph.D
Dissertation in Department of Mechanical Engineering: Stanford University, 2000.

[66] J. D. Plummer, M. D. Deal, and P. B. Griffin, Silicon VLSI Technology: Prentice Hall,
2000, Ch. 7, 8.

[67] T. Nishida and C.-T. Sah, "A Physical Based Mobility Model for MOSFET Numerical
Simulation," IEEE Trans. Electron Devices, vol. 34 (2), pp. 310-320, 1987.

[68] H. Nyquist, "Thermal Agitation of Electric Charge in Conductors," Phys. Rev., vol. 32, pp.
110-113, 1928.

[69] J. B. Johnson, "Thermal Agitation of Electricity in Conductors," Phys. Rev., vol. 32, pp.
97-109, 1928.

[70] F. N. Hooge, l/f Noise is No Surface Effect," Phys. Lett. A, vol. 29, pp. 13 9-140, 1969.

[71] E. Simoen and C. Claeys, "On the Flicker Noise in Sub Micron Silicon MOSFETs," Solid
State Electronics, vol. 43, pp. 865-882, 1999.

[72] A. McWhorter, l/f noise and Germanium Surface Properties," in Semiconductor Surface
Physics: University of Pennsylvania, Philadelphia, 1957, pp. 207-228.

[73] Analog Devices Inc, www.analog.com.

[74] M. Akbar and M. A. Shanblatt, "Temperature Compensation of Piezoresistive Pressure
Sensors," Sensors andActuators A, vol. 33, pp. 155-162, 1992.










[75] K. Suzuki, T. Ishihara, M. Hirata, and H. Tanigawa, "Nonlinear Analysis of a CMOS
Integrated Silicon Pressure Sensor," IEEE Trans. Electron Devices, vol. 34, pp. 1360-
1367, 1987.

[76] R. F. Pierret, Semiconductor Device Fundamentals:~dd~~ddd~~dd~~ Addison-Wesley, 1996, Ch. 5, 6.

[77] R. C. Jaeger, Introduction to M~icroelectronic Fabrication, 1993, pp. 57.

[78] M. E. Law and S. M. Cea, "Continuum Based Modeling of Silicon Integrated Circuit
Processing: An Obj ect Oriented Approach," Computational materials Science, vol. 12, pp.
289-308, Nov 1998.

[79] SRIM, www.srim.org.

[80] S. M. Sze and G. Gibbsons, "Avalanche Breakdown Voltage of Abrupt and Linearly
Graded p-n junctions in Ge, Si, GaAs, and GaP," Appl. Phys. Lett., vol. 8, pp. 1 11, 1966.

[81] S. M. Sze, Physics of Semiconductor Devices, 2nd ed.: John Wiley & Sons, Inc, 1981, pp.
193.

[82] R. C. Hibbeler, M~echanics of2aterials, Third ed.: Prentice Hall, 1997, pp. 160

[83] J. D. Plummer, M. D. Deal, and P. B. Griffin, Silicon VLSI Technology: Fundamentals,
Practice, and Modeling, Prentice Hall, 2000.

[84] M. Papila, R. T. Haftka, T. Nishida, and M. Sheplak, "Piezoresistive Microphone Design
Pareto Optimization: Tradeoff Between Sensitivity and Noise Floor," I. Microelectromech.
Syst., vol. 15 (6), pp. 1632-1643, December 2006.

[85] A. Partridge, "Lateral Piezoresistive Accelerometor with Epipoly Encapsulation," Ph.D
Dissertation in Department of Electrical Engineering, Stanford University, 2003.

[86] Mathworks Inc, MATLAB R2006b ed, 2006.

[87] J. F. Schutte and A. A. Groenwold, "A Study of Global Optimization Using Particle
Swarms," J Global Opt., vol. 31 (1), pp. 93-108, 2005.

[88] R. T. Haftka and Z. Gurdal, Elements of Structural Optimization: Kluwer Academic
Publishers, 1992.

[ 89] B. El-Kareh, Fundamentalsd~~~dd~~~ddd~~ of Semiconductor Processing Technologies, 3rd ed.: Kluwer
Academic Publisher, 1998.

[90] Unaxis, www.unaxis.com.

[91] STS, www.stsystems.com.

[92] M.-C. M. Lee, J. Yao, and M. C. Wu, "Silicon Profile Transformation and Sidewall
Roughness Reduction Using Hydrogen Annealing," M~EMS '05, Miami, FL, USA, 2005.










[93] R. Legtenberg, H. Jansen, M. d. Boer, and M. Elwenspoek, "Anisotropic Reactive lon
Etching of Silicon Using SF6/02/CHF3 Gas Mixtures," J. Electrochem. Soc., vol. 142, pp.
2020-2028, 1995.

[ 94] M. Ohring, The Materials Science of Thin Films: Academic Press, 1992.

[ 95] C.-T. Sah, Fundamentalsd~~~dd~~~ddd~~ ofSolid-State Electronics: World Scientific, 1993.

[96] Stanford Research Systems, http ://www.thinksrs.com/products/SIM928 .htm.

[97] V. Chandrasekaran, A. Cain, T. Nishida, L. N. Cattafesta, and M. Sheplak, "Dynamic
Calibration for Thermal Shear-Stress Sensors with Mean Flow," Exp. in Fluids, vol. 39,
pp. 56-65, 2005.

[98] R. Dieme, G. Bosman, M. Sheplak, and T. Nishida, Source of Excess Noise in Silicon
Piezoresistive Microphones," J. Acoust. Soc. Am., vol. 119, pp. 2710-2720, May 2006.

[99] M. G. Jones and P. E. Stiede, "Comparison of Methods for Determining Specific Acoustic
Impedance," J. Acoust. Soc. Am., vol. 101(5), pp. 2694-2704, 1997.

[100] J. N. Reddy, Theory and Analysis ofla~stic Plates: Taylor and Francis, 1999, pp. 25.









BIOGRAPHICAL SKETCH

Yawei Li received her BS and MS degree in Aerospace Engineering at Beijing University

of Aeronautics and Astronautics, China. She worked with China Aerospace Corporation before

she joined University of Florida. She also received MS (2003) in Aerospace Engineering and

ME (2006) in Electrical Engineering from University of Florida, respectively.

She is currently a Ph.D student in the Department of Mechanical and Aerospace

Engineering at the University of Florida. Her current research focuses on the sensor modeling,

design optimization, fabrication, and characterization of MEMS-based piezoresistive sensors that

enable the measurement and control of wall shear stress in turbulent flow.





PAGE 1

SIDE-IMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT BOUNDARY LAYER MEASUREMENT By YAWEI LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 1

PAGE 2

2008 Yawei Li 2

PAGE 3

To my husband Zhongmin and my parents 3

PAGE 4

ACKNOWLEDGMENTS Financial support for the research project is provided by National Science Foundation (CTS-04352835 and CMS-0428593) and AFOSR gr ant (F49620-03-C-0114). A doctoral dissertation is never the work of an individual, but instead a mira cle that encompasses the efforts of many people. I would like to recognize a numbe r of people who have helped me in various ways during my time in University of Florida. First and foremost, I extend my sincerest gratitude to my advisor, Dr. Mark Sheplak, who gave me the opportunity to work in MEMS resear ch field. I sincerely appreciate his guidance, continuous encouragement and support in my resear ch, tirelessly sharing with me his expertise and wisdom. His profound knowledge in MEMS, fl uids, acoustics and so on is the invaluable source I always rely on. I also wish to extend gracious thanks to my committee members, Drs. Toshikazu Nishida, Louis N. Cattafesta, Bhavani V. Sankar and Davi d Arnold for their instru ction and assistance on this interdisciplinary project. They are always generous on their time and expertise, and I am grateful for their efforts. I would give special thanks to professors in Department of Electrical and Computer Engineering, Material Science Engineering a nd Mechanical and Aerospace Engineering at University of Florida, especi ally Dr. Mark Law and his stude nt Ljubo Radic, Dr. Kevin Jones and Dr. Raphael Haftka for th eir invaluable suggestions on my device fabrication, process simulation and design optimization. I would espe cially like to thank Dr. Melih Pepila at Sabanchi University (Turkey) and Dr. Jaco F. Schutte for th eir suggestions in optimization design. My thanks go to Dr. Venketaraman Chandrasek aran at Sensata Technologies, Sean Knight in University of South Florida, Alvin A Bar lian in Stanford University and Core Systems 4

PAGE 5

Company for their help in device fabrications, and Keck Pathamma vong at Engent for his help in device packaging. I would also express my tha nks to Al Ogden, Dr. Ivan Kravchenko and Bill Lewis at UFNF for the facility maintenance and help on the fabrication. I was fortunate enough to have great co lleagues throughout my graduate school experience. My thanks go to IMG members, especially Hongwei Qu for his suggestions and discussions in device fabricatio n; Brandon Bertolucci, Alex Phi pps, David Martin for their kind help and assistance in device package design, Vijay Chandr asekharan, Qi Song, Benjamin Griffin and John Griffin for their kind help in device characterization, Matt Williams, Benjamin Griffin, Brandon Bertolucci and Brian Homeijier for their great editing and suggestions in my dissertation writing. It has been a pleasure to have work with them, and I will carry these invaluable memories on rest of life. Finally, I reserve the special thanks to my fa milies for their support and encouragement. I am always grateful to my husband, Zhongmin Liu for his endless love and support in my life. My parents always encouraged me to be the best and do my best on what I want to do. I would like to thank them for believing me every time I said I would graduate next year. Without their love and support this dissert ation would not be possible. 5

PAGE 6

TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES.......................................................................................................................10 ABSTRACT...................................................................................................................................14 CHAPTER 1 INTRODUCTION................................................................................................................. .16 Motivation for Wall Shear Stress Measurement.....................................................................16 Wall Shear Stress.............................................................................................................1 7 Turbulent Boundary Layer..............................................................................................19 Research Objectives............................................................................................................ ....22 Dissertation Overview.......................................................................................................... ..24 2 BACKGROUND................................................................................................................... .29 Techniques for Shear Stress Measurement.............................................................................29 Conventional Techniques................................................................................................30 MEMS-Based Techniques...............................................................................................31 Floating Element Sensors....................................................................................................... 32 Sensor Modeling and Scaling..........................................................................................32 Error Analysis and Challenges........................................................................................34 Effect of misalignment.............................................................................................34 Effect of pressure gradient.......................................................................................35 Effect of cross-axis vibration and pressure fluctuations..........................................36 Previous MEMS Floating Element Shear Stress Sensors.......................................................38 Capacitive Shear Stress Sensors......................................................................................38 Optical Shear Stress Sensors...........................................................................................40 Piezoresistive Shear Stress Sensors.................................................................................42 A Fully-Bridge Side-Implanted Piez oresistive Shear Stress Sensor......................................43 3 SHEAR STRESS SE NSOR MODELING.............................................................................53 Quasi-Static Modeling.......................................................................................................... ..54 Structural Modeling.........................................................................................................54 Small Deflection Theory.................................................................................................55 Large Deflection Theory.................................................................................................56 Energy method.........................................................................................................57 Exact analytical model.............................................................................................57 Lumped Elemen t Modeling....................................................................................................58 6

PAGE 7

Finite Element Analysis........................................................................................................ ..60 Piezoresistive Transduction....................................................................................................62 Piezoresistive Coefficients..............................................................................................64 Piezoresistive Sensitivity.................................................................................................66 Electromechanical Sensitivity.........................................................................................68 Noise Model............................................................................................................................69 Thermal Noise.................................................................................................................6 9 1 f Noise........................................................................................................................70 Device Specific Issues............................................................................................................72 Transverse Sensitivity.....................................................................................................72 Temperature Compensation.............................................................................................73 Device Junction Isolation................................................................................................74 Summary.................................................................................................................................78 4 DEVICE OPTIMIZATION....................................................................................................91 Problem Formulation............................................................................................................ ..91 Design Variables.............................................................................................................91 Objective Function..........................................................................................................93 Constraints.......................................................................................................................94 Candidate Flows.....................................................................................................................95 Methodology...........................................................................................................................96 Optimization Results and Discussion.....................................................................................97 Sensitivity Analysis........................................................................................................... .....98 Summary...............................................................................................................................100 5 FABRICATION AND PACKAGING.................................................................................105 Fabrication Overview and Challenges..................................................................................105 Fabrication Process............................................................................................................ ...105 Sensor Packaging for Wind Tunnel Testing.........................................................................110 6 EXPERIMENTAL CHARACTERIZATION......................................................................118 Experimental Characterization Issues...................................................................................118 Experimental Setup............................................................................................................. ..119 Electrical Characterization............................................................................................119 Dynamic Calibration.....................................................................................................120 Noise Measurement.......................................................................................................121 Experimental Results............................................................................................................122 Electrical Characterization............................................................................................122 Dynamic Calibration Results and Discussion...............................................................122 Summary...............................................................................................................................126 7

PAGE 8

7 CONCLUSION AND FUTURE WORK.............................................................................137 Summary and Conclusions...................................................................................................137 Future Work..........................................................................................................................138 Temperature Compensation...........................................................................................139 Static Characterization...................................................................................................141 Noise Measurement.......................................................................................................142 Recommendations for Fu ture Sensor Designs......................................................................142 APPENDIX A MECHANICAL ANALYSIS...............................................................................................145 Small Deflection............................................................................................................... ....145 Large Deflection-Energy Method.........................................................................................147 Large Deflection-Analytical Method....................................................................................149 Stress Analysis................................................................................................................ ......152 Effective Mechanical Mass and Compliance.......................................................................153 B NOISE FLOOR OF THE WHEATSTONE BRIDGE.........................................................157 C PROCESS TRAVELER.......................................................................................................160 Masks....................................................................................................................................160 Process Steps........................................................................................................................160 D PROCESS SIMULATION...................................................................................................166 E MICROFABRICATION RECIPE FO R RIE AND DRIE PROCESS.................................169 F PACKAGING DRAWINGS................................................................................................170 LIST OF REFERENCES.............................................................................................................173 BIOGRAPHICAL SKETCH.......................................................................................................180 8

PAGE 9

LIST OF TABLES Table page 1-1 Summary of typical skin friction contributions for various vehicles.................................25 1-2 Parameters in the turbulent boundary layer.......................................................................25 3-1 Material properties and geometry parameters used for model validation..........................79 3-2 Resonant frequency and effec tive mass predicted by LEM and FEA...............................79 3-3 First 6 modes and effective mass predicte d by FEA for the representative structure........79 3-4 Piezoresistive coefficients fo r n-type and p-type silicon...................................................79 3-5 Piezoresistive coefficients for n-type and p-type sili con in the <110> direction..............80 3-6 Space parameter dimensions for junction isolation...........................................................80 4-1 The candidate shear stre ss sensor specifications.............................................................102 4-2 Upper and lower bounds associated with the specifications in Table 4-1.......................102 4-3 Optimization results for the cases specified in Table 4-1................................................103 6-1 LabVIEW settings for noise PSD measurement..............................................................128 6-2 The optimal geometry of the shear stress sensor that was characterized.........................128 6-3 Sensitivity at different bias voltage for the tested sensor................................................128 6-4 A comparison of the predicted versus real ized performance of the sensor under test for a bias voltage of 1.5V.................................................................................................129 E-1 Input parameters in th e ASE on STS DRIE systems.......................................................169 E-2 Anisotropic oxide/nitride etch recipe on the Unaxis ICP Etcher system.........................169 E-3 Anisotropic aluminum etch recipe on the Unaxis ICP Etcher system.............................169 9

PAGE 10

LIST OF FIGURES Figure page 1-1 Schematic of wall shear stress in a la minar boundary layer on an airfoil section.............26 1-2 Schematic representation of the boundary layer transition process for a flat-plate flow at a ZPG ....................................................................................................................26 1-3 Schematic of typical velocity profile fo r low-speed laminar and turbulent boundary layers [9]............................................................................................................................27 1-4 The structure of a t ypical turbulent boundary layer.........................................................27 1-5 Estimates of Kolmogorov microscales of length and time as a function of Reynolds number based on a 1/7th power-law profile.......................................................................28 2-1 Schematic cross-sectional view of the floating element based sensor.............................46 2-2 Schematic plan view and cross-section of a typical floating element sensor ...................46 2-3 Integrated shear force variation as a function of sensor resolution for different element areas.................................................................................................................. ....47 2-4 Schematic illustrating pressure gradient effects on the force balance of a floating element........................................................................................................................ .......47 2-5 Schematic cross-sectional view of the capacitive floating element sensor .......................48 2-6 Plan-view of a horizontal-electrode capacitive floating element sensor ..........................48 2-7 Schematic top-view of a differen tial capacitive shear stress sensor .................................49 2-8 A schematic cross-sectional view of an optical differential shutter-based floating element shear stress sensor ...............................................................................................49 2-9 Schematic top and cross-sectional view of a Febry-Perot shear stress sensor ..................50 2-10 Top and cross-sectiona l view of Moir optical shear stress sensor ..................................50 2-11 A schematic top view of an axial piezoresistive floating element sensor .........................51 2-12 A schematic top view of a laterally-impla nted piezoresistive shear stress sensor ............51 2-13 A schematic 3D view of the side-implant ed piezoresistive floating element sensor.........52 3-1 Schematic top view of the structure of a piezoresistive floating element sensor..............81 3-2 The simplified clamped-clamped beam m odel of the floating element structure..............81 10

PAGE 11

3-3 Lumped element model of a floating elem ent sensor: (a) spring-mass-dashpot system (mechanical) and (b) equivalent electrical LCR circuit.....................................................81 3-4 Representative results of displacement of tethers for the representative structure............82 3-5 Representative load-deflection characteri stics of analytical models and FEA for the representative structure......................................................................................................82 3-6 Verification of the analyt ically predicted stress profile with FEA results for the representative structure......................................................................................................83 3-7 The mode shape for the representative structure...............................................................83 3-8 Geometry used in computation of Eulers angles..............................................................84 3-9 Polar dependence of piezoresistive coeffici ents for p-type silic on in the (100) plane......84 3-10 Polar dependence of piezoresistive coeffici ents for n-type silic on in the (100) plane......85 3-11 Piezoresistive factor as a function of impurity concentra tion for ptype silicon at .................................................................................................................................85 300K 3-12 Schematic illustrating the relevant geomet ric parameters for piez oresistor sensitivity calculations........................................................................................................................86 3-13 Schematic representative of a deflected side-implanted piezoresistive shear stress sensor and corresponding resistance changes in Wheatstone bridge.................................86 3-14 Wheatstone bridge subjec ted to cross-axis accelera tion (a) and pressure (b)....................87 3-15 Schematic of the double-bridge temp erature compensation configuration.......................87 3-16 Top view schematic of the side-implanted piezoresistor and p++ interconnect in an n-well (a) and equivalent electric circuit indicating that the sensor and leads are junction isolated (b)...........................................................................................................88 3-17 Doping profile of n-well, p++ interconnect, and piezoresistor using FLOOPS simulation..................................................................................................................... ......88 3-18 Cross view of isolation wi dth between p++ interconnects................................................89 3-19 Cross view of isolat ion width between p++ inte rconnect and piezoresistor......................89 3-20 Top view of the isolatio n widths on a sensor tether...........................................................90 3-21 Top view schematic of the side-implanted piezoresistor with a metal line contact...........90 4-1 Flow chart of design optimization of the piezoresistive sh ear stress sensor....................104 11

PAGE 12

4-2 Logarithmic derivative of objective function min with respect to parameters................104 5-1 Process flow of the side-implanted piezoresistive shear stress sensor............................112 5-2 SEM side view of side wall trench after DRIE Si...........................................................113 5-3 SEM side view of the notch at the interface of oxide and Si after DRIE........................113 5-4 SEM top view of the trench after DRIE oxide and Si......................................................114 5-5 SEM top views of the trench after DR IE oxide and Si with oxide overetch...................114 5-6 SEM top views of the trench with silic on grass through a micromasking effect due to oxide underetch................................................................................................................115 5-7 SEM side view of the trench after DRIE oxide and Si....................................................115 5-8 Photograph of the fabricated device................................................................................116 5-9 A photograph of the device with a close up view of the side-implanted piezoresistor...116 5-10 Photograph of the PCB embedded in Lucite package.....................................................117 5-11 Interface circuit board for offset compensation...............................................................117 6-1 The bridge dc offset voltage as a functi on of bias voltages for the tested sensor............130 6-2 An electrical schematic of the inte rface circuit for offset compensation.........................130 6-3 A schematic of the experimental setup for the dynamic calibration experiements.........131 6-4 Forward and reverse bias char acteristics of the p/n junction...........................................131 6-5 Reverse bias breakdown voltage of the P/N junction......................................................132 6-7 The nonlinearity of the I-V curve in Figure 6-6 at different sweeping voltages.............133 6-8 The output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 kHz as a function bias voltage..........................................................133 6-9 The normalized output voltage as a functi on of shear stress magnitude of the sensor at a forcing frequency of 2.088 kH z for several bias voltages.........................................134 6-10 Gain and phase factors of the frequency response function............................................134 6-11 The magnitude and phase angle of the refl ection coefficient of the plane wave tube.....135 6-12 Outputreferred noise floor of the measur ement system at a bias voltage of 1.5V.........136 12

PAGE 13

7-1 Pressure drops versus length between taps in the flow cell.............................................144 7-2 Experimental setup of static calibration...........................................................................144 A-1 The clamped beam and free body diagram. a) Clamped-clamped beam. b) Free body diagram of the beam. c) Free body diagram of part of the beam.....................................156 A-2 Clamped-clamped beam in large deflection....................................................................156 A-3 Clamped-clamped beam in small de flection (a) and free body diagram of the clamped beam (b).............................................................................................................15 6 B-1 The Wheatstone bridge....................................................................................................15 9 B-2 The thermal noise model of the Wheatstone bridge........................................................159 B-3 The 1 f noise model of the Wheatstone bridge..............................................................159 E-1 The drawing illustrating the Lucite packaging................................................................170 E-2 The aluminum plate for the plane wave tube interface connection.................................171 E-3 Aluminum packaging for pr essure sensitivity testing......................................................172 13

PAGE 14

Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SIDE-IMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT BOUNDARY LAYER MEASUREMENT By Yawei Li August 2008 Chair: Mark Sheplak Major: Aerospace Engineering In this dissertation, I discuss the devi ce modeling, design optimization, fabrication, packaging and characterization of a micromachin ed floating element piezoresistive shear stress sensor for the time-resolved, direct measurement of fluctuating wall shea r stress in a turbulent flow. This device impacts a broad range of appli cations from fundamental scientific research to industrial flow control and biomedical applications. The sensor structure integrates side-implanted, diffused resistors into the silicon tethers for piezoresistive detection. Temperature compensa tion is enabled by integrating a fixed, dummy Wheatstone bridge adjacent to the active shear-str ess sensor. A theoretical nonlinear mechanical model is combined with a piezoresistive sens ing model to determine the electromechanical sensitivity. Lumped element modeling (LEM) is used to estimate the resonant frequency. Finite element modeling is employed to verify the qua si-static and dynamic models. Two dominant electrical noise sources in the piezoresistive shear stress sensor, 1 f noise and thermal noise, and amplifier noise were considered to determ ine the noise floor. These models were then leveraged to obtain optimal sensor designs for se veral sets of specificatio ns. The cost function, minimum detectable shear stress (MDS) formulated in terms of sensitivity and noise floor, is 14

PAGE 15

minimized subject to nonlinear constraints of geometry, lineari ty, bandwidth, power, resistance, and manufacturing limitations. The optimization results indicate a predicted optimal device performance with a MDS of and a dynamic range greater than 75 dB. A sensitivity analysis indicates that the device performance is mo st responsive to varia tions in tether width. 0.1 mPa O The sensors are fabricated using an 8-ma sk, bulk micromachining process on a silicon wafer. An n-well layer is formed to control th e space-charge layer thickness of reverse-biased p/n junction-isolated piezoresisto rs. The sensor geometry is r ealized using reactive ion etch (RIE) and deep reactive ion etch (DRIE). H ydrogen annealing is employed to smooth the sidewall scalloping caused by DRIE. The piezoresistors are achieved by side-wall boron implantation. The structure is finally released from the backside using the combination of DRIE and RIE. Electrical characterization indica tes linear junction-isolated resistors, and a negligible leakage current (< ) for the junction-isolated diffused piezoresistors up to a reverse bias voltage of -10 V. Using a known acoustically-exc ited wall shear stress for calibration, the sensor exhibited a sensitivity of a noise floor of 0.12 A 4.24 V/Pa 11.4 mPa/Hz at 1 kHz, a linear response up to the maximum testing range of and a flat dynamic response up to the testing limit of These results, coupled with a wind-tunnel suitable pack age, result in a suitable transducer for turbulence measurements in lo w-speed flows, a first for piezoresistive MEMSbased direct shear stress sensors. 2 Pa 6.7 kHz 15

PAGE 16

CHAPTER 1 INTRODUCTION This chapter provides an introduction to wall shear stress and motivation for its measurement. Then the scaling tu rbulent boundary layer is reviewed as it applies to dictating the requirements for wall shear stress sensors. Th e research objectives and contributions are presented. This chapter ends with the dissertation overview. Motivation for Wall Shear Stress Measurement The quantification of wall shear stress is importa nt in a variety of engineering applications, specifically in the development of aerospace and naval vehicles. These vehicles span a wide range of Reynolds numbers Re from low (unmanned air vehicles for homeland security surveillance and detec tion) to a very high (hypersonic vehicles for rapid global and space access). Across the range, unsteady, complex flow phenomena associated with transitional, turbulent, and separating boundary layers play an important role in aerodynamics and propulsion efficiency of these vehicles [1, 2]. Furthermor e, since shear stress is a vector field, it may provide advantages over pressure sensing in active flow control applications involving separated flows [3]. Re Re Re The accurate measurement of the wall shear st ress is of vital impor tance for understanding the critical vehicle characteristics, such as lift, drag, and propulsion efficiency. Therefore, the ability to obtain quantitative, time-resolved sh ear stress measurements may elucidate complex physics and ultimately help engineers improve the performance of these vehicles [4]. Viscous drag or skin friction drag is formed due to shea r stress in the boundary layer. The viscous loss is highly dependent on the physical aerodynamic/hydr odynamic system; typical viscous losses for different systems are listed in Table 1-1 [5]. For aircraft, reducing skin friction by 20% results in a 10% annual fuel savings, and for underwater ve hicles, a reduction of skin friction drag of 20% 16

