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Silicon-Micromachined Thermoelectric Generators for Power Generation from Hot Gas Streams

Permanent Link: http://ufdc.ufl.edu/UFE0041166/00001

Material Information

Title: Silicon-Micromachined Thermoelectric Generators for Power Generation from Hot Gas Streams
Physical Description: 1 online resource (258 p.)
Language: english
Creator: Boniche, Israel
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: efficiency, energy, etching, exchanger, films, fins, gas, generators, gold, heat, hot, mems, metals, microelectromechanical, microfabrication, nickel, polyimide, polymer, power, resistance, seebeck, silicon, tcr, temperature, thermocouple, thermoelectric, thermoelements, thin, voltage
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Silicon-Micromachined Thermoelectric Generators For Power Generation Using Hot Gas Streams The demand for long-lasting wireless electronic devices with increasing functionality has spurred research of alternative power sources to traditional batteries. Additionally, there is great interest for energy harvesting devices that can locally generate power for wireless sensor networks from ambient environmental energy. To this end, thermoelectric generators are attractive for their capability to directly convert heat energy into electrical energy, with no moving parts. As a result, they are silent, reliable, and require no maintenance. This dissertation focuses on the development and characterization of miniaturized radial thermoelectric generator systems to directly convert waste thermal energy from hot gas streams into electrical energy. For example, a hot gas line in an automobile or aircraft could be used for a self-powered wireless temperature sensor. Alternatively, a thermoelectric generator could be coupled with a small-scale heat engine or combustor for conversion of hydrocarbon fuels into electrical energy. In this dissertation, a radial thermoelectric generator configuration is investigated. The structure consists of coin-sized silicon-micromachined chip modules that, when stacked, form a cylindrical heat exchanger with finned surfaces on both the inner and outer sides. Hot exhaust gas flows through the finned central channel heating the inner surface, and outer annular fins keep the outer surfaces cool. This design readily accommodates hot gas flow, which overcomes one of the primary inadequacies of the typical parallel-plate thermoelectric module design. Each module consists of two thermally isolated concentric silicon rings connected by a thin polyimide membrane that supports radially oriented thin-film thermoelements. This radial device design was first modeled using analytic heat transfer and electrical models. Using PbTe semiconductor thermoelements, model predictions indicate reasonably high power outputs and power densities (e.g. 1.3 mW and 27 mW/cm^3) could be expected from gas flows at 400 Celsius. To demonstrate the concept, micromachined generators consisting of thin-film metals (Au and Ni) were fabricated and tested. The 13-mm-diameter, 0.36-mm-thick (48 mm^3) modules demonstrated 0.8 microWatts of power generation (power density of 17 microWatts/cm^3) using a 195 Celsius hot gas stream. While limited, these results provide model validation and serve as a stepping-stone toward higher-performing modules using semiconductor thermoelements.
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 Israel Boniche.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Arnold, David.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041166:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041166/00001

Material Information

Title: Silicon-Micromachined Thermoelectric Generators for Power Generation from Hot Gas Streams
Physical Description: 1 online resource (258 p.)
Language: english
Creator: Boniche, Israel
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: efficiency, energy, etching, exchanger, films, fins, gas, generators, gold, heat, hot, mems, metals, microelectromechanical, microfabrication, nickel, polyimide, polymer, power, resistance, seebeck, silicon, tcr, temperature, thermocouple, thermoelectric, thermoelements, thin, voltage
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Silicon-Micromachined Thermoelectric Generators For Power Generation Using Hot Gas Streams The demand for long-lasting wireless electronic devices with increasing functionality has spurred research of alternative power sources to traditional batteries. Additionally, there is great interest for energy harvesting devices that can locally generate power for wireless sensor networks from ambient environmental energy. To this end, thermoelectric generators are attractive for their capability to directly convert heat energy into electrical energy, with no moving parts. As a result, they are silent, reliable, and require no maintenance. This dissertation focuses on the development and characterization of miniaturized radial thermoelectric generator systems to directly convert waste thermal energy from hot gas streams into electrical energy. For example, a hot gas line in an automobile or aircraft could be used for a self-powered wireless temperature sensor. Alternatively, a thermoelectric generator could be coupled with a small-scale heat engine or combustor for conversion of hydrocarbon fuels into electrical energy. In this dissertation, a radial thermoelectric generator configuration is investigated. The structure consists of coin-sized silicon-micromachined chip modules that, when stacked, form a cylindrical heat exchanger with finned surfaces on both the inner and outer sides. Hot exhaust gas flows through the finned central channel heating the inner surface, and outer annular fins keep the outer surfaces cool. This design readily accommodates hot gas flow, which overcomes one of the primary inadequacies of the typical parallel-plate thermoelectric module design. Each module consists of two thermally isolated concentric silicon rings connected by a thin polyimide membrane that supports radially oriented thin-film thermoelements. This radial device design was first modeled using analytic heat transfer and electrical models. Using PbTe semiconductor thermoelements, model predictions indicate reasonably high power outputs and power densities (e.g. 1.3 mW and 27 mW/cm^3) could be expected from gas flows at 400 Celsius. To demonstrate the concept, micromachined generators consisting of thin-film metals (Au and Ni) were fabricated and tested. The 13-mm-diameter, 0.36-mm-thick (48 mm^3) modules demonstrated 0.8 microWatts of power generation (power density of 17 microWatts/cm^3) using a 195 Celsius hot gas stream. While limited, these results provide model validation and serve as a stepping-stone toward higher-performing modules using semiconductor thermoelements.
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 Israel Boniche.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Arnold, David.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041166:00001


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1 SILICON MICROMACHINED THERMOELECTRIC GENERATOR S FOR POWER GENERATION FROM HOT GAS STREAMS By ISRAEL BONICHE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUI REMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Israel Boniche

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3 To my parents for giving me the strength and motivation to complete this work

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4 ACKNOWLEDGMENTS I would like to thank the Army Research Laborat ory (ARL) at Adelphi, MD for the financial support of this work under cooperative agreement W911NF 062 0004. In particular, I want to acknowledge Mr. Bruce R. Geil, Dr. Brian C. Morgan, Dr. Patrick J. Taylor and Dr. Nibir K. Dhar for their feedback in our discussions. Also, I am deeply thankful to Dr. Anne E. Donnelly, director of the National Science Foundation South East Alliance for Graduate Education and the Professoriate (NSF SEAGEP) at the University of Florida (UF), for motivating me to pursue a Ph. D. degree and providing financial support for my studies. Also, I am thankful for having Dr. David P. Arnold as my advisor. His support has allowed me to overcome many challenges and his motivation has encouraged me to be better. Similarly I would like t o thank my committee members, Dr. Toshikazu Nishida, Dr. Mark Sheplak and Dr. Subrata Roy for their guidance and input on this work. Moreover, I want to take the opportunity to thank the UF NanoFabrication staff for their technical support with various mi crofabrication tools and cleanroom processes, namely, Al Ogden, Bill Lewis, Ivan Kravchenko, and Dr. David Hayes. Moreover, I am grateful to be part of the Interdisciplinary Microsystems Group (IMG) at UF. I enjoyed all of the activities we shared as a gr oup including the summer lunch BBQs outside the lab, intramural basketball, soccer and ultimate Frisbee games. Also, I want to thank all of my friends at IMG for their helpful insights on this work. To name a few, I give thanks to Dr. Vijay Chandrasekharan and Matt Williams for their helpful feedback on MatLab optimization. Also, I want to thank Naigang Wang, Erin Patrick, Dr. Sheetal Shetye, and Dr. Robert Dieme for their help with microfabrication processes. In particular, I want to thank Christopher D. M eyer and Sivaraman

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5 Masilamani for their valuable work and assistance on the development of thermoelectric generator (TEG) technologies, and for our countless discussions. Also, I want to thank Eric Viale for his help with electrical measurements of thermoelectric films and work on a LabVIEW program to record multiple temperature measurements. Also, I want to thank Ryan J. Durscher for our many discussions on heat transfer and for making aluminum fixtures in the machine shop as part of the test setup of the TEGs. Lastly, I want to thank my parents, Antonia and Raul Boniche, my sister Elizabeth Boniche, and my brother, David H. Boniche, for their endless love and support throughout my graduate studies. They continue to inspire me to pursue my dreams.

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6 TABLE OF CONTENTS Page ACKNOWLEDGMENTS .................................................................................................. 4 TABLE OF CONTENTS .................................................................................................. 6 LIST OF TABLES ............................................................................................................ 9 LIST OF FIGURES ........................................................................................................ 11 ABSTRACT ................................................................................................................... 20 CHA PTER 1 INTRODUCTION .................................................................................................... 22 1.1 Background .................................................................................................... 22 1.2 Introduction to Thermoelectrics ...................................................................... 27 1.2.1 Seebeck Effect .................................................................................... 27 1.2.2 Peltier Effect ........................................................................................ 28 1.2.3 Thomson Effect ................................................................................... 29 1.2.4 Joule Heating ....................................................................................... 30 1.2.5 Scaling Factor ...................................................................................... 31 1.2.6 Thermoelectric Fig ures of Merit ........................................................... 32 1.2.7 Thermoelectric Efficiency .................................................................... 36 1.3 Prior Microscale Thermoelectric Devices ....................................................... 37 1.3.1 Out of Plane (Parallel Plate) Designs .................................................. 38 1.3.2 In Plane Designs ................................................................................ 44 1.4 Proposed Radial Thermoelectric Device ........................................................ 51 1.5 Research Objectives ...................................................................................... 53 1.6 Dissertation Outline ........................................................................................ 54 2 DEVICE DESIGN .................................................................................................... 56 2.1 Device Overview ............................................................................................ 56 2.2 Device Model ................................................................................................. 61 2.2.1 Thermal Model ..................................................................................... 65 2.2.2 Electrical Model ................................................................................... 68 2.3 Thermopile Design ......................................................................................... 70 2.3.1 Objective Function ............................................................................... 71 2.3.2 Design Variables ................................................................................. 71 2.3.3 Constraints .......................................................................................... 72 2.3.4 Fixed Variables .................................................................................... 73 2.3.5 TemperatureDependent Variables ..................................................... 74 2.4 Radial Device Performance ............................................................................ 76 2.4.1 Discussion of Thermal Performance .................................................... 81

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7 2.4.2 Discussion of Semiconductor Designs ................................................ 84 2.4.3 Discussion of Semiconductor Metal Hybrid Designs ........................... 85 2.4.4 Discussion of AllMetal Designs .......................................................... 86 2.5 Selected Designs for Fabrication and Testing ................................................ 87 2.6 Summary ........................................................................................................ 90 3 DEVICE FABRICATION ......................................................................................... 92 3.1 Fabrication Overview ...................................................................................... 92 3.2 Fabrication of Radial TEG Modules ................................................................ 95 3.2.1 Patterning of Polyimide ........................................................................ 96 3.2.2 Patterning the First Set of TE Legs .................................................... 100 3.2.3 Patterning the Second Set of TE Legs .............................................. 101 3.2.4 Silicon Etching ................................................................................... 102 3.3 Fabrication of Dummy Modules .................................................................... 103 3.4 Fabrication of a Stacked TEG Cylinder ........................................................ 105 3.5 Summary ...................................................................................................... 108 4 EXPERIMENTAL CHARACTERIZATION ............................................................. 109 4.1 Electrical Characterization of ThinFilms and Thermopile ............................ 109 4.1.1 Thin Film Electrical Resistivity Measurements .................................. 110 4.1.2 Thin Film Thermal Conductivity Estimates ........................................ 114 4.1.3 Module Thermopile Resistance Measurements ................................. 116 4.1.4 Module Thermal Conductiv ity Estimates ........................................... 118 4.2 Characterization of Integrated Resistive Temperature Sensors for Internal Temperature Measurements ........................................................................ 119 4.2 .1 Experimental Methods ....................................................................... 120 4.2.2 Uncertainty Analysis .......................................................................... 123 4.2.3 Summary of Results .......................................................................... 128 4.3 Characterization of Single Radial TEG Modules Using a Hot Gas Stream ... 129 4.3.1 Experimental Setup ........................................................................... 130 4.3.2 Thermal Performance ........................................................................ 132 4.3.3 Thermoelectric Performance ............................................................. 139 4.4 Characterization of Stacked TEG Modules Using a Hot Gas Stream ........... 151 4.4.1 Thermal Performance ........................................................................ 151 4.4.2 Thermoelectric Performance ............................................................. 155 4.5 Summary of Results ..................................................................................... 160 5 MODEL VALIDATION ........................................................................................... 162 5.1 Thermal Model of Stacked Structure ............................................................ 162 5.2 Thermoelectric Performance ........................................................................ 170 5.3 Summary of Results ..................................................................................... 176 6 CONCLUSIONS AND FUTURE WORK ............................................................... 178 6.1 Conclusions .................................................................................................. 178

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8 6.1.1 Research Summary ........................................................................... 178 6.1.2 Summary of Device Performance ...................................................... 179 6.1.3 Research Contributions ..................................................................... 183 6.2 Recommendations and Future Work ............................................................ 183 6.2.1 Obstacles .......................................................................................... 183 6.2.2 Potential Improvements ..................................................................... 187 APPENDIX A THERMAL ENERGY (POWE R) FROM A GAS STREAM .................................... 190 B EXPERIMENTAL RESULTS OF RADIAL TEG MODULES .................................. 192 C MATLAB FUNCTIONS .......................................................................................... 238 LIST OF REFERENCES ............................................................................................. 252 BIOGRAPHICAL SKETCH .......................................................................................... 258

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9 LIST OF TABLES Table page 1 1 Characteristics of thermoelectric devices based on thin films. ........................... 50 2 1 Lower and upper bounds used for the des ign variables. ................................... 73 2 2 Representative material properties considered in the radial design model. *Extrapolated properties for comparison to the other materials. ......................... 75 2 3 Design variables and respective geometries for thermopiles as a function of gas temperature. Values at a design constraint boundary are denoted in bold. Inner p and nleg widths are given by P*r1 and N*r1, respectively. TAMB = 22 C ...................................................................................................... 77 2 4 Thermoelectric performance for thermopiles as a function of gas temperature. Device power factor ( DPF ) using the module inner wall surface a t ri, the midradius surface at rmid, and the outer surface at rf, respectively. TAMB = 22 C ...................................................................................................... 79 2 5 Thermoelectric performance for TEG modules as a function of gas temperature. C = (TGas TAmb)/TGas. Also, TAMB = 22 C. .................................... 80 2 6 Comparison of the thermal isolation between the radial TEG of this work and other miniature TEG designs fabricated on silicon substrates. ........................... 83 2 7 Selected TEG designs for fabrication and tests with different geometries based on thinfilm Au and Ni. .............................................................................. 88 2 8 Theoretical performance of thin film metal TEG modules for fabrication and tests TAMB = 22 C. ............................................................................................ 89 2 9 Theoretical performance of thinfilm metal TEG modules for fabrication and tests. C = (TGas TAmb)/TGas. Also, TAM B = 22 C ................................................. 89 3 1 Dimensions of the van der Pauw (VDP) crosses and TLM (mesa) structures. 107 4 1 Measurements of thinfilm Ni an d Au electrical resistivity ( ) with van der Pauw crosses, TLM, and Ni ring structures at 25C. ........................................ 114 4 2 Estimated thermal conductivities ( ) for thin films Ni and Au based on measured resistivity ( ) values. ........................................................................ 115 4 3 Two point probe dc current measurements and model estimates of electrical resistance at room temperature for various TEG modules using AuNi thermoelement pairs. The percentages of the total thermopile resistance attributed to the legs and interconnects are indicated in parentheses. ............. 116

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10 4 4 Estimates of the thermopile thermal conduction resistance at 25 C based on estimated thermal con ductivities from electrical resistivity measurements. Legs thermal resistance includes both Au and Ni thinfilm legs. Substrate thermal resistance includes polyimide/oxide membrane and air. ...................... 119 4 5 Extracted TCR parameters for the inner and outer Ni resistive rings of TEG modules. ........................................................................................................... 128 4 6 Comparison between TEG modules with various TE leg pairs including TAMB C. ............................................................................................................... 139 4 7 Comparison between TEG modules with various TE leg pairs including Seebeck coefficient estimates. TAMB C. ...................................................... 144 4 8 Seebeck coefficient (thermoelectric power) of AuNi thermoelement pair after ~1 month for a single radial TEG module ( n =65 leg pairs). .............................. 145 4 9 Thermoelectric performance of TEG modules w ith various TE leg pairs. TAMBC. ........................................................................................................ 148 4 10 Thermoelectric performance between a single and a stacked TEG module ( n =65 metal leg pairs). TAMB2.5 C. ........................................................... 161 6 1 Comparison of the thermal isolation and electrical performance between the proposed radial TEG and a few of the other miniature TEG designs fabricated on silicon substrates. ....................................................................... 182 B 1 Thin Film thickness of sputtereddeposited Au and Ni on various regions of the van der Pauw crosses. ............................................................................... 195 B 2 A B) Resistance of various van der Pauw crosses to determ ine electrical resistivity. Thermal conductivity is estimated from the WiedemannFranz law. 196 B 3 Resistance measurements of the inner and outer Ni ring resistances to determine electrical r esistivity. Thermal conductivity is estimated from the WiedemannFranz law. ..................................................................................... 197 B 4 Thermopile thermal conduction resistance at 25 C based on estimated thermal conductivities from electrical resistivity measurements. Legs thermal resistance includes both Au and Ni thinfilm legs. Substrate includes polyimide/oxide membrane and air gap. ........................................................... 197 B 5 Extracted parameters for the inner and outer Ni ring of radial TEG modules. .. 198 B 6 Resistance measurements of the inner and outer Ni ring resistances to determine the temperature coefficient of resistance, TCR. ............................... 198