PAGE 17

would result in a 6.8% increase in speed [5]. Therefore, shear stress measurement attracts attention in sensor-actuator syst ems for use in active control of the turbulent boundary layer with an aim of minimizing the skin friction [6]. Wall Shear Stress When a continuum viscous fluid flows over an object, the no slip boundary condition at the surface results in a velocity gradient within a very thin boundary layer [7]; the streamwise velocity increases from zero at the wall to its free -stream value at the edge of the boundary layer. The velocity profile is shown in Figure 1-1 The viscous effects are confined to the boundary layer, while outside of the boundary layer the flow is essentially inviscid [7]. Two classes of surface forces act on the aerodynamic body: th e normal force per unit area (pressure) and the tangential force per un it area (shear stress) For a Newtonian flow, the wall shear stress is proportional to the velocity gradient at the wall. P w The boundary layer is classified as laminar or turbulent depending on Reynolds number or flow structure [7]. A laminar boundary la yer forms at low Reynolds numbers and is characterized by its smooth and orderly motion, where microscopic mixing of mass, momentum and energy occurs only between ad jacent vertical fluid layers. A turbulent boundary layer forms at high Reynolds numbers and is characteri zed by random and chaotic motion [8]. The macroscopic mixing traverses seve ral regions within the boundary layer. There is a transition range between laminar and turbulen t boundary layers, partially lamina r and partially turbulent, as shown in Figure 1-2 In the transition range, the flow is very sensitive to small disturbances [8]. Typical velocity profiles for low speed lamina r and turbulent boundary layer are shown in Figure 1-3 Due to the intense mixing, the turbulent boundary layer has a fuller velocity profile; thus, the shear stress in the turb ulent boundary layer is larger than in a laminar boundary layer. 17

PAGE 18

The boundary layer thickness, x is defined as the distance fr om the wall to the point at which the velocity is 99% of the free-stream ve locity [7]. The laminar boundary layer thickness in a zero pressure grad ient flat-plate flow is given by Blasius as [7] 5.0 x x R e (1-1) where x R e is the free stream Reynolds number and given by Ux x is the streamwise distance, U is the free stream velocity, and is the kinematic viscosity of the fluid. For turbulent flow, the boundary layer thickness is estimated by the 1/7th power law velocity profile is [7] v 170.16xx Re (1-2) The shear stress is related to skin friction by the skin-friction coefficient 21 2w fC U (1-3) The wall shear stress w for a one dimensional laminar fl ow is given by Newtons law of viscosity [7], 0 w y du dy (1-4) where is the dynamic viscosity of the fluid and is the local streamwise velocity in the boundary layer. For turbulent flow, the shear stress is decompos ed into mean shear stress u w and fluctuating shear stress w in terms of the Reynolds decomposition, www (1-5) The mean skin friction for laminar and turbulent flow are given by [7] 18

PAGE 19

, 22 0.664w flplate x C U R e (1-6) and ,0.027ftplate xC Re 1 7 (1-7) respectively. Equation (1-2) and (1-7) are based on the assumption of the 1/7th power law form of the velocity profile proposed by Prandtl [7], 1 7uy U (1-8) These formulas are in reasonable agreement with tu rbulent flat-plate data and are appropriate for a general scaling analysis [7]. Turbulent Boundary Layer To understand the temporal and spatial resolu tion requirements for the shear stress sensor, we need to understand the relevant time and length scales asso ciated with a turbulent boundary layer. There are two regions in a turbulent bound ary layer: the inner laye r and outer layer [9] The semi-log plot of the structure of a t ypical turbulent boundary layer is shown in Figure 1-4 The outer layer (wake region), is turbulent (eddy) shear-dominated and the effect of the wall is communicated via shear stress. The inner 20% of the boundary layer is defined as the inner layer, where viscous shear dominates. The overlap layer smoothly connects the inner and outer layer. There are three regi ons within the inner layer: 05 y viscous sublayer (or linear) region uy 54 y 5 buffer region 450.2 y log region 1 ln uy k B where is the Karman constant and k B is the intercept. They are universal constants with and [7]. The non-dimensional velocity u 0.41 k 5.0 B is defined as 19

PAGE 20

*uuu (1-9) where is given by *u wu (1-10) u is the mean velocity, and is the density of the fluid. The non-dimensional distance y is defined as ** y ylyuv (1-11) where *lvu is the characteristic viscous length scal e. A turbulent flow possesses different length scales. The largest eddies are on the order of the boundary layer thickness, while the smallest eddies can approach the Kolmogorov length scales [8]. Kolmogorovs universal equilibrium theory states that the small scale mo tions are statistically i ndependent of the slower large-scale turbulent structures, but depend on the rate at which the energy is supplied by largescale motions and on the kinematic viscosity [8]. In addition, the rate at which energy is supplied is assumed to be equal to the rate of dissipation. Thus, the small eddies must have a smaller time scale and are assumed to be locally isotropic. Therefore, the dissipation rate and kinetic viscosity are parameters governing sma ll scale motions. The scaling relationships between the small and large scale structur es in a boundary layer flow are [4, 8, 10] 34 34~eu Re (1-12) and 12 12~eu Tu Re (1-13) 20

PAGE 21

where and T are the Kolmogorov length a nd time scales respectively, is the eddy velocity (typically [4]. Substitution of Equation eu ~0.01e U uO (1-2) into Equation (1-12) and Equation (1-13) leads to estimates of the Kolm ogorov microscales in terms of Re x 1114~20xxRe (1-14) and 47400 ~xx TRe U (1-15) The relationship between the Kolmogorov micr oscales and Reynolds number is given in Figure 1-5 for a zero pressure gradient turbulent boundary layer with 50 ms U and at a distance downstream of the leading edge assuming a 1 m x 17th power-law velocity profile. In order to detect the wall sh ear stress generated by the sm allest eddies in a turbulent boundary layer, the sensor size must be of th e same order of magnitude as the Kolmogorov length scale [10], and have a flat frequency range greater than the reciprocal of the Kolmogorov time scale [4]. These microscales are rough estim ates, so some researchers used the viscous length scale and time scale, *l *tu *2 to estimate the required se nsor size and bandwidth [11, 12]. For example, Padmanabahn et al. [11] used in their sensor design, and Alfredsson et al.[12] used and in their experiments. Gad-el-Hak and Bandyopadhyay [13] reported these viscous scales are on the same order of the Kolmogorov scales. *4 l *10 l *8 l *2 l If the sensor size is larger than the Kolmogorov length scal e, the fluctuating component will be spatially averaged, which results in spectral attenuation and a corresponding underestimation of the turbulent parameters [14, 15]. It has been reported that the sensor smaller than wall units were free from spatial averaging effects [16] while the sensor lager than wall units suffered shear stress underestimation [17]. Equation 20 30 (1-12) and (1-13) indicate that as 21

PAGE 22

the Reynolds number increases, the sensor size shoul d decrease and the bandwidth of the sensor should increase. For example, at 710xRe the Kolmogorov length scale is and the characteristic frequency is From experiments and nu merical simulation results, and Gad-el-Hak stated that a sensor size of 3-5 times of Kolmogorov length is reliable for accurate turbulence measurem ent [10]. A summary of parameters and their analytical expressions for a zero pressure gradient turbulent boundary layer are listed in 65 m 3.7 kHz Lofdahl Table 1-2 [7, 8]. In addition, roughness is another factor that ma y disturb the turbulent boundary layer. The roughness height due to the flatne ss of the device die in the package, misalignment in tunnel installation, and gap size is denoted by s k and the characterized roughness is given by s sku k (1-16) In turbulent flow if the roughness protrudes above the thin viscous layer, causing wall friction to increase significantly [7]. If 5sk 4sk the wall surface is deemed hydraulically smooth and the roughness does not significantly dist urb the turbulent boundary layer [7]. Research Objectives The goal of this dissertation is to devel op a robust, high resolution, and high bandwidth silicon micromachined piezoresistive floating element shear stress sensor for turbulent boundary layer measurement. The shear stress sensor should possess high spatial and temporal resolution and a low minimum detectable signal (MDS). To date, the quantitative, time-resolved, continuous, direct measurement of fluctuating shear stress has not yet been realized [4]. Further effort is required to developed standard, reliable MEMS shear-s tress sensors with quantifiable uncertainties. The detailed description of the choice of the piezoresistive sensing scheme is discussed in Chapter 2. 22

PAGE 23

Depending on the application, there are severa l challenges in the de velopment of this device. An ideal shear stress sensor should have a large dynamic range ( 80 dB O ), large bandwidth and a spatial resolution of 10 kHz O 100 m O to capture the spectra of the fluctuating shear stress without sp atial averaging. The resolvable shear stress would to be on the order of resulting in force resolution of 0.1 mPa O 10 pN O for the desired spatial resolution of In addition, an ideal sensor should be packaged to allow for flush-mounting on the measurement wall surface to avoid flow disturbances. 100 m O Traditional intrusive instruments suffer from insufficient spatial and temporal resolution. Microelectromechanical systems (MEMS) tech nology offers the potential to meet these requirements by extending silicon-based integr ated circuit manufacturing approaches to microfabrication of miniature structures [4 ]. From the perspective of measurement instrumentation, the small physical size and reduce d inertia of microsensors vastly improves both the temporal and spatial measurement resolution relative to conventional macroscale sensors. Thus, MEMS shear stress sensors offer the pos sibility of satisfying transduction challenges associated with measuring very small forces while maintaining a larg e dynamic range and high bandwidth. The previous research in MEMS shear stress sensors [18-25] is di scussed in detail in Chapter 2. Three transduction schemes have been developed for direct measurement of shear stress: capacitive [18, 21, 24], optical [20, 22, 23] and piezoresistiv e [19, 25]. These previously developed sensors possess performance limitations and cannot be used for quantitative shear stress measurements. 23

PAGE 24

This research effort is the combination of multidisciplinary design and optimization, fabrication, packaging and calibration, which results in a truly fl ush-mounted, MEMS direct wall shear stress sensor. The contribu tions to the above efforts are: Development of electromechanical m odeling and nonlinear constrained design optimization to achieve good sensor pe rformance for aerospace applications. Development and execution of a novel micro-fabrication process accounting for p/n junction isolation and high-quality el ectrical and moisture passivation. Development of a sensor package that can be flush-mounted on the wall surface. Realization and preliminary charact erization of a functioning device. Dissertation Overview This dissertation is organized into seven chap ters and five appendices. Chapter 1 provides the motivation for the topic of this dissertation. Background information regarding previous shear stress measurement technol ogy is discussed in Chapter 2. Sensor modeling is discussed in Chapter 3. This includes the electromechanical modeling, finite element analysis for model verification as well as specific de sign issues. Chapter 4 discusse s device optimization subjected to manufacturing constraints and specifications. Chapter 5 descri bes the detailed fabrication process and device packaging. Expe rimental characterization setups and results are presented in Chapter 6. The conclusion and future work are presented in Chapter 7. Information supporting this dissertation is given in appendices. Appendix A provides detailed derivations of the quasi-static beam models and dynamic models. The detailed modeling of the noise floor of the fully active Wheatstone bridge is discussed in Appendix B. A fabrication process flow is presented in A ppendix C. The process simulation using FLOOPS [26] is given in Appendix D. The recipes for pl asma etching are given in Appendix E. Finally, packaging details, vendors, and engineeri ng drawings are provided in Appendix F. 24

PAGE 25

Table 1-1. Summary of typica l skin friction contributions for various vehicles [5]. Vehicles Typical viscous loss Supersonic fighter 25-30 % Large transport aircraft 40 % Executive aircraft 50 % Underwater bodies 70 % Ships at low/high speed 90-30 % Table 1-2. Parameters in the turbulent boundary layer. Parameters Analytical expression Free stream velocity ms U U Typical eddy velocity mseu ~0.01euU Streamwise distance m x x Kinematic viscosity Reynolds number based on streamwise distance xUx Re Boundary layer thickness m 170.16xxRe Momentum thickness m 7 72 Reynolds number based on momentum thickness R e U Re Reynolds number based on boundary layer thickness eu Re Skin friction coefficient f C 170.027fxCRe Wall shear stress Paw 21 2wfCU Kolmogorov length scale m 34~ Re Kolmogorov time scale s T 0.5~eRe T u 25

PAGE 26

P y x uy w x Figure 1-1. Schematic of wall shear stress in a laminar boundary layer on an airfoil section. Figure 1-2. Schematic representation of the bounda ry layer transition process for a flat-plate flow at a ZPG [7]. 26

PAGE 27

Turbulent Laminar Velocity y u Figure 1-3. Schematic of typical velocity profile for low-spee d laminar and turbulent boundary layers [9]. Figure 1-4. The structure of a typi cal turbulent boundary layer [8]. 27

PAGE 28

105 106 107 108 109 101 102 103 Kolmogorov Length Scale ( m )Reynolds Number Rex 102 103 104 Kolmogorov Time Scale 1/T (Hz) 1/T Figure 1-5. Estimates of Kolmogorov microscales of length and time as a function of Reynolds number based on a 1/7th power-law profile. 28

PAGE 29

CHAPTER 2 BACKGROUND This chapter provides an overview of the techniques for shear stress sensor measurement with a focus on floating element sensors. Previo us MEMS shear stress sensors are reviewed and their merits and limitations discussed. A side-imp lanted piezoresistive shear stress sensor is then proposed to achieve high spatial and tempor al resolution and quantifiable uncertainties. Techniques for Shear Stress Measurement The current techniques empl oyed in shear stress measur ement are grouped into two categories: direct and indirect [27]. Indirect techniques in fer the shear stress from other measured flow parameters, such as Joulean heati ng rate for thermal sensors, velocity profile for curve-fitting techniques or Doppler shift for op tical sensors [27]. The uncertainty in these measurements is dominated by the validity of the model relating the flow parameter to wall shear stress [27]. The direct technique measures th e integrated shear force generated by wall shear stress on surface [4]. This technique includes th ree areas: floating-element skin friction balance techniques, thin-oil-film techniques and liquid crystal techniques. The floating-element skin friction balance techniques are a ddressed in this dissertation. A floating element sensor directly measures the integrated shear force produced by shear stress on a flush-mounted movable floating element [27]. Direct measurem ent techniques are more attractive since no assumptions must be made about the relationshi p between the wall shear stress and the measured quantity and/or fluid prop erties. In addition, direct sensors can be used to calibrate indirect devices. Conventional shear stress sensors and MEMS-b ased shear stress sensors are described in the following sections, with specific focu s on the MEMS floating element technique. 29

PAGE 30

Conventional Techniques Many conventional techniques have been develo ped to measure the wall shear stress [28], including indirect measurement techniques su ch as surface obstacle devices and heat transfer/mass transfer-based devices, and dire ct measurement techniques such as a floatingelement skin friction balance. Several review papers [27-29] catalog the merits and drawbacks of these devices in various flow situations and a wide range of applications. The indirect conventional techniques are summar ized in the following paragraph. Surface obstacle devices include the Preston tu be, Stanton tube/razor blade and sub-layer fence. These devices are easy to fabricate a nd favorable in thick tu rbulent boundary layers. However, they are sensitive to the size and geom etry of the obstacle in the turbulent boundary layer. The device can only measure mean shear stress, and unable to measure the time-resolved fluctuating shear stress. In addition, they rely on an empirical co rrelation between a 2-D turbulent boundary layer profile and property measured. Heat transfer/mass transfer-bas ed devices include hot films and hot wires. They have advantages of fast response, high sensitivity and simp le structure. However, they are sensitive to temperature drift, have tedious calibration pr ocedures, and suffer calibration repeatability problems due to heat loss to the substrate/air. In general, these device s are considered to be qualitative measurement tools [4]. The direct measurement techniques, known as skin friction balance or floating element balance, have been widely used in wind tunnel measurements since the early 1950s [28]. These techniques measure the integrated shear fo rce produced by the wall shear stress on a flushmounted laterally-movable floating element [29]. The typical device is shown in Figure 2-1 The floating element is attached to either a disp lacement transducer or to part of a feedback 30

PAGE 31

force-rebalance configuration. Winter [28] catal oged the limitations of this technique, which are summarized as follows: Compromise between sensor spatial resolution and de tectable shear force. Measurement errors associated with misalignment, necessary gap and pressure gradient. Cross-axis sensitivity to acceleration, pr essure, thermal expansion and vibration. Some of these limitations can be significantly mitigated if the dimension of the device is reduced, which is a motivation for the devel opment of MEMS floating element sensors. MEMS-Based Techniques MEMS is a revolutionary new field that extends silicon integrated circuit (IC) micromachining technology for fabrication of mi niature systems. The MEMS-based sensors possess small physical size and large usable ba ndwidth. The utilization of these devices broadens the spectrum of applications, which range from fundamental scientific research to industrial flow control [6] and biomedical applications [30]. From the fluid dynamics perspective, MEMS-b ased sensors provide a means of measuring fluctuating pressure and wall shear stress in turbulent boundary layers because the micromachined sensors can be fabricated on th e same order of magnitude of the Kolmogorov microscale [10]. and Gad-el-Hak reviewed MEMS-bas ed pressure sensors for turbulent flow diagnosis [10] including background, design cr iteria, and calibration procedures. Recently, Naughton and Sheplak reviewed modern skin-fric tion measurement techniques, such as MEMSbased sensors, thin-oil film inte rferometry and liquid crystal coatings. They summarized the theory, development, limitations, uncertainties and misconceptions surrou nding these techniques [4]. Lofdahl Several microfabricated shear stress sensors of both direct and indirect types have been reported. The indirect MEMS wall shear-stress sensors include thermal devices [31-34], laser31

PAGE 32

based sensors [35], micro-pillar s [36, 37] and micro-fences [38] Thermal shear stress sensors operate on heat transfer princi ples. Laser Doppler sensors operate on the measurement of Doppler shift of light scattere d by particles passing through a di verging fringe pattern in the viscous sublayer of a turbulent boundary layer to yield the veloci ty gradient. Micro-pillars are based on a sensor film with micropillars arrays that are essentially ver tical cantilever arrays within the viscous sublayer. Th ese sensors employ optical techni ques to detect the wall shear stress in the viscous sublayer via pillar tip deflection. Micro-fe nces employ a cantilever structure to detect the shear stress vi a piezoresistive transduction. Direct shear stress sensors include floatingelement devices [18-25]. Three transduction schemes have been used in floating element sensors: capacitive [18, 21, 24], piezoresistive [19, 25] and optical [20, 22, 23]. Floating Element Sensors Sensor Modeling and Scaling The typical MEMS floating element sh ear stress sensor is shown in Figure 2-2 The floating element, with a length of width of and thickness of is suspended over a recessed gap by four silicon tether s. These tethers act as restoring springs. The shear force induced displacement of the floating element is determin ed by Euler-Bernoulli beam theory to be [11] (the detailed derivation is given in Appendix A) eL eW tT 32 1 4weet tt ttee L WLLW ETWLW (2-1) where and are tether length, width a nd thickness respectively, and tL tW tT E is the elastic modulus of tether material. The mechanical sensitivity of the sensor with respect to the applied 32

PAGE 33

shear force, weeFWL is directly proportional to the m echanical compliance of the tethers 1 k [18] 32 11 1 4tt y ttee t L LW C kFETWLW (2-2) The trade-off associated with spatial resoluti on versus decreasing shear stress sensitivity is illustrated in Equation (2-1) and Figure 2-3 For example, a sensor with floating element area of the integrated shear fore is 100 m100 m 10 pN O for a shear stress of 1 mPa O which requires the tethers to have a high compliance to get an apprec iable element detection. The compliance is limited by the maximum shear stress achievable before failure occurs or before nonlinearity in the force-displacement relations hip [4] becomes substantial. The minimum detectable shear stress is determined by the sensitivity and the total sensor noise [39]. Assuming a perfectly damped or under-damped system, the bandwidth is proportional to the first resonant frequency, kM where M is the effective mass, eet M LWT (2-3) where is the density of the floating elemen t material and it is assumed that Therefore, the shear stress sensitivit y-bandwidth product is obtained as eettLWLW 3 211 4t eettL ELWTW kM (2-4) The sensitivity-bandwidth product is a parameter useful in inve stigations of the scaling of mechanical sensors. MEMS technology enables the fabrication of sensors with small thickness and low mass, in addition to large compliance and a superior sensitivity-bandwidth product comparable to conventional techniques [4]. A MEMS floating element has lengths of 33

PAGE 34

1000 meeLWO and whereas conventional floating element lengths are Therefore, with the scaling of ma ss alone, MEMS-based sensors have a sensitivity-bandwidth product at least three-or ders of magnitude larg er than conventional sensors. MEMS-based sensors also possess spat ial resolution at least one-order of magnitude higher than conventional sensors, which is vital for turbulence measurements to avoid spatial averaging [4]. 10 mtTO 1 cmeeLWO Error Analysis and Challenges Compared to conventional techniques, MEMS shear stress sensors have a negligible misalignment error. This error is limited by th e flatness of the device die [18] because the floating element, tethers and substrate are fabri cated monolithically in the same wafer. Other sources of misalignment include packaging and tu nnel installation, with pa ckaging the dominant source [4]. Packaging-induced compressive or tensile force may drastically alter the device sensitivity [18]. The necessary gap between the wall and floating element is also reduced, with a typical gap size smaller than [4]. 5 m Effect of misalignment Misalignment of the floating element results in the element not being perfectly flushmounted with the wall surface, which disturbs th e flow field around the sensor. The effective shear stress is estimated by integrating the stagnation pressure 2 yu over the floating element surface and dividing by th e element area [39] to get 2 0 k s y MA eudz L (2-5) 34

PAGE 35

where s k is the height of protrusion or recession above or below the wall. Streamwise velocity is obtained via relationship be tween shear stress and velocity gradient in the sublayer, yu y wu z (2-6) where and are the density and dynamic viscosity of the fluid, respectively, and z is the distance from the wall. Substituting Equation (2-6) into Equation (2-5) to obtain the effective shear stress yields 3 21 3 s w MA ek L (2-7) For a sensor with 1000 meL 10 msk under the surface, and 5 Paw in air, the misalignment error is about 0.12%. Therefore it may be neglected. Effect of pressure gradient Error due to a pressure gradient is also greatly decreased for MEMS sensors. As illustrated in Figure 2-4 there are two sources which introduce pre ssure gradient errors; one is the recessed gap beneath the floating element and the other is the net pressure force acting on the lip of the floating element [26]. The net force acting on the lip of the floating element is given as p teteedP FTWPTWL dy (2-8) The associated effective shear stress is obtained by dividing by the sensor area, eeWL p tdP T dy (2-9) The pressure gradient also introduces a shear stress underneath the floating element that can be estimated to first-order by assuming fully-developed Poiseuille flow, 35

PAGE 36

2ggdP dy (2-10) where is the height of the recesse d gap beneath the floating element. The total effective shear stress acting on the floating element is g **1 22t effw t wT dPg g T dy (2-11) where wdP dy is called Clausers equilibrium parame ter, which is employed to compare the external pressure gradient to wall friction in a turbulent boundary layer [7]. The displacement thickness is a parameter quantifying the mass flux defic it due to viscous effects. As indicated in Equation (2-11) the error is dependent on the gap si ze and thickness of the floating element and independent of the size of the floating elem ent. The smaller ga p and thickness of the MEMS sensors result in smaller e rrors compared to conventional floating element sensors; the MEMS sensors provide approximately a two-or der of magnitude improvement in lip force induced error. To get a more accurate estimate of these errors, direct numerical simulation of the flow around the sensor is required. Effect of cross-axis vibration and pressure fluctuations Errors due to stream-wise acceleration scale favorably for low mass MEMS sensors [28]. The equivalent shear stress due to acceleration is approximated as eet a ffeeWLTa FMa Ta AAWL t (2-12) where is the acceleration and a f A is the surface area of the fl oating element, respectively. Equation (2-12) indicates that the effective shear st ress due to stream-wise acceleration is proportional to the tether thickness. Assuming the stream-wise acceleration is 1 g, for a 36

PAGE 37

proposed optimum sensor design with element dimensions of 1 000 m1000 m50 m and the tethers dimension of 1, the effective stress is found to be 1.14 in the 000 m30 m50 m Pa y -direction. Depending on the aerodynamic body acceleration levels, local acceleration measurements in conjunction with coherent pow er data analysis may be used to mitigate acceleration effects [40]. The stream-wise deflection is obtained from c cMa y M aC k (2-13) where and are the stream-wise stiffness and compliance of the tether s, respectively. Therefore, the stream-wise acceleration sensitivity is proportional to Assuming flow over the floating element in the -direction ( ck yC yC y Figure 2-4 ), the cross-axis compliances according to small-deflection beam theory are 4t x ttL C E WT (2-14) and 31 4t z tt L C E WT (2-15) The ratios of transverse compliances to compliance in the flow direction are 2 y t xtC L CW (2-16) and 2 y t ztC T CW (2-17) If and the compliance in the ~50 mttTWO ~1 mmtLO x -direction is four orders of magnitude less than the complia nce in the flow direction ( y -direction). Since the deflection is proportional to the compliance in the associat ed direction, the transverse deflection ( x -direction) 37

PAGE 38

is four-orders of magnitude smalle r than in the flow direction ( -direction). Therefore, the transverse acceleration effect in y x -direction is negligible. However, the compliances in the and z y -directions are of the same order, and thus tr ansverse acceleration eff ects in the z direction must be taken into account. This can be mitigated by using piezoresistive transduction scheme via a fully-active Wheatstone bridge configuration. The transverse acceleration and pressure in the -direction supplies a common mode signal to the Wheatstone bri dge, which can be rejected by the differential voltage output. It is critical to minimize the pressure sensitivity as pressure fluctuations in wall-bounded turb ulent flows are much larger in magnitude than wall shear stress fluctuations [41]. Hu et al. [41] found that the wall pressure fluctuations is (depending on frequency) higher than the fluctua tions for the streamwise wall shear stress, and higher than that for spanwise component. The detailed discussion is given in Chapter 3. z 720 dB 1520 dB Previous MEMS Floating Element Shear Stress Sensors Previous research in the floating element shear stress sensor is review ed in this section. This review is divided into capacitive, optical and piezoresistive sensing in terms of transduction schemes. Their respective performance merits and drawbacks are discussed. Capacitive Shear Stress Sensors Realizing the merits of scali ng shear stress sensors to the microscale, Schmidt et al. [18, 39] first reported the development of a micromac hined floating element shear stress sensor with an integrated readout for applications in lo w speed turbulent boundary layers, As shown in Figure 2-5 the sensor was comprised a square floating element (50 0 m500 m32 m ) suspended by four tethers (1000 m5 m32 m ) and fabricated usi ng polyimide/aluminum surface micromachining techniques. A differentia l capacitive scheme was employed to sense the 38

PAGE 39

deflection of the floating element. This differe ntial capacitive scheme is insensitive to the transverse movement to first order. The sens or was calibrated in a laminar flow using dry compressed air up to a shear stress of 1 P. The achieved minimum detectable shear stress was with a bandwidth of 10. The measurement data was in agreement with the design model. However, the sensor was sensitive to electromagnetic interference (EMI) due to the high input impedance, and suffered from the sensi tivity drift due to mois ture-induced polyimide property variation. In addition, the capacitive sensing scheme was limited to nonconductive fluids. a 0.1 Pa kHz Pan et al. [21, 42] presented a force-feedback capacitive design that monolithically integrated sensing, actuation a nd electronics control on a single chip using polysilicon-surfacemicromachining technology. The sensor has a comb finger structure with folded beam suspension. The folded beam provided higher sens itivity and internal stress relief. The floating element motion was measured by a differential cap acitive sensing scheme while the folded beam served as mechanical springs ( Figure 2-6 ). A linear measurement sensitivity of 1.02 VPa over a pressure range of to 3.7 was achieved in a 2-D continuum laminar flow channel. No dynamic response, linearity and noise floor result s were reported. In addition, the front wire bonds may disturb the flow in turbulent flow measurements. 0.5 Pa Zhe et al. [24] developed a floating elemen t shear stress sensor using a differential capacitive sensing technique, with an optical technique as a self-test. The sensor was fabricated on an ultra-thin ( ) silicon wafer using wafer bonding and DRIE techniques. As shown in 50 m Figure 2-7 the sensor consisted of two sensor elec trodes, two actuation el ectrodes, a floating element (20in width and 500 in length) and a cantilever beam ( in length). The shear stress was detected by a cantilever beam deflection, with a mechanical sensitivity of 0 m m 3 mm 39

PAGE 40

1 mPa This sensor was capable of measuring a shear force as small as 5 n that corresponded to a shear stress of 50. The static calibration in a rectangular channel shows a minimum detectable shear stress of with 8% uncertainty up to which is the limit of the calibration technique. No fr equency response results were reported. N mPa 0.04 Pa 0.2 Pa Optical Shear Stress Sensors Padmanabhan et al. [20] developed two genera tions of differential optical shutter-based floating element sensors for turbulent flow measurement. As shown in Figure 2-8 the floating element (120 and 500 m120 m7 m m500 m7 m ) is suspended 1. above the silicon substrate by four tethers. Two photodiodes were integrated into the substrate under the leading and trailing edges of th e opaque floating element. The floating element motion induced by shear force causes the photodiodes shuttering. Under uniform illumination from above, the normalized differential photocurrent is proportional to the lateral displacement of the element and the wall shear stress. The sensor could measure a wall shear stress from up to 10, with a sensitivity of 0 m 3 mPa Pa 0.4 VmPa (without integration of detection electronics ). The dynamic response of the sensor was quantified up to the characterization limit of [43]. The measured shear stress was consiste nt with predicted theoretical va lues. The sensor showed very good repeatability, long-term stability, minimal drif t, and EMI immunity. The main drawback to this sensor was that vibrations of the light source relative to the sens or resulted in erroneous signals. 4 kHz Tseng et al. [22] developed a novel Febry-Pero t shear stress sensor that employed optical fibers and a polymer MEMS-based structur e. The sensor was micromachined using micromolding, UV lithography and RIE processes. As shown in Figure 2-9 a membrane was used to protect the inner sensing parts and support the floating element displacement 40

PAGE 41

measurement. The displacement of the floating element (40 high, wide) induced by the wall shear stress on the membrane (1 0 m 200 m .5 mm1.5 mm20 m ) was detected via an optical fiber using Fabry-Perot interferometer. The sens or was tested in a steady laminar flow between parallel plates and the results demonstrated a shear stress resolution of 0.65 Panm The minimum detectable shear stress was The fragile sensing parts were not exposed to the testing environment, making the sensor suitable for applications in harsh environments. This sensor was not tested in flows. The dynamic response and linearity of this sensor are questionable due to the potential buckling of diaphr agm. Furthermore, cross-axis sensitivity due to vibration and pressure may be significant given the geometry of the sensing element. 0.065 Pa Horowitz et al. [23] develope d a floating-element shear stre ss sensor based on geometric Moir interferometer ( Figure 2-10 ). The device structure consisted of a silicon floating element (1280) suspended above a Pyrex wafer by four tethers ( ). The sensor was fabricated via DRIE and a wafer bonding/thin back process. When the device was illuminated throu gh the Pyrex, light was reflected by the top and bottom gratings, creating a translation-dependent Moir fringe pattern. The shift of the Moir fringe was amplified with respect to the elem ent displacement by the ratio of fringe pitch G to the movable grating pitch The sensor die was flush-mounted on a Lucite plug front side, and the imaging optics and a CCD camera was inst alled on the backside for the displacement measurement. Experimental characteriza tion indicated a stat ic sensitivity of m400 m10 m 2.0 m 545 m6 m10 m 2g 0.26 mP a a resonant frequency of 1.7, and a noise floor of kHz 6.2 mPaHz Drawbacks to this sensor included an optical packaging scheme not f easible for wind tunnel measurement and limited bandwidth. 41

PAGE 42

Piezoresistive Shear Stress Sensors Shajii et al. [19] and Goldberg et al. [ 44] extended Schmidts work to develop a piezoresistive based floating element sensor for polymer extrusion feedback control ( Figure 211 ). The polyimide/aluminum composite floating el ement was replaced by single crystal silicon. These sensors were designed for operation in high shear stress 1 kPa100 kPa high static pressure (up to ) and high temperature (up to 300) flow conditions. The floating element size was 120 in Ngs design, and 500 40 MPa C m140 m m500 m in Goldbergs design. The element motion was sensed by axial surface pi ezoresistors in the tethers via configuration these piezoresistors to a half White stone bridge. This sensor was not suitable for turbulent flow measurement due to low sensitivity as it was de signed for maximum shear-stress levels 5 ordersofmagnitude larger than those in a typical turbulent flow. However, Goldberg et al. [44] developed a backside contact st ructure to protect the wire-bon ds from the harsh external environment, which reduced the flow disturban ce and associated measurement uncertainty for turbulence measurement. Barlian et al [25] developed a piezoresistive shear stress sens or for direct measurement of shear stress underwater. The si dewall-implanted piezoresistors measured the integrated shear force, and the top-implanted piezor esistors detected the pressure ( Figure 2-12 ). The displacement of the floating element was detected using a Wheatstone bridge. The experimental measurements indicated the in-pla ne force sensitivity ranged from 0.0410.063 mVPa while the predicted sensitivity was 0.068 mVPa The transverse sensitivity was 0.04 mVPa with a corresponding transverse resonant frequency of 18. This was done by using a mechanical cantilever as an input. The dynamic analysis wa s performed using a lase r Doppler vibrometer with a piezoelectric shaker to drive the in-plane or out-of-plan e motion. The in-plane resonant .4 kHz 42

PAGE 43

frequency was experimentally found to be 19 compared to a predicted value of 13.4. The integrated noise floor was 0.16 over bandwidth of 1 kHz kHz V Hz100 kHz The sensitivity of the piezoresistors to changes in temperature was investigated in a de-ion ized (DI) water bath, and the temperature coefficient of sensitivity was found to be o0.0081 k C No electrical characteristics of p/n junction isolation and flow characteri zation are reported and no fluid mechanics characterization was performed. A Full-Bridge Side-Implanted Pi ezoresistive Shear Stress Sensor According the above discussion, the most su ccessful MEMS floating element sensor to date used integrated photodiodes to detect the lateral displacement via a differential optical shutter [20]. This sensor can de tect the shear stress as low as 1.4. However, it is not suitable for wind tunnel testing because the sens ing system is sensitive to tunnel shock and vibration. The capacitive transduction techniqu e integrated the mechanical sensor and electronics on one chip to eliminate the parasi tic capacitance [45], and has the capability to measure small signals. Unfortunately, the sensitivity drifted due to the charge accumulation in the electrodes [18], which can be mitigated by hermetic sealing [46] or by employing metal electrodes. However, the shear stress sensor must be exposed to the flow for shear stress measurement and wind tunnels are typically not humidity controlled environments. mPa The piezoresistive transduction scheme is wide ly used in commercial pressure sensors and microphones due to its low cost, simple fabricat ion, and higher reliabi lity than capacitive transduction. In addition, piezoresistive techno logy can resolve sufficiently small forces up to [47]. Shajii et al. [19] proposed a backsi de-contact, piezoresistive sensor to measure very high shear stress in a polymer extruder. Ax ial mode piezoresistive transducers [19, 25] for high-shear industrial applicati ons have been fabricated us ing standard ion-implantation 1510N O 43

PAGE 44

techniques, but more sensitive bending-mode transducers require that the piezoresistors be located on the tether sidewall. This concept ha s been proposed by Sheplak et al.[48] and applied by Barlian et al. who presented an integrated pressure/shear stress sensors for underwater applications [25]. The authors did not present a comprehensive fluid-induced shear stress characterization of their sensor Rather, the sensor was sta tically characterized using a mechanical cantilever and dynamically charac terized using an acceleration input. In a conference paper, the authors presented some wa ter flow results possessing a large uncertainty and an unexplained sensitivity that was larger than the value predicted by beam mechanics [49]. None of these devices have successfully tr ansitioned to wind tunnel measurement tools because of performance limitations and/or packag ing impracticalities [2]. For use in a wind tunnel, the sensor package must be flush m ounted in an aerodynamic model, robust enough to tolerate humidity variations and immune to el ectromagnetic interferen ce (EMI). We have attempted to address these limitations via the de velopment of a fully-active Wheatstone bridge side-implanted piezoresistive sensor. This approach was motivated by the following two sideimplanted piezoresistive transduc er concepts. Chui et al. [ 50] first presented a dual-axis piezoresistive cantile ver using a novel oblique ion implantation technique. Later, Partridge et al. [51] leveraged the side-implant process to fabr icate a high performance lateral accelerometer. The device structure developed in th is dissertation is illustrated in Figure 2-13 which shows an isometric view of the floating element, sidewall implanted p-type silicon piezoresistors, heavily doped end-cap region, and bond pads. In this transduction scheme, the integrated force produced by the wall shear stress on the floating el ement causes the tethers to deform and thus induces a mechanical stress field. The piezoresistor s respond to the stress field with a change in resistance from its nominal, unstressed value due to a change in the mobility (or number of 44

PAGE 45

charge carriers) within the pi ezoresistor [52]. The conversio n of the shear stress induced resistance change into an electrical volta ge is accomplished via configuration of the piezoresistors into a fully-active Wheatstone bridge to increase the sensitivity of the circuit compared to half bridge configuration. This bridge requires the presence of a bias current through the piezoresistors, typicall y, it is driven by constant volta ge excitation. This sensor is designed to measure shear stress only and to m itigate pressure sensitivity. An on-chip dummy bridge located next to the sensor is used for temperature corrections. Ideally, common mode disturbances do not have any effect while differential disturbances are linearly converted into the br idge output. To achieve a differe ntial signal, the piezoresistors are oriented such that the resi stance modulation in each resistor of a given leg is equal in magnitude but opposite in sign. These conditions are achieved by placing the side implanted resistors facing one another such that when one resi stor is in tension, the other is in compression. This results in equal mean resi stance but opposit e perturbation. Once the transduction scheme is selected, the mechanical models and transduction sensing models need to be developed to get sensor performance, such as sensitivity, linea rity, bandwidth, noise floor, dynamic range, MDS. The detailed di scussion of the electrom echanical modeling is given in Chapter 3. 45

PAGE 46

Figure 2-1. Schematic cross-sectional view of the floating element based sensor. Figure 2-2. Schematic plan view and cross-section of a typical floating element sensor [4]. 46

PAGE 47

10-2 100 102 10-12 10-10 10-8 10-6 10-4 10-2 Shear Stress w (Pa)Shear Force (N) 100X100 m2 250X250 m2 500X500 m2 1X1 mm2 2X2 mm2 10-3103 Figure 2-3. Integrated shear fo rce variation as a function of sensor resolution for different element areas. Figure 2-4. Schematic illustrating pressure gradient effects on the force balance of a floating element. 47

PAGE 48

Embeded Conductor Floating Element Cps1Cps2CdpVDS Passivated Electrodes Csb1Csb2Silicon on chip off chip Sense Capacitor Sense Capacitor Drive Capacitor Figure 2-5. Schematic cross-sectional view of the capacitive floating element sensor developed by Schmidt et al. [18]. Release Holes Floating Element Tether Expanded View of Comb Finger Structures C1 C2 VV+ Figure 2-6. Plan-view of a hor izontal-electrode capacitive fl oating element sensor [21]. 48

PAGE 49

Figure 2-7. Schematic top-vi ew of a differential capacitiv e shear stress sensor [24]. Figure 2-8. A schematic cross-sectional view of an optical differentia l shutter-based floating element shear stress sensor [11]. 49

PAGE 50

Figure 2-9. Schematic top and cross-sectional vi ew of a Febry-Perot sh ear stress sensor [22]. Tethers Aluminum Gratings (Floating Element & Base Gratings) Reflected Moir Fringe Floating Element Silicon Pyrex Laminar Flow Cell Incident Incoherent Light Figure 2-10. Top and cross-sectional view of Moir optical shear stress sensor [23]. 50

PAGE 51

Flow 180 m 120 120 m 10m m Figure 2-11. A schematic top view of an axial piezoresistive floating element sensor [19]. Figure 2-12. A schematic top view of a laterally-implanted piezoresistiv e shear stress sensor [25]. 51

PAGE 52

R R R R R R R RoVBV1V2V Figure 2-13. A schematic 3D view of the side-i mplanted piezoresistive floating element sensor. 52

PAGE 53

CHAPTER 3 SHEAR STRESS SENSOR MODELING This chapter presents the electromechani cal modeling of the ME MS side-implanted piezoresistive shear stress sensor. These mode ls are leveraged for use in finding an optimal sensor design (detailed discussion in Chapter 4). Formulation of th e objective function for performance optimization begins with structural and electronic device models of the shear stress sensors. The structural response directly dete rmines the mechanical sensitivity, bandwidth, and linearity of the dynamic response. The piezore sistor design determines the overall sensitivity and contributes to the electronic noise floor of the device. The organization of this chapter is as follows. First, the mechanical modeling is discussed, including quasi-static modeling and dynamic response analysis. Linear and non-linear quasi-static behaviors are presented. Lumped element modeling is employed to find the dynamic behavior of the sensor. These analytical models were verified using finite element analysis (FEA) in CoventorWare. Second, the piezoresistive sensing electrom echanical model is developed, where the resistance and piezoresistive sensitivity for nonuniform doping are derive d via stress averaging and a conductance-weighted piezores istance coefficient. Two domi nant electrical noise sources in the piezoresistive shear stress sensor, 1 f noise and thermal noise, as well as amplifier noise are considered to determine the noise floor. Finally, some device specific issues are addressed, including transverse sensitivity, acceleration sensitivity, pressure sensitivity, junction isolation issues and temperature compensation via a dummy bridge. 53

PAGE 54

Quasi-Static Modeling In this section, the sensor structure is disc ussed and modeled. Quas i-static models for small and large floating element deflections that make use of Euler-Bernoulli beam theory and the von Krmn stain assumption, respectively, are presented. Two methods are used in large deflection analysis, an energy method and an exact analytical method. Structural Modeling Floating element sensors are composed of four tethers and a square floating element. A schematic of the piezoresistive sh ear stress sensor is shown in Figure 3-1 The floating element is suspended above the surface of the silicon wafer by tethers, each of which is attached at its end to the substrate. Side-impla nted boron in the sidewalls of the tethers forms the four piezoresistors. These resistors are aligned in th e <110> direction and loca ted near the edge zone of the tethers to achieve the maximum sensitiv ity. Two resistors are oriented along opposite sides of each tether. When the fluid flows over the floating element, the integrated shear force causes the tethers to deform a nd induces a bending stress. For the mechanical analysis, the floating elements and tethers are assumed to be homogeneous, linearly elastic, and symme tric. In practice, this is not strictly valid as the beam is partially covered by thin silicon dioxide and si licon nitride layers. The floating element is assumed to move rigidly under the applied shea r stress, and the motion is permitted in-plane only. The tethers are assumed to be perfectly clamped on the edge. The effects of pressure gradient and gap errors are i gnored. Furthermore, the Youngs modulus and Poisson ratio are assumed to be constant and do not change with processing. 54

PAGE 55

Small Deflection Theory Assuming that the tethers can be modeled as a pair of clamped-clamped beams with a length of subjected to a uniform distributed load (per unit length) and a central point load [39], as shown in ttLW tT 2tL Q P Figure 3-2 The distributed load is due to the shear stress acting on the tethers and is given as wtQW (3-1) The point load, is the effect of the resultant shear force on the floating element and is given by P 2weePWL (3-2) where the factor of 1/2 comes from the symmet ry of the problem. The maximum deflection and bending stress distribution is obt ained using Euler Bernoulli beam theory. The detailed derivation is given in Appendix A. The la teral displacement of the beam is given by 22 34 3()38282 (0) 4w eettt eett t t ttwx WLLWLxWLWLxWxxL EWT Pa (3-3) where is the Youngs modulus of silicon in the 168 EG 110 direction [53]. The maximum deflection occurs at the center of the beam and is obtained by substituting t x L into Equation (3-3) to get 312 4weet tt tteeWLLWL E TWWL (3-4) This corresponds to the floating element displ acement. The second term in the brackets of Equation (3-4) is a correction for the distributed wa ll shear stress on the tethers. Equation (3-4) indicates that the important parameters affecti ng the scaling of the device are the area of the floating element, ratio of the tether lengt h to the tether width, eeWL tLW t and ratio of the area 55

PAGE 56

of a tether to that of the floating element, tteeWLWL If the tether surface area the stiffness is approximated as tteeWLWL 311 4t weett L kWLETW (3-5) This indicates that the stiffness is proportional to the tether thickness and ra tio of the tether width and length. The bending stress di stribution through the width and le ngth of the tether is given by 2 20 263 233 ,1 0 42t weet tt tt tt l t ttt ee eeteet x L WLL WLWLWL yx x xy yW WTWWLWLLWLL ,(3-6) where is at the end of the beam, and 0 x 0y is on the side wall surface. Equation (3-6) indicates that the maximum shear stress is locate d at the end of the beam and on the side wall surface ( in ,xy 0 Figure 3-2 ). Linear Euler-Bernoulli beam theory [54] fails for sufficiently large wall shear stresses because the mid-plane of the beam is strained [46]. The beam grows stiffer as the deflection becomes large. Furthermore, the nonlinear motion generates undesired harmonic distortion in the frequency domain. The sensor is required to maintain a li near relationship between shear stress and displacement in order to preserve spectral fidelity for time resolved measurement. This requirement places a nonlinear constraint in the sensor design optimization (discussed in Chapter 4). A large deflection mechanical model was therefore developed for use in determining this constraint. Large Deflection Theory Large deflection theory provides a measure of the maximum shear stress that may be measured while maintaining mechanical linearit y. Two analysis techniques are pursued to 56

PAGE 57

determine the nonlinear mechanical behavior of th e sensor: the strain en ergy method [46] and an exact analytical method. The detailed derivations are given in Appendix A. Energy method The deflection predicted by the strain energy method [46] is obtained by assuming a trial function which meets both the clamped boundary condition and symmetry condition of the beam, 1cos 2t NL tLx wx L (3-7) where N L is the floating element deflection. The tria l function is substituted into the expression for strain energy in the beam and the principle of minimum potential en ergy is applied. The result is 23 term3 1 44NL weet tt NL tt t NLWLLWL WETWW 1 2e eL (3-8) Comparing this result to Equation (3-4) one can see that cubic nonlinearity term has been added. The mechanical response of the floating element sensor will be linear provided that the nonlinear term is small with respect to unity; that is if the displacement of the sensor is small in comparison to the tether width, 21NLtW The nonlinear term is cubic and therefore represents a Duffing spring behavior or stiffening of the beam as deflections become large. This means that the nonlinear deflection is smaller th an the ideal linear deflection for large shear stresses. Exact analytical model In the large deflection model, the neutral axis tension force is taken into account. The average axial tension force is ob tained by integrating the neutral axis strain along the length of aF 57

PAGE 58

the beam. It then serves as a constitutive equa tion between axial force and strain. The detailed model development procedure is given in Appe ndix A. The maximum deflection predicted by the exact analytical method is obtaine d using von Krmn strain assumption, 2cosh()1 sinh() cosh()+ 2 sinh()22 22tt AL t t t aat aLQ PP P LQ LL FFL F t aL P L F (3-9) where the axial force is given by aF 2 02Lt tt a tdwx ETW F dx Ldx (3-10) and is given by 3=12attFETW (3-11) There are five variables, four boundary condi tions and one constitutive equation. But the equation is indeterminate, so the final solution is obtained using an ite rative technique to find and therefore obtain the maximum deflection. Lumped Element Modeling Lumped element modeling is used to represen t the fluidic to mechanical transduction of the shear stress sensor and fac ilitates the prediction of the dynamic response. The main assumption of LEM is that the length scale of th e physical phenomena of interest is be much larger than the characteristic length scale of the device [55]. For the shear stress sensor, this means that the bending wavelength of the beam mu st be much larger than the length of the tethers. The LEM provides a simple way to estimate the dynamic response of a system for low frequencies, up to just beyond the first resona nt frequency, which is appropriate for design purposes [56]. 58

PAGE 59

There are several types of elements in the lumped element model. For example, in a lumped mechanical system, mass represents the st orage of kinetic energy compliance of a spring (inverse of stiffness) represents the storage of potential energy, and a damper represents the loss of energy through dissipation. Si milarly, in lumped electrical systems, generalized potential energy is stored in a capacitor, generalized kinetic energy is stored in an inductor, and energy is dissipated via a resistor. From a LEM perspective, the two sets of te thers are modeled as a spring possessing an effective compliance In an impedance analogy, this compliance shares a common displacement with the effective mass meC me M of the tethers and floating element as well as the damper, d R of the system. The main source of damp ing is the viscous damping underneath the element, and thermoelastic damping, compliant boundaries and vibrati on radiation to the structure boundaries are neglected in this research. Therefore, the sensor is modeled as a springmass-dashpot system, as schematically shown in Figure 3-3 In the equivalent circuit, the voltage and current are analogous to force and velocity, respectively. The motion of the massspring-dashpot system is described by the cl assic second-order differential equation, 2 2() 1me d medd FtMRC dtdt (3-12) Therefore, the frequency response func tion of the device is found to be 21 () () 1medmej Hj Fj j MjRC (3-13) where the angular frequency 2 f f is the cyclic frequency, and 1j Assuming a lightly damped system, the first resonant frequency r f is 59

PAGE 60

1 2r memef CM (3-14) The detailed derivation of the lumped elemen ts is given in Appendix A. The effective mechanical compliance is determined by equating th e potential energy stored in the beam to that of an equivalent lumped system and is 321 1214 21tt tt tt t me tt ee ee eeLWLWLWL C ETWWLWLWL 26 4 5 (3-15) The effective mass is obtained by eq uating the kinetic energy of the sensor to that of a lumped system and is 23149422381024 11 315315 315tt tt tt tt mesieet ee ee ee eeWLWLWL WL MWLT WLWLWLWL 22 (3-16) where 32331 kgmsi is the density of silicon [53]. Finite Element Analysis To verify the analytical models, a finite element analysis with a clamped boundary condition on the edge of the tethers is perfor med. The material properties of silicon and the geometry of a representati ve structure are given in Table 3-1 Finite element analysis is performed in CoventorWare using the multi-mesh model by partitioning the continuum solid model into plate and tether volumes. A fine mesh is used in the tethers because of the large stress gradients with respect to those found in the plate. These volumes are joined to form one volume via RigidLink after meshing. The mesh is composed of parabolic Manhattan brick elements. A mesh refinement study revealed sufficient elements dimensions are 3 in length, width and thickness within the tethers, m,0.5 m and 1 m 60

PAGE 61

respectively, and 10 within the plate. Since the device is symmetric, only half of the structure is analyzed in the model, with 6600 elements in the analysis. m,10 m,1 m A representative displacement field of the tethers at 5 Paw is shown in Figure 3-4 The comparison in Figure 3-4 indicates that the nonlinear analyti cal model is in agreement with FEA simulation results. Figure 3-5 shows the maximum displacement of the floating element as a function of applied shear stress for analytical linear and nonlinear models, nonlinear energy method model and FEA model. This comparison in Figure 3-5 indicates that al l results are in agreement in the linear range ( approximately), while the nonlinear analytical model, nonlinear energy method model and FEA models agree in this nonlinear deflection region. 50 Pa Figure 3-6 shows the stress distribution usi ng analytical linear model (Equation (3-6) ) and FEA results along the tether le ngth on the sidewall surface ( 0y ) for the representative structure. Figure 3-6 demonstrates that the analytical model is in agreement with the FEA model. The bending stress varies from tensile to compressive in a parabolic distribution along the tether length. Figure 3-6 shows that the maximum stress occurs on the edge zone ( ) of the tether. ,xy 0 The resonant frequenc y obtained from LEM (12.44) and FEA (12.47) agree well, as shown in kHz kHz Table 3-2 The next 5 modes were also found using FEA and are given in Table 3-3 The first six mode shapes are shown in Figure 3-7 The in-plane resonant frequency (second mode) is 17.08, greater than the out-of-plane resonant frequency (first mode) because the tether width is greater than the tether thickness for the verification studies ( kHz Table 31 ). Clearly, the representative dimensions used for model verification are not a preferred design, let alone an optimized design. 61

PAGE 62

Piezoresistive Transduction In 1954, Smith [52] discovered the piezoresistan ce effect in silicon and germanium. The piezoresistance effect is defined as the change of semiconductor resistivity due to a change in carrier mobility that results from an applied mechanical stress. In piezoresistive transduction, the resistance modulation is a function of the a pplied stress and piezoresistive coefficients ij [57]. For the cubic crystal structure of silicon under small strain, the corr elation of normalized piezoresistivity and stress for reduced tensor notation reduces to 1111212 2121112 3121211 23 44 23 13 44 13 12 4412000 000 000 1 00000 00000 00000 1 2 3 (3-17) where is the change in resistivity, i are normal stresses along the cubic crystal axes, and 100 ij are shear stresses. For a given resistor geometry, there are two piezoresistive coefficients used for piezoresistive sensing analysis in terms of stre ss orientation with respect to the current. The longitudinal piezoresistive coefficient captures th e effect of an applied stress in the same direction as the current, and the transverse piezo resistance coefficient captures the effect of an applied stress in the direction perpendicular to the current. The longitudinal and transverse piezoresistive coefficients in terms of the funda mental piezoresistive coe fficients and direction cosines are given by, respectively [58], 222222 114412111111112lmlnmnl (3-18) and 222222 12441211121212llmmnnt (3-19) 62

PAGE 63

where 111,, lmn is the set of direction co sines between the longitudina l direction an d the crystal axis, and is the set of direction cosines betw een the transverse direction and the crystal axis. The direction cosines are given in terms of Eulers angles [59] 222,, lmn 111 222 333lmncccssscccssc lmnccsscscsccss lmncsssc (3-20) where cos c sin s and etc. The geometry of the Eulers angle is shown in Figure 3-8 In this research, a wafer is used, thus 100 0 0 and sweeps from 0 to 180 degree in Figure 3-8 Therefore, the matrix (3-20) reduces to, (3-21) 111 222 3330 0 001 lmncs lmnsc lmn The piezoresistive coefficients, 111244, and are given in Table 3-4 for both p-type and n-type piezoresistors at room temperatur e for low doping concentrations. For this piezoresistive device, the floating element sensor features integrated sideimplanted diffused resistors [25, 50, 51] in the el ement tethers for piezoresistive detection. In this transduction scheme, the integrated force produced by the wall shea r stress on the floating element causes the tethers to deform and thus create s a mechanical stress field in the tethers. The piezoresistors respond to the mechan ical stress field with a change in resistance from its nominal unstressed value [46] as indicated by llttR R (3-22) 63