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11 LIST OF FIGURES Figure page 1 1 Estimate of thermal power content of a hot gas stream, qGas A vailable, (assuming air) for various temperatures and mass flow rate (g/s) ...................... 26 1 2 Sketch of a thermocouple consisting of two dissimilar conducting materials joined by a metal. A) A voltage is generated from the due to Seebeck effect. B) TE cooling (by pumping heat from cold to hot side) from current flow due to Peltier effect. .................................................................................... 28 1 3 Diagram of a typical TE device with (p and n) thermocouples sandwiched between hot and cold thermally conductive plates. Alternating pand n legs are connected by a metal interconnect. .............................................................. 31 1 4 Typical values of the unitless figure of merit (z T) over a ra nge of temperature for various A) ptype and B) ntype doped materials. ..................... 34 1 5 Commercially available bulk thermoelectric device (12 x 13 x 3.5 mm3) from TE Technology, Inc. using Bi2Te3 alloy s (model no. TE 650.6 1.5). .................. 37 1 6 TE device fabricated by electrochemical deposition of thick films of (Bi,Sb)2Te3 alloys with Cr/Au and Ni interconnects on SiO2/S i substrates. ......... 39 1 7 TE couples are sandwiched between two soldered silicon substrates to form the TE device. The insert shows the alignment of the pand ntype components prior to soldering. ........................................................................... 40 1 8 Angle view of a CMOS based TEG in a silicon substrate using thin films of poly Si or poly SiGe. ........................................................................................... 41 1 9 TE couples are sandwiched between two solder ed silicon substrates to form the TE device. The insert shows the alignment of the pand ntype components prior to soldering. ........................................................................... 42 1 10 a) An out of plane heat flux TEG using thin film planar p/n type TE couples between two polyimide sheets, and b) cross section view of device along the A B line. .............................................................................................................. 43 1 11 Thin films of sputtered metal on a flexible polyimide membrane that can be co iled up for TE power generation. ..................................................................... 44 1 12 Planar TE generator on glass substrate (22 x 24 mm2) using thin films of p/n typ e BiTe alloys. ................................................................................................ 45 1 13 Microstructured TE generator in silicon with improved heat flow path. .............. 46

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12 1 14 TE generator on a thin silicon membrane (with low heat adhesive for membrane stabilization) and bonded aluminum ( Al) as heat fins. ...................... 47 1 15 a) Cross section of 2stage planar microcooler, and b) topview and c) closed up view of center region of a 5stage cooler using thin films. .................. 48 1 16 A planar TE microcooler on a flexible polyimide membrane with N i/Al contacts. ............................................................................................................ 49 1 17 A) Top view of thermoelectric generator w ith hot center and cold outer silicon rings connected by a polyimide membrane. B) Cross section view (A A) of stacked radial devices to form a cylindri cal structure. ........................................ 52 2 1 A) Top view of thermoelectric generator with hot center and cold outer silicon rings connected by a polyimide membrane. B) Cross section view (A A) of stacked radial devices to form a cylindri cal structure. ........................................ 57 2 2 Cylindrical heat exchanger formed by stacking siliconmicromachined modules with longitudinal inner fins and annular outer fins (13 mm in diameter). A thin polymer membrane connects the concentric silicon rings. .... 59 2 3 Fabrication process flow of a radial TE generator module in a silicon substrate. ............................................................................................................ 60 2 4 A) An overview diagram illustrating the heat flow rates in TEG devic e. B) A coupled thermal electrical circuit model of a TEG. ............................................. 63 2 5 Thermal and electrical circuit models of a radial TEG. The output voltage is proportional to the temperature difference across the thermoelements. Arrows indicate that the thermal resistances of the inner and outer silicon rings a re negligible. ........................................................................................... 64 2 6 Top view of a radially oriented thermoc ouple segment. ..................................... 69 2 7 Power and power density as a function of gas temperature for radial TEG modules composed of p/nBi2Te3, p/n PbTe, Cr Ni, or Au Ni t hermoelements. ................................................................................................ 81 3 1 A) Top and cross section views (A A) of a TEG module (n=18 leg pairs) including resistive thin film Ni for internal temperature measurements of the inner and outer silicon rings. B C) TEG modules with n=65 and n=90 leg pairs. D) Te st module with only resistive Ni ring structures. ............................... 93 3 2 Fabrication process of a radial TE generator module in a silicon substrate. ....... 98 3 3 TEG modules fabricated on silicon substrates using thinfilm Au Ni as thermoelements. Also included resistive thin film Ni for temperature sensing

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13 of the inner and outer silicon rings. Inner and outer diameters are 5 mm and 13 mm, respectively. ......................................................................................... 103 3 4 A) Top view of a dummy module structure. B) Backside view of dummy modules used for stacking. Inner diameter aperture is 5 mm, and outer diameters are 9 mm and 13 mm. ...................................................................... 104 3 5 Stacking of a TEG module (13mm) between 15 dummy modules (9 mm and 13 mm in diameter) to form a cylindrical structure for hot gas stream tests. ..... 106 3 6 Cross section and topview diagram of van der Pauw crosses and TLM (mesa) structures used to estimate thinfilm resistivity (Au and Ni) and specific contact resistivity (Au/Ni). .................................................................... 107 4 1 Characterization of the integrated (A) inner and (B) outer Ni resistive thermal sensors on a dummy module (no thermoelements) for internal temperature measurements. ................................................................................................. 122 4 2 Least squ are fit of resistance temperature data on a dummy module (no thermoelements) using mean coefficients obtained from a Monte Carlo (MC) simulation. ........................................................................................................ 125 4 3 Monte Carlo simulation distributions used to extract (A) slope ( m ), and (B) intercept ( b ) for least square fit, and thus, TCR of the inner resistive thermal sensors on a dummy module (no thermoelements). ......................................... 127 4 4 Test setup for thermal and electrical characterization of single radial TEG modules using a heat gun as a source for a hot gas stream. ........................... 132 4 5 Inner and outer resistive Ni ring resistances on a radial TEG (with no thermoelements) for internal temperature measurements. ............................... 135 4 6 Inner and outer silicon ring temperatures determined from integrated Ni ring resistances on a radial TEG (with no thermoeleme nts). ................................... 136 4 7 Silicon ring temperature difference as a function of gas temperature for a radial TEG (with no thermoelements). .............................................................. 138 4 8 Silicon ring temperature difference as a function of gas temperature for various TEG modules. ...................................................................................... 139 4 9 Opencircuit voltage as a function of gas temperature for various TEG modules having small uncertainties in the voltage ( 0.6 mV) and TGAS ( 2.5 C). ................................................................................................................... 141 4 10 Opencircuit voltage as a function of silicon ring temperature difference for various TEG modules. ...................................................................................... 142

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14 4 11 Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from the slope of the opencircuit voltage and temperature difference for a radial TEG ( n =65 thermoelements ). ......................................... 144 4 12 Electrical resistance of a stacked TEG module ( n =65) as a function of gas temperature during tests with a heat gun. ........................................................ 146 4 13 Power output for single TEG modules as a function of gas temperature by using resistive loads matching the TEG device resistance. ............................ 148 4 14 Load voltage for various resistive loads over different gas temperatures for a single TEG module ( n =65). ............................................................................... 150 4 15 Power output for various resistive loads over different gas temperatures for a single TEG module ( n =65). ............................................................................... 150 4 16 Stacked cylinder structure composed of an active TEG ( n =65) between 15 dummy TEG modules ( n =0) for hot gas stream tests. ...................................... 151 4 17 Inner and outer Ni ring resistances as a function of gas temperature for a single and a stacked TEG module (n=65). ....................................................... 153 4 18 Inner and outer silicon ring temperature as a function of gas temperatur e for a single and a stacked TEG module (n=65) including least square fit lines. ..... 154 4 19 Temperature difference between the inner and outer silicon rings as a function of gas temperature for a single and a stacked TEG module (n=65). ... 155 4 20 Comparison of the opencircuit voltage vs. gas temperature for a single and a stacked TEG module ( n =65) ............................................................................ 156 4 21 Comparison of the opencircuit voltage as a function of silicon ring temperature difference for a single and a stacked TEG module including a least square fit line with slope, m = 0.93, and Au Ni =14.3 0.9 V/K ............. 157 4 22 Power output to resistive loads vs. gas temperature for a single and a stacked TEG ( n =65) module including a least square (quadratic) fit lines. ....... 158 4 23 Load voltage for various resistive loads over different gas temperatures for a stacked TEG ( n =65) module. ............................................................................ 159 4 24 Power output for various resistive loads over different gas temperatures for a stacked TEG ( n =65) module. ............................................................................ 160 5 1 Th ermal and electrical model of a stacked TEG with one active TEG module sandwiched between dum my modules (no thermoelements) to form a cylindrical structure for hot gas stream tests. .................................................... 163

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15 5 2 Estimate of the heat transfer rate, qStack, coupled into the stacked cylinder. ..... 166 5 3 Estimate of the convective thermal resistances, ConvCold and ConvHot on the cold and hot side, respectively of a stacked cylinder. ....................................... 167 5 4 Estimate of the convective heat transfer coefficient, hCold, on the cold side of a stacked cylinder. ............................................................................................ 168 5 5 Estimate of the convective heat transfer coefficient, hHot, on the hot side of a stacked cylinder. ............................................................................................... 168 5 6 Experimental data (points) and model predictions (solid lines) for the inner and outer silicon ring temperatures for the stacked TEG. ................................. 169 5 7 Experimental data (points) and model predictions (solid line) for the between inner and outer silicon rings radially through the stacked TEG. ......... 170 5 8 E xperimental data (points) and model predictions (solid lines) of load voltage ......................................... 172 5 9 E xperimental dat a (points) and model predictions (solid lines) of power ........... 173 5 10 M odel estimates of power delivered to various loads using extracted thin film resistivity and measured TEG resistance (1.63 k ). Better approximation to the data is obtained at lower than at higher temperatures. ............................... 174 6 1 Dia gram of power converter sys tem consisting of a dc/dc converter and feedback/control circuit. TEG energy at the input is converted at the output, which can then be stored in a capacitor or delivered to a load through a dc regulator. .......................................................................................................... 181 B 1 Resistance (R) vs. contact spacing (d) between Au/Ni pads for estimates of film resistivity and contact resistivity using the TLM method. ........................... 192 B 2 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on a dummy radial TEG (no thermoelements). ......................................................... 199 B 3 Characterizati on of the inner and outer resistive thermal sensors on radial TEG ( n =65 thermoelements) for internal temperature measurements. ............ 200 B 4 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the inner resistive thermal sensors on radial TEG (n=65 thermoelements) for internal temperature measurements. ... 201

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16 B 5 Monte Carlo si mulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on radial TEG ( n =65 thermoelements) for internal temperature measurements. ... 202 B 6 Characterization of the inner and outer resistive thermal sensors on radial TEG ( n =18 thermoelements) for internal temperature measurements. ............ 203 B 7 Monte Carlo si mulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the inner resistive thermal sensors on radial TEG ( n =18 thermoelements) for internal temperature measurements. ... 204 B 8 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on radial TEG ( n =18 thermoelements) for internal temperature measurements. ... 205 B 9 Characterization of the inner and outer resistive thermal sensors on radial TEG ( n =90 thermoelements) for internal temperature measurements. ............ 206 B 10 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the inner resistive thermal sensors on radial TEG ( n =90 thermoelements) for internal temperature measurements. ... 207 B 11 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on radial TEG ( n =90 thermoelem ents) for internal temperature measurements. ... 208 B 12 Inner and outer resistive Ni ring resistances (as gas temperature increases and decreases) on a radial dummy TEG (no thermoelements) for i nternal temperature measurements. ............................................................................. 209 B 13 Inner and outer resistive Ni ring resistances on a radial TEG ( n =18 thermoelements) for internal temperature measurements. ............................... 210 B 14 Inner and outer silicon ring temperatures determined from integrated Ni ring resistances on a radial TEG ( n =18 thermoelements). ...................................... 210 B 15 Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from the opencircuit voltage and temperature difference for a radial TEG ( n =18 thermoelements). ......................................................... 211 B 16 Load voltage vs. T for TEG with n=18 leg pairs. ............................................ 211 B 17 Delivered power for TEG module with n=18 leg pairs using matched load. ...... 212 B 18 Module electrical resistance vs. gas temperature for TEG with n=18 l eg pairs. 212 B 19 Measurement of the inner and outer resistive Ni ring resistances on radial TEG ( n =65 thermoelements) for internal temperature measurements. ............ 213

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17 B 20 Inner and outer silicon ring temperatures determined from integrated Ni ring resistances on radial TEG ( n =65 thermoelements). ......................................... 213 B 21 Load voltage vs. ................. 214 B 22 least square sense. .......................................................................................... 214 B 23 Re test 30 days later of the inner and outer resistive Ni ring resistances on a radial TEG ( n =65 thermoelements) for internal temperature measurements and for functionality over time. .......................................................................... 215 B 24 Re test of the inner and outer silicon ring temperatures determined from integrated Ni ring resistances on a radial TEG ( n =65 thermoelements) for functionality over time. ...................................................................................... 216 B 25 Re test of the thermoelement pair Seebeck coefficient ( Au Ni) from the open circuit voltage and temperature difference for a radial TEG ( n =65 thermoelements) for functionality over time. ..................................................... 216 B 26 Re test Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from the open circuit voltage and temperature difference for a radial TEG ( n =65 leg pairs). ..................................................... 217 B 27 Re functionality over time. ......................... 217 B 28 Re te over time. ............................................. 218 B 29 Third test of the inner and outer resistive Ni ring resistances on a radial TEG ( n =65 leg pairs) for internal temperature measurements. ................................. 218 B 30 Third test of the inner and outer silicon ring temperatures determined from integrated Ni ring resistances on a radial TEG ( n =65 leg pairs). ...................... 219 B 31 Third test of the thermoelement pair Seebeck coefficient ( Au Ni) from the opencircuit voltage and temperature difference for a radial TEG ( n =65 leg pairs). ............................................................................................................... 219 B 32 Third test Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from the open circuit voltage and temperature difference for a radial TEG ( n =65 leg pairs). ..................................................... 220 B 33 Inner Ni ring resistance vs. load resistance at various temperatures. Error bar is +/ 3.3 Ohms. ................................................................................................ 220

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18 B 34 Outer Ni ring resistance vs. load resistance at various temperatures. Error bar is +/ 3.3 Ohms. .......................................................................................... 221 B 35 Inner Ni ring resistance vs. load resistance at various temperatures. Error bar is +/ 3.3 Ohms, and Ring temperatue is ~ 6.5 C. ............................................. 221 B 36 Outer Ni ring resistance vs. load resi stance at various temperatures. Error bar is +/ 3.3 Ohms, and Ring temperatue is ~ 6.0 C. ...................................... 222 B 37 Temperature difference vs. load resistance at various temperatures. Error bar is +/ 3.3 Oh ms, and Ring temperatue is ~ 8.5 C. ...................................... 222 B 38 Inner and outer resistive Ni ring resistances on a radial TEG ( n =90 thermoelements) for internal temperature measurements. ............................... 223 B 39 Inner and outer silicon ring temperatures determined from integrated Ni ring resistances on a radial TEG ( n =90 thermoelements). ...................................... 223 B 40 Therm oelement pair Seebeck coefficient ( Au Ni) from the opencircuit voltage and temperature difference for a radial TEG ( n =90 thermoelements). ............. 224 B 41 Monte Carlo simulations used to determine the thermoelement pair Seebeck coeff icient ( Au Ni) from the opencircuit voltage and temperature difference for a radial TEG ( n =90 thermoelements). ......................................................... 224 B 42 Load voltage of resistive load (1.55 k ) as a function of temperature difference for a radial TEG ( n =90 thermoelements). ......................................... 225 B 43 Electrical power delivered to a test resistive load (1.55 k ) as function of temperature difference for a radial TEG ( n =90 thermoelements). .................... 225 B 44 Monte Carlo simulations of the slope to determine the Seebeck coefficient of the stacked TEG ( n =65 leg pairs). .................................................................... 226 B 45 Sample load voltage vs. gas temperature for a stacked TEG (n=65). .............. 226 B 46 Opencircuit voltage vs. gas temperature for a stacked TEG (n=65). ............... 227 B 47 Inner Ni ring resistance for various loads and temperatures for a stacked TEG (n=65). ...................................................................................................... 228 B 48 Outer Ni ring resistance for various loads and temperatures for a stacked TEG (n=65). ...................................................................................................... 229 B 49 Inner silicon temperature for various loads and temperatures for a stacked TEG (n=65). ...................................................................................................... 230 B 50 Ou ter silicon temperature for various loads and temperatures for a stacked TEG (n=65). ...................................................................................................... 231