PAGE 64

where and R are the resistivity and resistance of the piezoresistor, respectively, signifies the perturbation in the resist ance and resistivity due to the piezoresistive effect, l is the bending stress along the beam, and t is the transverse stress. For a beam subjected to pure bending, Equation (3-22) simplifies to llR R (3-23) Piezoresistive Coefficients The piezoresistive coefficients depend on crys tal orientation, doping type and level, and temperature. This dependence is typically expr essed as a product of th e coefficients low-doped room temperature value 0 and a piezoresistive factor [59] (,)PNT 0,( NTPNT ,) (3-24) where is the doping co ncentration and T is the temperature. For a N 100 wafer, the dependence of the piezoresistive coefficien t on the crystal direction is given in Figure 3-9 and Figure 3-10 for p-type and n-type piezore sistors, respectively. This indicates that the maximum piezoresistive coefficient for p-type silicon is in the 110 direction, while for n-type silicon the maximum is in the 100 direction. Also note that n-ty pe silicon has a larger achievable piezoresistive coefficient than p-type silicon. The longitudinal and tr ansverse piezoresistive coefficients l and t in the 110 direction for n-type and ptype silicon are given in Table 3-5 [52]. As shown in Table 3-5 piezoresistors in p-type silicon are more sensitive than for n-type in the 110 direction, which is parallel or perpendicular to the flat of a 100 wafer. In this design, the p-type piezoresistors are c hosen due to its high sensitivity in the 110 direction and 64

PAGE 65

because of the lower temperature sensitivity at higher doping concentrations compared to n-type piezoresistors [60]. Many theoretical [59] and experimental [61-63] studies have repor ted the dependence of the piezoresistive factor on doping concentration at room temperature. Kandas model [59] is most popular and is accurate for low c oncentrations. However, when compared to experimental data [61-63], Kandas model under predicts the roll-off of for concentrations above For doping concentration above the fundamental piezoresistive coefficient is expressed as a pr oduct of its lightly-doped room temperature value (,)PNT (,)PNT 17-310 cm 17-310 cm 0 and the experimentally fitted piezoresistive factor [47], (,)PNT 0.2014 22-3 001.5310 cm ,(,)logNTPNT N (3-25) The piezoresistive factor is plotted in Figure 3-11 versus concentration at room temperature. The piezoresistive coefficient is also temperature dependent. At higher doping concentrations, there will be a reduction in both thermal noise and 1 f noise compared to lower doping concentrations [47]. In addition, the temper ature dependence of the piezoresi stance coefficient is reduced significantly as the concentr ation increases at low doping concentration. For doping concentrations above the piezoresistance coefficient is almost independent of temperature variation [61]. Howe ver, the sensitivity degrades due to the reduced piezoresistive coefficient at a high doping level [62]. Thus, th ere is a tradeoff between sensitivity and noise floor. This tradeoff suggests optimization is necessa ry to obtain the best performance, as will be discussed in chapter 4. 20-310 cm 65

PAGE 66

Piezoresistive Sensitivity For the structure shown in Figure 3-12 the side-implanted piezoresistors are fabricated by first implanting p-type impurities (boron) into th e sidewall, followed by a diffusion step to drivein and to electronically activate the impurities. The impurities diffuse laterally, and the resulting impurity concentration profile decreases from the su rface of the side wall to the junction depth. If the unstrained impurity prof ile as a function of depth, Ny is known, the piezoresistive coefficient profile ()y can be determined. As shown in Equation (3-6) the stress varies along the beam, and varies across the junction depth, j y as well. Therefore, the product of the stress and the piezoresistive coefficient distributions need to be integr ated in the electromechanical model. Several models have been developed for piezo resistive sensitivity. Tortonese [64] and Harley [65] built a two-step model for non-uni form doping concentration and formulated an efficiency factor to be inserted into the numerator of the surface sensitivity equation. In integrating across the beam, their model does no t account for the junction isolation of diffused resistors. Senturia [46] presents the piezo resistive coefficient de pendence of the doping concentration, but does not account for stress variation as a function of depth. S zes model [57] addresses stress variations across the resistors ( -direction) and incor porates a conductanceweighted piezoresistance coefficient. Sze, how ever, did not account for th e stress variation along the piezoresistor ( y x -direction). Based on Harleys wo rk, a new model was developed by involving stress averaging along the tether length and across the dept h of piezoresistor, and using a conductance-weighted piezoresistive coefficient. Two issues need to be consid ered in calculating the piezores istive response. One is that the piezoresistors are typically formed by diffu sion, thus have a non-uni form doping profile with 66

PAGE 67

respect to junction depth. The second issue is that piezoresistors also span a finite area on the device, and hence have non-uniform stress with respect to length and depth. The derivation of the resistance of the piezoresis tor begins with the non-uniform doping concentr ation that varies from the sidewall surface to the junction depth ( -direction). The stress varies in this direction as well. As shown in y Figure 3-12 the resistor can be considered as a stack of slices, where each slice has a slightly different doping concentra tion and stress. The current flow is in x direction, so the slices ( ) are connected electrically in parallel because they share the same potential. The stress also varies along the length of the resistor ( dy x direction). Thus, the resistor is also segmented along its length. These segments ( ) are connected in series due to the same current flow. The mechanical model assumes that thus the differential resistance of a unit cell for a small segment and a small slice with width of is given by dx and ttLW tT dx dy rW 1 ,e unit unit r x ydx dRxy dGxyWdy (3-26) where it is assumed that at the surface and 0y 2tyW at the neutral axis. In Equation (3-26) ,e x y is the stressed resistiv ity determined by [46] (,)()1()(,)ee oll x yyyx y (3-27) where ()eo y is the unstressed resistivity and (,)l x y is given in Equation (3-6) For nonuniform doping, ()eo y is given by [66] 1 () ()()eo pAy yqNy (3-28) where is the electronic charge of an electron and 191.60210 q C ()py is the boron mobility. In this research, the mobility is obtained from [67]. To simply the calculation process, 67

PAGE 68

we use conductance 1 G R rather than resistance in the deri vation. The total conductance for segment is obtained by summing the conductance of each unit dx 0 01 ()1()(,)j jy y r slice unit eo llWdy dGdG dxyyxy (3-29) The total resistance is determined by summing the resistance of the small segments, dx 01 1/ ()1()(,)Rr Rr j RRLL LL slice y LL r eo ll R RdG Wdy yyxy dx (3-30) where is the overlap end cap and it does not change the resistance value. The total unstressed resistance is similarl y found by integrating along the leng th of the resistor using the unstressed resistivity, 10 mRL 01 1 ()Rr Rr j R RLL LL slice y L L r eo R dG dx Wdy y (3-31) Then the resistance modulation is obtained by arranging Equation (3-30) and (3-31) 0 0() 1 1 ()1()(,)y j LL Rr eo y j L r R eo lldy y RRRR dx RRL dy yyxy (3-32) Electromechanical Sensitivity The four side-wall implanted piezoresistors form a full Wheatstone bridge circuit that provides sensitivity enhancement for a small change in resistance. As illustrated in Figure 3-13 when the tether deflects in the y direction, piezoresistors 1 a nd 3 experience a compressive stress while 2 and 4 experience a tensile stress. These resistors experience a change in resistance 68

PAGE 69

of R and R respectively. For an ideal bridge, 13 R RRR and 24 R RRR so that the output voltage, for a given bias voltage is oV BV 41 3412 oRR B B R VV RRRRR V (3-33) The sensitivity of the piezoresistive sensor is de fined as the change of ou tput voltage per unit of applied shear stress and for a linear sensor is expressed as o EM wwVV S o (3-34) Substituting in Equation (3-33) the electromechanical sensitivity is rewritten as B EM wVR S R (3-35) Noise Model The key sources of the electrical noise in piezoresistive sensors are thermal noise, low frequency 1 f noise, and amplifier noise [ 65]. Physical fluctuations of the floating element at an equilibrium temperature, T, can result in random motion of the device; however, the contribution of thermomechanical displacement noi se has been found to be much smaller than the electronic noise sources excep t at mechanical resonance [47] For an ideally balanced Wheatstone bridge, the bi as source noise will be common mode rejected. Thermal Noise Thermal noise, also known as Nyquist or J ohnson noise, is produ ced when electrons are scattered by thermal vibration of the lattice stru cture [68]. Since higher temperatures lead to increased vibrational motion, thermal noise power spectral density (PSD) is directly proportional to temperature. Moreover, thermal noise is present in thermodynamic equilibrium, and its PSD is independent of frequency si nce random thermal vibrations ar e not characterized by discrete 69

PAGE 70

time constants. The thermal noise PSD ( ) is modeled by Nyquist [68], which was experimentally verified by Johnson [69], as vTS 4 vTBSkT R (3-36) where 1.38e-23 Bk JK is the Boltzmann constant, R is the total resistance in the resistor, and is the temperature in Kelvin. In a piezoresistor, the rms noise voltage, due to thermal noise is obtained by taking the square root of the thermal noise PSD integrated over the bin width of interest T tRV 2 1 f ff [68], 2 14f tR vT B fVSdfkTR f (3-37) 1 f Noise The dominant noise source for most ion-implanted piezoresistors is 1 f noise. Hooge [70] first reported that the 1 f noise PSD of a piezoresistor is inversely proportional to the total number of carriers in the resistor when an external dc bias voltage is applied, and is given by 2 1 H R vf cV S Nf (3-38) where is the voltage across the resistor, is the total number of ionized carriers in the resistor, RV cN f is frequency, and H is Hooge parameter, with the ex perimental values ranging from to [71]. Hooges parameter is sensitive to bulk crystalline silicon imperfections and the interface quality. Low frequency noise occurs under non-equilibrium conditions and its spectra is proportional to the square of the app lied voltage. Two physical mechanisms have been proposed to account for the low frequency noise: random trapping/detrapping of carriers at the 6510 3210 70

PAGE 71

surface and bulk electronic traps, and random mobility fluctuations [72]. The noise power of 1 f noise is obtained by integrating Equation (3-38) over a frequency range of operation 2 2 1 1lnHR fR cVf V Nf (3-39) The total number of ionized car riers in the resistors for th e piezoresistor geometry in Figure 3-12 is given as (3-40) 0()jy crrANLWNyd y where is the -type doping concentration. As indicated in Equation ()ANy p (3-39) 1 f noise increases for small volumes and hi ghly resistive piezoresistors. In this dissertation, th e typical input noise of a low noise amplifier at 1k, Hz 4 nVHz [73], is used in the noise floor model. For an ideally balanced Wheatstone bridge assuming a unity gain amplifier, the total rms output noise voltage is NV 2 2 2 11 ln449 4HB NB cVf Vk T R f Nf e f (3-41) where the first, second and third terms in Equation (3-41) are the contribution of 1 f noise, thermal noise, and the amplifier noise, respec tively. The detailed derivation of Equation (3-41) is given in Appendix B. Since narrow bin turbulence spectra are desired, a figure of merit bin width of centered at 1 k is used in this dissertation; therefore, and 1 Hzf Hz 1999.5 Hz f 21000.5 Hz f The minimum detectable shear stress (MDS) or input noise, min is the minimum shear stress that the shear stress sensor can resolv e in the presence of noise and is defined as 71

PAGE 72

minN EMV S (3-42) The dynamic range (DR) is then given by max min20log DR (3-43) Device Specific Issues In this section, a few specific design issues are addressed, including transverse sensitivity, acceleration sensitivity, pressure sensitivity, temperature compensation and device junction isolation issues. Transverse Sensitivity Transverse sensitivity was di scussed in Chapter 2 (Equation (2-16) ), and restated here briefly. Recall that the transver se mechanical sensitivity in the x -direction can be neglected due to the large differences in bending versus axial s tiffness, while transverse mechanical sensitivity in the direction is of the same order as in the flow direction. The z x -direction also possesses electromechanical rejection for an ideally balanced bridge. Assuming the flow is in the direction, when the sensor is subjected to an x-axis acceleration, piezoresistors 1 and 2 experience a tensile stress while 3 and 4 experience a compressive stress. These resistors experience a change in resistance of y R (piezoresistors 1 and 2 and R (piezoresistors 3 and 4), respectively ( Figure 3-14 (a)). The resistances in the bridge become 12 R RRR 34 R RRR The output voltage, for a given bias voltage is given by oV BV 3 1 12340 2222oR RR RR V RRRRRRRR R (3-44) 72

PAGE 73

When the fluctuating pre ssure load acts in the direction, the stress distribution in all four tethers is the same, leading to equal resistance perturbations ( z R ) in all four piezoresistors. The reaction of the Wheatstone bridge due to pressure is shown in Figure 3-14 (b). The total pressure effect is to supply a common mode signal into this differential sensing scheme, which does not affect the voltage output. Therefore, the ideal elect romechanical sensitivity due to the x-axis load and pressure disturbance is ideally equal to zero. In reality, there will still be transverse sensitivity due to bridge mismatch. Temperature Compensation The output voltage of a piezore sistive sensor is dependen t on temperature due to the thermal sensitivity of the resistance, strain a nd piezoresistive coefficient [46]. In this dissertation, it is assumed that the thermal coe fficient of resistance will dominate over thermal strain effects and changes in the piezoresistive co efficient. The typical temperature coefficient of resistance for a laterally implan ted sensor is reported to be o0.0081 k C which is much larger than the shear stress sensitivity [25]. Since it is impossible in practice to have absolute temperature control in a wind t unnel, temperature compensation of the output signal must be employed. In it important that the temperature is measure as close as possible to the sensing element to avoid compensation errors due to temperat ure gradients in the flow. In this thesis, the temperature compensation of the resistors are ach ieved using a double bridge configuration [74]. As shown in Figure 3-15 two Wheatstone bridges are used on one chip; one is the active Wheatstone bridge with output that is a function of shear stress a nd temperature, while the other is a dummy compensation Wheatstone bridge with output that acts as a thermometer and only depends on temperature. The dimension of the co mpensation bridge resistors is identical to the active bridge and is kept as close as possi ble to the active bridge (safe distance of 10 0 m 73

PAGE 74

suggested for the peripheral circuits [75] ). The detailed temperature compensation procedure for the non-ideal case of a sta tically unbalanced bridge is discussed in Chapter 6. For ideally balanced Wheatstone bridge, the power supply noise is just a common mode signal to the bridge and would not affect the bridge voltage ou tput. In most physically realized devices, the bridge is not exactly balanced. Therefore, the powe r supply noise contribution to the noise scales with the bridge offset volta ge output normalized by the bias voltage. Device Junction Isolation One design issue is the difficulty of realizing a junction-isolat ed, laterally diffused resistor in the sidewall of a tether. As shown in Figure 3-16 the p-type piezoresi stor (with resistance S R ), the p++ interconnects (with resistance L R ) and the n-type substrate form a p/n diode. For an ideal p/n diode, the leakage cu rrent is negligible in the reve rse bias region [76]. When the reverse voltage exceeds a certain value, the reve rse current will increase rapidly and the diode will breakdown. To ensure the current flows exclusively through the p-type regions, the p/n junction must be reverse-biased for all possi ble bias voltages along the entire length of the piezoresistor and interconnect. Th is section addressed design issues associated with this design constraint. Two issues must be taken into account in th e design: (1) maintaini ng junction isolation and (2) avoiding p/n junction breakdow n while achieving the desired piezo resistor sensitivity. When a voltage is applied between the two p++ interc onnects, the p/n junction voltage varies linearly with position due to a linear volta ge drop across a distribu ted resistance. For junction isolation, the p/n junction must be reverse-bi ased at all spatial locations. Under reverse bias, a p/n junction develops a space charge layer due to the depletion of carriers [76]. In order to maintain electrical is olation, it is necessary to ensure that the space 74

PAGE 75

charge layers for adjacent p-type regions extending into the n-ty pe substrate do not overlap or punch-through. The space charge layers punch-through will cause the corresponding p regions to become shorted, resulting in a non-functi onal device. Assuming uniform doping, the acceptor concentration in the p re gion is assumed to be and the donor concentra tion in the n region is assumed to be AN D N The space charge layer widths on the p-side p x and n-side n x are given as a function of the junction voltage [76], jV 2Si D p j AADN b i j x V qNNN V V (3-45) and 2Si A nj bij DADN x V qNNN V V (3-46) where 12 Si1.04510 Fcm is the silicon permittivity, and th e intrinsic number of electrons is 10310 cmin in silicon at room temperature. The built-in voltage is given as 2lnAD bi iNN kT V qn (3-47) In order to electrically isolate the p++ regions, the en tire length of the p/n junction must be reverse-biased The space charge layer width in the p and n region, 0jV p x and n x respectively, increases with reverse bias. The to tal space charge width on the n side is given by jnjnBjWVxVxVV (3-48) If the total space charge layer width on the n side, jWV increases to the width between the piezoresistor and the p++ interconnect, or to the width between the p++ interconnects, the space charge layers will punch-through, causing the corresponding p regions to be shorted. 1L 2L 75

PAGE 76

To avoid punch-through, 1 jWVL must be satisfied fo r all junction voltages, Additionally, lateral diffusion that occurs during high temperature process steps, leading to an increase in the actual width of the p-type region compared to the designed width, must be taken into account. Therefore, the total isolation wi dth is approximated by jV 2isoj dnjnBjWVLxVxVV (3-49) where is the lateral diffusion width estimated from the net effect of high temperature process time on the diffusion length (thermal budget) [77]. The total thermal budget dL tot D t is equal to the sum of the diffusion time, D t products for all high temperature cycles affecting the lateral diffusion, i tot i D t Dt where and are the diffusion coefficient and time associated with each processing step. iD it In this design, the doping profile is non-unifo rm, and the acceptor c oncentration in the p region and the donor concentration in the n region ANy DNy vary with depth, as shown in Figure 3-17 The non-uniform doping prof iles are obtained by FLOOPS simulation [78], where sidewall boron implantation in amorphosized si licon is simulated by SRIM [79] and then imported to FLOOPS The cross-sectional vi ew of the isolation widt h for a doping profile at a bias voltage of 10 V is shown in Figure 3-18 and Figure 3-19 which are associated with the A-A and B-B cuts shown in Figure 3-20 The dimensions of the tether width the sidewall implanted piezoresistor depth the p++ interconnect width and the space parameters, and are listed in tW 4L 3L 1L 2L 5L Table 3-6 for the actual device. There is a tradeoff between the p++ interconnect widths, and and the punchthrough width A large value of and is desired to reduce the lead resistance. The 3L 4L 1L 3L 4L 76

PAGE 77

resulting narrow gap, may cause p/n junction punch-through. On the edge of the tethers, the p++ interconnects are tilted degrees from the tether centerline to increase the isolation gap spacing. For the worst case, at left and 0 V on the right, as shown in 1L 24 10 VjV Figure 3-20 there is about between adjacent p++ interconnect s assuming a lateral diffusion of Meanwhile, a crossover between the piezoresistor and p++ interconnects must be avoided. As shown in 9 m ~1.1 m Figure 3-19 the space charge layer of the piezoresistor in the n-well increases as the depth increases. If the space be tween the piezoresistor and the p++ interconnect is too close, there will be crossover and the p-region will punch through. A top view of the isolation width is shown in Figure 3-20 The blue region is the tether, the cyan region is the p++ interconnects, the green region is the piezoresistor, and the pink lin e is the final isolation width considering lateral diffusion and spac e charge diffusion to the n-well at (worst case). 10 VjV In order to minimize the space charge width in the n-well, one can increase the doping concentration of the n-well, D N There is, however, a tradeoff between increased n-well doping concentration and reduced reverse breakdown volta ge. With increasing doping, the internal electric field increases and th e reverse junction breakdown volta ge decreases [80, 81]. The breakdown voltage decreases from to ~1 when the impurity concentration increases from to ~50 V 0 V 16-31.010 cm 17-31.010 cm The curvature of the tether corner and the cu rvature of the junction regions must also be considered. A sharp corner dramatically increa ses the mechanical stress, which could lead to possible failure of the material s [82]. Additionally, a sharp corner in the p/n junction may increase the local electric fiel d and decrease the breakdown voltage [83]. Thus, the corner is rounded. The stress concentration factor, K, de pends on the fillet radius for a given thickness [82] and is relatively high when the ratio of the fillet radius and tether width is less than 0.5. In 77

PAGE 78

this design, K is chosen as 0.9. In addition, 4 slots in the substrate near the edge of each tether are designed to relieve stress concentrati ons that arise duri ng fabrication [51]. In order to avoid thes e issues, a metal contact design is employed, where the metal lines run on the top of the tethers to connect either side of the laterally implanted piezoresistors, as shown in Figure 3-21 Because there are two deep trenches on both sides of the tether for tether release, the fabrication process of this design is very challenging and is discussed in detail in Chapter 5. 50 m Summary Electromechanical modeling of a side-impla nted piezoresistive floating element shear stress sensor has been developed for aerospa ce applications. Two Wheatstone bridges are employed, an active bridge for shear stress sensing and a dummy bridge for temperature compensation. The predicted sensitivity, noise floor, dynamic range and MDS have been modeled and verified by FEA. To accurately resolve the fluctuating shear st ress in a turbulent boundary layer, the shear stress sensor is desired to possess a small size, large usable bandwidth and a low MDS. MDS depends on the geometry of sensors and piezoresistors, dopant profile, process parameters, and sensor excitation. To achieve a low MDS, it is favorable to maximize sensitivity and minimize noise. However, there are tradeoffs between se nsitivity and noise floor. It is necessary to perform design optimization to balance these conf licting requirements. Additionally, the sensor design is constrained by temporal and spatial resolution requirements as well as structural limits. The detailed optimization is discussed in Chapter 4. 78

PAGE 79

Table 3-1. Material properties [53] and geometry para meters used for model validation. Density of silicon 3kg/mSi 2330 Youngs modulus in [110] orientation GPa E 168 Poisson ratio p 0.27 Length of tethers mtL 400 Thickness of the tethers mtT 3 Width of the tethers mtW 4 Length of the square floating element meL 150 Table 3-2. Resonant fre quency and effective mass predicted by LEM and FEA for the representative structure given in Table 3-1 Frequency kHz Effective Mass kg LEM 12.44 1.66e-10 FEA 12.47 1.72e-10 Table 3-3. First 6 modes and effective mass pr edicted by FEA for the representative structure given in Table 3-1 Mode Domain Frequency kHz Effective Mass kg 1 12.47 (translational in -direction) z 1.72e-10 2 17.08 (translational in -direction) y 1.74e-10 3 34.95 (rocking mode about x -axis) 6.82e-10 4 162.33 (rocking mode about -axis) y 1.81e-11 5 170.11 (rocking mode about -axis) z 1.84e-11 6 219.50 (translational in x -direction) 1.70e-11 Table 3-4. Piezoresistive coefficients for n-type and p-type silicon [53]. 11 (10-11Pa-1) 12 (10-11Pa-1) 44 (10-11Pa-1) n-type -102.2 53.4 -13.6 p-type 6.6 -1.1 138.1 79

PAGE 80

Table 3-5. Piezoresistive coeffici ents for n-type and p-type sili con in the <110> direction [53]. l (*10-11Pa-1) t (*10-11Pa-1) n-type -31.2 -17.6 p-type 71.8 -66.3 Table 3-6. Space parameter dime nsions for junction isolation. tW tL 2L 3L 4L 5L 30 m 9 m 13.6 m 15 m 1 m 33 m 80

PAGE 81

Figure 3-1. Schematic top view of the structure of a piezoresistive floating element sensor. P Q 0 x Floating Element Tether Wt Lt y LtLeWe/2 WtTt 2Lt Figure 3-2. The simplified clamped-clamped b eam model of the floating element structure. Figure 3-3. Lumped element mode l of a floating element sensor: (a) spring-mass-dashpot system (mechanical) and (b) equivalent electrical LCR circuit. 81

PAGE 82

0 0.2 0.4 0.6 0.8 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Normalized Tether Length x/LtDisplacement ( m ) FEA Nonlinear Analytical Figure 3-4. Representative resu lts of displacement of tethers for the representative structure given in Table 3-1 at 5 Paw 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Wall Shear Stress w (Pa) Maximum Displacement ( m) Nonlinear Linear Energy FEA Figure 3-5. Representative load -deflection characteristics of an alytical models and FEA for the representative structure given in Table 3-1 and 5 Paw 82

PAGE 83

0 0.2 0.4 0.6 0.8 1 -1 -0.5 0 0.5 1 Normalized Tether Length x/LtBending Stress ( MPa ) FEA Linear Analytical Figure 3-6. Verifi cation of the analytically predicted stress profile (Equation (3-6) ) with FEA results for the representative structure of Table 3-1 and 5 Paw Translational in -direction Translational in -direction Rocking mode about z y x -axis Rocking mode about -axis Rocking mode about -axis Translational in y z x -direction Figure 3-7. The mode shape for the representative structure of Table 3-1 and 5 Paw 83

PAGE 84

z x y*y* z x Figure 3-8. Geometry used in co mputation of Eulers angles [59]. 2e-010 4e-010 6e-010 8e-010 30 210 60 240 90 270 120 300 150 330 180 0 t l <110> <110> Figure 3-9. Polar dependence of pi ezoresistive coefficients for p-t ype silicon in the (100) plane. 84

PAGE 85

5e-010 1e-009 1.5e-009 30 210 60 240 90 270 120 300 150 330 180 0 l t <100> <100> Figure 3-10. Polar dependence of piezoresistive coefficients for ntype silicon in the (100) plane. 1016 1017 1018 1019 1020 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Boron Concentration (cm-3)Piezoresistance Factor Kanda Harley Figure 3-11. Piezoresistive factor as a function of impurity concen tration for ptype silicon at [47]. 300K 85

PAGE 86

Figure 3-12. Schematic illustrating the releva nt geometric parameters for piezoresistor sensitivity calculations. Figure 3-13. Schematic representative of a defl ected side-implanted piezoresistive shear stress sensor and corresponding resistance changes in Wheatstone bridge. 86

PAGE 87

VBR1R2R3R4 Vo VBR1R2R3R4 Vo(a) (b) Figure 3-14. Wheatstone bridge subjected to cross-axis acceler ation (a) and pressure (b). Figure 3-15. Schematic of the double-bridge temperature compensation configuration. 87

PAGE 88

+ + -n++ p++ p++ RSRLRL (a) (b) Figure 3-16. Top view schematic of the side-impla nted piezoresistor and p++ interconnect in an n-well (a) and equivalent elec tric circuit indicating that the sensor and leads are junction isolated (b). 0 0.5 1 1.5 2 105 1010 1015 1020 1025 Depth(um)Doping Concentration(cm-3) nwell p++ interconnect piezoresistor Figure 3-17. Doping profile of n-well, p++ interconnect, and piezore sistor using FLOOPS simulation. 88