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19 B 51 Silicon rings temperature difference for various loads and temperatures for a stacked TEG (n=65). ........................................................................................ 232 B 52 Experimental data (points) and model predictions (solid lines) of opencircuit voltage versus gas temperature for the stacked TEG. ...................................... 233 B 53 Experimental data (points) and model predictions (solid lines) of load voltage ......................................... 233 B 54 Experimental data (points) and model predictions (solid lines) of opencircuit voltage versus ........................................................... 234 B 55 Experimental data (points) and model predictions (solid lines) of delivered ersus ...................................... 234 B 56 Model estimates of voltage across various loads using extracted thin film resistivity and measured TEG resistance (1.63 k ). Better approximation to the data is obtained at lower than at higher temperatures. ............................... 235 B 57 Model estimates of voltage across various loads using extracted thin film resistivity and estimated TEG resistance (2.24 k ). Be tter approximation to the data is obtained at lower than at higher temperatures. ............................... 236 B 58 Model estimates of power delivered to various loads using extracted thin film resistivity estimated TE G resistance of (2.24 k ). Better approximation to the data is obtained at lower than at higher temperatures. ..................................... 2 37

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20 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 SILICON MICROMACHINED THERMOELECTRIC GENERATOR S FOR POWER GENERATION FROM HOT GAS STREAMS By Israel Boniche May 2010 Chair: David P. Arnold Major: Electrical and Computer Engineering The demand for long lasting wireless electronic device s with increasing functionality has spurred research of alternative power sources to traditional batteries. Additionally, there is great interest for energy harvesting devices that can locally generate power for w ireless sensor networks from ambient environmental energy. To this end, t hermoelectric generators are attractive for their capability to directly convert heat energy into electrical energy, with no moving parts. As a result, they are silent, reliable, and require no maintenance. This dissertation focuses on the development and characterization of miniaturized radial thermoelectric generator system s to directly convert w aste thermal energy from hot gas streams into electrical energy. For example, a hot gas line in an automobile or aircraft could be used for a self powered wireless temperature sensor. Alternatively, a thermoelectric generator could be coupled with a small scale heat engine or combustor for conversion of hydrocarbon fuels into electrical ener gy. In this dissertation, a radial thermoelectric generator configuration is investigated. The structure consists of coin sized silicon micromachined chip modules that, when

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21 stacked, form a cylindrical heat exchanger with finned surfaces on both the inner and outer sides. Hot exhaust gas flows through the finned central channel heating the inner surface, and outer annular fins keep the outer surfaces cool. This design r eadily accommodates hot gas flow, which overcomes one of the primary inadequacies of the typical parallel plate thermoelectric module design. Each module consists of two thermally isolated concentric silicon rings connected by a thin polyimide membrane that sup ports radially oriented thin film thermoelements. This radial device design was firs t modeled using analytic heat transfer and electrical models. Using PbTe semiconductor thermoelements, model predictions indicate r easonably high power output s and power densities (e.g. 1.3 mW and 27 mW/cm3) could be expected from gas flows 400 C To demo nstrate the concept, micromachined generators consisting of thinfi lm metals (Au and Ni ) were fabricated and tested. The 13mm diameter, 0.36mm thick (48 mm3) modules demonstrated 0.8 W of power generation (power density of 17 W/cm3) using a 195 C hot gas stream. While limited, these results provide model validation and serve as a stepping stone toward higher performing modules using semiconductor thermoelements.

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22 CHAPTER 1 INTRODUCTION 1.1 Background Recent advances in micromachining methods have enabled the fabrication of smaller, lighter, more compact and fu nctional portable electronics. While the U.S. Army1In part icular, the U.S. Army is interested in the development of energy dense power supply systems for the soldier and other mobile applications. A recent study by the National Research Council calls for more emphasis on the development of efficient, low power designs (~2 W) for f uture land warrior electronics [6] To improve power/energy usage of electronic devices, three options are available: 1) use less, that is, design systems that require less energy to function, 2) increase energy density of portable energy sources, and/or 3) harvest or recl aim energy to charge batteries for extended lifetime. The first choice is limited since not all electronic devices or systems can be scaled down in power due to fundamental power requirements. On the other hand, the second choice has motivated interest in developing and using higher energy density sources such as l i thium ion batteries or logistical Army fuel (e.g. JP 8). has benefited tremendo usly from this increase in capability, the power requirements to operate these devices require soldiers to carry an unacceptable amount of batteries. In addition to the battery, alternative energy sources involving microscale heat engines, micro fuel cells solar cells, micro thermophotovoltaic, and thermoelectric generators [1 5] are being explored to improve system performance and operation lifetime, and enable soldiers to carry out long duration missions 1 The U.S. Army Research Laboratory was the primary sponsor of this research, so the motivation for this work is described in the context of Army mission goals.

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23 However, this approach still requires the soldier to carry a s ignificant number of batteries. Also, to use the chemical energy from the f uel requires additional systems such as heat engines and electrical generators that convert to mechanical and el ectrical energy, respectively. The third option of harvesting or scavenging energy from the environment is not intended to entirely replace the previous two options, but rather complement them. For instance, energy reclaimed from the environment can be used to recharge batteries, which results in carrying less batteries and reducing the logistical burden of having to resupply. Furthermore, wasted energy recovered from a system e.g. from vehicle exhaust, can be recycled to generate supplemental power Consequently, energy harvesting, which is of great interest to the Army, has the potential for a wide array of applications from powering networks of autonomous microsensors or other small scale electronics to largescale systems such as communication devices and unmanned air vehicles (UAVs) [4, 5] Some of the more popular energy scavenging methods include usi ng solar cells and collectors, vibrational devices, electromagnetic based devices (induction antennas), and thermoelectric (TE) devices [5, 7 9] These energy scavenging approaches are intended for low power applica tions, in the range of milliwatts to Watts of power. Some of the challenges for solar cell devices include the dependence on daylight solar lightingpower generation is typically very low when indoors. Vibrational and electromagnetic based devices are appealing, but they typically output low ac voltages and low net output power, thus necessitating advanced power electronic circuits. If a persistent heat source is available, thermoelectric generators (TEGs) can output relatively large and stable dc voltages, and

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24 relatively large output power levels, simplifying and improving the efficiency of the required power management electronics. TE devices are solidstate devices that directly convert heat energy into elec trical energy, and vice versa. The lack of moving parts and the ability to create electrical power from any heat source enable a reliable and versatile power generation mechanism. TE devices are especially interesting to the Army for stealth operations since they operate in silence They also require little or no maintenance, emit no harmful gas or waste products into the environment, and can be reliable in extreme conditions. TEGs have historically only been employed in very niche applications including powering of deepspace probes using radioacti ve (heat) sources, powering of unattended low power wireless sensors and control systems, and, more recently, powering wrist watches and hearing aids (with body heat). TE heaters and coolers have also been used for thermal management applications such as h eat signature reduction, spot chip cooling, laser chillers, and temperature control of telecommunication systems and medical instruments. Consequently, TE devices have found scattered utility in industrial, commercial, and military applications [8]. Historically, one reason TEG devices have been restricted to very specific applications is due to low thermal to electrical conversion efficiencies, t ypically below ~10% [5, 8]. More recently, new material structures have been developed for higher thermoelectric efficiencies. Materials engineers have evolved classic thermoelectric alloys such as group IV (PbTe) or group V (Bi2Te3) chalcogenides into more complex nanostructured materials such as AgPbmSbTe2+ m (LAST m) and Bi2Te3/Sb2Te3

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25 su perlatices [10 12] Improvements in the thermoelectric performance (or figure of merit) o f these materials have been achieved mainly by reducing the thermal conductivity (to reduce thermal losses). These recent breakthroughs have fueled a resurgent interest in TE power generation. The focus of this dissertation is to explore and develop small scale (~ cubic centimeter) TEG systems to directly convert waste thermal energy into electrical energy from hot gas exhaust streams. For instance, a thinfilm based micromachined TEG could be coupled to the hot gas stream of a microcombustor or micro heat engine for electrical power generation using the thermal energy [2]. Alternatively, a TEG device could supply power to a wireless sensor node using heat from a steam or coolant line, e.g. in an automobile or aircraft. Figure 11 shows estimates of the thermal energy that is transported by a hot gas stream. Specifically, the thermal power content (in Watts) of a hot gas stream qGas_Available, (assuming air) is shown for various temperatures and assumed mass flow rates (g/s) [2, 5, 10, 13] Further details are provided in Appendix A. Even for a net thermal to electrical conversion efficiency of ~5% 10%, up to several Watts of electrical power could potentially be generated for low power microelectronic and/or sensors applications [5, 8] The concept to thermoelectrically harvest energy from a hot gas stream seems fairly straightforward. However, the actual useful power from the hot gas stream is determined by s everal factors. One of the challenges is being able to effectively couple the heat energy from the hot gas flow into the structure of the TEG. Another challenge is to pattern suitable materials and make electrical contacts that are thermally and

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26 electrica lly stable over a range of temperature for sustained performance. Furthermore, it is important to consider the necessary voltage and current requirements to interface a real energy harvesting system. For instance, the intermediate power management circuit or dc dc step up converter at the output of the TEG will consume electrical energy, which must be accounted to properly power a system (e.g. wireless sensor systems). These and other challenges will be discussed further throughout this dissertation. 0 200 400 600 800 1000 1200 25 100 200 300 400 500 600 700 800 900 1000 P (W) Temperature ( C) 0.1 g/s 0.5 g/s 1 g/s Steam line AP aircraft engine (2.5 cu. cm) Microcombustor (0.07 cu. cm) Automobile exhaust > 1 kW 10's kW Fig ure 1 1 Estimate of thermal power content of a hot gas stream qGas A vailable, (assuming air) for various temperatures and mass flow rate (g/s). In the remainder of this chapter, a typical TE G structure is first shown followed by a description of the thermoelectric phenomena. Then, an overview and comparison of previously investigated small scale TE devices is presented. This is followed by the description of a novel micromachined thermoelectric device with a radial structure,

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27 which builds upon the previous art and addresses some of the limitations encountered by previous designs. Lastly, the research objectives and research plan are discussed 1.2 Introduction to Thermoelectrics 1.2.1 Seebeck Effect A thermoelectric couple (or thermocouple) consists of two dissimilar conductors, often p type and ntype doped semiconductors, connected at one enddenoted the junction as shown in Figure 1 2 The first TE effect, known as the Seebeck effect [14, 15] occurs when the junction is heated while the other side is kept cool, so as to create a temperature difference ( Hot TCold) across the thermocouple ( Figure 1 2 a) The resulting generates an electromotive force (or voltage potential) along the TE materials, which is given by, ()ocPNVT ( 1 1 ) wherePand N are the absolute Seebeck coeffi cients or thermoelectric powers (com monly in V/K) for the pand ntype material respectively (often pand ndoped semiconductors). The sign (polarity) of the Seebeck coefficient is generally positive valued for the pleg and negativevalued for the nleg Similarly, some metals exhibit p ositive valued Seebeck coefficients such as Cr and Cu, while others show negativevalued coefficients such as Ni. The magnitude of the individual Seebeck coefficients for semiconductors can be up to hundreds of microvolts per degree Kelvin, while that for metals is usually <100X than semiconductors [10]

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28 A B Figure 1 2 Sketch of a thermocouple consisting of two dissimilar conducting m aterials joined by a metal. A) A v oltage is generated from the due to Seebeck effect. B) TE cooling (by pumping heat from cold to hot side) from current flow due to Peltier effect. 1.2.2 Peltier Effect In addition to the Seebeck effect two other TE phenomena (Peltier effect and Thomson effect) occur when electric current (I) flows through the thermocouple, such as when a loa d (in Figure 1 2 a) or a current sourc e ( Figure 1 2 b) is connected to close the circuit. The first phenomen on results in heat being absorbed or released at the junction of dissimilar conductors due to the Peltier effect [10, 16, 17] The material properties and current direction determine whether heat is absorbed or released. For instance, when current flows for instance, from the pleg to the n leg ( in a clockwise sense ) in Figure 1 2 b, the rate of heat released, in watts (W), at the upper hot portion of thermocouple due to the Peltier effect i s given by H PeltierPMHot MNHotq TITI ( 1 2 ) which reduces to H PeltierPNHotq TI ( 1 3 ) V oc

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29 where M, P, N, are the Seebeck coefficients of the metal, ptype, and ntype materials, respectively and THot is the hot side temperature. Similarly, the rate of heat released at the lower portion of the thermocouple is C PeltierMPCold NMColdq TITI ( 1 4 ) which simplifies to C PeltierPNColdq TI ( 1 5 ) where TC old is cold side temperature. The negative rate of heat release i ndicates that heat is absorbed, i.e., the lower portion is cooled. Additionally, from Kelvins second law, the absolute Peltier and Seebeck coefficients are related by T ( 1 6 ) where T is the absolute temperature 1.2.3 Thomson Effect The second th erm oelectric effect that occurs with current flow is the Thomson effect [10, 16, 17] While the Peltier effect describes heat absorption/liberation at the junction of two dissimilar conductors, the Thomson effect describes heat absorption/liberation along the length of a single conducting material in which a temperature gradient is also present The heat rate per unit length of material (units of W/m) is given by dqdT I dxdx ( 1 7 ) where is the Thomson coefficient (V/K) for a single homogeneous conductor The overall sign (being positive if heat is released and negative if absorbed) depends on the

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30 direction of the current and temperature gradient relative to each other. Additionally, the Thomson and Seebeck coefficients are related as follows: d T dT ( 1 8 ) Generally, the Thomson effect is of relatively l ittle importance in TE devices [10] For instance, i f the Seebeck coefficient is fairly constant over a given temperature range, then the Thomson coefficient in Equation 18 is generally small, and so too the heat absorption/liberation. 1.2.4 Joule Heating All three thermoelectric effects are reversible, i.e., heat can be generated or absorbed by reversing the thermal gradient and/or current flow. In contrast, Joule heating, which results from electric current flow through the TE couple is a lossy and irreversible process, that is, heat is always released, and giv en by JouleqIR ( 1 9 ) where R i s the thermocouple resistance. To a first order approximation, it has been shown that the heat generated from resistive heating (Joule heating) will flow equally out of each end of the thermocouple [10, 15] When the thermocouple is used as a generator as shown i n Figure 1 2 a, heat flows into the thermocouple, in which some is partially rejected at the cold side and some is converted to electrical power (when a resistive load is connected). That is, due to the Seebeck effect, an opencir cuit voltage, Voc, is generated from the temperature gradient, and by connecting a load, current will flow, and electrical power is delivered to the load. On the other hand, when the thermocouple is used as a heat pump as shown in Figure 1 2 b, an amount of electric power (from the electric current source) is supplied

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31 to the thermocouple, which results in heat being pumped away from the cold side to a hotter side. 1.2.5 Scaling Factor In practice, many thermocouples are connected toget her forming a thermopile to boost the output voltage or increase the heating pum ping capability of a TE device. A standard parallel plate TE device design (as shown in Figure 1 3 ) consists of an array of thermoco uples sandwiched between two rigid, thermally conducting parallel plates. These couples are connected electrically in series, and thermally in parallel to form the thermopile. Specifically, connecting n thermocouple pairs in series scales the opencircuit voltage by a factor of n The electrical resistance also scales by n When a load is connected to the open ends, thus closing the circuit, an electrical current will flow through each of the legs Since the same current flows through each thermocouple junc tion, the Peltier heat flow scales by n Similarly, Joule heating and Thomson heat flow scale by n Figure 1 3 Diagram of a typical TE device with (p and n) thermocouples sandwiched between hot and cold thermally conductive plates. Alternating pand n legs are con nected by a metal interconnect [18] [Adapted from Strasser, M. 2004. Micromachined CMOS thermoelectric generators as onchip power supply. ] L A V oc +

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32 When a TE device is used as a generator, electrical power is supplied due to the generated output voltage and current resultin g from an applied temperature gradient. Maximum electrical power is delivered when the electrical resistance of the generator matches that of the load, LL LV P R ( 1 10) Maximum power is delivered to the load, when the load resistance is matched to that of the TEG, R which yields, OC MaxLV PVI R ( 1 11) where VL = VOC I R is the voltage when connected to a load, I = VOC/2R i s the electrical current in the circuit for matched resistances 1.2.6 Thermoelectric Figures of Merit The performance or the heat transformation characteristic is embodied in the thermoelectric figure of merit ( z ), where for an individual TE material (por n type) is given by z ( 1 12) having units of (K1), and commonly reported in literature [10] and used in this dissertation. The performance of TEG devices is improved by using thermoelectric materials with high Seebeck coefficients to generate large voltages, low electrical resistivity to minimize electrical resistance, and low thermal conductivity to maintain a large temperature differential across the thermocouple.

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33 Of the three material properties defining z the thermal conductivity is usually the most difficult to measure, since it requires more elaborate test structures and measur ement methods T hus for simplicity, another commonly employed figure of merit (for a single material) is the film power factor ( FPF) given by FPF ( 1 13) which relates just the electrical properties, ignoring the thermal conductivity, and having units of (W/cm K2). Thus, for high conversion efficiency, materials with high figures of merit, ( z ) are desirable, where typical values are generally 1x103 to 3x103 K1 [16] Since the Seebeck coefficient, thermal conductivity, and electrical conductivity are all functions of temperature, z also varies with temperature. As a result different materials are preferred in different temperat ure ranges. For convenience, the unitless figure of merit (z T) is oftentimes reported to compare between materials at a specified temperature T as shown in Figure 1 4 As a guide, typical values of z T are shown in ( a) for p type and in (b) for ntype materials, although specific values depend on the film quality and deposition method. For instance, Bi2Te3 alloys have highest z T at lower temperatures (including room temperature), while PbTe and TAGS (tellurium, antimony, germaniu m, silver) alloys are generally preferred for medium temperature applications. Lastly, SiGe and La2Te3 alloys have the highest z T in the high temperature range [10]

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34 A B Figure 1 4 Typical values of the unitless figure of merit (z T ) over a range of temperature for various A) ptype and B) ntype doped materials [10] [Adapted from Rowe, D.M. 2006. Thermoelectric handbook: macro to nano. ] The discussion so far has described various figures of merit for a single material A thermocouple requires at least two materials. Thus for a particular thermocoupl e another figure of merit, ZT C, can be defined [10] as PN TC LegsLegsZ KR ( 1 14)

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35 where KLegs is the thermal conductance of the two legs in parallel, and RLegs is the electrical resistance of the two legs in series, each given by NN PP Legs PNA A K LL ( 1 15) NN PP Legs PNL L R AA ( 1 16) where L and A are the electrical resistivity, length, and cross sectional ar ea for each leg, respectively. Since the ZT C given above involves physical dimensions, it is not specifically a figure of merit for a pair of materials (p and n), but ins tead for a geometrically defined thermocouple. It has been shown [7, 10] that when the following relationship is satisfied (thus minimizing the product KLegsRLegs), NPPN PNNPLA LA ( 1 17) a figure of merit for a pair of materials can be written as PN MaterialPair PPNNZ ( 1 18) Furthermore, a metric used to compare power output between devices of different size and operating at different temperatures is given by the device power factor ( DPF ) with units of (W/cm2 K2), and given by P DPF TA ( 1 19) which normalizes the output power by the temperature difference squared and the device surface area, A (where the heat is absorbed) [18, 19] Typical commercially available macroscale TE modules have DPF ~ 1 10 W/cm2 K2 [20, 21]

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36 1.2.7 Thermoelectric Efficiency For thermoelectric power generati on, the thermal to electrical efficiency for the TEG module is defined as the ratio of the electric output power Pelec divided by the heat flow rate into the hot side of the TEG module, qHot, elec Module HotP q ( 1 20) If the thermocouple figure of merit, ZTC, is known, the theoretical maximum TEG module efficiency can be written in terms o f the Carnot efficiency and material properties as [5, 8] 1MaterialC Cold HotM T M T ( 1 21) where 1TCAVGMZT ( 1 22) a nd TAVG = ( THot TCol d)/2, is the average temperature between the two thermal reservoirs (hot and cold side). Also, C is the Carnot efficiency, which thermodynamically limits the maximum generator efficiency, and is given by HotCold C ColdTT T ( 1 23) where the temperature is in absolute values (K), corresponding to the thermal reservoirs in which the device oper ates (e g. gas temperature and ambient temperature). I n practice Module is less than Material, since the former account s for module structure (e .g. packing density of thermoelements and thermal interface with heat source and sink ) which determines the heat flow rate coupled to the hot side. On the other hand, the lat ter provides a theoretical upper limit based on the Carnot limit and materials. For

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37 example, considering ZTC TAVG 1 and TCold = 298 K in Equation 1 22, the factor (M1)/(M+TCold/THot) = 0.17 for THot TCold. This factor equals 0.21 for THot = 2 TCold, and up to 0.29 for THot >>TCold [5, 8]. Thus, a conversion efficiency, Material ~ 25% of the ideal Carnot efficiency is feasible using TEGs. 1.3 Prior Microscale Thermoelectric Devices As shown in Figure 1 5 c ommercially available TE modules are commonly manufactured from bulk materials that are mechanically diced and soldered between two ceramic plates. However there is difficulty and limitations in miniaturizing these devices due to cutt ing, assembling, and fitting of couples in a small area [20, 21] In recent years, research has been directed to develop novel microfabrication methods and materials for application in both power generation and refrigeration [10, 22, 23] Figure 1 5 Commercially available bulk thermoelectric device (12 x 13 x 3.5 mm3) from TE Te chnology, Inc. using Bi2Te3 alloys (model no. TE 650.6 1 .5) [20] [Adapted from TE Technology, Inc. 2008. http://www.tetech.com ] Microfabricated TE devices are particularly attractive for microscale power generation or cooling because of their potential for integration with other microf abricated systems (e.g. electronics, sensors, MEMS). Additionally, the thermoelectric TE couples Contact wires

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38 thermoelectric performance may be improved by using thin films TE materials (as opposed to bulk) with high f igur e s of merit ( z T ) [24, 25] However there are many challenges for integrating advanced TE thin films into micromachined platforms to yield functional micro coolers or power sources. For instance, the utilization of oxidized sili con (SiO2/Si) substrates offers reliable dielectric isolation from the bulk silicon and compatibility with many other MEMS processing technologies (e.g. surface micromachining, deep silicon etching, etc.). Unfortunately the adhesion of the TE films on SiO2/Si is expected to be a significant challenge. For example, thermal stress is a significant issue because of the large mismatch in thermal coefficient of expansion (TCE ) between the TE films and oxidized silicon [26] Another challenge is designing and integrating suitable heat exchange structures for maximizing thermoelectric performance. Also, if microscale TE devices are to be built, then maintaining large temperature gradients ( ) across small distances and structures ( micrometers to hundreds of micrometers) may present significant technological challenges. The next two sections describe prior efforts for realizing micromachined TE devices, both micro coolers and power generators. Designs using conventional out of plane (parallel plate) configurations are reviewed first. This is followed by a discussion of devices designed for inplane heat transfer. 1.3.1 Out of Plane (Parallel Plate) Designs In an effort to miniaturize TE devices, G. J. Snyder et al., at the Jet Propulsion Laboratory, el ectrochemical ly deposited (Bi, Sb)2Te3 alloys as shown in Figure 1 6 to

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39 fabricate a TE microcooler with TE film s of up to 40 m thick [27] The parallel plate device showed cooling of 2 K for an applied current of 110 mA. Figure 1 6 TE device fabricated by electrochemical deposition of thick films of (Bi,Sb)2Te3 alloys with Cr/Au and Ni interconnects on SiO2/Si substrates [27] [Adapted from Snyder, G.J. 2003. Thermoelectric microdevice fabricated by a MEMS like electrochemical process. ] Similarly, H. Bttner et al. reported another out of plane microcooler (0.8 mm x 1.4 mm) using 20 m thick film s with 3 p/npairs of cosputtered Bi2Te3 alloys. That device achieved a higher thermal gradient (or net cooling ) of ~11 K using a current of 800 mA [28] T he alloys were patterned on two separate SiO2/Si substrates, which were then aligned, assembled, and soldered at a wafer or chip level, as shown i n Figure 1 7 One difficulty of this flip chip fabrication approach developed by MicroPelt, was that it required matching of the p and ntype film thicknesses and precise control of substrate bonding. Nonetheless a nother device consisting of 12 p/n TE couples, with same dimensions as the microcooler, was tested for power generation. The generator showed a maximum power output of 0.67 W at an applied of 5 K, corresponding to a device Metal contacts Substrate TE material

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40 power factor ( DPF ) of 2.4 W/cm2 K2. The semiconductor materials exhibited film power factor ( FPF) values of up to 25.3 W/cm K2 and 15.7 W/cm K2 for p type and nt ype thick films, respectively. Figure 1 7 TE couples are sandwiched between two soldered silicon substrates to form the TE device. The insert shows t he alignment of the pand ntype components prior to soldering [28] [Adapted from Bottner, H. 2004. New thermoelectric components using Microsystems technologies. ] Yet other researchers at Infineon Technologies AG, investigated micromachining a CMOS compatible TE G ( 1 cm2) in silicon substrates [18, 29] as shown in Figure 1 8 Patterned TE layers of up to 0.4 m were produced by chemical vapor deposition (CVD) of p/n poly Si couples and of p/npoly SiGe couples As a result, a peak electrical power output of ~1 W (and corresponding voltage of 5 V) was achieved with an out of plane of 5 K. Specifically, generators based on poly Si exhibited a DPF of 0.043 W/cm2 K2, while those based on poly SiGe exhibited a DPF of 0.035 W/cm2 K2. Even though the device power output Substrates Thermocouples

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41 demonstrated the feasibility of combining a TEG on a standard CMOS process. Additionally, heat loss through the silicon structure limit ed the m aximum temperature difference. From a film power factor view, t he pand npoly Si TE layers showed higher values, of 4.8 and 4.0 W/cm K2, respectively, than the p and npoly SiGe which exhibited lower FPF of 1.9 and 2.5 W/cm K2. Figure 1 8 Angle vi ew of a CMOS based TEG in a silicon substrate using thin films of pol y Si or poly SiGe [29] [Adapted from Strasser, M. 2002. Miniaturized therm oelectric generators based on poly Si and poly SiGe surface micromachining. ] Moreover, J. F Li and coworkers proposed a more ambitious design of a TEG by micropacking Bi Sb Te alloys (300 m high) shown in Figure 1 9 into a si ngle silicon mold to fit 10,000 couples in an area of 100 mm2 [30] T he thermoelements were susceptible to cracking during sa mple preparation and processing, that no power measurements were reported. Nonetheless, the effort indicated that high packing density of thermoelements was feasible with m icromachined silic on molds

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42 Figure 1 9 TE couples are sandwiched between two soldered silicon substrates to form the TE device. The insert shows the alignment of the pand ntyp e components prior to soldering [30] [Adapted from Li, J. F. 2003. Microfabrication of thermoelectric materials by silicon molding process ] Another alternative approach by N. Sato et al. was to microfabricate TE devices on flexible polymers, for application on curved surfaces, as shown in Figure 1 10 [31] Thermocouples were fabricated on a polyimidecopper substrate using RF magnetron sputtering of chromel (ptype) and constantan (ntype) e ach 1.25 m in thickness. Thin film FPF of 6.58 and 24.6 W/cm K2 were obtained for the pand nty pe TE materi als, respectively. Overall, the prototype generator, had only 9 thermocouples and showed a low DPF of 1.1x105 W/ cm2 K2.

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43 Figure 1 10. a) An out of plane heat flux TEG using t hin film planar p/ntype TE co uples between two polyimide sheets, and b) cross section vi ew of device along the A B line [31] [Adapted from Sato, N. 2005. Fabrication and evaluation of a flexible thermoelectric device using metal thin films ] Moreover, J. We ber et al. have explored another unconventional method such as fabricating thermoelements on a flexible polymer that can be coiledup as shown in Figure 1 11 [32] Thin films of sputtered antimony (1 m) and bismuth (6 m) were patterned on a 12.5 m polyimide (Kapton) membrane as the substrate. A test device (1 cm2) consisting of 30 thermo couples had an output power of 0.8 W for a of 5 K. As a result, the generator showed a DPF of 0.032 W/cm2 K2. Hand assembly made it difficult to coilup the generator perfectly, resulting i n uneven top and bottom surface, and thus po or the rmal contact to a hot source or a heat sink.

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44 Figure 1 11. Thin films of sputtered metal on a flexible polyimide membrane that can be co iled up for TE power generation [32] [Adapted from Weber J. 2006. Coin size coiled up polymer foil thermoelectric power generator for wearable electronics ] 1.3.2 In Plan e Designs Other efforts have focused on developing inplane devices mainly to function as energy sources for electric devices requiring small energy consumption (in the microWatt range). For example, M. Takashiri et al. fabricated TE devices on glass subst rates (Corning 7059) by flash evaporation of p type BiTeSb and ntype BiTeSe thin film alloys up to 1 m as seen i n Figure 1 12 [33] The planar TE device achieved a peak power output of 0.21 W (voltage of 0.83 mV) for a temperature difference of 30 K, m ainly limited by the device internal resistance of 8.5 k r (DPF) was estimated at 7x105 W/cm2 K2. For these flash evaporated materials, film power factor (FPF) values of up to 15.9 W/cm K2 and 21.5 W/cm K2 were obtained for p type and ntype thin films, respectively. Also, I. H. Kim et al. fabr icated a planar generator simi lar in structure as that shown i n Figure 1 12, using flash evaporated pBi0.5Sb1.5Te3 and nBi2Te2.4Se0.6 thin film alloys up to 4 m thick on a glass substrate [34] This device (with 15 TE couples) had a single DPF of 16x105 W /cm2 K2.

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45 Figure 1 12. Planar TE generator on glass substrate (22 x 24 mm2) using thi n films of p/n type BiTe alloys [33] [Adapted from Takashiri, M. 2007. Fabrication and characterization of bismuthte lluride based alloy thin film thermoelectric generators by flash evaporation method. ] Nonetheless, there are challenges involved with microfabricating TEG s on polymer or glass substrates including mechanical stability of the structure and patterning/etc hing of the substrate. These concerns make it difficult to integrate such TEGs to other MEMS based or (CMOS) complementary metal oxide semiconductor systems. Overall, the fabrication of TE devices on silicon platforms offers a tremendous advantage due to the possibility of monolithic onchip integration and a high density of couples in a small area. More advanced inplane microfabrication methods were explored for integrating TE films on silicon substrates. For instance, t o improve the inplane within the silicon structure (while still applying a cross plane heat flux), T. Huesgen et al. designed a similar silicon based generator with electroplated Cr/Au metal on top of TE device to conduct heat from the top surface to the hot TE couple juncti on [19] shown i n Figure glass Al contact p leg n leg Contacts

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46 1 13. The metal wa s deposited within trenches patterned with SU 8 photoresist (20 m) which also provided th ermal isolation Additionally, the bottom silicon was selectively etched (removed) using a deep reactiveion etching tool (DRIE) to thermally isolate the hot junction f rom the cool bottom substrate. A second wafer wa s bonded on the cool backside of the dev i ce for better thermal contact. The couples wer e formed with ndoped poly Si (0.7m) and sputtered Al metal (0.25 m), having FPF of 18.5 and 0.7 W/cm K2, respectively. Due to problems with the Al processing (such as over etching and thus degrading the A l legs) resulted in high de Consequently, the performance of the device was limited to a DPF of 0.016 W/cm2 K2 compared to simulated values that indicated DPF of up to 0.36 W/cm2 K2. Also, the paper discussed that, if TE couples of BiSbTe alloys were patter ned then, a DPF of up to 0.81 W/cm K2 was theoretically possible. Figure 1 13. Microstructured TE generator in silic on with improved heat flow path [19] [Adapted from Huesgen, T. 2008. Design and fabrication of MEMS thermoelectric generators with high temperature efficiency ]

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47 Similarly, TEGs fabricated in silicon by HSG IMIT and Kundo aimed to also reduce t he heat loss through the substrate by etching the silicon from underneath the thermopile to a 10 m thin layer of silicon where the thermopile consisted of aluminum (Al) and of n doped silicon (1 m layer with FPF estimated at 64.3 W/cm K2) [35] as shown in Figure 1 14. Moreover, to enhance heat transfer and maintain a larger across the thermopile, Al docking elements were bonded with an adhesive to the silicon chip resulting in better coupling to hot and cool regions As a result, a device peak power of 1.5 W resulted from a of 10 K. Moreover, a high packing density of thermo couples ( n = 1000) was achieved in a 16 mm2 area with total device resistance of he DPF of the device was estimated at 0.091 W/cm2 K2. Figure 1 14. TE generator on a thin silicon membrane (with low heat adhesive for membrane stabilization) and bo nded aluminum (Al) as heat fins [35] [Adapted from Glosch, H. 1999. A thermoelectric converter for energy supply ] Al docking elements Thermopiles Silicon chip Stabilizator Heat flow

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48 Also, A. Gross et al. fabricated a multi stage microcooler (9 x 9 mm2) seen in Figure 1 15, using co evaporated thin films of bismuth telluride (2.9 m) and antimony telluride (3.3 m), that are 30 m long x 130 m wide, w ith Cr/Au metal contacts [36] Up to five stages are implemented using a planar layout with the stages arranged as a series of concentric circles around the center cool region. Furthermore, t he stages are thermally isolated by selective DRIE etch of silicon from underneath the TE couples, and added support is provided by anodically bonding to a Pyrex glass/silicon substrate. As a result, c ooling of up to 3.8 K was observed by using a 2 stage arrangement with a supply current of 5.2 mA, while the 5stage slight increased in cooling of up to 3.45 K but requi red a lower curr ent of 3.2 mA. Figure 1 15. a) Cross section of 2stage planar microcooler, and b) topview and c) closed up view of center region of a 5 stage cooler using thin films [36] [Adapted from Gross, A. 2008. A multistage in plane microthermoelectric cooler ]

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49 Alternativel y, L.M. Goncalves et al. fabricated a planar Peltier microcooler as seen i n Figure 1 16, on a flexible Kapton polyimide (12 m) substrate using thick films of co evaporated nBi2Te3 and pSb2Te3 (10 m), each with film power fact ors of ( FPF) of 16 and 22 W/cm K2, respectively [37] A temperature difference of about 4 K (in a mini vacuum) was achieved using a current of 4 mA supplied to the device. Figure 1 16. A p lanar TE microcooler on a flexible polyimi de membrane with Ni/Al contacts [37] [Adapted from Goncalves, L.M. 2006. Flexible Thin film Planar Peltier Microcooler ] In summary various TE devices have been microfabricated using a combination of thin films and micromachining approaches as summarized in Table 1 1 These devices showed that micro coolers and generators are a feasible option for low power applications However, the performance was often limited by high internal or contact resistance or by relatively low temperature gradients across t he TE couples due to heat conduction through the silicon substrate. As an alternative, glass or polymer substrates (with l ower thermal conductance than silicon) were used to reduce heat losses but at