PAGE 89

0 5 10 15 20 0 0.4 0.8 1.2 1.6 2 Depth (m)Isolation Width (m) p++ p++ Piezoresistor n-well Figure 3-18. Cross view of isolation width between p++ interconnects (A-A cut in Figure 3-20 ). 0 2 4 6 8 10 12 14 0 0.4 0.8 1.2 1.6 2 Depth (m)Isolation Width (m) p++ Piezoresistor 4.8 m n-well Figure 3-19. Cross view of isolation width between p++ interconn ect and piezoresistor (B-B cut in Figure 3-20 ). 89

PAGE 90

Figure 3-20. Top view of the isolation widths on a sensor tether. Figure 3-21. Top view schematic of the side-imp lanted piezoresistor with a metal line contact. 90

PAGE 91

CHAPTER 4 DEVICE OPTIMIZATION This chapter presents the nonlinearly constr ained design optimization of a micromachined floating element piezoresistive shear stress sensor. First, the problem form ulation is discussed, including the objective functi on and constraints based on fl ow conditions. Next, the optimization methodology is outlined. The op timization results are then presented and discussed. Finally, a post-opt imization sensitivity analysis of the objective function is performed. Problem Formulation The objective function is selected based on tradeoffs identified between the sensitivity and noise floor of the shear stress sensor. The c onstraints are formed due to physical bounds, manufacturing limits and opera tional requirements [84], a nd are dependent on the flow conditions of the desired applications. The objective function and constr aints are functions of the de sign variables, including the geometry of the floating element structure and the piezoresistors, the surface doping concentration, and sensor excitati on. The detailed discussion of the design variables chosen is presented in next subsection. Design Variables The objective function and constraints depend on geometry of sens ors structures and piezoresistors, process related parameters, and sensor operational parameters. The geometry parameters include tether length tether width tether thickness, floating element length and piezoresistor length piezoresistor width The process related parameters include piezoresistor surface concentration and junction depth (assuming a uniform doping profile). The sensor operational para meter is the supplied bias voltage. tL tW tT eL rL rW SN jy 91

PAGE 92

The geometry parameters of the sensor stru cture determine the mechanical characteristics of the sensor, such as sensitivity, linearity and bandwidth. Design issues related to the tether width and tether thickness are addressed here. As discu ssed in Chapter 3, the minimum tether width is set to to avoid p/n junction punch thr ough. The tether thickness must be larger than the tether width to ensure that th e cross-axis resonant freq uency is larger than the in-plane resonant frequency. As shown in the representative structure in tW tT tW 30 m Table 3-1 the first mode is out of plane due to the tether thickness larger than the tether width. The increases in tether thickness results in bending stress decreases (Equation (3-6) ), and thus sensitivity decreases (Equation (3-23) ). On the other hand, the piezoresi stor related parameters, such as piezoresistor length piezoresistor width and p/n junction depth rL rW j y and surface concentration are related to noise floor and sensitivity. SN For each design optimization, different tether thickness, junction depth and tether width may be achieved, but all designs are fabricated in one wafer due to economic constraints. Thus these parameters for each design mu st be set to the same value. In this research, the tether thickness is set to 50 considering the sensitivity of the shear stress sensor and SOI wafer availability. Due to the rough si dewall surface near the buried oxide layer after DRIE process and no passivation on the bottom of the te thers after final release, the high m 1 f noise and current leakage became issues in the piezoresistor design [85]. Partridge et al .[51] investigated the accelerators with piezoresist ors implanted in the top 15 (total thickness), 5 of the flexures, and found that 3 case has large sensitivity and low m m 3 m m 1 f noise. In this research, piezoresistor width 5 mrW is chosen to avoid current leakage while maintaining high 92

PAGE 93

performance. A junction depth of 1 m jy is chosen taking account the piezoresistor and p++ interconnection and the manu facturing constraint. In summary, six design variables are include d in the optimization design, and they are tether length tether width floating element length and piezoresistor length piezoresistor surface doping concentration and bias voltage tL tW eL rL SN B V Objective Function As stated in Chapter 1, to accurately rec ognize the fluctuating wall shear stress in the turbulent boundary layer, the measurement de vice must possess sufficiently high spatial and temporal resolution as well as a low MDS, which is defined as the ratio of noise floor to the sensitivity. Therefore, lowering the noise floor and increasing se nsitivity are favorable in shear stress sensor design to achiev e a low MDS [84]. Some parame ters, such as junction depth, surface doping concentration and bias voltage, a ffect both sensitivity and noise floor creating tradeoffs between these performance parameters The following discusses the tradeoffs in sensitivity and noise floor a nd the arrival at th e MDS as the objective function of the optimization. Junction depth, j y and surface doping concentration, are two major factors involved in processing that affect sensit ivity and noise floor. As disc ussed in chapter 3, changes in while keeping SN SN j y constant invoke tradeoffs between noise and sensitivity. If increases, the resistivity of the piezoresistor decreases and the total carrier number increases. This leads to the reduction of thermal noise and SN 1 f noise. Conversely, sensitivity decreases due to the reduction of the piezoresistive coefficient l from high doping concentration (Equation (3-23) ). 93

PAGE 94

The bias voltage B V also affects both sensitivity and noise floor. As B V increases, the sensitivity increases (Equation (3-35) ) because the output voltage is directly proportional to the bias voltage. The voltage noise contribution from 1 f noise also increases squarely as indicated by Equation (3-38) By establishing the MDS as the objective f unction, a balance between noise floor and sensitivity is achieved. Previous researchers have investigated the potential and methods in piezoresistive sensor optimizati on. Harley and Kenny [47] pres ented an informal graphical design optimization guidelines in the form of de sign charts by varying the dimensions of the cantilever, the geometry of the piezoresistor, doping level, and proce ss issues related to sensitivity and noise floor. Papila et al. [84] performed a piezore sistive microphone Pareto design optimization, in which the tradeoff between pressure sensitivity and electronic noise is investigated. The Pareto curve indicated that th e MDS in units of pressu re is the appropriate parameter for performance optimization. Constraints The constraints are determined by physical bounds, fabrication lim its and performance requirements [84]. The constraints used in th is optimization and their associated physical explanations are listed below: Piezoresistor geometry: 0.4rtLL as discussed in Chapter 3, stress changes sign at the longitudinal center of the tether (shown in Figure 3-6 ). Thus, the sensitivity will be reduced if the length of the pi ezoresistor is larger than 2tL As a result, the maximum piezoresistor length is limited to of the tether length 40% Resistance: 3SLRR represents a balance betw een the sensor resistance S R being 3 times larger than the interconnect resistance L R but small enough to minimize electromagnetic in terference (EMI). Frequency: minr f f puts a bandwidth constraint in the design. The constraint changes with flow conditions. 94

PAGE 95

Power consumption: where 0.1owP 2owBSLPVRR When increases to a large value, the temperature of the piezoresistor will increase due to Joul e heating resulting in voltage drift and eventually electromigration. owP Nonlinearity: 3%NLLNL device linearity is required to keep spectral fidelity for time-resolved measurements. In-plane resonant frequency: To avoid disturbing the flow at the sensor resonance, the tether thickness is required to be larger than tether width to ensure the onset of the in-plane resonant frequency o ccurs before the out of plane. In this dissertation, the minimum tether width is 30 and its upper bound is set to 40, thus the tether thickness is set to 50. tTW t tT tW m m m Lower bounds (LB) and upper bounds (UB): ,,,,,tterSBLBLWWLNVUB present the limitation of the design variables. LB and UB are given in Table 4-2 based on the candidate shear stress design specifications and design issues related to fabrication. In summary, both the objective function and c onstraints are nonlinear. Therefore, the optimal performance design deals with solving the constrained nonlinear optimization problem. Candidate Flows Several sensor specifications associated w ith various flow phenomena, ranging from low speed flow to supersonic and hypersonic flow, are listed in Table 4-1 Here max is the maximum shear stress to be measured and constrained by non-linearity, min f is the minimum resonant frequency to provide adequa te temporal resolution and is the maximum floating element size that determines the lowest tolerable spatial resolution, is the minimum tether width that is limited by the junction isolation, and is the minimum thickness that is constrained by the in-plane resonant frequency. The temporal and spatial resolution maxeL mintW tT min f and are chosen to approach the Kolmogorov time and length scales, but are sufficiently c onservative to yield a proof of concept device. maxeL 95

PAGE 96

Methodology The design problem is formulated to find the optimum dimensions of the floating element and tethers, geometry and surface doping concentr ation of piezoresistors, and bias voltage for each candidate flow. Mathematically, the optim ization seeks to minimize the MDS subject to constraints. The key points rega rding the optimization of the minimum detectable shear stress, min are summarized below: Design variables: , tL tW eW rL B V and SN Objective function: minimize minFX where X is the design variable vector. Constraints: 10.410rtgLL ; 2min10rgff ; 313SLgRR 0 ; 2 410 10BSLgVRR ; 50.0310NLL NLg ; 10, 6,8,...,11iiigLBxi ; 10, 12, 13...17ji igxUBj where ,,,, and itterSB x LWWLNV Since the magnitudes of de sign variables differ by several order of magnitude ( Table 4-2 ), all variables are non-dimensiona lized to avoid singularities in the program. This nonlinear constrained optim ization is implemented using the function fmincon in MATLAB (2006b) [86] optimization Toolbox, which employs sequential quadratic programming (SQP) for nonlinear constrained problems and calcula tes the gradients by finite difference method. The optimum value of for different designs might be different. All designs, however, are fabricated on one wafer. Therefore, surface concentration, for all designs must be set to the same value. In this dissertation, the optimal for first three cases were the same and is This value was chosen as the surface concentration for SN SN SN 19-3=7.710 cmSN 96

PAGE 97

all designs. The optimization was re-implemented using this fixed conc entration following the same steps described above. The SQP method is a local optimizer and is hi ghly dependent on the initial value. The initial designs are selected randomly, and a numbe r of local optimum solutions from different initial designs were obtained. The solution iden tifies one best design points as the optimal solution. A global optimization algorithm using partic le swarms [87] is also employed to investigate the possibility of improving the optimum solutions. It is found that global optimization solution is very similar to the optimization results obtained by fmincon function. The global optimization results have a large computational cost. Optimization Results and Discussion In the optimization, the doping pr ofile is assumed to be uniform to simplify the modeling. The Gaussian profile is more accurate than a uniform profile, but it is not employed in this research to avoid computationa l cost. The doping concentration for p++ interconnect is achieved as with a junction depth of 1 for all designs. In this research, the material properties of silicon is fixed. 20-32.0 cm m The resulting optimizati on design is shown in Table 4-3 The highlights are active constraints. Since the low resistance result s in low thermal noise, but the power dissipation increases. Therefore, the power constraint is always active (close for case 9). For each device, the dynamic range from the optimum design is in excess of Kuhn-Tucker conditions [88] are conducted to check the optimality and ac tive constraints, which are stated as follows: 75 dB Lagrange multipliers j are nonnegative, and satisfy equation (4-1) 10 i=1,2...mgn j j j iig F xx (4-1) 97

PAGE 98

where g n is the total number of constraints, and is the total number of design variables. Lagrange multipliers m j are obtained by the fmincon MATLAB function. The corresponding j is zero if a constraint is not ac tive. The active constraints for each case are indicated in bold font in Table 4-3 Once the optimum design for uniform doping is obtained, non-uniform doping profiles are applied to achieve the final perf ormance of the sensor. The optim ization flow chart is shown in Figure 4-1 The non-uniform doping profiles are obt ained by FLOOPS simu lation [26], where sidewall boron implantation to amorphous silic on is simulated by SRIM simulation [79] and imported to FLOOPS. The surface concentratio n of the piezoresistor, the piezoresistive interconnection, and n-well are achieved to and respectively, as shown in 19-37.7 cm 20-32.0 cm 16-37 cm Figure 3-17 The results indicate th at non-uniform doping profiles yield approximately a decrease in dynamic range. Therefore, implementing a Gaussian profile as part of the optimization would resu lt in a more accurate model and thus optimal design. 5 dB Sensitivity Analysis Due to parameter uncertainty caused by process, min may achieve different values than theoretical optimization. The sensitivity analysis is implemen ted to understand sensitivity of MDS to the variations of the de sign variables, constrai nts, and fixed parameters at the optimum design. Therefore, sensitivity analysis is a post-optimization step, which involves two parts: Sensitivity of the objective function to de sign variables at the optimum design. Sensitivity of the objective functions to the fixed parameters at the optimum design, where the effect of a change in the active constr aints on the objective f unction is taken into account. 98

PAGE 99

For the sensitivity analysis with respect to the design variables, logarithmic derivative [88] is employed to measure the sensitivity of MDS to uncertainty of design parameters at the optimum design, min min minlog logi ii x xx (4-2) where ,,,, and itterB S x LWWLVN For the sensitivity analysis with respect to the fixed parameters, equation (4-2) is invalid if the nonlinear inequality constraints are active. Lagrange multipliers based on the Kuhn-Tucker conditions [88] is employed to calculate the sensitiv ity of the optimal so lution to the fixed parameters. Assuming that the objective f unction and the constraints depend on a fixed parameter p so that the optimization problem is defines as, jminimize such that g,0 j=1,2...17.FXp Xp (4-3) The gradient of with respect to is given as [88], F p T ag dFF dppp (4-4) where denotes the active cons traint functions and ag 0ag from Kuhn-Tucker conditions. The equation (4-4) indicates that the Lagrange multipliers are a measure of the effect of a change of the constraints to the objective function. Lagrange multipliers 0 for active constraints, otherwise it is obtained by 1TTNNNF (4-5) where and are defined as N F j=1,2...17, i=1,2...6j ig N x (4-6) 99

PAGE 100

and F F= i=1,2...6ix (4-7) The sensitivity of min to uncertainty of the fixed parameters is given as minmin min min T ag p pppp (4-8) can be obtained from the output of fmincon function directly. The fixed parameters are ,,,jrtpyWTN S For case 1, power is the active inequality constraint, and the associated Lagrange multiplier, 0.0026179 is obtained from MATLAB calcu lation. Therefore, Equation (4-2) is employed to calculate the sensitivity of MDS to uncertainty of design parameters ( and tL tW eW rL B V ) at the optimum design. Equation (4-8) is employed for the fixed parameters ( and ). jy rW tT SN Figure 4-1 shows the sensitivity of min to uncertainty of the design variables and fixed parameters for case 1, i.e., 10% change of the tether width causes 19% change of the minimum detectable shear stress. It is illustrated that min is sensitive to variation of tether width, tether length, floating element width, and junction depth, The MDS is less sensitive to variation of piezoresistor length In summary, tW tL eW jy rL min is very sensitive to uncertainties of tether and element dimensions, junction depth and width of the piezoresistors, and less sensitive to uncertainties of piezoresistor length. Summary This section described the c hoice of objective function and a ssociated constraints. The optimization has been implemented for nine designs, from low Reynolds number flow to supersonic and hypersonic flow. The optimization results indicate that the dynamic range exceeds 75 for all designs based on a uniform doping profile. Accounting for non-uniform dB 100

PAGE 101

doping profile results in a 5 d decrease in dynamic range. The sensitivity analysis indicates that the MDS is very sensitive to uncertainties of tether and element dimensions, junction depth and width of the piezoresistors, and less sensitivity to uncertainties of piezoresistor length. B 101

PAGE 102

Table 4-1. The candidate shea r stress sensor specifications. Low Speed Supersonic, High Re Hypersonic, Underwater Device 1 2 3 4 5 6 7 8 9 maxPa 5 5 5 50 50 100 100 500 500 minkHz f 5 5 10 10 50 50 100 100 200 max meL 1000 1500 1000 1000 1000 1000 500 500 500 min mtW 30 30 30 30 30 30 30 30 30 mtT 50 50 50 50 50 50 50 50 50 Table 4-2. Upper and lower bounds asso ciated with the sp ecifications in Table 4-1 Design Variables and -UB LB Flow Description mtL mtW meL mrL VBV -3cmSN minPa minkHz f 1 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 5 5 2 100 1000 30 40 100 1500 50 400 5 10 5e+18 2e+20 5 5 3 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 5 10 4 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 50 10 5 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 50 50 6 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 100 50 7 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 100 100 8 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 500 100 9 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 500 200 102

PAGE 103

Table 4-3. Optimization results for the cases specified in Table 4-1 (bold for active constraints). Parameter Case1 Case2 Case3 Case 4 Case5 Case6 Case7 Case8 Case9 maxPa 5 5 5 50 50 100 100 500 500 mtL 1000 1000 1000 991.2 343.6 348.7 308.8 500.4 500 mtW 30 30 30 30 30 30.7 30 30 30 meW 1000 1500 983.5 996.1 1000 993.3 499.1 250.2 100 mrL 228.5 228.5 228.5 228.5 98.8 99.9 88.6 126.8 117.7 VBV 10 10 10 10 6.8 6.8 6.5 7.6 6.0 WowP 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.07 kHzrf 9.8 6.60 10 10 50.53 50.01 130.15 104.07 231.11 SR 851 851 851 851 368 372 330 470 438 LR 149 149 149 149 94 94 89 105 102 VPaMS 3.65e-5 7.92e-5 3.54e-5 3.58e-5 6.64e -6 6.40e-6 1.47e-6 1.13e-6 4.20e-7 nVNV 21.1 21.1 21.1 21.1 11.0 10.97 10.95 11.19 9.54 minmPa 0.58 0.27 0.60 0.33 1.66 1.72 7.44 9.88 2.28e-2 dB DR 78.7 85.4 78.5 103.7 89.6 95.3 82.6 94.1 86.8 103

PAGE 104

Figure 4-1. Flow chart of design optimization of the piezo resistive shear stress sensor. Lt Wt We Tt VB Ns yj Wr Lr -1.5 -1 -0.5 0 0.5 1 1.5 2 dmin/dxi*xi/min Figure 4-2. Logarithmic de rivative of objective function min with respect to parameters (Case1). 104

PAGE 105

CHAPTER 5 FABRICATION AND PACKAGING The fabrication process and packaging of the side-implanted piezoresistive shear stress sensor are presented in this chapter, with the ai d of masks and schematic cross section drawings. A detailed process flow is given in Appendi x C, which lists all the process parameters, equipments and labs for each step. The detaile d packaging approach for wind tunnel testing is also presented. Fabrication Overview and Challenges The first generation of the shear stress sensor is fabricated in an 8-mask, silicon bulkmicromachining process. All the masks are generated using AutoCAD 2002 and manufactured in Photo Sciences, Inc (PSI). It is described in detail in the following sections. Some challenges in this process are addressed before starting the process flow: Side-implanted piezoresistors: boron is side implanted into the silicon tethers to form the piezoresistors with an oblique angle of normal to the top surface. The traditional piezoresistor is formed by top implantation. The doping profile for side-implantation is simulated via FLOOPS, and the accuracy of the profile n eeds to be judged only after device testing. o54 Trench filling: 50m-deep trenches were etched on the top surface to define the tethers. Trench filling is requ ired to obtain good photoresist coverage before subsequent deposition and patterning of the metallization layer. Junction isolation: the space between piezoresi stors and p++ interconnects should be larger than the isolation width to avoid p/n punch through, as discussed in chapter 3. Fabrication Process The fabrication process starts with a 100-mm (100) si licon-on-insulator (SOI) wafer with a 50m-thick 1~5 -cm n-type silicon de vice layer above a 1.5m-thick buried silicon dioxide (BOX) layer. The corresponding bac kground doping concentration is from to The total wafer thickness is 45. A brief overview of the process is as follows. The four side-implanted piezoresistors are first formed by boron oblique implantation. 15-32.510 cm 14-3510 cm 0 m 105

PAGE 106

The structure of the sensor is then defined by DR IE Si etch. Thermal dry oxide is grown for high quality passivation. Al-Si (1%) is deposited and patterned to form the bond pads. PECVD nitride is deposited as a moisture barrier layer. Finally, the structure is released from the backside via DRIE Si and RIE of the oxide and nitride. The process flow is broken down into 8 major steps as follows: a. The n-well formation: the fabrication begins with the formation of the n-well by a phosphorus blanket implantation ( Figure 5-1 (2)). An energy of 150 and a dose of are used to achieve a surface concentration of keV 12-24.010 cm 16-36.510 cm to control the spacecharge layer thickness of the reverse-biased p/n junction-isolated piezoresistors. b. Reverse bias contact: a 100 thin oxide layer is then deposited via plasma-enhanced chemical vapor deposition (PECVD) and patterned, then etched vi a buffered oxide etch (BOE) in preparation of the reverse-bias contact implant. This step al so creates alignment marks on the top surface. Phosphorus is th en implanted with energy of 80 and dose of to achieve a n++ region with a surface concentration of nm keV 13-29.010 cm 18-31.810 cm ( Figure 5-1 (4)). The device is then annealed at 1000 for minutes to drive-in the inpurities. C 450 c. Piezoresistor interconnects: the oxide is selectively remove d by BOE. Then, a two-step Ge preamorphization implant is performed to mi nimize the effect of random channeling tail caused by the subsequent high-dose boron implan tation [66], which provides a heavily doped Ohmic body contact. The preamorphization implant energies are 16 and respectively, and a dose of This preamorphization is to ensure no more than 2% of the implanted boron dose penetrates into the substrate [89]. Then boron is impl anted into the silicon with a dose of and an energy of 50 to provide Ohmic contacts ( 0keV 50 keV 15-210 cm 16-21.210 cm keV Figure 5-1 (5)). The resulting surface con centration and junction depth, jp x while taking into account the 106

PAGE 107

thermal budget of the entire process, are simulated by FLOOPS to be and 1 respectively. The interconnect region begins from the edge of the tether and distributes symmetrically along the cente rline of the tethers to minimize the sensitivity error, with a larger width on the end cap to decrease the resistan ce. The FLOOPS simulation file is given in Appendix D. 20-31.9610 cm m d. Nested mask release: a 1 oxide layer is deposited via PECVD and patterned via reactive ion etch (RIE) [90] to serve as a nested mask for the deep reactive ion etch (DRIE) [91] that defines the tether s and floating element ( m Figure 5-1 (7)). New alignment marks are also created in this step. e. Side wall etch and side wall implantation: the wafers are then patterned using the mask SIM ( Figure 5-1 (8)). To ensure good contact be tween the piezoresistor and the p++ interconnect, the SIM mask has a 4 overlap with the p++ inte rconnect on the edge of the tether, 10 overlap with the p++ inte rconnect on the end cap, and 4 overlap with sidewall. Prior to DRIE, the native oxide or oxide residues are et ched via BOE about one 1minute. The Si is then etch ed vertically to approximately deep by DRIE to form the trenches for the sidewall oblique implant, as shown in m m m 8 m Figure 5-2 (scanning electron microscope (SEM) top view). The trench width is set to 51.1 mtan548.5 m to achieve a 5 implant, where 54 is the implant tilt angle from the normal axis, and 1.1is the thickness of the oxide layer. The sidewall impl antation is restricted on the top 5 to ensure the silicon surface on which the boron implanted is smooth a nd avoid forming the current leakage path on the bottom [85]. This can reduce the m m m 1 f noise at low frequency [85] The basic recipes on STS DRIE system and Unaxis RIE sy stems are shown in Appendix E. 107

PAGE 108

The extruded oxide resulting from the DRIE is etched via BOE (6:1) for one minute, as shown via the scanning electron microscope image in Figure 5-3 This avoids the protruded oxide blocking the implant dosage to the side wall. Hydrogen annealing (1000 10 mTorr for 5 minutes) [92] is performed to smooth the scallops on the sidewa lls that arise from the DRIE process, which will improve the noise floor [25]. A oxide layer is thermally grown as a thin implant oxide layer on the sidewall, which must be accounted for in the thermal budget. C 0.1 m After a two-step Germanium pr eamorphization implant, boron is then implanted with an energy of a dose of (two times of the simulation dose to compensate the solubility loss at high dosage ) and an oblique angle of 54 to achieve a 5 shadow side wall implantation (shown in 50 keV 16-2210 cm m Figure 5-1 (9)). f. Tether definition: the oxide on the trench bottom is then etched via DRIE while the oxide on the sidewall is left to pr otect the doped sidewall, as shown in Figure 5-4 This is a timecontrolled process: an over-etch will expose silic on on the edge of the sidewall of the tether ( Figure 5-5 ), while an under-etch will create a silicon grass effect [93] after the subsequent DRIE silicon etch due to the oxide residues that acts as a micromask ( Figure 5-6 ). The channels/trenches are then etched via DRIE w ith the BOX as an etch stop, as shown in Figure 57 (note the rough surface is caused by the dicing saw) The tether sidewall oxide is then etched for two minutes by BOE (6:1). Subsequen tly, the wafers are annealed at 1000 for 60 min to drive in the boron to form the piezoresistors. A thin dry oxide layer was thermally grown at 975 as an electrical passivation layer. The temperature 975 is selected to avoid excessive diffusion and excessive compressive stress when the temperature is below 9 [94]. Meanwhile, the boron is segregated into the oxide from the silicon. C 0.1 m C C 50 C 108

PAGE 109

g. Metallization and nitride passivation: since there are 50m-deep trenches on the wafer for tether release, it is necessary to fill the trench to achieve good phot oresist coverage before subsequent wafer patterning. A two-step trench filling process is performed as follows: first, a thin layer of photoresist AZ1512 is coated and so ft baked, then a thick photoresist AZ9260 is coated and soft baked; second, the wafer is flood exposed for 300 seconds and developed using developer AZ400 until the surface is clear. Thus, the trench can be reduced from to only deep if following the above process once or twice. 50 m 5~6 m After filling the trenches with photoresist, the oxide is patterned and then etched via BOE (6:1) to open contact vias for Al sputtering. This step is very critical for the quality of the metal contact. Since the boron laden silicon dioxide etches much sl ower than the standard oxide etching ( 1000 Amin ), an over etch is required to remove a ll oxide to ensure an Ohmic contact. Any residual oxide left ov er will result in Schottky diode effect. A 1m-thick layer of Al-Si (1%) is sputtered and patterned via RIE to form the metal interconnects ( Figure 5-1 (12)). A 200-nm-thick, low-stress silicon nitride layer is deposited via PECVD to from a protective moisture barrier. The bond pads are exposed by patterning and plasma etching the silicon nitride via RIE. h. Backside release: to protect the device, the front side of the wafer is coated with a 10m-thick photoresist layer. The wafers are then patterned from the backsi de using front-to-back alignment. The structure is released from the backside using DRIE up to the BOX layer ( Figure 5-1 (14)), along with an oxide and nitride etch using RIE ( Figure 5-1 (15)). Finally, a postmetallization anneal is performed in forming gas (4% 96% ) at for 1 hour [95]. This annealing allows the aluminum to react with the native oxide to remove the tunneling oxide, and allow the hydrogen to passivate the interface tr aps. This improves the contact resistance and 2H 2N 450 C 109