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50 the expense of limited integration to other siliconbased devices and batch fabrication using well established siliconbased micromachining technology. Table 1 1 Characteristics of thermoelectric devices based on thin films Materials Fabrication Method FPF W/cmK2 Substrate Device Size mm 2 DPF W/ cm2K2 Notes Ref BiTe 2.9 m (SbTe) 3.3 m co evaporated -Pyrex glass/Si 18 -=3.45K I=3.2mA Au/Cr contacts [36] Bi 2 Te 3 (Sb2Te3) 10 m co evaporated 16 (22) Kapton polyimide 12 m 4 -=4K I=4mA Ni/Al [37] BiTeSb (BiTeSe) 1 m flash evaporated 15.9 (21.5) Glass 528 7x10 5 P=0.21W =30K Al [33] BiSbTe (BiTeSe) 4 m flash evaporated -Glass 880 16x10 5 P=2.2W =42K Al [34] p/n poly Si p/npoly SiGe 0.4 m CVD 4.8 (4.0) 1.9 (2.5) SiO 2 /Si 100 pol y Si: 0.043 poly SiGe: 0.035 P=1W =5K Tungsten/Al [18, 29] n poly Si (0.7 m) (Al) (0.25 m) CVD sputtered 18.5 (0.7) Si 100 0.016 if p/n BiSbTe: 0.81 P=0.014W =0.95K Au/Cr, Al [19] n doped Si 1 m (Al) CVD 64.3 Si 16.5 0.091 P=1.5W =10K Al [35] Antimony 1 m (Bismuth) 6 m sputtered -Kapton polyi mide 12.5 m 100 0.032 P=0.8W =5K [32] Chromel Constantan 1.25 m sputtered 6.58 (24.6) Polyimi de/Cu (35/25 m) 1600 1.1x10 5 P=0.14W =29K [31]

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51 Furthermore, almost all of the previously investigated devices we re designed for heat transfer by conduction, that is, the TE device was intended to be sandwiched (or stacked) b etween the heat source (such as a hot plate or a heater element ) and the heat sink. This direct contact is important to maintain a temperature gradient on the device. In the case of this dissertation, the heat source is not in the form of a hot surface but in the form of hot gas streams As a result, the standard parallel plate planar geometries of the previously investigated TE devices are not well suited for effective coupling to this available energy. This motivates the present investigation. 1.4 Proposed R adial Thermoelectric Device The design presented in this work is similar in function, but different in structure and fabrication to previous designs. The proposed generator shown i n Figure 1 17, consists of silicon micromachined c hip modules that, when stacked, form a cylindrical heat exchanger with finned surfaces on both the hot and cold sides This design uses a radial configuration with a tubular structure forming a hot inner cylin der and a cold outer cylinder. Hot gasses pass through the finned central silicon channel heating the inner surface while outer annular fins keep the outer surface s cool vi a natural or forced convection. A large, uniform temperature gradient ( ) is thus established across the radially oriented thermoelements within each module. Each module in the stack consists of two thermally isolated concentric silicon rings connected by a 5 m thick polyimide membrane that supports patterned TE thin films. The thermoelectric generator i s formed by patterning radially oriented thermoelectric elements on the substrate as opposed to the checkerboard configuration of typical TE

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52 devices. This approach offers direct and easy inline coupling for power generation from hot gas streams. A B Figure 1 17. A) Top view of thermoelectric generator with hot center and cold outer silicon rings connected by a polyimide membrane. B ) Cross sect ion view (A A) of stacked radial devices to form a cylindrical structure [38] [ Reprinted with permission from Boniche, I. 2009. Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] r o r i r 1 r 2 tsi t ox t poly Hot Gas tN Fin Extension (every 4th layer) r f tP

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53 This structure offer s several key advantages for the intended application. High thermal performance is achieved by the low thermal conductance of the polyimide membrane and enhanced fluidsolid heat transfer via the silicon fins. Additionally, the cylindrical design readily accommodates hot gas flow, overcoming one of the primary inadequacies of the typical parallel plate configuration. Moreover, the ability to stack modules enables scalability in the design, so that multiple modules can be connected for larger power output. T his technology is intended for self powered sensors/systems wherever hot gas or liquid lines are present, e.g. automobiles, aircraft, or industrial environments [10] 1.5 Research Objectives The primary focus of this research is to develop a thinfilm based TE generator for power generation from hot exhaust streams. To accomplish this, efforts are focused on (1) designing and modeling a micromachined TEG system with integrated hot and cold heat exchangers, (2) developing microfabrication strategies to enable thinfilm TE materials to be integrated into micromachined silicon systems, (3) fabricating and characterizing prototype TEG systems, and (4) evaluating experimental measurements for comparison to model predictions. The outcome of this work is a technology demonstration of a power producing thin film metal TEG module using hot exhaust gas streams as a step towards TEG systems using better performing semiconductors Additionally, design, modeling and fabrication capabilities will be developed to enable future T E integration into not only micro machined generators, but also other compact heat sources such as highpower

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54 electronics, optoelectronics, microcoolers, etc. The contributions of this work include the following: Design and modeling of a radial TEG module f or power generation by convective coupling to a hot exhaust gas stream C hallenges involved developing analytic (electrical and thermal) model s, determining important parameters for the design, and evaluating fabrication and system level constraints Micr ofabrication process flow for TEG modules using thinfilm metals on micromachined polymer/silicon substrates. Challenges included depositing thin film metals on polymer layers, patterning of numerous series connected TE leg pairs, releasing of individual m odules from the silicon substrate, and stacking TE modules Experimental characterization of individual TE G modules and stacked structure. Challenges included making accurate resistance, temperature, and voltage measurements and quantifying the uncertainty of the measured and calculated values. 1.6 Dissertation Outline This dissertation is divided into six chapters. Chapter 1 provides an introduction of the field of thermoelectricity, describing basic principles, its usefulness and relevance as a potential source of energy. Past work in thin TE films and devices is also discussed in detail. Also, the research goals and expected contributions of this work are outlined. Chapter 2 describes the development of analytic (electrical and thermal) model s to predict the performance of a miniaturized radial TEG module that convectively couples to hot gas streams The advantages and limitations of the model s used in the design are also described. Ch apter 3 discusses the process flow and fabrication of a thermoelectric generator (TEG) module using thin film metal (Au and Ni) thermoelements on micromachined silicon substrates. Also, additional dummy modules (no thermocouples) are fabricated for tests of a stacked structure.

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55 Chapter 4 describes the experimental characterization methods for the fabricated TEG modules. Electrical and thermal measurements of thinfilm metals are described in detail, including characterization of integrated Ni resistive rings for internal temperature measurements. Voltage and temperature measurements are made on various TEG modules. Additionally, uncertainty analysis on the thermal and electrical measurements is described. Chapter 5 focuses on the thermal characterization and model validation. Estimates of thin film thermal and electrica l properties are used in the models and compared to experimental measurements. Chapter 6 summarizes the contributions of this work and provides recommendations on improvements to the fabrication, assembly and testing of TEG modules. Furthermore, insights into the development of higher performing hybrid TEG modules (semiconductor and metal thermoelements) and all semiconductor TEG modules are outlined.

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56 CHAPTER 2 DEVICE DESIGN With kind permission from Springer Science+Business Media: J. Elec. Mat., Design of a Miniaturized Thermoelectric Generator using Micromachined Silicon Substrates, Vol. 38, No.7, 2009, 12931302, I. Boniche et al. Chapter 1 discussed the general principles of thermoelectricity and its relevance as a potential energy conversion. Also, previous work in thin TE films and devices was discussed along with technical limitations Chapter 2 now focuses on the design of a radial TEG module that is more suitable for p ower generation using hot gas streams 2.1 Device Overview Chapter 1 described the structure and operation of a typical macroscale TE module consisting of an array of thermocouples sandwiched between two rigid, thermally conducting plates. Here, the design of a radial TEG for direct coupling to hot exhaust streams is now described in more detail. As shown in Figure 2 1 t he structure consists of silicon micromachined chip modules that when stacked, form a cylindrical heat exchanger with finned surfaces on both the hot and cold sides. The structure serves to sustain a large, uniform temperature difference ( T ) across a radially oriented thermopile within each module. Each module in the stack consists of two thermally isolated concentric silicon rings connected by a 5thick polyimide membrane that supports patterned TE thin films. Hot exhaust gas flows t hrough the finned central channel heating the inner surface, and outer annular fins keep the outer surfaces cool via natural or forced convection.

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57 A B Figure 2 1 A ) To p view of thermoelectric generator with hot center and cold outer silicon rings connected by a polyimide membrane. B) Cross section view (A A) of stacked radial devices to form a cylindrical structure [38] [Reprinted with permission from Boniche, I. 2009. Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] ro r i r 1 r 2 tsi t ox t poly Hot Gas tN Fin Extension (every 4th layer) r f tP

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58 As mentioned in Chapter 1, one advantage of this structure is that a high T can be achieved by combining the low thermal conductance of the poly imide membrane and the enhanced fluidsolid heat transfer via the silicon fins. For instance, polyimide layers have a high decomposition temperature (~600 C), low coefficient of thermal expansion (CTE ~3x106 K1), and low thermal conductivities ( 0.14 W/mK ) [39] Moreover, polyimide can be deposited on silicon platforms and patterned with standard microfabricati on methods. Also, silicon substrates allow for batch fabrication of the radial chip modules, which can then be stacked into a robust cylindrical structure to readily accommodate hot gas flow. At the same time, the ability to stack modules enables scalabil ity in the design so that more modules can be connected for more power. The feasibility of tailoring silicon substrates with polymer membranes as thermally insulating platforms for radially oriented inplane thinfilm TE generators was previously demonstr ated by another student, Sivaraman Masilamani [40, 41] Individual silicon chips, with no thermoelements, were stacked to form a cylindrical structure as seen i n Figure 2 2 This work expands on those efforts by evaluating the overall device performance with the inclusion of thermoelements (the prior proof of concept demonstrators did not include thermoelements).

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59 Figure 2 2 Cylindrical hea t exchanger formed by stacking siliconmicromachined modules with longitudinal inner fins and annular outer fins (13 mm in diameter). A thin polymer membrane connects the concentric silicon rings [40] [Ada pted from Masilamani, S. 2007. Design of a tubular microfabricated power generation system for hot exhaust streams ] The proposed fabrication process of radial TEG modules is described here and shown in Figure 2 3 The process starts with a ~ 345 m thick, doubleside polished, thermally oxidized silicon wafer. Annular polyimide rings are first patterned on the topside of the wafer ( Figure 2 3 a). The first thermoelements are then deposited (sputtered, evaporated, molecular beam epitaxy (MBE), etc.) and patterned (wet etch, dry etch, or lift off) ( Figure 2 3 b), followed by the second thermoelements to complete the thermopile ( Figure 2 3 c). A n electrically insulating layer of silicon dioxide or polyimide can then be deposited on top of the thermopile for electrical isolation between stacked silicon chips. After patterning of the coating layer, the exposed top and bott om side oxides are removed with a plasma etch or a (BOE) bufferedoxide wet etch ( Figure 2 3 d). After completing the topside processing, a deep reactive ion etch (DRIE) is performed on the back side to form the fin arr ays and hot gas channel ( Figure 2 3 e).

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60 Simultaneously, the silicon is selectively etched away from underneath the thermopile, stopping on the oxide to maximize thermal isolation. More specific fabrication details are included in Chapter 3. A. Spin and pattern polyimide membrane on SiO2/Si B. Deposit and pattern first TE legs C. Pattern second TE legs to complete thermocouple D Coat TE legs with protective polyimide or SiO2 layer E. Backside DRIE of silicon for thermal isolation creating inner and outer silicon ring, and central channel Figure 2 3 Fabrication process flow of a radial TE generator module in a silicon substrate. 2 nd TE leg 1 st TE leg Silicon SiO 2 Polyimide

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61 After the wafer level fabrication, t he individual chip modules are then manually aligned, stacked, and bonded into a cylindrical structure using a hightemperatureresistant, thermally conductive epoxy. Other more advanced chip bonding techniques are also possible. Electrical connections are made to the contact pads either by soldering thin wires or by gold wire bonding. Throughsilicon vias or other advanced interconnects may also be included to en able interconnections between the stacked module layers 2.2 Device Model Analytic heat transfer and electrical models were developed based on the radial configuration. During operation, heat from a source will flow into the hot side of the TEG module, where some of it will be released at the cold side, and some will be converted to electrical power when a resistive load is co nnected to the TEG as depicted i n Figure 2 4 T he heat flow rate into the hot side of the TEG module, qHot, is given by [10] 1 Hot PNHot TEG TEGT qnTIIR ( 2 1 ) Similarly, the heat flow rate out of the cold side of the TEG, qCold is given by 1 Cold PNCold TEG TEGT qnTIIR ( 2 2 ) The first term on each equation represents heat flow by conduction, determined by the temperature difference, ( THot TCold) between the hot and cold side, and the thermal resistance of the module,TEG. The second term is the Peltier heat transport, which can flow in either direction depending on electrical current, I flow direction, n is the number of thermoelement pairs, and PN is the overall Seeb eck coefficient of the TE pairs. The

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62 last term is the Joule resistive heating, which manifests as thermal energy due to current flow, and is assumed to flow equally out of the hot and cold sides. A coupled thermal elect rical model for a TEG is shown i n Figure 2 4 where the opencircuit voltage generated, VOC, due to the Seebeck effect is proportional to T When a resistive load is connected, current w ill flow and electrical power, PL is delivered to the load. Also, the heat energy converted to electrical power, PL, can be determined from the heat flow rate into the hot side and out of the cold side of the TE leg pairs as follows [10] : LHotColdPqq ( 2 3 ) To simplify the analysis, several simplifying assumptions were made. First, a onedi mensional (1D) radial conduction through the thermocouples, polyimideoxide layers and underlying air gap was assumed with forced convection on the inner and outer finned surfaces. Radiation exchange between the two silicon rings and to ambient w as cons idered negligible since the temperature differences are moderate. This assumption will be verified later in this chapter. Second, as discussed in Chapter 1, the Thomson effect has some influence on the thermal distribution but is of relatively little i mportance in TE devices. Generally, for a small temperature range of T the Seebeck coefficient ( ) may not change significantly, so that the Thomson coefficient ( ) may be small and negligible [8]. Third because of the relatively small amounts of power being converted in the designs explored in this dissertation, the heat contributions of the Peltier and Joule heating are assumed small compared to heat conduction. Thus the total heat transfer

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63 rate (in Watts) through the TEG is dominated by the conduction term, T/TEG and qHot ~ qCold. A B Figure 2 4 A ) An overview diagram illustrating the heat flow rates in TEG device. B ) A coupled t hermal electrical circuit model of a TEG. TEG Module Peltier Heat P L q Cold T Cold Side T Hot Side q Hot Heat Conduction Joule Resistive Heat TEG n PN T Hot I T Hot T Cold n PN T Cold I R TEG I 2 R TEG I 2 R TEG R L V oc =n PN (T Hot T Cold ) I qHot q Cold

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64 With these simplifying assumptions, the thermal and electrical models can be decoupled, thus simplifying the design equations. Essentially, the assumption is that the temperatures and heat flow in the thermopile are fixed by the thermal interface (gas temperatures, heat source/sink performance, etc.) and not largely affected by the small thermoelectric currents induced in the TEG. These assumptions will be verified later. The simplified equivalent electrical an d thermal model for a single layer (module) in the stack is shown in Figure 2 5 First, the thermal model is derived below, foll owed by the electrical model. Figure 2 5 Thermal and electrical circuit models of a radial TEG. The output voltage is proportional to the temperature difference across the thermoelements. Arrows indicate that the thermal resistances of the inner and outer silicon rings are negli gible [38] [Reprinted with permission from Boniche, I. 2009. Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] q Hot R TEG V oc =n( P N )(T Hot T Cold ) T AMB T GAS N Polyimide ConvectionHot T Hot T Cold ,, SiRingCold ConvectionCold P Oxide ,, SiRingHot T 1 T 2 Air Conduction

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65 2.2.1 Thermal Model By analysis of the equivalent thermal circuit, the total heat transfer ra te, qHot, is given by ,, GASAMB Hot ConvhotConductionConvcoldTT q ( 2 4 ) where 1 11111Conduction PolyOxAirPN ( 2 5 ) is the parallel combination of the conductive thermal resistances S pecifically P, N Poly Ox and Air are conductive thermal resistances of the pand ntype legs, polyimide, oxide and underlying air gap, respectively, while, ConvHotand ConvColdare the convective thermal resistances on the inner and outer silicon rings. Due to the relatively large cross sectional area and high thermal conductivity of the silicon rings, their associated conduct ive thermal resistances, ,, SiRingHot and ,, SiRingCold are negligible compared to the other resistances, and thus ignored. Later results will confirm this assumption. T he temperature difference T between the concentric silicon rings is given by, HotColdHotConductionTTTq ( 2 6 ) and by rear ranging Equations 24 and 26 as follows: ,, GASAMB Conduction ConvHotConductionConvCold TT T ( 2 7 ) the temperature difference can be written as

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66 ,, 1GASAMB ConvHotConvCold Conduction TT T ( 2 8 ) Thus, the convective thermal resistances sh ould be much smaller than the conductive resistances ( ConvHot + ConvCold << Conduction ) to maximize T. Essentially, the largest T is desirable across the thermoelement pairs. Each of the aforementioned thermal resistances depends on geometric parameters, material properties, and in the case of the convective terms, the flow properties. From a top view of the device ( Figure 2 1 a), the total angle subtended on the surface by a thermocouple pair is given by NETn ( 2 9 ) where n is the total number of thermocouple or leg pairs. The angles subtended by the individual pand ntype legs are given by P and N. Thus, the unitless filling ratios FP and FN are defined as the angular fraction covered by each leg (por n type) for a given thermocouple angle, NET P P NETF ( 2 10) N N NETF ( 2 11) Using t hese defined quantities, the cumulative radial conductive thermal resistances for the different radial structures can be written as follow: 1ln P PPPr r Ft ( 2 12)

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67 1ln N NNN r r Ft ( 2 13) 1ln Poly PolyPolyr r t ( 2 14) 1ln Ox OxOxr r t ( 2 15) 1ln Air SiAirr r t ( 2 16) where tS i, tO x, tP oly, tP, and tN are respectively the thickness of the silicon, oxide layer, polyimide membrane, and thermoelement films (pand ntype). Similarly, O x, P oly, P, N, and A ir are thermal conductivities of the mentioned films and of the air gap. Also, the convective thermal resistances are given by, 1 ConvHot iSiHotrth ( 2 17) ,1 ConvCold oSiColdrth ( 2 18) where hH ot and hC old are the convective heat transfer coefficients associated with the inner and outer silicon surfaces, respectively. By s ubstituting Equations 212 to 218 into Equation 28 the temperature gradient across the concentric silicon rings, and therefore across the thermocouples, can be expressed in terms of the material properties and geometric dimensions to yield,

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68 11 11 1 lnGASAMB Poly N Ox P airPPNNPoly Ox Si Si Si SiiHotoColdTT T t tt t FF r ttttrhrh r ( 2 19) 2.2.2 Electrical Model The electrical model can be represented by a simple Thveninequivalent consisting of a voltage source and a resistance. The opencircuit thermally induced voltage generated by the thermopile is given by, oc PNVnT ( 2 20) where n is the number of series connected thermocouple pairs, T is the temperature difference between the silicon rings (as given by Equation 2 24 ), P and N are the Seebeck coefficients of the p and ntype thermoelements. Thus, large T results in higher voltage output from the TEG module. Also t he electrical r esistance of a TEG module ( RTEG = R ) is given by the series resistance of the pand ntype thermoelement resistances as follows, PNicoiciRnRRRR ( 2 21) where RP and RN are the resistances along the radial direction of the pieshaped thermoelements, while Rico and Rici are the outer and inner interconnects, respectively, along the circumferential direction ( Figure 2 6 ). Any interfacial contact resistance is considered negligible due to the large (overlap) contact area of the pand nt ype leg interconnects as shown i n Figure 2 1 a. Overall, the total resistance can be expressed as,

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69 11 ln ln PN PNETPN NNETPN PP NN P Nrr rr rr Rn tt tw tw ( 2 22) with elect rical resistivitie s, P and N, corresponding to the p and ntype legs, and w2 and w1 their respective interconnect widths. This equation can be rewritten in terms of the unitles s angular filling factors (Equations 210 and 211) as 1 1 ln 1 PN NN PP PPNN PNr FF r r r Rn FtFtntwtw ( 2 23) Figure 2 6 Top view of a radially oriented thermocouple segment [38] [Reprinted with permission from Boniche, I. 2009. Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] By considering matched resistance between the TE generator and the load, the maximum output power per module is given by ocV P R ( 2 24)

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70 Thus thermoelements with high electrical resistivity results in lower power available for a load connected to the TEG module. In conclusion, the power, P is now expressed in terms of the five variables of interest, namely, n, tP, tN, FP, and FN. Lastly, th e device power factor ( DPF ), with units of (W/ cm2K2) and described in Chapter 1, compares the power output between devices of different size and operating at different temperatures [18, 19] given by P DPF TA ( 2 25) For the radial TEG, the surface area of interest is a cylindrical wall surface. H eat is absorbed through the cylinder inner wall ( Ai = 2 ritS i), but flows out through the outer wall with different surface area ( Ao = 2 rftS i). Conse quently, the mid radius surface area Amid = 2 rmidtS i where rmid (the average between ri, and rf) is used to calculate a mid radius DPF to compare performance between TEG devices. 2.3 Thermopile Design It is well known that TE films with high Seebeck coefficients (and opposite in sign), low thermal conductivity, and low electrical resistivity are desired for high TE conversion efficiency as described by the figure of merit ( z) However, in the design of a functional TEG module, there are numerous components and interrelated physical phenomena which create a large design space with many tradeoffs as discussed in the following sections Also, other factors must be considered such as electrical contact reliability at high temperatures, fabrication process limitations, and required voltages and source resistance to drive a given electrical load.

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71 To design suitable structures and to evaluate these tradeoffs, t he model equations derived in the previous section were first implemente d in MATLAB (shown in Appendix C ) to predict the thermoelectric performance of the radial generator. Then, a constrained, nonlinear optimization routine was implemented using the fminc on function in the MATLAB Optimization Toolbox in order to aid in the design of the thermopile layout. The objective function was to maximize power ( P ), subject to the constraints of device geometry, as well as microfabrication and system level constraint s. As a starting point for design and eventual experimental validation, the substrate and polyimide/oxide layer thickness, all radial dimensions, and the thermopile interconnect widths were fixed (as shown in Section 2.3.4). The general dimensions followe d from the previous study [41] of the heat exchanger platform, which was proven to be mechanically robust and thermally insulating. The interconnect widths ( w1, w2) of the TE legs were patterned to a conservative width to ensure interconnect con tact and limit their ( parasitic) resistance. The free design variables were the thermopile variables: number of thermocouple pairs ( n ), the thermoelement film thickness ( tP and tN), and the angular filling fraction of each thermoelement leg on the device s urface ( FP and FN). The design can be formalized as follows: 2.3.1 Objective Function T he design object ive was to maximize power P Mathematical ly, the design problem wa s actually the minimization of the negative of P 2.3.2 Design Variables n number of thermocou ple or leg pairs tP thickness of p type thermoelement tN thickness of n type thermoelement

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72 FP angular fill fraction for ptype thermoelements FN angular fill fraction for ntype thermoelements 2.3.3 Constraints The lower and upper bounds for the design variables LB tP, tN, FP, and FN) UB are summarized in Table 2 1 The minimum number of leg pairs wa s 1, while the maximum wa s set to 500 to have a reasonable number for fabrication. Also, eac h thermoelement film thick ness ( tP, tN) wa s bounded within 0.1 10 m, which is a re asonable range for thin films. Lastly the angular fill fractions ( FP, FN) we re bounded within 0 100 % but we re also constrained by microfabrication constraints as described below Both the spacing between the TE legs and their individual widths we re constrained by the minimum feature size that can be reliably patterned on silicon with photolithography. The minimum width and spacing we re each set to be 10 m. Specifically, the spacing between the TE legs wa s constrained as follows: 1 10 PNrFF m n ( 2 26) Also, each TE leg width wa s constrained to, 1 10PrF m n ( 2 27) 1 10NrF m n ( 2 28) Since the free design parameters were numerically in different scales and have different units, convergence of the optimization routine was improved by nondimensionalizing the parameters of interest using their respective lower bounds ( LB ) and upper bounds ( UB ) as follows [42] :

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73 nLB n UBLB ( 2 29) P PtLB t UBLB ( 2 30) N NtLB t UBLB ( 2 31) P PFLB F UBLB ( 2 32) N NFLB F UBLB ( 2 33) That is, the fmincon algorithm searched for optimum parameters in a unitless search space, although at every step for instance, the constraints and power were checked using the variables with their respective units (dimensionalized variables). Table 2 1 Lower and upper bounds used for the design variables [38] [Reprinted with permission from Boniche, I. 2009. Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] Design Variables Leg Pairs ( n ) t P (m) t N (m) F P (%) F N (%) Lower Bound (LB ) 1 0.1 0.1 0 0 Upper Bound (UB) 500 10 10 100 100 2.3.4 Fixed Variables Mechanical dimensions : The silicon substrate, oxide, and polyimide thicknesses considered for this work we re: tS i = 345 m, tO x = 0.4 m, and tP oly = 5 m (shown i n Figure 2 1 ) Dimensions of a single module we re fixed at ri = 2.5 mm, r1 = 3 mm, r2 = 4 mm, ro = 4.5 mm, and rf = 6 .5 mm. These dimensions were based on previously fabricated heat exchangers (shown i n Figure 2 2 ), having a suitable inner channel diameter so as to not choke the hot gas flow from a small model airplane engine [40,

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74 41] Also, the width of each inner ( w1) and outer ( w2) interconnect along the circumferent ial direction wa s set to 100 m (10X the minimum leg width). The optimization routine wa s not restricted to these values; these we re only representative values in accordance with the proposed fabrication flow. Convective coefficients : Also, convective heat transfer coefficients of hH ot = 100 W/m2K and hC old = 100 W/m2K we re used for the inner and outer silicon surfaces, respectively. These we re approximate values that were experimentally extracted for the micromachined radial silicon heat exchangers (witho ut TE elements as shown i n Figure 2 2 ) consisting of outer annular fins and of eight inner longitudinal fins [40, 41] 2.3.5 Temperature D ependent Variables Thermal and electrical material properties : Table 2 2 provides a summary of the thermal and electrical material properties for the semiconductors (PbTe, Bi2Te3) [40] and pure metals (Cr, Ni, Au) [44, 47] that were considered in the simulations. These properties are fairly representative of the materials that conventionally are used to make TE generators. The p and ntype semiconductor films were assumed to have the same material properties, but opposite Seebeck polarity. Note that the Seebec k coefficient ( ), electrical resistivity ( ), and thermal conductivity ( ) all vary with temperature. As a result, the simulations were repeated using the material properties at different temperatures. For the sake of simplicity, the material properties were fixed by the assumed gas temperature. For example, for an assumed gas temperature of 400 C, the material properties at 400 C were used, even though the entire structure would not be at 400 C. That is, material property temperature dependence between the hot and cold sides of the TEG was not considered.

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75 Table 2 2 also includes estimates of the unitless figure of merit ( zT ) and film power factor ( FPF) at various temperatures given by [8] zTT ( 2 34) FPF ( 2 35) Table 2 2 Representative material properties considered in the radial design model [8, 39, 4346] *Extrapolated properties for comparison to the other m aterials [38] [Reprinted with permission from Bonic he, I. 2009.] Material (p/n) Temp T (C) Absolute Seebeck coefficient | | (V/K) Electrical resistivity ( m) Thermal conducti vity (W/mK) FPF ( W/cmK2) Material z T Unitless ) Bi 2 Te 3 100 200 300* 400* 200 190 205 175 12x10 6 14x106 23x106 27x106 1.7 1.7 1.6 1.6 33.3 25.8 18.3 11.3 0.73 0.72 0.65 0.48 PbTe 100 200 3 00 400 85 125 165 200 8x10 6 12x106 20x106 27x106 2.6 2.0 1.5 1.2 9.0 13.0 13.6 14.8 0.13 0. 31 0.52 0.83 Ni 100 200 300 400 22 25 23 20 10.5x10 8 17x108 23x108 31x108 83 75 68 67 46.1 36.8 23.0 12.9 0.02 0.02 0.02 0.01 Cr 100 200 300 400 20 18 17 1 7 15 x10 8 19x108 24x108 29x108 92 87 82 76 26.7 17.1 12.0 10.0 0.01 0.01 0.01 0.01 Au 100 200 300 400 2.3 2.8 3.0 3.2 2.9 x10 8 3.8x108 4.6x108 5.6x108 312 306 300 292 1.8 2.1 2.0 1.8 2 x10 4 3 x104 4 x104 4 x104 Air (1 atm) 100 200 300 400 0.03 2 0.039 0.045 0.051 Polyimide 0.14 SiO 2 1.4 Silicon 148

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76 In addition, material properties are provided for polyimide, oxide and air (at atmospheric pressure) [39, 44, 46] While t he thermal conductivity of air was assumed temperaturedependent, t he thermal conductivities of the supporting layer (silicon, oxide and polyimide) we re assumed to not vary significantly over the test temperature range. 2.4 Radial Device Performance Using the abovedescribed analytical model and optimization framework, the performance of the radial generator was considered using thinfilm semiconductors (PbTe, Bi2Te3). Even though semiconductors have better performance compared to metal films, some fabrication difficulties arise, such as depositing and patterning both pand ntype thin films on the same substrate. Also electrical contact resistance and reliability has been problematic in prior studies Thus, the performance of hybrid designs consisting of p t ype semiconductor and metal (Ni) legs were also considered and compared. To further simplify the fabrication process, designs consisting of dissimilar metals (Cr, Ni and Au) as TE legs were also simulated. Thus, a comparison is presented among the various designs helping to quantify tradeoffs between performance and ease of fabrication. As part of the optimization routine, the fmincon function requires initial guesses for the five design variables shown in Table 2 1 Several different initial guesses were attempted for each design, and each converged to the same parameters. This indicates the optimizer likely converged to a global minimum (the optimum design), as opposed to a local minima (sub optimal design).

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77 Table 2 3 summarizes the optimal para meters ( n tP, tN, FP, FN) for combinations of semiconductor and metal thin fi lms over the range of hot gas streams from 100 400 C. All values at a design boundary are indicated in bold. Als o, the values for Bi2Te3 at 300 C and 400 C are based on extrapolated parameters, shown in Table 2 2 to compare with those of PbTe. Table 2 3 Design variables and r espective geometries for thermopiles as a function of gas temperature. Values at a design constraint boundary are denoted in bold. Inner p and nleg widths are given by P*r1 and N*r1, respectively. TAMB = 22 C [38] [Adapted from Boniche, I. 2009. Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] Material (p/n) T emp T (C) Leg pairs n ) t P (m) t N (m) F P (%) F N (% ) p leg inner width (m) n leg inner width (m) Leg spacing (m) Bi 2 Te 3 100 200 300 400 62 59 54 52 10 10 10 10 10 10 10 10 47 47 47 47 4 7 47 47 47 141 150 162 168 141 150 162 168 10 10 10 10 PbTe 100 200 300 400 103 66 52 46 10 10 10 10 10 10 10 10 45 4 7 47 48 45 47 47 4 8 81 133 168 191 81 133 168 191 10 10 10 10 Bi 2 Te 3 / Ni 200 400 99 77 10 10 2.8 4.0 84 88 5 4 159 212 10 10 10 10 PbTe/ Ni 200 400 130 64 10 10 2.3 4.7 79 90 7 3 114 263 10 10 10 10 Cr / Ni 100 200 300 400 471 471 471 471 0.7 0.8 0.8 0. 9 0.6 0.8 0.9 1.0 25 25 25 25 25 25 25 25 10 10 10 10 10 10 10 10 10 10 10 10 Au / Ni 100 200 300 400 471 471 471 471 0.2 0.2 0.2 0.2 0.7 0.8 1.0 1.1 25 25 25 25 25 25 25 25 10 10 10 10 10 10 10 10 10 10 10 10

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78 The performances of the designs at various temperatures are summarized in Table 2 4 and Figure 2 7 which also included power and power density. The power density, PD, for a single module is given by D f PP P Volumert ( 2 36) wher e t is the thickness of the module, and rf is the outermost radius ( includ ing the outer annular fins). The module diameter is 13 mm, and the thickness 0.36 mm, for a total volume of 48 mm3. Table 2 5 included the figure of merit, and various efficiencies, defined in sections 1.2.6 and 1.2.7. The thermocouple pair figure of merit, ZTC, introduced i n section 1.2.6, is given by Legs TC PN LegsZn R ( 2 37) where Legs and RLegs are the total thermal and electrical resistances of n thermocouple pairs, respectively. The figure of merit is a metric traditionally used to indicate that materials with high Seebeck coefficients, high thermal conductivities, and low electrical resistance are desirable for improved thermoelectric performance. Similarly, the unitless thermocouple figure of merit, is given by ZTCTAVG, as discussed in section 1.2.7, and here, TAVG = ( TGAS + TAmb)/2 is the average temperature between the thermal reservoir in which the device operates. More detailed discussion of the heat transfer and the overall device performances are included in the next few sections.