PAGE 110

reduces the electrical nois e floor [25]. The fabricated device is shown in Figure 5-8 and the close view of the piezoresistors is shown in Figure 5-9 The trenches between each device were patterned and created during back side release, thus the die can be easily separated by tweezers. Sensor Packaging for Wind Tunnel Testing After fabrication, the individual die (6.) were then packaged in a custom printed circuit board (PCB) ( ) designed for modularity. The PCB layout was performed using Protel and was manufactured by a commercial ve ndor, Sierra Proto Express. The MEMS device die and PCB were then packag ed by Engent Inc. The MEMS die are flushmounted into a machined cavity in the PCB a nd sealed with epoxy at the perimeter. The aluminum bond pads are then bonded to gold pa ds on the PCB. Subsequent to the bonding process, the wire bonds are cove red by non-conductive epoxy to protect the wire bonds from the gas flow in the calibration wind tunnel or flow cell. The roug hness of the epoxy is less than and is located (3.2) downstream of the sensing element to mitigate flow disturbances. The PCB package is then flush-mounted into a Luc ite package, which in turn is flush mounted in an aluminum plat e to minimize flow disturbance. 2 mm.2 mm 20 mm mm 300 m mm Figure 5-10 shows the PCB embedded in the Lucite package. Copper wires (gauge 26) pass from underneath up through the vias in the PCB and are soldered to PCB via rings. The wire is reinforced by the glue on the backside of the Lucite package. An interface circuit board was designed for offset compensation and signal amplification, as shown in Figure 5-11 This board includes two sets of compensation circuitry: one for active bridge, another for dummy bridge. Each circuit has two amplifying stages: the first stage is used to null the amplified offset, a nd the second stage is to amplif y the compensated signal. The detailed description of the interf ace circuit for offset compensation is given in Chapter 6. This 110

PAGE 111

board is attached on the backside of the device package and supported by two screws that connect it to the Lucite packaging. The copper wires for the signal output and voltage supply from the Lucite plug are soldered to this board. There are eight BNC connectors for the amplified signal outputs and power supplies. 111

PAGE 112

Figure 5-1. Process flow of the side-implanted piezoresistive shear stress sensor. 112

PAGE 113

Figure 5-2. SEM side view of side wall trench after DRIE Si. Figure 5-3. SEM side view of the notch at the interface of oxide and Si after DRIE. 113

PAGE 114

Figure 5-4. SEM top view of the trench after DRIE oxide and Si. Figure 5-5. SEM top views of the trench af ter DRIE oxide and Si with oxide overetch. 114

PAGE 115

Figure 5-6. SEM top views of the trench with si licon grass through a micromasking effect due to oxide underetch. Figure 5-7. SEM side view of th e trench after DRIE oxide and Si. 115

PAGE 116

Figure 5-8. Photograph of the fabricated device. Figure 5-9. A photograph of the de vice with a close up view of the side-implanted piezoresistor. 116

PAGE 117

Figure 5-10. Photograph of the P CB embedded in Lucite package. Figure 5-11. Interface circuit board for offset compensation. 117

PAGE 118

CHAPTER 6 EXPERIMENTAL CHARACTERIZATION Preliminary electrical and fl uidic characterization were performed to determine the performance of the shear stress sensor and to partially compare to the analytical models discussed in Chapter 3. The expe rimental setup for sensor charac terization is described and then the results are presented. The experiments incl ude measurement of characteristics of p/n diode, system noise, sensor sensitivity and linearity, and frequency response. Experimental Characterization Issues There are two complicating issues in characterizing the sensors: the initial offset voltage output without shear stress applied and the temperat ure sensitivity of the bridge output. These two issues directly affect the measurement resolution and static sensitivity. Therefore, offset compensation and temperature compensation mu st be employed for the static calibration experiments. The motivation and methodology for offset compensation is discussed in the following paragraphs. The temperature compensation was not performed and will be discussed in Chapter 7. For a balanced Wheatstone bridge, the differentia l voltage output of the sensor is directly proportional to the applied shear stress. In re ality, the Wheatstone bridge is not perfectly balanced due to uncertainty in the fabrication process. As shown in Figure 6-1 the dc offset exists without applied shear stress, and is directly propor tional to the bias vo ltage. The offset is typically 10 mVV O or even larger in some device die. The optimization results in Chapter 4 indicate that the normalized sensi tivity of the sensor designs is 1 VVPa O Such a small sensitivity requires high gain amplification pr ior to being sampled by data acquisition board. However, a dc offset will cause amplifier saturation even at a relatively low gain. Therefore, it is imperative to minimize or eliminate the o ffset to maximize the dynamic range of the 118

PAGE 119

measurement system. An approach for the interface circui t readout is discussed as follows for dc offset compensation. The interface circuit consists of a precision programmable instrumentation amplifier AD625 and a high speed precision Op Amp AD 711 from Analog Devices [73], as shown in Figure 6-2 The gain of the AD625 is set by adjusting exte rnal resistors F R and G R and is given by 4FGRR 1 The AD711 acts as a unity buffer. Th e initial offset voltage goes through the amplifier AD625 with a set gain of 21. Then the amplified offset voltage is precisely controlled by adjusting the input of the AD711, which is pr ovided by a Stanford Research Systems SIM928 isolated voltage source [96]. SIM928 is an ultra low noise voltage source (10 at 1 k bandwidth) that provides a stable low-noise voltage reference with mV resolution. Unfortunately, there was an error in the second amplifier stage of the PCB and a decision was made to just proceed with AC shear stress cal ibrations to demonstrate proof of concept functionality. Vrms Hz Experimental Setup In this section, the experimental setup fo r the shear stress sensor characterization is discussed. A probe station is used to measure the current-volta ge (I-V) characteristics of the sensor. A plane wave tube (PWT) is then used to determine the sensor linearity, sensitivity and frequency response. Then sensor system noise is measured with dynamic calibration setup in the plane wave tube with speaker amplifier off. Electrical Characterization Electrical characterization in cludes measurement of the bridge impedance and leakage current of the junction-isolated devices, as well as the breakd own voltage. All measurements 119

PAGE 120

were made using an Agilent 4155C semiconductor parameter analyzer and a wafer level probe station. As discussed in Chapter 5, the p/n junctions are formed by the p-type piezoresistor and the p++ interconnects with the n-well. To ensure that the current flows en tirely through the p-type regions, the p/n junction must be reverse biased and the leakage current should be ne gligible. In this experiment, the reverse bias characteristics of the p/n junction were measured to determine the leakage current from the piezoresistors to th e n-type substrate. Th e resistance is extracted from the I-V characteristics of the piezoresistors in the p/n forward bias region. Dynamic Calibration The frequency response and linearity were deduc ed using Stokes layer excitation of shearstress in a plane-wave tube (PWT). This technique utilizes acoustic plane waves in a duct to generate known oscillating wall sh ear stresses [97]. This technique relies on the fact that the particle velocity of the acousti c waves is zero at the wall due to the no-slip boundary condition. This leads to the generati on of a frequency-dependent boundary layer thickness and a corresponding wall shear stress. Therefore, at a given location, the relationship between the fluctuating shear stress and acoustic pressure is theoretically know n. The acoustically-generated wall shear stress for the frequenc y range of excitation in this paper is approximated by [97] 2' 'jtkx wallpjv e c t a n h j (6-1) where is the amplitude of the acoustic perturbation, 'p 1j v is the kinematic viscosity, is the angular frequency, k c is the acoustic wave number, 2b is the nondimensional Stokes number and is the half height of the duct. b 120

PAGE 121

A conceptual schematic of the dynami cal calibration setup is shown in Figure 6-3 The plane wave is generated by a BMS 4590P compressi on driver (speaker) that is mounted at one end of the PWT. The PWT consists of a rigidwall 1x1 duct with an anechoic termination (a 30.7 long fiberglass wedge), which is respon sible for supporting acous tic plane progressive waves propagation along the duct [97]. The se nsor and a reference microphone (B&K 4138) are flush-mounted at the same axial position from the driver. The usable bandwidth for plane waves in the PWT is defined by the cut-on frequency of the first higher order mode which is 6.7 in air and in helium. The compensated output voltage from the AD625 interface circuit is ac-coupled and amplified 46 dB by the SR560 low noise preamplifier. A B&K PULSE Multi-Analyzer System (Type 3109) is used as the microphone power supply, data acquisition unit, a nd signal generator for the source signal in the plane wave tube. kHz 20 kHz Noise Measurement A noise measurement is necessary to determ ine the minimum detectable signal (MDS). The sensor is mounted on the sidewall of the plan e wave tube and the speaker amplifier is turned off. This provides a reasonable estimate of the en tire sensor system noise floor as installed in a calibration chamber. The compensated voltage output is amplified by the AD625 and the SR560 low noise preamplifier (ac coupled ), and then fed into the SRS 785 spectrum analyzer [98]. The spectrum analyzer measures the noise power spec tral density (PSD), us ing a Hanning window to minimize PSD leakage. The measured noise PSD includes the sensor noise and the setup noise, including noise from sources such as EMI, the amplifier, the spectrum analyzer, and the power supply. LabVIEW is used for data acquisition an d manipulation. The noise PSD is measured in three overlapping frequency spans from 10 to 1024. The settings for three frequency ranges are listed in Hz Hz Table 6-1 121

PAGE 122

Experimental Results Electrical Characterization As shown in Figure 6-4 I-V characterization results indica te a negligible leakage current (< ) up to a reverse bias voltage of -10 V. The reverse bias breakdown voltage for the P/N junction is around 20 V or greater ( 0.12 A Figure 6-5 ). I-V measurements of the diffused resistors across the Wheatstone br idge are shown in Figure 6-6 for a representative design in Table 6-2 One curve is for the resistors across the bias voltage port and ground, a nother is for the resistor s across the output ports and The nonlinearity of the I-V curve is obtained subtract ing the actual voltage in the VB-GND curve (or V1-V2) from a linear cu rve fit (fit between 1V 2V 0.5 V to 0.5 and extended to ), then normalizing by the linear curve and multiplyi ng by 100. The nonlinearity is shown in V 10 V Figure 67 The linear variation of current with voltage below 5 V (3% nonlinearity in Figure 6-7 ) indicates Ohmic behavior of the piezoresistors and p ++ interconnects. The average resistances across the bridge are 397 and 41 1 respectively, while the predicted value for the individual resistor is 1 k. The smaller than predicted resistances may due to the high implant dosage (double of the simulation value to a void solubility loss). The asymmetry of curve may be due to the Schottky effect. The as ymmetry may also be due to residual heating as the voltage was swept from -10 V to 10 V instead of performing two test s sweeping the voltage from 0 to 10V and 0 to -10 V. The root cause of this asymmetry re quires further study. V1-V2 Dynamic Calibration Results and Discussion The dynamic sensitivity and lineari ty of the sensor were test ed with a single tone of as a function of increasing sound pressure levels (SPL). The chosen frequency of is far enough below the expected resonan ce so that it is a reasonable approximation 2.088 kHz 2.088 kHz 122

PAGE 123

of the static sensitivity. In this measurement, the frequency span was with a frequency resolution of 32 H. 3000 linear averages with 0% overlap were taken to minimize the random error. The sensor wa s operated at bias voltages of 1.0, 1.25 Vand 1.5. This is substantially lower than the optimized bias volta ge of 10 V because elect ronic testing indicated nonlinearities in the current-voltage relationship at excitation voltages abov e 4.5 V from resistor self-heating. Any resistor self-heating will lead to temperature-resistive voltage fluctuations due to unsteady convective coo ling [38]. In other words, the direct sensor will behave somewhat like an indirect sensor. To avoi d this phenomenon, testing was limited to bias voltages of 1.5 and below. 0.2-6.4 kHz z V V V The dynamic sensitivity is the ratio of the differential sensor output voltage to the input wall shear stress. Ideally, the lateral displacem ent of the floating element will be solely a function of the acoustically genera ted wall shear stress. In practi ce, however, it is known that there will be an additional displacement due to the local pressure gradient forces generated by traveling acoustic waves across th e floating element [43]. The ma gnitude of the effective shear stress including pressure-gradien t effects for a purely-traveling acoustic wave in a duct is [43] 22 1 2wall effgff ft (6-2) The second and third terms of Equation (6-2) represent the error due to the fluctuating flow beneath the element and the net fluctuating pres sure force acting on the lip (assuming a square element). Accounting for the fact that the actual shear stress is proportional to f the magnitude of the error terms is proportional to f The second term of Equation (6-2) assumes that so that the flow underneath the elem ent can be approximated by fully-developed pressure-driven flow in a slot. For the current sensor, eL g 400 mg and Clearly, 1000 meL 123

PAGE 124

this approximation is invalid and the flow beneath the element is sufficiently complex and must be evaluated using computationa l techniques. Therefore, only an estimate for the pressure gradient force acting on the thickness can be provided. The maximum error for this term is ( 7.5 dB 2.4wall ) at the highest frequency tested, The error terms are also 6.7 kHz /2 out of phase with the actual shear stress. By adjusting the SPL from 123 dB to 157, the induced shear stress varies from to dB 0.04 Pa 2.0 Pa Figure 6-8 shows output voltages response to the shear stress variation at different bias voltages. The slopes of the plots shown in Figure 6-8 indicate the dynamic sensitivity of the sensor at different bias volta ges. For all bias cond itions, the sensors respond linearly up to and the sensitivities are 2.0 Pa 2.905 VPa 3.602 VPa and 4.242 VPa at bias voltages of 1.0 V, 1.25 V and 1.5 V, respectively. The normalized sensitivity is defined as the ratio of sensitivity to applied bias voltage. For a Wheatstone bridge without resist or self-heating, the normalized se nsitivity is a constant. If resistor self-heating is occurring, a power-law dependence on the pow er dissipation is expected. The slopes of Figure 6-9 are the normalized sensitivities at bias voltages of 1.0 V, 1.25 V and respectively, which are 1.5 V 2.905 VVPa 2.882 VVPa and 2.828. The predicted normalized sensitivity is VVPa 3.65 VVPa Note that for Figure 6-9 the initial offset voltages were subtracted for normalized slope comparison purposes. The close match in normalized sensitivities (<3% vari ation) indicates that the sensor is responding solely to the piezoresistive effects and not unsteady convective cooling. This piezoresistive effect is a combination of shear stress sensitivity, pressure gradient sensitivity and normal pressure sensitivity. 124

PAGE 125

The frequency response at a bias voltage of 1.5 was also investigated in this experiment. For this test, the generator is set to a random signal with a span of and a center frequency of to ensure that all harmonics up to 6 kH are captured. A 200 line FFT is used corresponding to frequency resolution of At each measurement frequency, 2000 linear averages are taken with 0% overlap. The input shear stress is desired to be The theoretical SPL for each measuremen t frequency obtained via Equation V 6.4 kHz 3.4 kHz z 32 Hz 0.3 Pa (6-1) By adjusting the SPL at specific frequency, the targ et shear stress is then achieved. The normalized frequency res ponse function of the shear stre ss sensor is given as [43] out wallVf Hf f V (6-3) where is the sensor output with a known input, outVf wall f is obtained via Equation (6-1) and V is the flat band sensitivity. For this experiment, the sensitivity at from the linearity test was used for normalization. 2.088 kHz Figure 6-10 demonstrates the magnitude and phase of the actual frequency response function of the shear stress sensor for a nominal input shearstress magnitude of 0.. The gain factor is flat and is between 3 Pa 3.01 dB to for this test. The phase is flat up to It is noted that the ga in factor at frequency of is not 0 d, which may be due to the setup and temperature variation in these two measurements. These results ar e not corrected for nonidealities in the anechoic termination which results in a finite reflected wave [97]. In addition, there is some su spicion that the results above are corrupted by the scattered evanes cent field near the termination. Regardless, there is no apparent resonance in this sensor up to 0.09 dB 4.552 kHz 2.088 kHz B 4.552 kHz 6.7 kHz To check the wave reflection effect on the measurement, the two-microphone method [99] is used to measure the reflection coefficient, as shown in Figure 6-11 The frequency spans from 125

PAGE 126

0.2 Hz to 6.4 kH. The FFT line is set to 400 gi ving a frequency resolution of 16 H. 1000 linear averages with 0% overlap are taken. Th e results indicated that the magnitude of the reflection coefficient is comparativel y large when the frequency is below 1 k. Therefore, the frequency in the measurement for both lin earity and frequency response are above 1 k to minimize the uncertainty. z z Hz Hz The lower end of the dynamic range of the se nsor is ultimately limited by the device noise floor. The output-referred noise floor of the sensor and measurement system is shown in Figure 6-12 for a bias voltage of 1.5. As expected, the noise spectrum is dominated by V 1 f noise indicating that the signal-to-noise ratio for this sensor is a strong functi on of frequency. At (with 1 Hz bin) the output-referred noise floor of the sensor a nd measurement system is 1 kHz 48.2 nV Hz which corresponds to the minimum detectable shear stress of 11.4 m. Pa Summary Preliminary electrical and dynamic characterization and the noise determination are presented to demonstrate device functionality. At a bias voltage of 1.5, the dynamic characterization of the device reveal ed a linear response up to at least and a flat response up to the frequency testing limit of The theoretically predic ted resonant frequency is Noise floor measurements indicate that V 2.0 Pa 6.7kHz 9.8 kHz 1 f noise dominates and the minimum detectable shear stress at 1 kHz is 11. Therefore, the experimentally verified dynamic range is 11 m. The theoretically predicted upper e nd of the dynamic range at 3% static non-linearity is 5 Pa. The upper ends of the dynamic range and bandwidth, however, could not be verified due to constraints in the calibration apparatus. A summary of the experimental results compared to the predicted results for a bias voltage of 1.5 V are listed in .4 mPa Pa-2 Pa Table 6-4 The normalized sensitivity is close to the predicted de sign value, but resistor heating precluded using 126

PAGE 127

higher bias voltages, thus lowering th e maximum allowable sensitivity by 16.5 dB. Furthermore, the noise floor is roughly a factor of 7 higher than predicted. This may be due to the noise floor measured is the total system noise, which includes setup noise and sensor noise, whereas the predicted valu e is just due to the se nsor and the AD 625 circuit. There are also substantial differences in the pr edicted versus realized bridge impedance which means that the voltage noise of the resistors may al so be higher than predicted. 127

PAGE 128

Table 6-1. LabVIEW settings for noise PSD measurement Frequency Range (Hz) Bin Width ( ) Hz Number of Averages 10-200 0.25 2300 200-1600 2 4000 1600-102400 128 30000 Table 6-2. The optimal geometry of the shear stress sensor that was characterized. Parameters Design Values Target Shear Stress maxPa 5 Tether Length mtL 1000 Tether Width mtW 30 Tether Thickness mtT 50 Floating Element Width meW 1000 Piezoresistor Length mrL 228.5 Piezoresistor Width mrW 5 Piezoresistor Depth mjy 1 Table 6-3. Sensitivity at different bias voltage for the tested sensor. Bias Voltage (V) Sensitivity mVPa 1.5 0.27 2.95 0.71 3.1 0.93 4.8 3.0 128

PAGE 129

Table 6-4. A comparison of the predicted versus realized perfor mance of the sensor under test for a bias voltage of 1.5V. Parameters Theoretical Value Experimental Result Normalized Sensitivity VVPa 3.65 2.83 Noise Floor nV 6.5 48.2 MDS mPa 1.2 11.4 Bandwidth kHz 9.8 >6.7 Resistance 1000 397 maxPa 5 >2 129

PAGE 130

0 1 2 3 4 5 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 Bias Voltage( V )Offset Voltage ( V ) Figure 6-1. The bridge dc offs et voltage as a function of bias voltages for the tested sensor. Figure 6-2. An electrical schematic of th e interface circuit for offset compensation. 130

PAGE 131

Figure 6-3. A schematic of the experimental setup for the dynamic calibration experiements. -10 -8 -6 -4 -2 0 2 -2 0 2 4 6 8 10 Bias Voltage ( V )Current ( A ) Reverse Bias Forward Bias Figure 6-4. Forward and reverse bias characterist ics of the p/n junction. 131

PAGE 132

-20 -15 -10 -5 0 -10 -8 -6 -4 -2 0 2 Bias Voltage ( V )Current ( A ) Figure 6-5. Reverse bias breakdow n voltage of the P/N junction. -10 -5 0 5 10 -30 -20 -10 0 10 20 30 Bias Voltage( V )Current( mA ) y = 2.52*x 0.01 R2 = 0.9992 y = 2.43*x + 0.273 R2 = 0.9990 VB-GND V1-V2 Linear Fitting VB GND Linear Fitting V1 V2 Linear Fitting Figure 6-6. I-V characteristic s of the input and output term inals of the Wheatstone bridge. 132

PAGE 133

-10 -5 0 5 10 -2 0 2 4 6 8 10 12 Voltage (Volts)Nonlinearity (%) V1-V2 VB-GND Figure 6-7. The nonlinearity of the I-V curve in Figure 6-6 at different sweeping voltages. 0 0.5 1 1.5 2 0 1 2 3 4 5 6 7 8 9 Shear Stress (Pa)Output Voltage ( V) y = 3.602*x + 0.01884 y = 4.242*x + 0.0231 y = 2.905*x + 0.004146 VB=1 V VB=1.25 V VB=1.5 V Figure 6-8. The output vo ltage as a function of shear stress ma gnitude of the sensor at a forcing frequency of 2.088 kHz as a function bias voltage. 133

PAGE 134

0 0.5 1 1.5 2 0 1 2 3 4 5 6 Shear Stress (Pa)Normalized Output Voltage ( V/V) y = 2.905*x 0.3113 for VB=1.0V y = 2.882*x 0.2964 for VB=1.25V y = 2.828*x 0.2914 for VB=1.5V VB=1.0 V VB=1.25 V V-B=1.5 V Linear Fitting Figure 6-9. The normalized output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 kHz for several bias voltages. 1 2 3 4 5 6 -10 0 10 Frequency (kHz)|H(f)| (dB) 1 2 3 4 5 6 -50 0 50 Frequency (kHz)Phase (Deg) Figure 6-10. Gain and phase factors of the frequency response function. 134

PAGE 135

1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 |R|Freq [kHz] 1 2 3 4 5 6 -200 -100 0 100 200 Phase [deg]Freq [kHz] Figure 6-11. The magnitude and phase angle of th e reflection coefficient of the plane wave tube. 135

PAGE 136

101 102 103 104 105 100 101 102 103 Noise Floor (nV/Hz)Frequency (Hz) System "Thermal Noise" System Noise Figure 6-12. Outputreferred noise floor of the measurement system at a bias voltage of 1.5V. 136

PAGE 137

CHAPTER 7 CONCLUSION AND FUTURE WORK Summary and Conclusions A proof-of-concept micromachined, floating el ement shear-stress sensor was developed that employs laterally-implanted piezoresistors for the direct measurement of fluctuating wall shear stress. The shear force on the element induces a mechanical stress field in the tethers and thus a resistance change. The piezoresistors are arranged in a fully-active Wheatstone bridge to provide rejection to common mode disturbances, su ch as pressure fluctuat ions. A dummy bridge located next to the sensor is used for temperature corrections. The device modeling, optimal design, fabrication process, packaging and comprehensive calibration were presented. Mechanical models for small and large defl ection of the floating element have been developed. These models are combined with a pi ezoresistive model to determine the sensitivity. The dynamic response of the shear stress sens or was explored by combining the above fundamental mechanical analysis with a lumped-element model. Finite element analysis is employed to verify the mechanical models and lumped-element model results. Dominant electrical noise sources in the piezoresistive shear stress sensor, 1 f noise and thermal noise, together with amplifier noise, are considered to determine the noise floor. These models are then leveraged to obtain optimal sensor designs for m easuring shear stress in se veral flow regimes. The cost function, minimum detectable signal (MDS) formulated in terms of sensitivity and noise floor, is minimized subject to nonlinea r constraints on geometric dimensions, linearity, bandwidth, power, resistance, and manufacturing constraints. The optimization results indicate that the predicted optimal device performance is improved with respect to existing shear stress sensors, with a MDS of O(0.1 mPa) and dyna mic range greater than 75 dB. A sensitivity 137

PAGE 138

analysis indicates that the devi ce performance is most respons ive to variations in tether geometry. The process flow used an 8-mask bulk micromachining process, involving PECVD, thermal oxidation, wet etch, sputtering, DRIE and RIE fabrication techniques. After fabrication, the die was packaged for wind tunn el testing in a custom printe d circuit board for modularity. An interface circuit board was designed for amplification and offset compensation. Then the sensor was calibrated electrically and dynamically. Electrical characterization indicates linear junction-isolated resistors, and a negligible leakage current (<0.12) for the junction-isolated diffused piezoresistors up to a reverse bias voltage of -10 V. Using a known acoustically-excited wall shear stress for calibration at a bias voltage of 1.5, the sensor exhibited a sensitivity of a noise floor of A V 4.24 V/Pa 11.4 mPa/Hz at 1 kHz, a linear response up to the maximum testing range of and a flat dynamic re sponse up to the testing limit of6.7 kH. These results coupled with a wind-tu nnel suitable package are a significant first step towards the development of an instru ment for turbulence meas urements in low-speed flows. The system noise is 2 Pa z 48.2 nVHz at 1 k (with 1 Hz bin), and is roughly 7 times higher than predicted. Static heating lim itations limited the maximum bias voltage to 1.5 instead of 10. Hz V V Suggestions for Future Work Future work should focus on the comprehensive characterization of the sensor to determine absolute performance and to compare against all of the theoretical predictions. An uncertainty analysis of all experime nts and accurate measurement of the sensor geometry are required to enable this comparison. Specifically, a temperatur e compensation approach must be realized that will enable the static calibration of the sensor as well as any dc measurement application. The 138

PAGE 139

resonant frequency of the sensor s must be determined. Sensitiv ity to vibration and pressure fluctuations must also be determined. Detailed noise measurements that isolate the contribution from the piezoresistor should be carried out. Finally, the flow around the floating element will be investigated via numerical si mulations to provide an improved estimate of pressure gradient induced errors. In the following subsection, several suggestions for carrying out these measurements are discussed below. Temperature Compensation The sensitivity of the shear stress sensor chan ges with temperature due to the variation of the piezoresistive coefficient with te mperature, as indicated in Equation (3-23) and (3-24) In sensor static calibration in a 2-D laminar cell, the sensitivity is de fined as the slope of the curve of voltage output versus shear stress. However, due to the temperature effect, the output voltage is a function of shear stress and temperature. Thus the temperature induced voltage output should be subtracted from the ac tive bridge voltage output. For the identical active and dummy Wheatstone bridge, the temperature effect on them should be same Therefore, the temperature effect on the active bridge in the static calib ration can be removed by subtracting the voltage output of the dummy bridge. Unfortunately, the active bridge and dummy br idge are not identical due to Wheatstone mismatch. So the voltage output dependence of the temperature need to be measured for both active bridge and dummy bridge. The output voltage of the active bridge is a function of shear stress and temperature variations, while the du mmy bridge depends on temperature variation only. The measured output volta ges in the laminar flow are ,awVT for the active bridge and for the dummy bridge, respectively. The sl ope of the voltage vs. temperature curve is dVT TaS 139