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79 Table 2 4 T hermoelectric performance for ther mopiles as a function of gas temperature. Device power factor ( DPF ) using the module inner wall surface at ri, the midradius surface at rmid, and the outer surface at rf, respectively. TAMB = 22 C [38] [Adapted from Boniche, I. 2009. Desig n of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] Material (p/n) T emp. T (C) Voltage Voc (V) T (C) T Hot (C) R P (mW) DPF (W/cm 2 K 2 ) P D (mW/cm3) Inner Mid Outer Bi 2 Te 3 100 200 300 400 0.73 1.4 2.1 2.2 28 61 93 121 68 125 181 235 1.0 0.97 1.3 1.5 0.13 0.48 0.79 0.83 3.1 2.4 1.7 1.1 1.7 1.3 0.94 0.58 1.2 0.92 0.65 0.41 2.8 10.0 16. 5 17.4 PbTe 100 200 300 400 0. 42 0.95 1.6 2.4 24 58 95 131 66 123 182 241 1.8 1.0 1.1 1.1 0.03 0.22 0.61 1.3 0.80 1.20 1.30 1.40 0.45 0.67 0.70 0.77 0.31 0.46 0.49 0.53 0.53 4.5 12.8 26.7 Bi 2 Te 3 / Ni 200 400 1.1 1. 5 51 101 118 223 1.3 1.4 0.23 0.42 1.64 0 .76 0.91 0.42 0.63 0.29 4.7 8.7 PbTe/ Ni 200 400 0.95 1. 5 49 107 117 227 2.0 0.95 0.11 0. 60 0.87 0.96 0.48 0.53 0.33 0.37 2.3 12.5 Cr / Ni 100 200 300 400 0.44 0.94 1.3 1.5 22 46 68 8 7 64 116 165 213 16 19 22 25 0.003 0.01 0.02 0.02 0.11 0.10 0.07 0.06 0 .06 0.05 0.04 0.03 0.04 0.04 0.03 0.02 0.06 0.24 0.40 0.49 Au / Ni 100 200 300 400 0.25 0.61 0.83 0.95 22 46 68 87 64 115 165 213 13 16 18 22 0.001 0.006 0.01 0.01 0.05 0.05 0.04 0.03 0.03 0.03 0.02 0.01 0.02 0.02 0.01 0.01 0.03 0.12 0.20 0.22

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80 Table 2 5 T hermoelectric performance for TEG modules as a function of gas temperature. C = (TGas TAmb)/TGas Also, TAMB = 22 C Material (p/n) T emp. T (C) ZTC (K1) x104 Unitless ZTCTAVG Carnot Eff., C (%) Material (%) q Hot (mW) Module =P/qHot (%) Bi 2 Te 3 100 200 300 400 20 15 11 7.1 0.66 0.58 0.50 0.34 21 38 49 56 2.9 5.1 6.0 5.6 17.3 40.8 64.5 89.5 0.76 1.2 1.2 0.93 PbTe 100 200 300 400 3.5 6.5 9.1 12.0 0.12 0.25 0.39 0.60 21 38 49 56 0.64 2.5 5.2 8.5 18.7 41.9 63.9 86.2 0.14 0.52 0.96 1.5 Bi 2 Te 3 / Ni 200 400 6.5 3.1 0.25 0.15 38 56 2.5 2.7 44.3 96.4 0.51 0.43 PbTe/ Ni 200 400 3.1 4.6 0.12 0.22 38 56 1.3 3.8 45.0 94.2 0.25 0.63 Cr / Ni 100 200 300 400 0.40 0.32 0.23 0.16 0.013 0.012 0.010 0.008 21 38 49 56 0.08 0.14 0.16 0.15 19.5 45.8 73.1 101 0.015 0.021 0.026 0.023 Au / Ni 100 200 300 400 0.17 0.16 0.12 0.07 0.006 0.006 0.005 0.004 21 38 49 56 0.03 0.07 0.08 0.07 19.5 45.8 73.1 101 0.006 0.012 0.013 0.010

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81 Figure 2 7 Power and power density as a function of gas temperature for radial TEG modules composed of p/nBi2Te3, p/n PbTe Cr Ni, or Au Ni thermoelements [38] [Adapted from Boniche, I. 2009. Design of a Miniaturized Thermoelectric Generator Using Micromachined Silicon Substrates ] 2.4.1 Discussion of Thermal Performance For the ev aluated test cases (Table 23 and Table 24) the individual conductive thermal resistances for the supporting polyimide and oxide membranes, Poly and Ox are >65x103 K/W, and the net thermal resistances of t he p /n type legs and air gap, P, N and Air are each estimated at ~ 3 x103 K/W. Also, the convective thermal resistance s on the inner and outer silicon ring s, ConvHot and ConvCold are each ~ 1 .5 x103 K/W. On the other hand, the conductive thermal resistances through the inner and outer silicon ring s, ,, SiRingHot and ,, SiRingCold respectively ~1 K/W, are negligibl e as previously assumed. Thus, the net thermal resistance, Conduction, of the device between THot and TCold (as shown in Figure 2 5 ) is ~ 9 00 K/W determined mainly by the pand nCr Ni Au Ni PbTe Bi 2 Te 3

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82 type TE legs, and air gas Also, note that in the absence of leg pairs, the total thermal resistance is now determined by the polyimide/oxide membrane and air gap (~3x103 K/W). Thus, a TEG module with no leg pairs ( n =0) sustains a higher T between the inner and outer silicon rings than those with patterned metal legs. These results indicate that greater thermal isolation (~2 orders of magnitude) can be achieved with the radial TEG structure compared to other miniature devices with planar or vertically oriented TE elements, as summarized in Table 2 6 Even though the polyimide/oxide supporting membrane results in high thermal resistances for good thermal isolation between the silicon rings ( Figure 2 1 ), the convective t hermal resistances are still comparable, which results in significant unwanted temperature differentials between the hot gas and inner silicon ring, and between the outer silicon ring and ambient ( Table 2 4 ). Thus, it is still possible to increase the across the TE elements (and thus increase output power) by improving convective heat transfer and/or by using better TE or support structure materials.

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83 Table 2 6 Comparison of the thermal isolatio n bet ween the radial TEG of this work and other miniature TEG designs fabricated on silicon substrates Refs. Materials Fabrication Method Device Size ( mm 2 ) Thermal Resistance (K/W) DPF ( W/cm2K2) [30] p and n Bi Sb Te (300 m) Micropacking alloy powders 100 for the device: 2 -[19] n poly Si (0.7 m) Al (0.25 m) CVD and sputtered 100 for the device: 2 0.016, but with p/n BiSbTe: 0.81 [35] n doped Si 1 m Al CVD 16.5 supporting (10 m) Si membrane: 27 0.091 This work PbTe, BiTe, or hybrid with metals M olecular beam epitaxy sputtered, or evaporated 132.7 for t he device: ~9 00 Supporting poly/ox membrane/air: ~3 000 up to 1.7 at mid radius, rmid Furthermore, the heat contributions by the Peltier and Joule effects were estimated after obtaining the optimum parameters shown i n Table 2 3 and Table 24. First, for each optimum design, the total Joule heating, determined by multiplying the TEG resist ance ( R ) with the square of the current (I) was < 1% of the total heat transfer rate, qHot (calculated using Equation 24 ). For instance, for the pand nBi2Te3 design at T =100 C, the total Joule heating is only 0.13 mW compared to a total heat transfer rate of ~ 17.3 mW. The Peltier heat flow (released or absorbed) at the junctions which is the product of N P junction temperature T current I and number of TE couples n was also calculated as described in Equations 12 to 1 5. For t he all metal designs, the Peltier heat flow was negligible (< 1%) compared to the total qHot.

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84 On the other hand, the hybrid semiconductor metal designs showed that the Peltier heat flow was ~ 4% 6 % compared to the total heat rate qHot, with the upper bound occurring at the higher values of Seebeck coefficient. Furthermore, a maximum of ~18 % (or 3.2 mW) of qHot was calculated for the Bi2Te3 semiconductor designs, which occurred at the higher Seebeck coefficient values when T = 100 C. Similarly, a Pe ltier heat flow of up to 12 % ( or 10 mW), resulted for the PbTe semiconductor designs for higher values when T = 400 C. Lastly, for all designs, radiation exchange between inner and outer silicon rings and between module and envi ronment (Equations in Appendix C ) was estimated up to ~8 % of total flow rate, qHot, at the highest temperature ( 400 C ). Nonetheless, it is expected to be less significant for lower temperatures. In summary although the Joule heating was negligible for all designs, the Peltier heat flow released/absorbed at the junctions was ~10% for some of the designs. To provide more ac curate thermoelectric predictions especially for the semiconductor designs these effects should be included in the design models. None theless, the decoupled thermal and electrical models provide a good first order estimate of the performance of the TEG suitable for guiding preliminary fabrication efforts 2.4.2 Discussion of Semiconductor Designs For the semiconductor designs, as the hot gas increases from 100 to 400 C, the optimum leg pairs decreases from 62 to 52 for the Bi2Te3 designs and from 103 to 46 for the PbTe designs. The film thickness constantly hits the upper bound of 10 m (given a total substrate thickness of 350 m) with a minimum spacing of 10 m between the TE leg pairs. Since for each design the material properties are considered equal f or both p and ntype, the angular fill factors ( FP, FN) and film thicknesses ( tP, tN) are also equal.

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85 That is, p and ntype semiconductors result in the same amount of surface area coverage. As shown in Table 2 2 b oth semiconductor materials show power factor ( FPF) between 9 and 33 W/cmK2, which is similar those reported in previous works [19, 33] For the Bi2Te3 design, the power P increases as the hot gas temperature in creases from 0.13 mW at 100 C to 0.83 mW at 400 C Similarly, the power of the PbTe design incr eases with temperature from 0.03 to 1.3 mW. As summarized in Table 2 4 the performance of the Bi2Te3 exceeds that of the PbTe, except for the test case of T = 400 C. This is consistent with the thermocouple unitless figure of merit ( ZTCTAVG) of Bi2Te3 exceeding that of PbTe below 400 C (Table 25). Also, t he Bi2Te3 and PbTe module conversion efficiencies, Module, are estimated up to 1.2% and 1.5%, respectively. Similarly, the TEG device power factor ( DPF ) using Bi2Te3 thin films exceeds that of PbTe designs, except at 400 C and is estimated at up to 1.7 W/cm2K2 (calculated using the midradius, rmid, wall surface area) for the low temperature of 100 C. The DPF for the radial generator is similar to that of a thick film based (20 m) parallel plate generator [28] and to macroscale TE devices [20, 21] but is ~ 2X higher than the performance of a generator based on thin BiTe alloy films on polymer/silicon substrates [19] Additionally the TEG module exceeds by up to ~1000X the performance of similar thin film planar devices on glass substrates [33, 34] 2.4.3 Discussion of Semiconductor Metal Hybrid Design s For hybrid semiconductor metal designs, as the hot gas increases from 200 to 400 C, the optimum film thickness for the semiconductor hits the upper bound of 10 m T he Ni metal thickness ( tN) increases from 2.8 m to 4.0 m for the Bi2Te3/Ni designs

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86 and from 2.3 m to 4.7 m for the PbTe/Ni designs. Both hybrid designs show minimal spacing of 10 m between TE leg pairs. Also, t he angular fill factor, FP for both Bi2Te3 and PbTe increases to above 7 9 %, while FN decreases to below 7 % for the metal. At 200 C, the Bi2Te3/Ni design has a higher performance ( P = 0.23 mW ) thermocouple ZTCTAVG of 0.25 than the PbTe/Ni design. While at 400 C, the latter has a higher performance ( P = 0.60 mW ) thermocouple ZTCTAVG of 0.22 as expected. Also, both semiconductor metal hybrid radial designs exhibit comparable DPF to those predicted for an all semiconductor generator [19] To maximize the power the design routine is striving to minimize the metal leg (with large and low ) cross section, while maximizing the semiconductor leg (with low and large ). By doing so, the thermal losses through the leg pairs are minimized to maintain a high temperature difference, while keeping the electrical resistance from increasing too large by making the leg pairs wider and/or thicker. In other words, t he design routine balances the thermal and electrical resistances, subject to the design constraints. Specifically, the design routine strives for larger for higher voltage and power by reducing the cross section of materials with large thermal conduct ivity ( ) such as that of the metal. On the other hand, the routine increases the cross section of the semiconductor leg (having high ) to reduce the electrical resistance and thus increase power. 2.4.4 Discussion of All M etal Design s Lastly, allm etal TEG design s (CrNi and AuNi) result in a large number of leg pairs (471 pairs), with a minimum spacing of 10 m, but only require a film thickness below 1.1 thermocouple ZTCTAVG remains relatively low (< 0. 013), with a

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87 maximum power P = 0.02 mW an d power density, PD = 0.49 mW/cm3 at 400 C. Overall, the DPF of a radial design based metal thin films is over an order of magnitude worse than those based on semiconductors However, the all metal thinfilm TEG module can be fabricated with a much simpler material set 2.5 Selected Designs for Fabrication and Testing The previous sections showed estimates of the performance of TEG modules using various materials. Also, these sections provided insight into what is possible by using optimized thermopile lay outs and highperforming materials on the radial polymer/silicon platforms. As a step towards demonstrating the concept while ensuring first run success, three different simpler designs based on thinfilm metals were selected for fabrication and testing. Even though the semiconductor designs yielded high er performance, these films would require a more advanced deposition method such as molecular beam epitaxy (MBE) [47] On the other hand, the metal thinfilm designs were selected for simpler fabrication and deposition methods such as evaporation or sputtering. The geometries for the selected designs are shown in Table 2 7 The material properties from Table 2 2 were used to estimate the AuNi TEG module performance, as summarized in Table 2 8 and Table 2 9 Au and Ni thin films were selected due to a comb ination of low electrical resistivity good adhesion to the polyimide layer, and good solder ability for electrical contacts [48] Additionally, the AuNi system exists as a two solid phase (mixture), up to ~800 C, under equilibrium conditions [49, 50] For a given temperature, the intermediate design ( n =65) showed higher power output and power density (up to 4.5 W and 97.5 W/cm3) assuming matched load, than the other two

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88 designs. Meanwhile, a design with more leg pairs ( n =90) generated the highest voltage for a given temperature. For instance, at 200 C, the design with n=90 pairs generated an opencircuit voltage of 177 mV, while the modules with n=18 and n=65 pairs yielded 13 mV and 77 mV, respectively. Although, low efficiencies, Module, are obtained using thin film metal, the simpler material set enables the evaluation of the proposed radial design on silicon substrates. Table 2 7 Selected TEG designs for fabrication and tests wi th different geometries based on thinfilm Au and Ni. Leg Pairs, n 18 65 90 Au width at r 1 ( m) 377 50 10 Ni width at r 1 ( m) 377 40 10 Leg spacing ( m) 90 90 90 Inner/outer interconnect width ( m) 100 100 100 Angular fill factor F p (%) 40 20 5 Ang ular fill factor F N (%) 40 15 5 Au thickness t P ( m) 0.5 0.5 0.5 Ni thickness t N ( m) 0.5 0.5 0.5

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89 Table 2 8 Theoretical performance of thinfilm metal TEG modules for fabrication and tests TAMB = 22 C. Au/Ni Leg Pair n T emp. T (C) Voltage Voc (mV) T (C) T Hot (C) R ( DPF (W/ cm2K2) P D ( W/ cm3) P ( W) 18 100 5.1 12 58 15 0.032 9 0.42 200 13.3 27 103 24 0.027 40 1.9 300 19.5 42 149 32 0.018 65 3.0 400 23.6 57 194 42 0.011 72 3. 3 65 100 29.9 19 62 345 0.019 13.9 0.65 200 76.7 42 113 540 0.016 58.6 2.7 300 111 65 164 718 0.010 91.2 4.2 400 132 87 214 955 0.006 97.5 4.5 90 100 71.4 33 71 2000 0.006 13.6 0.63 200 177 71 131 3120 0.005 53.7 2.5 300 247 106 189 4140 0.003 79.3 3.7 400 288 138 246 5490 0.002 80.8 3.8 Table 2 9 Theoretical performance of thinfilm metal TEG modules for fabrication and tests C = (TGas TAmb)/TGas. Also, TAMB = 22 C Au/Ni Leg Pair n T emp. T (C) Z TC (K1) x106 Unitless ZTCTAVG x103 Carnot Effi., C (%) Material x103 (%) q Hot (mW) Module =P/qHot x103 (%) 18 100 11.2 3.7 21 21.8 23 1.8 200 9.8 3.7 38 43.5 53 3.5 300 6.7 2.9 49 46.5 82 3.7 400 4.1 2.0 56 38.7 112 3.0 65 100 9.3 3.1 21 18.1 21 3.2 200 8.1 3.1 38 36.0 47 5.8 300 5.5 2.4 49 38.2 74 5.8 400 3.4 1.6 56 32.1 101 4.5 90 100 11.2 3.7 21 21.8 16 4.0 200 9.8 3.7 38 43.5 37 6.7 300 6.7 2.9 49 46.5 60 6.2 400 4.1 2.0 56 38.7 84 4.5

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90 2.6 Summary This chapter proposed a radial TE generator design and its performance for various TE thin films using hot gas streams (100 400 C). The cylindrical, stackable, silicon based design facilitates planar batch microfabrication and direct fluidic coupling to hot exhaust streams It was shown that p and ntype semiconductor thermoelements yielded reasonably high power s and power densities (e.g. 1.3 mW and 26.7 mW/cm3 at 400 C) from mo dules 13 mm in diamet er and 0.36 mm thick (48 mm3). Also, m ultiple modules could potentially be stacked to achieve tens of milliwatts of power for inline, heat powered sources. The optimization, however, indicates the requirement for fairly thick semiconductor films, but within reason for electrodeposition or molecular beam epitaxy (MBE) deposition methods. The pand ntype semiconductor films constantly hit the upper bound of 10 This motivates the need to explore thick film deposition technologies and/or thi nner substrates. For ease of fabrication or to demonstrate the concept allmetal Cr Ni and AuNi designs may be preferred, with predicted power of up to 0.02 mW but only requiring film thickness below 1 m. These preliminary performance predictions were compare d to other reported devices. Overall, the device power factor ( DPF ) of the radial generator is similar to that of a thick film based (20 m) parallel plate generator [28] and to macroscale TE devices [20, 21] However, the DPF of the radial TEG is > 2X than the performance of a generator based on thin BiTe alloy films on polymer/silicon substrates [19] Furthermore, the radial generator shows ~1000X higher performance than similar thin film planar devi ces on glass substrates [33, 34]

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91 Finally, there is much room for continued design and optimization for similar miniat urized thermoelectric modules. This work assumed the use o f thin films due to fabrication and size constraints, but similar design analysis could be performed for thicker films by relaxing the upper bound constraint on the film thickness. Additional constraints (e.g. minimum voltage, maximum resistance, etc.) could also be imposed to tailor the design depending on the requirements of an application. To expand the design space, additional design variables could also be included (e.g. heat exchanger parameters, substrate thickness, etc.) to further increase the performance of the generator modules. Nevertheless, three thinfilm metal TEG module designs with various leg pairs, n were selected for fabrication and analysis. The fabrication of these prototype modules is discussed in Chapter 3 followed by the experimental procedure in Chapter 4.