PAGE 140

for active bridge and for dummy bridge. In the static calibration, th e output voltage dependence of shear stress is given as TdS ,awawaVVTV T (7-1) Assuming that the slope of the curve remains constant and they are given as, vs. ToV 0 0 aa Ta ddVTVT S VTVTS T d (7-2) Substituting from Equation aVT (7-1) into (7-2) and rearranging it, the shear stress dependent output voltage is obtained as 0,Ta awawa dd TdS VVTVTVTVT S 0 (7-3) where 0 aVT is the initial voltage value at room temperature. The Equation (7-3) indicates that and must be obtained in order to get TaS TdS awV Preliminary experiments prior to employing dc offset nulling were performed to determine the temperature sensitivity. Unfortunately, the large dc offset limited the quality of the results. The ex perimental set up is as follows. The voltage output dependence of temperature variation is conducted in two bath settings. Both bathes are filled with DI water. The out er bath is the chamber of Isotemp refrigerated circulator, and the inner bath is glass beaker. The packaged sensor is sitting on the top of the beaker. The beaker is used to protect the se nsor from flow circulat ion disturbance. The compensated voltage output is connected to a HP34970A data acquisition unit and DAQ card. A HP34970A digital voltage meter is used to minimize the 60 noise. LabVIEW is used for data acquisition. Hz 140

PAGE 141

Static Characterization Initially, we attempted to statically characte rize the sensor, but the temperature sensitivity and dc offset issues prevented any meaningful resu lts. The goal of the static characterization is to verify the sensor design and characterize th e sensitivity and linearity. After temperature compensation and dc nulling have been achieved, a static calibration can be performed. The flow cell design is such that an ideal one-dim ensional fully developed incompressible laminar flow exists between two semi-infinite parallel plates (Poiseuille flow between two parallel plates). For this case, the pressure drop is constant and the wall shear stress is given by the theoretical relation [7] 2whdP dx (7-4) where is the height of the channel in meters and P is pressure in Pascals. Detailed setup information can be found in [34]. h The incompressible flow is first verified be fore the sensor static calibration. The incompressible flow exhibits a linear pressure drop versus length for wall shear stress up to which is a necessary assumption for Equation 2 Pa (7-4) The pressure measurements are carried out using the Scannivalve pressure measurement system. This multiplexing valve system allows the pressure taps to be reached sequent ially to measure pressure drop between the first pressure tap and other taps downstream. The in let flow rate is regul ated using a mass flow controller (GFC4715). A linear pressure drop versus length is displayed in Figure 7-1 Figure 7-2 shows the experimental setup for the st atic calibration of the wall shear stress sensor. The sensor is flush-mounted on one wa ll of the laminar flow cell and oriented for measuring wall shear stress in th e flow direction. The corresponding pressure drops across two pressure taps and is measured using a differential pre ssure gauge, Heise pr essure meter. 1P 2P 141

PAGE 142

The voltage output is first fed into the compensa tion circuit. The compensated signal is then supplied to a HP34970A preci sion digital voltage meter to elim inate 60Hz noise from the power supply by averaging. The mass flow rates are controlled automatically by LabVIEW to obtain different pressure drops and co rrespondingly wall shear stress. LabVIEW is also used for data acquisition and manipulation. Noise Measurement In order to determine the isolat ed resistor noise characteristic s, the sensor is placed in a double-nested Faraday Cages to improve the elec tromagnetic interference (EMI) reduction [98]. The compensated voltage output is amplified by a SR560 preamplifier, a nd then fed into the spectrum analyzer (SRS785). The spectrum anal yzer (ac coupled) measures the noise power spectral density (PSD), using a Hanning window to avoid PSD leak age. The noise PSD of the sensor is obtained by subtracting the setup noise PSD from the total measurement noise PSD. The setup noise sources include EMI and noise from the amplifier, spec tra analyzer, and power source. Recommendations for Future Sensor Designs Based on lessons learned during the first gene ration shear stress sensor fabrication and characterization, there are several issues that need to be addressed in future designs. Specifically, issues regarding resistor self-heating and pressure sens itivity need to be addressed. In the sensor calibration, piezoresistor self-heating was clearly present when the dissipated power was greater than 10. A study of the normalized sens itivities indicated that selfheating could be avoided all together for a power dissipation limit of Therefore, the power dissipation limit in the design op timization should be decreased from 100 down to to avoid resistor self heating. The power limit will be a function of the tether geometry, but the order of magnitude in power reduction will provide a better estimate of appropriate mW 5.7 mW mW 10 mW 142

PAGE 143

biasing conditions for design purposes. A detailed nume rical study of the re sistor heating may also provide insight into this phenomenon, but this may be challe nging due to the complexity of the convective boundary conditions at the tether surface. For a balanced Wheatstone bridge, pressure fl uctuations should not affect the voltage output. Preliminary pressure calibrations, however, indicate that the pressure sensitivity is only lower than the shear stress sensitivity. In addition to achieving better control of the resistor implant process to balance the bridge, this can be mitigated by extending the sideimplanted resistor all the way down tether thic kness. The fabrication process should change correspondingly to protect the botto m of the piezoresistor with a high quality passivation. In current sensor design, the piezoresistor is implanted on the top of the tether thickness to avoid resistor current leakage. So in the fina l backside release step, the BOX layer was removed to release the structure a nd the tether bottom is exposed to the flow without any protection. This will cause sensitivity drifting if the piezoresistor is implanted on the whole tether thickness. A process flow must be designed to realize an electrically passivate d resistor that extends to the bottom of the resistor thickness. 10 dB O 5 m In general, improved test structures are need ed to provide additional information about the side-planted resistors. Specifically, a test struct ure must be added into the mask design to enable the measurement resistor doping profile via s econdary ion mass spectroscopy (SIMS). In addition, providing additional bond pads for each resistor will permit a resistor trim based approach to bridge balancing a nd temperature compensation [60]. 143

PAGE 144

1 2 3 4 5 6 7 20 40 60 80 100 120 140 Length (Inch)Pressure Drop (Pa) Testing Data linear Fitting Figure 7-1. Pressure dr ops versus length between taps in the flow cell. Piezoresistive Shear Stres Sensor P1P2 L Amplifier Mass Flow Controller SourceMeter u(y)Flow Cell Gas Pressure Meter Voltage MeterdPVolts DAQ PC (LabView) Compensation Circuit Figure 7-2. Experimental se tup of static calibration. 144

PAGE 145

APPENDIX A MECHANICAL ANALYSIS A clamped-clamped beam with a central point force and a distributed pressure load is shown in Figure A-1 (a). This is a second order stat ically indeterminate problem. Euler Bernoulli beam theory is used to predict the linear, small deflection behavior and Von Krmn strain is included in the nonlin ear, large deflection models. Two methods, an energy method and an exact analytical method, ar e used to solve the large de flection problem. Using EulerBernoulli beam theory, the stress distribution is also derived. Small Deflection Equilibrium equations may be written base d on the free body diagram of the symmetric structure, Figure A-1(b). The relatio nships between the resultant forces, A R and B R point load and distributed load Q are thus P 2AB t R RPQL (A-1) where 2weePWL wtQW and w is the wall shear stress. The nonlinear differential equation governing the beam deflecti on caused by bending is given as [82] 22 32 2() 1 x dwxdx E I dwdx M (A-2) where is the deflection in the direction, wx z E is the Youngs Modulus, I is the area moment of inertia given as 312ttITW and x M is the resisting moment in cross of x Writing the equation for moment equilibrium, 0DM yields 22xAA M MRxQx (A-3) 145

PAGE 146

where A M is the resisting moment, and A B M M due to the symmetry of the structure. Assuming the rotation dwdx is very small, Equation (A-2) is simplified to 2 2() x M dwx dxEI (A-4) Integrating Equation (A-4) yields the rotation and deflection of the beam along its length, 23 1111 26AAdwx M xRxQxc dxEI (A-5) and 2 34 1111 () 2624A AMx wx RxQxcxc EI 2 (A-6) where and are constants. There are three unknown quantities in Equations 1c 2c (A-5) and (A-6) A M and Therefore, three boundary conditions should be employed, 1c 2c 00 (clamped) w (A-7) 0 0 (clamped) dw dx (A-8) and 0 (symmety)tdwL dx (A-9) Substituting the above boundary conditions and A R from (A-1) into (A-6) one obtains 120 cc (A-10) and 211 43At t M PLQL (A-11) The displacement is then obtained by substituting Equation wx (A-10) (A-11) and momentum of inertia 312ttITW into (A-6) 22 34 t 338282, 0x 4w eettt eett t ttwx WLLWLxWLWLxWx EWT L (A-12) 146

PAGE 147

The maximum deflection at the center of the beam is given as 32 1 4weet tt Lt tteeWLLWL wL E TWWL (A-13) Large Deflection-Energy Method In a large lateral deflection, the beam experi ences bending and stretchi ng. The total strain is composed of bending and stretching strain [42] tbendingstrenching (A-14) where bending 2 2dw y dx y is the position upward. The axial strain at 2tyW is given as [100] 21 2adudw dxdx (A-15) The total change in beam length is given by 2 22 001 2LL tt adudw L dx dx dxdx (A-16) The integration of the first term is zero due to the clamped-clamped boundary condition. The axial stain is the total change in beam le ngth divided by the total length of the beam 2 2 01 24L t strentching ttLdw dx LLdx (A-17) The total strain is obtained as 2 2 2 2 01 4L t t tdwdw y dxLdx d x (A-18) For large deflection, a trial function in the form of a cosine is assumed, as it automatically satisfies the doubly clamped boundary condition and is a maximum at the center of the beam. The trial function is thus 147

PAGE 148

1cos 2t NL tLx wx L (A-19) where N L is the maximum deflection at the center of the beam. Substituting this model into (A-18) yields sin 2t NL ttLx dw dxLL (A-20) and 2 2 22cos 2t NL ttLx dw dxLL (A-21) Substituting Equation (A-20) into Equation (A-18) yields 22 2cos 21t NL NL t ttLx y LL 2 26tL (A-22) The strain energy density is given as 2 22 2 0 2 011 cos 222 16t t NL NL t ttLx UdEEy LLL 2 2 t (A-23) The strain energy is then obtained 2 2 0 002WL tt t tET UUdV dxdy (A-24) The total strain energy is obt ained by integrating Equation (A-24) to yield 24344 396256NLtNLt t ttW UET LL 3W (A-25) Based on the principle of virtual work, the total potential energy W is equal to the stored strain energy minus the work done by the external force K WUK (A-26) where K is given by 148

PAGE 149

2 01cos 2L t t NL NL t tLx KPQ dxPQL L (A-27) The equilibrium configuration is that in which the potential energy is minimized. The minimum is obtained when 4334 331 0 48642NLtNLt tw e ttWW dW ET WLWL dLL e w t t (A-28) Rearranging Equation (A-28) yields 23 442 1 96128 4NL wee ttt NL tte eWLWLL WETWL tW (A-29) Simplifying the above equation, 41 96 and 43 1284 yields an approxima te large deflection solution, 232 3 11 44NL wee ttt NL tte eWLWLL WETWL tW (A-30) Large Deflection-Analytical Method For large deflection, axial force in the beam is not zero as in the small deflection model, and serves as a constitutive equation in the m odeling analysis. Since the beam is symmetric, only half of the beam is analyzed, as shown in Figure A-3 For large deflections, taking axial force into account, the differen tial equation governing the b eam deflection caused by bending is given as aF 2 2() ()dwx E IM dx x (A-31) where the slope of beam caused by large deflection is assumed 1 dwdx and therefore 2dwdx is negligible. The moment M x is given by 149

PAGE 150

2 01 () ((0)()) 22aP M xQxxMFwwx (A-32) where 0 w is an unknown constant. Substituting Equation (A-32) into Equation (A-31) yields 2 2 0 2()1 () (0) 22adwx P EIFwxQxxMFw dx a (A-33) The above equation can be solved as a superposition of one general solution and a particular solution nw s w ()()()nswxwxwx (A-34) 12where ()Csinh()cosh()nwxxCx and 2 ()swxaxbxc assuming =aFEI Substituting s w into Equation (A-33) a, b, and c are obtained as 0 2 aQ a = and c = (0) 2F2aaM PQ bw FF aF Equation (A-34) can be rewritten as 2 0 12 2()sinh()cosh() (0) 22aaaaM QPQ wxCxCxxxw FFFF (A-35) for which the boundary conditions are: 0 =0 dw dx (A-36) () =0tdwL dx (A-37) and 0twL (A-38) For large deflection, the axial strain at 2tyW is nonlinear and is given as 2 01 2 x a xdu F dw dxdxEEA (A-39) 150

PAGE 151

where Integrating the above equation yields ttATW 2 0 01 2L t a tdu EA dw F dx Ldxdx (A-40) The first term in the integration is zero due to the doubly clamped boundary condition. Axial force in the neutral axis aF 2tyW is then obtained as 2 02L t a tEAdw F dx Ldx (A-41) There are five unknown variables: and thus five boundary conditions are needed to solve for these unknown variables. However, only three boundary conditions 120,,,,aCCFM (0)w (A-36) (A-38) and one constitutive equation (A-41) are available. Another condition is 00 ww The problem is indeterminate and an iterative tec hnique must be used to find the final result. First, we applied boundary conditions (A-36) (A-38) and the constitutive equation (A-41) into Equation (A-35) and solve it to get the maximum defl ection as a function of the axial force in the neutral axis, The detailed procedure for solving th is problem is given in the following. aF Substituting (A-35) into boundary conditions (A-36) and (A-37) yields 121 and cosh() 2 sinh()22t aatPP CCQ L FFL tP L (A-42) Substituting and into 1C 2C (A-35) and setting 0 x yields 0 21 cosh() sinh()22t tQP P t M QL L L (A-43) Substituting 0 M from (A-43) and and from 1C 2C (A-42) into (A-35) yields 2cosh()1 sinh() cosh() (0) 2 sinh()22 22tt aat aaPxP PQ P wx x QL Lxxw FFL FF (A-44) 151

PAGE 152

Substituting (A-38) into (A-44) yields deflecti on at the center, 2cosh()1 (0)sinh() cosh()+ 2 sinh()22 22tt ttt aat aLQ PP P wLQ LL FFL F t aL P L F (A-45) Derivative Equation (A-44) to obtain 1 sinh() cosh() cosh() 2sinh()22 2 tt atdwx PxP P xQ LLQ x dxF L P (A-46) Secondly, we solve the ma ximum deflection equation (A-45) by iterating An initial value is selected randomly and the fo llowing steps are performed to obtain the maximum deflection, aF -4 aF=10 Pa 0 w 1) Substitute into aF (A-46) to get dw dx where Fa EI 2) Substitute dw dx into (A-41) to obtain new aF 3) Repeat 1), 2) until the relative error 11FaFaFa16nnne 4) Substitute into aF (A-45) to find the maximum deflection 0 w Stress Analysis The bending stress along a beam (shown in (A-3) ) is given as [82] z x z M yF A I (A-47) where z I is the moments of inertia for the axis, and z 312zttITW In small deflection, the axial force A free body diagram of the clamped b eam is shown based on the discussion 0aF 152

PAGE 153

in the small deflections section, where A R and A M are obtained from Equation (A-1) and (A-11) respectively. The moment for a certain length from the edge of the beam is obtained as, 21111 4322zttt 2 M PLQLPQLxQx (A-48) Substituting Equation (A-48) into (A-47) and simplifying the equa tion to obtain the bending stress along the beam 0t x L0y at 2 2263 33 42weet tt tt tt x tt ee eeteetWLLWLWLWL x WTWLWLLWLL x (A-49) Effective Mechanical Mass and Compliance In this section, the mechanical lumped para meters for a clamped-clamped beam are found. These parameters include lumped compliance obt ained via the storage of potential energy and lumped mass obtained via the storage of kinetic en ergy. These results are used in Chapter 3 to develop the lumped element model of a laterally diffused piezoresistive shear stress sensor. Recall that the lateral disp lacement and maximum displacement of the clamped-clamped beam in small deflection given in Chapter 2, 22 34 3()38282 (0) 4w eett eett t t ttwx WLLWLtxWLWLxWxxL EWT (A-50) and 312 4weet tt t tteeWLLWL wL E TWWL (A-51) The kinetic co-energy K EW of a rectilinear system with a total effective mass m moving with velocity uis given as, *1 2KEWm 2u (A-52) For a simple harmonic motion, the velocity a nd displacement of the beam are related by 153

PAGE 154

uxjwx (A-53) where is the frequency and t t uL. ux is then expressed as jwL t twx uxuL wL (A-54) For an infinitesimal element on the beam with a mass of sittWTdx the kinetic co-energy K EdW is calculated using Equations (A-52) and (A-54) to be 2 *2 2 21 22sittt KE sitt tWTuL dWWTux wxdx wL (A-55) where s i is the density of silicon. Integrating Equation (A-55) over the beam gives the total kinetic co-energy of the system, 2 ** 2 2 002LL tt sittt KE KE tWTuL WdWwx wL ( ) dx (A-56) The reference point is t x L which corresponds to the maximum deflection of the beam twL The distributed deflectio n of the beam can be lumped into a rectilinear pi ston by equating the kinetic energy obtained in Equation (A-56) to the kinetic energy of th e rectilinear piston of mass tme M 22tmet KE M uL W (A-57) Equating Equation (A-57) and (A-56) yields effective mechanical mass as 2 2 02L t sitt tme tWT M wxdx wL (A-58) Since the velocity of the plate is tujwL the effective mechanical mass of the device is the sum of the mass of th e plate and the effective m echanical mass of the beam, 154

PAGE 155

meptmesieettme M MMLWTM (A-59) The strain energy stored in the beam due to its deflection can be expressed as 2 2 2 0()L t SEdwx WEId dx x (A-60) The strain energy of an equivalent spring is given by 211 2SE t meWw C L (A-61) where is the mechanical compliance of the beam. Equating Equation meC (A-61) and (A-60) yields 2 2 2 2 0() 2t me L twL C dwx E Id dx x (A-62) Substituting and in Equation wx twL (A-50) and (A-51) into (A-59) and (A-62) yields 23 2149422381024 1 315315315 12tt tt tt ee ee ee mesieet tt eeWLWLWL WLWLWL MWLT WL WL (A-63) and 2 3 212 1 2 64 14 15tt ee t me tt tt tt ee eeWL WL L C ETW WLWL WLWL (A-64) 155

PAGE 156

x y z Figure A-1. The clamped beam and free body di agram. a) Clamped-clamped beam. b) Free body diagram of the beam. c) Free body diagram of part of the beam. FaP/2 Q Lt M0 Figure A-2. Clamped-clamped beam in large deflection. My MAV x D A RAQ x=0 (a) (b) Figure A-3. Clamped-clamped beam in sma ll deflection (a) and free body diagram of the clamped beam (b). 156

PAGE 157

APPENDIX B NOISE FLOOR OF THE WHEATSTONE BRIDGE For a Wheatstone bridge shown in Figure B-1 assuming 1234 R RRRR we get 12BVV therefore the voltage across each resistor is 2RBBBVVVV 2 (B-1) The current through th e resistor is 2B RV I R (B-2) Assuming the noise sources are uncorrelated, the mean square noise can be solved as a superposition of the mean square thermal noise, the 1 f noise, and the amplifier noise. For thermal noise, the equivalent noise model is given in Figure B-2 The rms thermal voltage is given as 22 ,121 23 4444nthermal B B BVEEkTRRfkTRRfkT Rf (B-3) For 1 f noise, the equivalent noise model is given in Figure B-3 The mean square current noise is 2 2 2 1 11lnHR c I f I Nf (B-4) The mean square voltage noise 2 1 E is obtained as 2 222 11212EIIRR (B-5) Substituting Equation (B-4) and (B-2) into (B-5) to obtain 22 2 2 22 11 1121 22 2 22 12 22 11ln ln =ln ln 44HR HR cc HB HB ccIfIf ER NfNf VfVf 2R R R NRfNRf (B-6) 157

PAGE 158

Rearrange the above equation to get 2 2 2 1 1 =ln 8HB cVf E Nf (B-7) The rms 1 f voltage is obtained as 22 22 2 ,1 12 112lnln 84HB HB nf ccVfVf VEE NfNf 2 (B-8) The total noise floor is obtained via the superposition of the mean square noises 2 2 2 1ln449 4HB nB cVf Vk T R f Nf e (B-9) where the last term in the above equation is the low amplifier noise. 158

PAGE 159

Figure B-1. The Wh eatstone bridge. R1R2R4R3 V1V2 R1 R2 R4 R3 V1V2 E1E2 Figure B-2. The thermal noise m odel of the Wheatstone bridge. Figure B-3. The 1 f noise model of the Wheatstone bridge. 159

PAGE 160

APPENDIX C PROCESS TRAVELER Wafer: n-type <100> 1-5 ohm-cm, SOI wafer Start with SOI wafer (n-Si (100) 1-5 -cm) with 50 m silicon on 1.5um buried oxide (BOX). DI rinse Masks Reversed biased mask-------RBM Piezo contact mask-------PCM Nested mask-------NM Side implant mask-------SIM Bond pad cuts mask-------BPCM Metal mask-------MM Bond pad mask-------BPM Process Steps 1. n-well Implant Ion implantdopant = phosphorus, energy = 150 keV, dose = 4e12 cm-2. 7 degree tilt, blanket implantation. This forms the n-well. This needs to be simulated first. Piranha clean 2. PECVD oxide: deposit oxide 0.1m via PECVD 3. Reverse Bias Contact Coat and pattern photoresi st/oxide on front side o HMDS evaporation for 5min o Spin AZ1529 at 4000rpm for 50sec & softbake at 90 oven for 30min C o Pattern by mask RBM Exposure 60sec at 8.8mJ/cm2 Develop at AZ300MIF for 50sec Hard bake at 90 oven for 60min C 160

PAGE 161

BOE(7:1) : ~80sec to etch 0.1um oxide. This step puts alignment marks on the wafer Ion implantdopant =phosphorus, energy = 80 keV, dose = 9e13 cm-2. 7 degree tilt Ash strip photoresist RCA clean Thermal annealing at time=420sec in nitrogen 1000 CoT 4. Inplant Interconnection Contact Coat and pattern photoresi st/oxide on front side o HMDS evaporation for 5min o Spin AZ1529 at 4000rpm for 50sec & softbake at 90 oven for 30min C o Pattern by mask PCM, align to the alignment marks created via RBM Exposure 60sec at 8.8mJ/cm2 Develop at AZ300MIF for 50sec Hard bake at 90 oven for 60min C BOE(7:1) : 90sec to etch 0.1um oxide. This step puts alignment marks on the wafer Preamorphization Implant Ion implantdopant = Ge, energy = 160 keV, dose = 1e15 7 degree tilt -2cm Ion implantdopant = Ge, energy = 50 keV, dose = 1e15 7 degree tilt -2cm Ion implantdopant = boron, energy = 50 keV, dose = 1.2e16 7 degree tilt -2cm Ash strip photoresist Piranha clean 5. Nested Mask Release Deposit PECVD oxide 1 m Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1529 at 2000rpm for 50sec & softbake at 95 convection oven for 25min C o Pattern by mask NM, align to the alignment marks created via PCM Exposure 85sec at 7.9 mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90 oven for 60min C Plasma dry oxide etch. This step puts new alignment marks on the wafer 161

PAGE 162

BOE(6:1) oxide etch to re move the oxide residues 6. Etch Sidewalls Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1512 at 2000rpm for 40sec & softbake at 95 hotplate for 50sec C o Pattern by side implantion ma sk(SIM), align to the alignment marks created via NM Exposure 19sec at 4.5mJ/cm2 Develop at AZ300MIF for 70sec Hard bake at 90 oven for 60min C BOE(6:1) oxide for 2min DRIE silicon to deep ~8 m BOE(6:1) oxide for 60sec to av oid Piezoresistor and Piezo contact disconnection due to DRIE undercut Ash strip photoresist Piranha clean 7. Hydrogen Annealing P=for 5min in pure hydrogen for surface roughness reduction 1000 TC 5mTorr 8. Oxidation: thermal grown wet oxide 1000A at oT=1000C 9. Side Wall Implantation Preamorphization implant Ion implantdopant = Ge, energy = 160 keV, dose = 1e15 54 degree tilt -2cm Ion implantdopant = Ge, energy = 50 keV, dose = 1e15 54 degree tilt -2cm Ion implantdopant = boron, energy = 50 keV, dose = 1e16 54 degree tilt -2cm Piranha clean 10. Beam Definition Etch oxide by reactive ion etch via dielectric setting in STS DRIE silicon to BOX BOE(6:1) 2min to remove oxide (ensur e to remove 0.1um oxide on sidewall) 162

PAGE 163

11. Oxidation Piranha clean Annealing at for 60min in nitrogen oT=1000C Thermal dry oxide grown at for 235min oT=975C 0.1 m 12. Bond Pad Cuts Trench filling o Spin AZ1512 at 800rpm for 40sec & softbake at 95hotplate for 50sec C o Spin AZ9260 at 800rpm for 50sec & softbake at 90 oven for 30min C o Flood exposure Exposure 300sec at 7.9mJ/cm2 Develop at AZ400MIF till clear Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1512 at 0.5k/2k for 5/40sec & softbake at 95hotplate for 50sec C o Pattern by bond pad cuts mask(BPCM), align to the alignment marks created via PCM Exposure 45sec at 4.5mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90 oven for 60min C BOE(6:1) oxide for 15min Remove photoresist 13. Metalization Trench filling Desccum in oxygen plasma Deposit 1um Al-Si(1%) to av oid spiking via sputtering Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1529 at 0.2k rpm and stay for 2min. Then spin at 0.2k/2k rpm for 10/50sec with ramp rate of 100/500 rmp/s o Softbake at 90 oven for 30min C o Pattern by metal mask (MM), align to the alignment marks created via BPCM Exposure 100sec at 7.9mJ/cm2 Develop at AZ300MIF for 1min 30sec 163

PAGE 164

Hard bake at 90 oven for 60min C Etch Al by RIE Remove photoresist 14. Nitride Passivation Deposit 2000A PECVD silicon nitride Trench filling Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1512 at 4000rpm for 40sec & softbake at 95hotplate for 50sec C o Pattern by bond pad mask(BPM), align to the alignment marks created via MM Exposure 18sec at 4.5mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90oven for 60min C Etch nitride by RIE Remove photoresist 15. Final Release (a) Device wafer Spin AZ9260 on front side of the device wafer o Spin speed 200rpm, ramp rate 100rpm/s for 10s, wait for 1min. Run this recipe twice o Spin speed 4000rpm, ramp rate 1000rpm/s for 50s o Soft bake at 90 oven for 30min C HMDS on the backside Spin AZ9260 on backside of the device wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s o Soft bake in 90 oven for 30min C Pattern by back release mask(BRM), align to the alignment marks created via NM o Exposure 25sec in E VG520 mask aligner o Develop at AZ300MIF for 3min 40sec 164

PAGE 165

o Hard bake at 90oven for 60min C (b) Carrier wafer Spin PR AZ9260 on a carrier wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s Soft bake at 90 oven for 20-30min C Put some cool grease on the edge of the carrier wafer Bake on hotplate, 60 for 5min C Put the device wafer face down on the carrier wafer. Put on the hotplate, apply pressure using swab (c) DRIE Run DRIE, stopped until 50um silicon left Put the wafer on the hotplate 6 for 5min, separate from the carrier wafer 0 C Separate the wafer into individual dies (d) Process on individual dies Spin AZ9260 on a carrier wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s o Put the device die on the top of the carri er wafer, apply pressure using swab o Soft bake in 90 oven for 30min C DRIE to BOX layer RIE BOX layer for 15min, run BOE 5-10min to remove the residues RIE nitride for 6min Remove the device die using tweezers Put the device die in AZ400 PR stripper Plasma clean in Asher for 10min 165

PAGE 166

APPENDIX D PROCESS SIMULATION This chapter includes the FLOOPS proce ss simulation of the piezoresistor, p++ interconnects and n-well, as well as the reverser bias connections. (a). Piezoresistor This program simulates the doping profile of piezoresistor in the silicon layer after ion implantation, anneal and thermal oxidation. Th e boron is implanted into preamorphization Si layer with oxide as a screen layer. Its init ial doping profile is simulated by SRIM, and then imported to FLOOPS file for subs equent process simulation. line x loc=-0.1 spa=0.005 tag=SiO2top line x loc=0 spa=0.005 tag=top line x loc=1.5 spa=0.01 tag=bot region oxide xlo=SiO2top xhi=top region silicon xlo=top xhi=bot init #profile name=B_SRIM inf=/home/yawei/Floops_new/SRIM _B_50keV_0.1umSiO2_Si_only.txt sel z=B_SRIM*5 name=Boron sel z=log(Boron) layer etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=235 puts "### Oxide thickness after thermal oxide is [e xpr [interface oxide /si licon] [interface gas /oxide]] um." sel z=log10(Boron) plot.1d bound !cle label=PZR set cout [open /home/yawei/Floops_new/pzrda ta w] puts $cout [print.1d] close $cout sel z=log10(5.0e14) plot.1d !cle label=background sel z = Boron-5e14 puts "The Junction Depth is [interpolate silicon z=0.0]" set z=Boron layer (b). P++ interconnection and n-well #p++ surface concentration is ~1e+21 and n-well Ns~1e+16 # generate grid 166

PAGE 167

line x loc=0 spa=0.001 tag=top line x loc=1.0 spa=0.01 line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot init sel z=5e14 name=Phosphorus implant phosph dose=4.0e12 energy=150 tilt=7 #deposit 0.1um PECVD oxide deposit time=4 rate =0.030 oxide grid=10 puts "O xide thickness after PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." diffuse temp=1000 time=450 strip oxide implant boron dose=1.2e16 energy=50 tilt=7 #strip oxide #deposit 1um PECVD oxide deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD oxide is [expr [interface oxide /sil icon] [interface gas /oxide]] um." diffuse temp=1000 wet time=9.2 # oxide thickness is 1000A etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=235 sel z=log10(Phosphorus+1) plot.1d bound !cle color=blue label=nwell set cout [open /home/yawei/Floops_new/nwelld ata w] puts $cout [print.1d] close $cout sel z=log10(5e14) plot.1d !cle color=pink label=background sel z=log10(Boron+1) plot.1d bound !cle color=red label=p++ set cout [open /home/yawei/Floops_new/ohmicda ta w] puts $cout [print.1d] close $cout sel z = BoronPhosphorus layer puts "The Junction Depth is [interpolate silicon z=0.0]" (c). Reverse biased contact line x loc=0 spa=0.005 tag=top line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot init sel z=5.0e14 name=Phosphorus implant phosph dose=4.0e12 energy=150 #deposit 0.1um PECVD oxide deposit time=4.19 rate =0.0239 oxide grid=10 puts "Oxide thickness after PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." strip oxide smooth set t [open temp.P w+] 167

PAGE 168

sel z=Phosphorus puts $t [print.1d] close $t # start with a new grid ... si nce strip oxide removes the nodes near the surface where the new phosphorus profile is about to go set fo rmer_interface [interface gas /silicon] line x loc=$former_interface spa=0.0001 tag=top line x loc=0.1 spa=0.001 line x loc=1.0 spa=0.01 line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot init profile name=Phosphorus inf=temp.P # inplant phosphorus for reverse bias contact implant phosph dose=9.0e13 energy=80 tilt=7 sel z=log10(Phosphorus) plot.1d bound !cle color= red label=Profile_ini #Thermal Annealing 450min at T=1000 deg diffuse temp=1000 time=450 #deposit 1um PECVD oxide deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD oxide is [expr [interface oxide /sil icon] [interface gas /oxide]] um." # thermal grown oxide 1000A at T=975 deg diffuse temp=1000 dry time=9.2 etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=235 puts "### Oxide thickness after thermal oxide is [e xpr [interface oxide /si licon] [interface gas /oxide]] um." sel z=log10(5.0e+14) plot.1d bound !cle color= black label=background sel z=log10(Phosphorus+1) plot.1d bound !cle color=bl ue label=reverse_bias set cout [open /home/yawei/Floops_new/reversedata w] puts $cout [print.1d] close $cout layers 168

PAGE 169

APPENDIX E MICROFABRICATION RECIPE FO R RIE AND DRIE PROCESS Table E-1. Input parameters in the ASE on STS DRIE systems. Parameters 50 m Si etch 8 m Si etch 2SiO etch Coil power 600 W 600 W 800 W Platen power 12 W 12 W 130 APC (mTorr) 28 (fixed) 28 (fixed) 50 (auto) Etching process 11 6 Passivation process 6.5 4 6SF flow (sccm) 130 130 2O flow (sccm) 13 13 48CF flow (sccm) 85 85 Etching cycle Varies Varies Varies Passivation cycle Varies Varies Varies Table E-2. Anisotropic oxide /nitride etch recipe on the Unaxis ICP Etcher system. Parameters Oxide Nitride 3CHF flow (sccm) 45 -6SF flow (sccm) -15 2O flow (sccm) 3 5 RF2 power (W) 600 300 RF1 power (W) 100 100 Chamber pressure (mTorr) 15 20 Helium flow (sccm) 20 10 Table E-3. Anisotropic aluminum etch re cipe on the Unaxis ICP Etcher system. Parameters Settings Ar flow (sccm) 5 2Cl flow (sccm) 30 3BCl flow (sccm) 15 RF2 power (W) 500 RF1 power (W) 100 Chamber pressure (mTorr) 5 Helium flow (sccm) 20 169

PAGE 170

APPENDIX F PACKAGING DRAWINGS 25 12.70 20Measurements Units: mm SIDE VIEW TOP VIEW Insert O-ring 19.05 ?? 20 Note: Sharp Corner Is Required 6.35 R 15 R 25 Screw AMaterial: LuciteUsing device chip to ensure it flush-mounted Hole Through the Lucite to Take Out the PCB Package Holes Through the Lucite R3 Figure E-1. The drawing illustrating the Lucite packaging. 170

PAGE 171

Figure E-2. The aluminum plate for the plane wave tube interface connection. 171

PAGE 172

Figure E-3. Aluminum packaging for pressure sensitivity testing. 172

PAGE 173

LIST OF REFERENCES [1] P. J. Johnston, J. Allen H. Whitehead, and G. T. Chapman, "Fitting Aerodynamics and Propulsion into the Puzzle," Aerospace America, pp. 32-42, 1987. [2] W. Shyy, M. Berg, and D. Ljungqvist, "Fla pping and Flexible Wi ngs for Biological and Micro Air Vehicles," Prog. Aerosp. Sci., vol. 35, pp. 455-505, 1999. [3] M. Sheplak, L. Cattafesta, and Y. Tian, "Micromachined Shear Stress Sensors for Flow Control Applications," IUTAM Symposium on Flow Control and MEMS London, England 2007, pp. 67-73. [4] J. W. Naughton and M. Sheplak, "Modern Development in Shear Stress Measurement," Prog. Aerosp. Sci., vol. 38, pp. 515-570, 2002. [5] M. Gad-el-Hak, Flow Control : Cambridge University Press, 2000, pp. 209-210. [6] R. Rathnasingham and K. S. Breuer, "Activ e Control of Turbulent Boundary Layers," J. Fluid Mech., vol. 495, pp. 209, 2003. [7] F. M. White, Viscous Fluid Flow 2nd ed.: McGraw Hill, 1991, Ch.1, 4, 5, 6. [8] H. Tennekes and J. L. Lumley., A First Course in Turbulence : The MIT Press, 1972, Ch.1, 5. [9] Y. A. Cengel and J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications : McGraw-Hill 2006. [10] L. Lofdahl and M. Gad-el-Hak, "MEMS-Ba sed Pressure and Shear Stress Sensors for Turbulent Measurement," Meas. Sci. Tech., vol. 10, pp. 665-686, 1999. [11] A. Padmanabhan, "Silicon Micromachined Sensors and Sensor A rrays for Shear-Stress Measurements in Aerodynamic Flows," Ph.D Dissertation in Department of Mechanical Engineering, Massachussets Institute of Technology, 1997. [12] H. Alfredsson, A. V. Johansson, J. H. Haritonidis, and H. Eckelman, "The Fluctuating Wall-Shear Stress and the Velocity Field in the Viscous Sublayer," Phys. Fluids, vol. 31, pp. 1026-1033, 1988. [13] M. Gad-el-Hak and P. R. Bandyopadhyay, "Reynolds Number Effects in Wall-Bounded Flows," Appl. Mech. Rev., vol. 47, pp. 307-365, 1994. [14] J. M. Corcos, "Resolution of Pressure in Turbulence," J. Acoust. Soc. Am., vol. 35 (2), pp. 192-200, 1963. [15] T. A. Brungart, G. C. Lauchle, S. De utsch, and E. T. Riggs, "Outer-Flow Effects on Turbulent Boundary Layer Wall Pressure Fluctuations," J. Acoust. Soc. Am., vol. 105, pp. 2097-2106, 1999. 173

PAGE 174

[16] R. F. Blackwelder and J. H. Haritonidis, "Scaling of the Bursting Frequency in Turbulent Boundary Layer," J. Fluid Mech., vol. 132, pp. 87-103, July 1983. [17] W. W. Willmarth and L. K. Sharma, "S tudy of Turbulent Structure with Hot Wires Smaller than the Viscous Length," J. Fluid Mech., vol. 142, pp. 121-149, May 1984. [18] M. A. Schmidt, R. T. Howe, S. D. Sentur ia, and J. H. Haritonidis, "Design and Calibration of a Micromachined Floating-Element Shear-Stress Sensor," IEEE Trans. Electron Devices, vol. 35, pp. 750-757, 1988. [19] J. Shajii, K.-Y. Ng, and M. A.Schmidt, "A Microfabricated Floating Element Shear Stress Sensor Using Wafer-bonding Technology," J. Microelectromech. Syst., vol. 1 (2), pp. 8994, June 1992. [20] A. Padmanabhan, H. Goldberg, K. D. Breuer, and M. A.Schmidt, "A Wafer-Bonded Floating-Element Shear Stress Microsen sor with Optical Position Sensing by Photodiodes," J. Microelectromech. Syst., vol. 5 (4), pp. 307-315, 1996. [21] T. Pan, D. Hyman, and M. Mehregany, "M icrofabricated Shear Stress Sensors, Part 1: Design and Fabrication," AIAA J., vol. 37, pp. 66-72, 1999. [22] F.-G. Tseng and C.-J. Lin, "Polymer MEMS-Based FabryPerot Shear Stress Sensor," IEEE Sensors J., vol. 3, pp. 812-817, Dec. 2003. [23] S. Horowitz, T.-A. Chen, V. Chandrasekaran, K. Tedjojuwono, L. Ca ttafesta, T. Nishida, and M. Sheplak, "A Micromachined Geomet ric Moir Interferomet ry Floating-Element Shear Stress Sensor," IEEE Solid-State Sensor and Actuator Workshop 2004, pp. 13-18. [24] J. Zhe, V. Modi, and J. Kenneth. R. Farm er, "A Microfabricated Wall Shear-Stress Sensor with Capacitative Sensing," J. Microelectromech. Syst., vol. 14 (1), pp. 167-175, Feb. 2005. [25] A. A. Barlian, S.-J. Park, V. Mukundan, a nd B. L. Pruitt, "Design and Characterization of Microfabricated Piezoresistive Floating Element-Base d Shear Stress Sensors," Sensors and Actuators A, vol. 134 (1), pp. 77-87 2007. [26] M. E. Law and S. Cea, "Continuum Ba sed Modeling of Silicon Integrated Circuit Processing: An Object Oriented Approach," Computational Materials Science, vol. 12, pp. 289-308, August 1998. [27] J. I. Haritonidis, "The Measurement of Wall Shear Stress," Advances in Fluid Mechanics Measurements, Springer-Verlag, pp. 229-261, 1989. [28] K. G. Winter, "An Outline of the Techni ques Available for The Measurements of Skin Friction in Turbulent Boundary Layers," Prog. Aerosp. Sci., vol. 18, pp. 1-57, 1977. [29] T. J. Hanratty and J. A. Campbe ll, "Measurements of Wall Shear Stress," Fluid Mech. Measurements 1983, pp. 559-615. 174

PAGE 175

[30] T. K. Hsiai, S. K. Cho, P. K. Wong, M. Ing, A. Salazar, A. Seva nian, M. Navab, L. L. Demer, and C.-M. Ho, "Monocyte Recruitment to Endothelial Cells in Response to Oscillatory Shear Stress," FASEB J., vol. 17(12), pp. 1648-1657, September, 2003. [31] B. Oudheusden and J. Huijsing, "Integrated Flow Friction Sensor," Sensors and Actuators A, vol. 15, pp. 135-144, 1988. [32] E. Kalvesten, G. Stemme, C. Vieider, and L. Lofdahl, "An Integrated Pressure-Flow Sensor for Correlation Measurem ent in Turbulent Gas Flow," Sensors and Actuators A, vol. 52, pp. 51-58, 1996. [33] C. Liu, J.-B. Huang, A. Z. Z, F. Ji ang, S. Tung, Y.-C. Tai, and C.-M. Ho, "A Micromachined Flow Shear-Stress Sensor Based on Thermal Transfer Principles," J. Microelectromech. Syst., vol. 8 (1), pp. 90 99, March 1999. [34] M. Sheplak, V. Chandrasekaran, A. Cain, T. Nishida, and L. N. C. III, "Characterization of a Micromachined Thermal Shear Stress Sensor," AIAA J., vol. 40, pp. 1099-1104, 2002. [35] D. Fourguette, D. Modarress, F. Taugwalder, D. Wilson, M. Koochesfahani, and M. Gharib, "Miniature and MOEMS Flow Sensor," AIAA paper 2001-2982 2001. [36] C. Brcker, D. Bauer, and H. Chaves "Dynamic Response of Micro-Pillar Sensors Measuring Fluctuating Wall-Shear-Stress," Exp .in Fluids, vol. 42 (5), 2007 [37] C. Brcker, J. Spatz, and W. Schrder, "Feasability Study of Wa ll Shear Stress Imaging Using Microstructured Surfaces with Flexible Micropillars," Exp. in Fluids, vol. 39 (2), pp. 464-474, Aug. 2005. [38] T. V. Papen, H. Steffes, H. D. Ngo, a nd E. Obermeier, "A Micro Surface Fence Probe for the Application in Flow Reverse Area," Sensors and Actuators A, vol. 97-98, pp. 264-270, 2002. [39] M. A. Schmidt, "Microsensors for the Measurement of Shear Forces in Turbulent Boundary Layers," Ph.D Dissertation in Mechan ical Engineering, Massachussets Institute of Technology, 1988. [40] B. Carroll, E. Boulos, M. Sytsma, L. Cattafe sta, J. P. Hubner, and M. Sheplak, "Aero-Optic Measurement Facility Characterization," in 42nd Aerospace Sciences Meeting and Exhibit, AIAA Paper 2004-0936, Reno, NV, 2004. [41] Z. W. Hu, C. L. Morfey, and N. D. Sa ndham, "Wall Pressure and Shear Stress Spectra from Direct Simulations of Channel Flow," AIAA J., vol. 44 (7), July 2006 2006. [42] T. Pan, D. Hyman, and M. Mehregany, "M icrofabricated Shear Stress Sensors, Part 2: Testing and Calibration," AIAA J., vol. 37, pp. 73-78, 1999. 175

PAGE 176

[43] M. Sheplak, A. Padmanabhan, M. A. Schm idt, and K. S. Breuer, "Dynamic Calibration of a Shear-Stress Sensor Using Stokes-Layer Excitation," AIAA J., vol. 39 (5), pp. 819-823, May 2001. [44] H. D. Goldberg, K. S. Breuer, and M. A. Schmidt, "A Silicon Wafer-Bonding Technology for Microfabricated Shear-Stress Se nsors with Backside Contacts," IEEE Solid-State Sensor and Actuator Workshop Hilton Head, SC, 1994, pp. 111-115. [45] N. Maluf, An Introduction to Microelectro mechanical System s Engineering Norwood, MA: Artech House, 2000. [46] S. D. Senturia, Microsystem Design : Kluwer Academic Publishers, 2001, Ch. 10, 17, 18, 19. [47] J. A. Harley and T. W. Kenny, "1/f No ise Considerations for the Design and Process Optimization of Piezoresistive Cantilevers," J. Microelectromech. Syst., vol. 9 (9), June 2000. [48] M. Sheplak, L. Cattafesta, and T. Nish ida, "Microelectromechanical Floating Element Flow Sensor," U.S Patent Number : 6966231, Issued on November 22, 2005. [49] A. A. Barlian, R. Narain, J. T. Li, C. E. Quance, A. C. Ho, V. Mukundan, and B. L. Pruitt, "Piezoresistive MEMS Underw ater Shear Stress Sensors," MEMS' 06, Istanbul, Turkey, 2006, p. 626. [50] B. W. Chui, T. W. Kenny, H. J. Mamin, B. D. Terris, and D. Rugar, "Independent Detection of Vertical and Lateral Forces with a Sidewall-Implanted Dual-Axis Piezoresistive Cantilever," Appl. Phys. Lett., vol. 72 (11), pp. 1388-1394, 1998. [51] A. Partridge, J. K. Reynolds, B. W.Chui, E. M.Chow, A. M. Fitzgerald, L. Zhang, N. I. Maluf, and T. W.Kenny, "A High-Performan ce Plannar Piezoresistive Accelerometer," J. Microelectromech. Syst., vol. 9 (1), March 2000. [52] C. S. Smith, "Piezoresistance Effects in Germanium and Silicon," Physical Review, vol. 94, 1954. [53] M. Madou, Fundamentals of Microfabrication : CRC Press, 1997, Ch. 4. [54] A. H. Nayfeh and P. F. Pai, Linear and Nonlinear Structural Mechanics : John Wiley & Sons, Inc, 2004, pp. 183. [55] M. Rossi, Acoustics and Electroacoustic .: Artech House, 1988, pp. 245. [56] J. Merhaut, Theory of Electroacoustics : McGraw-Hill Inc., 1981, Ch. 1. [57] S. M. Sze, Semiconductor Sensors: Wiley-Interscience, 1994, pp. 160. 176

PAGE 177

[58] O. N. Tufte and D. Long, "Recent Devel opment in Semiconductor Piezoresistive Devices," Solid State Electronics, vol. 6, pp. 323-338, 1963. [59] Y. Kanda, "A Graphical Representation of the Piezoresistive Coefficients in Silicon," IEEE Trans. Electron Devices, vol. 29 (64), pp. 64-70, 1982. [60] J. Brysek, K. Petersen, J. Joseph R. Mallon, L. Christel and F. Pourahmadi, Silicon Sensors and Microstructures: Lucas NovaSensor, 1991, Ch. 4. [61] O. N. Tufte and E. L. Stelzer, "Piezore sistive Properties of Si licon Diffused Layers," J. Appl. Phys., vol. 34 (2), pp. 313-318, 1963. [62] W. P. Mason, J. J. Forst, and L. M. Tornillo, Recent Developments in Semiconductor Strain Transducers: New York, 1962. [63] D. R. Kerr and A. G. Milelnes, "Piezo resistance of Diffused Layers in Cubic Semiconductors," J. Appl. Phys., vol. 34 (4), pp. 727-731, 1963. [64] M. Tortonese, "Force Sensors for Scanni ng Probe Microscopy," Ph.D Dissertation in Department of Mechanical Engine ering: Stanford University, 1993. [65] J. A. Harley, "Advances in Piezoresistive Probes for At omic Force Microscopy," Ph.D Dissertation in Department of Mechanical Engineering: Stanford University, 2000. [66] J. D. Plummer, M. D. Deal, and P. B. Griffin, Silicon VLSI Technology : Prentice Hall, 2000, Ch. 7, 8. [67] T. Nishida and C.-T. Sah, "A Physical Based Mobility Model for MOSFET Numerical Simulation," IEEE Trans. Electron Devices, vol. 34 (2), pp. 310-320, 1987. [68] H. Nyquist, "Thermal Agitation of Electric Charge in Conductors," Phys. Rev., vol. 32, pp. 110-113, 1928. [69] J. B. Johnson, "Thermal Agita tion of Electricity in Conductors," Phys. Rev., vol. 32, pp. 97-109, 1928. [70] F. N. Hooge, "1/f Noise is No Surface Effect," Phys. Lett. A, vol. 29, pp. 139-140, 1969. [71] E. Simoen and C. Claeys, "On the Flicker Noise in Sub Micron Silicon MOSFETs," Solid State Electronics, vol. 43, pp. 865-882, 1999. [72] A. McWhorter, "1/f noise and Germanium Surface Properties," in Semiconductor Surface Physics : University of Pennsylvania, Philadelphia, 1957, pp. 207-228. [73] Analog Devices Inc, www.analog.com [74] M. Akbar and M. A. Shanblatt, "Tempera ture Compensation of Piezoresistive Pressure Sensors," Sensors and Actuators A, vol. 33, pp. 155-162, 1992. 177

PAGE 178

[75] K. Suzuki, T. Ishihara, M. Hirata, and H. Tanigawa, "Nonlinear Analysis of a CMOS Integrated Silicon Pressure Sensor," IEEE Trans. Electron Devices, vol. 34, pp. 13601367, 1987. [76] R. F. Pierret, Semiconductor Device Fundamentals : Addison-Wesley, 1996, Ch.5, 6. [77] R. C. Jaeger, Introduction to Microelectronic Fabrication 1993, pp. 57. [78] M. E. Law and S. M. Cea, "Continuum Based Modeling of Silicon Integrated Circuit Processing: An Object Oriented Approach," Computational Materials Science, vol. 12, pp. 289-308, Nov 1998. [79] SRIM, www.srim.org [80] S. M. Sze and G. Gibbsons, "Avalanche Breakdown Voltage of Abrupt and Linearly Graded p-n junctions in Ge, Si, GaAs, and GaP," Appl. Phys. Lett., vol. 8, pp. 111, 1966. [81] S. M. Sze, Physics of Semiconductor Devices 2nd ed.: John Wiley & Sons, Inc, 1981, pp. 193. [82] R. C. Hibbeler, Mechanics of Materials, Third ed.: Prentice Hall, 1997, pp. 160 [83] J. D. Plummer, M. D. Deal, and P. B. Griffin, Silicon VLSI Technology: Fundamentals, Practice, and Modeling, Prentice Hall, 2000. [84] M. Papila, R. T. Haftka, T. Nishida, and M. Sheplak, "Piezoresistive Microphone Design Pareto Optimization: Tradeoff Between Sensitivity and Noise Floor," J. Microelectromech. Syst., vol. 15 (6), pp. 1632-1643, December 2006. [85] A. Partridge, "Lateral Piezoresistive A ccelerometor with Epipoly Encapsulation," Ph.D Dissertation in Department of Electrical Engineering, Stanford University, 2003. [86] Mathworks Inc, MATLAB R2006b ed, 2006. [87] J. F. Schutte and A. A. Groenwold, "A Study of Global Optimi zation Using Particle Swarms," J. Global Opt., vol. 31 (1), pp. 93-108, 2005. [88] R. T. Haftka and Z. Gurdal, Elements of Structural Optimization : Kluwer Academic Publishers, 1992. [89] B. El-Kareh, Fundamentals of Semiconductor Processing Technologies 3rd ed.: Kluwer Academic Publisher, 1998. [90] Unaxis, www.unaxis.com [91] STS, www.stsystems.com [92] M.-C. M. Lee, J. Yao, and M. C. Wu "Silicon Profile Transformation and Sidewall Roughness Reduction Using Hydrogen Annealing," MEMS '05 Miami, FL, USA, 2005. 178

PAGE 179

[93] R. Legtenberg, H. Jansen, M. d. Boer and M. Elwenspoek, "Anisotropic Reactive Ion Etching of Silicon Using SF6 /02/CHF3 Gas Mixtures," J. Electrochem. Soc., vol. 142, pp. 2020-2028, 1995. [94] M. Ohring, The Materials Science of Thin Films : Academic Press, 1992. [95] C.-T. Sah, Fundamentals of Solid -State Electronics : World Scientific, 1993. [96] Stanford Research Systems, http://www.thinksrs.com/products/SIM928.htm [97] V. Chandrasekaran, A. Cain, T. Nishida, L. N. Cattafesta, and M. Sheplak, "Dynamic Calibration for Thermal Shear-Stress Sensors with Mean Flow," Exp. in Fluids, vol. 39, pp. 56-65, 2005. [98] R. Dieme, G. Bosman, M. Sheplak, and T. Nishida, "Source of Excess Noise in Silicon Piezoresistive Microphones," J. Acoust. Soc. Am., vol. 119, pp. 2710-2720, May 2006. [99] M. G. Jones and P. E. Stiede, "Comparison of Methods for Determining Specific Acoustic Impedance," J. Acoust. Soc. Am., vol. 101(5), pp. 2694-2704, 1997. [100] J. N. Reddy, Theory and Analysis of Elastic Plates : Taylor and Francis, 1999, pp. 25. 179

PAGE 180

BIOGRAPHICAL SKETCH Yawei Li received her BS and MS degree in Aerospace Engineering at Beijing University of Aeronautics and Astronautics, China. She wo rked with China Aerospace Corporation before she joined University of Florida. She also received MS (2003) in Aerospace Engineering and ME (2006) in Electrical Engineering from University of Florida, respectively. She is currently a Ph.D student in the Department of Mechanical and Aerospace Engineering at the University of Florida. Her current research focuses on the sensor modeling, design optimization, fabrication, and characteriza tion of MEMS-based piezo resistive sensors that enable the measurement and control of wall shear stress in turbulent flow.