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92 CHAPTER 3 DEVICE FABRICATION Chapter 2 focused on the design and optimization of a radial TEG using various combinations of TE thin films and whose structure is more suitable for power generation using hot gas streams In this chapter the silicon microfabrication process for the radial TE generator modules with integrated resistive structures for tem perature sensing is described in detail Additionally, the fabrication of dummy modules structures without thermocouples is also included. Lastly, the techniques used for stacking the TEG and dummy modules to form the stacked cylindrical device structure are also presented. 3.1 Fabrication Overview TEG modules (13 mm in diameter) were fabricated using thin film metal (Ni and Au) thermocouples, as shown in Figure 3 1 The microfabrication process involved a combinatio n of photolithography, reactiveion etching (RIE) of polyimide, metal deposition (sputtering), wet etching, metal lift off, and silicon deep reactive ion etching (DRIE). The overall module geometries we re based on the designs presented in Chapter 2. T hree different thermopiles designs were fabricated, where the number of thermocouples varied: n = 18, n = 65, and n = 90, as shown i n Figure 3 1 A to C. An additional device without thermocouples was also fabricated to characterize the thermal isolation capability of the supporting pol yimide/oxide membrane as shown i n Figure 3 1 D. The modules also included integrated Ni resistive structures for temperature sensing of the inner and outer silicon rings. These resistors simultaneously were fabricated using the same metals as used in the thermopile.

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93 A Figure 3 1 A) Top and cross section views (A A) o f a TEG module (n=18 leg pairs) in cluding resistive thin film Ni for internal temperature measurements of the inner and outer silicon rings. B C) TEG modules with n=65 and n=90 leg pairs. D) Test module with only resistive Ni ring structures. Outer resistive thermal sensor TEG terminals 1 st TE leg (Ni) 2 nd TE leg (Au) Hot inner finned silicon ring Leg spacing A A Polyimide membrane Cold outer an nular silicon ring Inner resistive thermal sensor Outer silicon ring Oxide Au leg Ni leg 0.35 mm 5 mm 1 mm 0.5 mm

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94 B C Figure 31. Continued

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95 D Figure 31. Continued Metal films were used (a) for fabrication simplicity and (b) because semiconductor TE materials were not readily available for this work. While the TE performance is limited by the use of metal thermocouples, the fabric ated structures are useful for demonstrating the radial design concept; for model validation; and as a stepping stone toward future, improved designs. 3.2 Fabrication of Radial TEG Modules The process uses double side polished silicon (100) substrates from Sil icon Quest Inc. that are 100 mm in diameter and ~ 345 m in thick ness. These substrates include a thermally grown silicon dioxide (SiO2) layer ~0.4 m in thickness on the front and back Inner silicon ring Outer silicon ring

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96 surfaces An overview of the process is shown in Figure 3 2 and described in detail in the following sections. 3.2.1 Patterning of Polyimide Prior to processing, a substrate is rinsed with acetone, methanol, isopropanol, and deionized water to remove any particles and any surface contamination. The w afer is then dehydrated in an oven at 110 C for 10 minutes. Next, an aminosilanebased solution ( DuPont VM 651) is used as an adhesion promoter to enhance polyimide adhesion to SiO2, and silicon [39] The solution is first diluted 1:200 (by volume) with deionized water and then, a puddle is dispensed and spun dry at 3000 rpm for 40 seconds on the topside of the s ubstrate. The substrate is then baked in an oven for 110 C for 10 minutes Similarly, a puddle of polyimide (PI 2611 from Microsystems Inc.) is then dispensed and allowed to spread on the substrate. The polyimide is slowly spun first at 500 rpm for 5 seconds to allow a uniform spread over the wafer and then, spun to a final speed of 3500 rpm for 35 seconds for a target film thickness of ~ 5 m To fully cure and set the final thickness, the polyimide is softbake at 110 C for 10 minutes on a programma ble hot plate, and the temperature is increased to 350 C at ~ 4 C/minutes. This maximum temperature of 350 C is held for 1 hr, and then the substrate is gradually cooled down to room temperature ( Figure 3 2 A ). As mentioned earlier in this work, a polyimide layer is used as part of the supporting structure for the TE legs because of advantageous properties such as good thermal and mechanical stability at high temperatures (~ 400 C). In particular, the cured pol yimide used in this work exhibits other desirable properties such as low stress (<2 MPa), low coefficient of

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97 thermal expansion (CTE 3 ppm/ C) and low moisture uptake (0.5 %) as compared to other polyimides [39] Next, oxygen plasma is used to pattern the polyimide. It was observed that the photoresist mask eroded considerably in O2 plasma, thus a layer of 0.1 m of Chromium (Cr) is sputtered on the polyimide to serve as a hard mask. After the Cr deposition, a positive tone photoresist ( AZ 9260 from Clariant ) is then spincoated at 2500 rpm for 40 seconds and soft bake in a hot plate at 110 C for ~165 seconds. Th en, the resist is exposed with a UV light source using Mask 1, and developed with diluted AZ 400K in deionized water (1:3 by volume) to form annular rings of resist (~ 9 m in thickness) over the Cr layer. Then, the Cr layer is patterned with a wet etch solution consisting of nitric acid (HNO3) and ceric ammonium nitrate (Chromium Etchant Type 1020 from Transene Co.) as shown i n Figure 3 2 B Next, the polyimide layer on the topside of the wafer is patterned with a dry etch method using both the photoresist and Cr film as hard mask ( Figure 3 2 C) The dry etch of the polyimide on the silicon wafer consists of an oxygen (O2) plasma in a RIE ICP (Unaxis) unit at 70 mTorr, with coil and electrode powers of 600 W and 2 00 W, respectively, and bac kside substrate cooling using 12 sccm of helium ( He ) gas. An etch rate of ~ 0.5 polyimide using 60 sccm of O2 [39] Once the polyimide layer is patterned, the substrate is immersed in a solution bath of buffer oxide etch (BOE 6:1) for ~ 5 minutes to remove the exposed SiO2 from the top and bottom sides ( Figure 3 2 D) Then, the Cr layer is completely removed with the wet etch solution mentioned above ( Figure 3 2 E) thus revealing a smooth polyimide film ~ 5 in thickness as measured with a surface stylus profilometer from Veeco Inc.

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98 The process flow above described the use of nonphotodefinable polyimide (PI 2611). In addition, a photodefinable polyimide (HD 8820) was also investigated, since it would require fewer steps to pattern the annular rings compared to the nonphotodefinable polyimide (PI 2611). However, it was observed that striations developed on various thin film metals including Cr, Ni, Ti, and Cu when deposited on HD 8820. Also, further proc essing resulted in visible cracking of the metal. Thus, PI 2611 was used as the supporting polyimide membrane for all of the modules reported in this dissertation. Silicon SiO2Polyimide A. Deposition of polyimide layer on SiO2/Si Chromium mask B. Deposit ion and patterning of chromium mask. Figure 3 2 Fabrication process of a radial TE generator module in a silicon substrate.

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99 Patterning of Polyimide C. Patterning of polyimide layer with O2 plasma. Patterning of SiO2 D. Removal and patterning of SiO2 layer with BOE solution Removal of Chromium mask E. Removal of chromium hard mask with nitric acid solution. Ni F. Deposition and patterning of 1st thin film (Ni) TE metal. Figure 32. Continued

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100 Au Ni G. Deposition and patterning of 2nd thin film (Au) TE metal. Silicon Au Ni Polyimide Oxide H. Backside silicon DRIE for ther mal isolation, channel formation and device release. Figure 32. Continued 3.2.2 Patterning the First Set of TE Legs After the patterning of the polyimide and oxide rings, the substrate is rinsed in solvents (acetone and methanol), followed by deionized water and then dehydrated in a hot plate at 110C for 30 seconds. A positivetone 9thick photoresist is patterned with Mask 2 for lift off deposition of the first set of thermoelement (TE) metal on the polyimide layer ( Figure 3 2 F). For metal deposition, the substrate surface is first rinsed and cleaned in hydrochloric acid (HCl) diluted in deionized water (1:10) for ~20 seconds. The substrate is then immediately loaded (in a metal sputtering tool) for dc sputter deposition of ~0.4 of nickel (Ni) at 350 W, chamber pressure of 5 mTorr, and deposition rate of ~0.2 nm/sec. Prior to deposition, the substrate is exposed to an in -

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101 situ gas plasma of O2 (90 sccm) and Ar2 (100 sccm) for 20 seconds at 300 W, which cleans and roughens the polyimide surface for improved metal adhesion. After the sputter deposition, thin film Ni legs are patterned on the polyimide by a lift off method in an acetone bath. After the lift off process, edge beads of photoresist still remained but were removed with a combination of rinsing the substrate in acetone, methanol and deionized water, and a gentle brush of the structures in acetone with a cleanroom swab. 3.2.3 Patterning the Second Set of TE Legs Next, the second set of thermoelements is deposited and patterned to complete the thermopile using Mask 3 ( Figure 3 2 G). Similar to the procedure followed for the first set of TE legs, the substrate is rinsed in solvents and dehydrated in a hot plate at 110C for 30 seconds. Another layer of 9 thick photoresist is patterned with Mask 3 over the polyimide layer. The substrate surface is also rinsed in a solution of HCl and deionized water (1:10) for ~20 seconds to clean the Ni and polyimide surfaces. The substrate is then loaded (in a metal sputtering tool) for dc sputter deposition of ~0.4 of gold (Au) at 150 W, chamber pressure of 5 mTorr, and deposition rate of ~0.4 nm/sec. Prior to deposition, an in situ gas plasma of only Ar2 (100 sccm) for 20 seconds at 300 W, cleans the Ni contact s and roughens the polyimide surface for improved metal adhesion. Note that, O2 plasma was not used to minimize oxidation on the Ni film. Then, the Au metal is patterned to complete the thermopile by a lift off method in an acetone bath. Excess resist is removed by repeated rinsing in solvents and deionized water.

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102 3.2.4 Silicon Etching After completing the thermopile fabrication on the topside, fin arrays and a hot gas channel are formed by a deep reactive ion etching (DRIE) of silicon from the backside of the wafer. This process also releases each die (or module) and simultaneously, selectively etches away silicon from underneath the thermopile, stopping on the oxide ( Figure 3 2 H). The details are described as follows. First, a posit ive tone 9 thick photoresist is spun on the backside and patterned with Mask 4. The photoresist backside features are aligned to the topside features using a back to front optical alignment with an EVG mask aligner. The topside of the substrate is attached to a plain silicon handle wafer to provide support during the latter DRIE using a thin (~2 m) S1813 photoresist spincoated at 2500 rpm for 40 seconds. The substrate, photoresist, and handle wafer stack is soft baked on a hot plate at 100 C for ~ 2min. Then, the stack is loaded (into an STS Deep RIE tool) for deep silicon etch (>350 m) using a Bosch etch process consisting of alternating silicon etching and passivation cycles with SF6 and C4F8, respectively at ~1 m/cycle. After completion, t he individual chip modules, shown in Figure 3 3 are carefully removed from the handle wafer by immersion in acetone, and rinsing with methanol and deionized water.

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103 Figure 3 3 TEG modules fabricated on silicon substrates using thinfilm Au Ni as thermoelements Also include d resistive thin film Ni for temperature sensing of the inner and outer silicon rings. Inner and outer diameters are 5 mm and 13 mm, respectively. 3.3 Fabrication of Dummy Modules In addition to the TEG modules, dummy modules of 9 mm and 13 mm in diameter were fabricated using a separate set of two masks. The first mask is used to pattern the polyimide into annular rings following the same process ste ps shown i n Figure 3 2 (A to E). The second mask is used to pattern the backside of the silicon substrate and release the devices following the same steps i n Figure 3 2 H. These structures have no thin fi lm metals and consist of a polyimide/oxide annular membrane (~ 5 m in thickness) connecting to two concentric silicon rings as depicted in Figure 3 4 These modules were used for thermal characterization and to enable a stacked c ylinder structure for hot gas flow tests. Single TEGs

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104 A B Figure 3 4 A) Top view of a dummy module structure. B) B ackside view of dummy modules used for stacking Inner diameter aperture is 5 mm, and outer diameters are 9 mm and 13 mm Polyimide membrane connecting inner and outer silicon rings Cold outer annular silicon ring Hot inner finned silicon ring

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105 3.4 Fabrication of a Stacked TEG Cylinder The overall design concept for the radial TEG system envisions a stacked cylindrical structure of multiple TEG modules. While fabricating and testing multiple stacked modules is le ft for future work, testing single TEG modules in a stacked structure is investigated. To demonstrate the concept, a stack was formed using only one active TEG module in a stack of dummy modules. To facilitate alignment, stacking, and bonding of the modules, a customedmade assembly jig using two stainless steel rods (1 mm in diameter and 35 mm in length) was used, as shown in Figure 3 5 Several dummy modules were bonded one at a time using a high temperature resistant, thermally conductive epoxy (JB Weld). The epoxy, which consists of a resin and a hardener mixed 1:1, is applied manually on the top surface of the inner and outer silicon using ~150m diameter needle tip. The top module is then slightly pressed onto the bottom chip to minimize any air gaps. For overall assembly of the stacked structures, two stacks of dummy modules t he top stack had 8 modules (one 13 mm in diameter, seven 9 mm in diameter while the bottom had 7 modules (one 13 mm in diameter, six 9 mm in di ameter) were first assembled separately, and left overnight to cure the epoxy ( Figure 3 5 A). Then, a TEG module (13 mm in diameter) was bonded between the two halves to complete the stacked cylinder for a total of 16 modules as sh own i n Figure 3 5 B C. This complete structure was then left overnight to allow the epoxy fully cure at ambient temperature. Lastly, the stack was carefully removed from the assembly jig. Prior to assembling the TEG module between the stacked devices, electrical connections were made by soldering thin Cu wires (gage 34) to the Au/Ni bond pads (~1mm x 2mm).

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106 A B C Figure 3 5 Stacking of a TEG module (13mm) between 15 dummy modules (9 mm and 13 mm in diameter) to form a cylindrical structure for hot gas stream tests. Additionally, Figure 3 6 shows a diagram of van der Pauw ( VDP ) crosses and transfer length method (TLM) test structur es [51] that were also simultaneously fabricated on the same silicon substrate, with corresponding dimensions shown i n Table 3 1 Specifically, van der Pauw crosses were used to estimate the thinfilm resistivit y of the deposited Au and Ni films. Similarly, the TLM structures with Au contacts on a Ni mesa were used to determine film resistivity and specific contact resistivity. More detail s are provided in Chapter 4. Soldered e lectrical contacts Stacked TEG module ~ 6mm ~ 13mm Alignment r od

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107 Figure 3 6 Cross section and topview diagram of van der Pauw crosses and TLM (mesa) structures used to estimate thinfilm resistivity (Au and Ni) and specific contact resistivity (Au/Ni). Table 3 1 Dim ensions of the van der Pauw (VDP ) crosses and TLM (mesa) structures. Features Dimensions Ni thickness, t Ni ( m ) 0.57 Au thickness, t Au (m ) 0.48 VDP pad size, p (m ) 310 VDP pad separatio n, L (m ) > 490 TLM Mesa width, w (m) 50 TLM Au Pad size, s (m ) 275, 300, 400 TLM Pad spacing, d (m) 35, 45, 44, 104, 155, 204 Ni t Ni SiO 2 / Silicon P o lyimide Au A A t Au A A d s w van der Pauw crosses TLM Structure L p

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108 3.5 Summary This chapter presented the fabrication procedure of various radial TEG devices in silicon substrates. Moreover, TEG modules with thin film metal structures were integrated for internal temperature measurements. Also, a stacked cylinder consisting of dummy TEG structures (no thermocouples) stacked with a TEG module was also fabricated for hot gas stream tests. T he challenges and advantages of integrating thin film metal thermocouples on polymer films and on silicon substrates were also discussed.

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109 CHAPTER 4 EXPERIMENTAL CHARACT ERIZATION Ch apter 3 discussed the process flow and fabrication of radial thermoelectric generator (TEG) modules using thin film metals as thermoelements. Additional modules without thermoelements coined dummy mod ules were also fabricated. This chapter focuses on the test procedures and experimental characterization of the devices using hot gas streams. First, electrical resistivities of the metal thin films were measured using onwafer electrical test structures The module thermopile resistances were then characterized. Next, the thermal resistive sensors integrated on the TEG and dummy modules were characterized by measuring the temperatureresistance behavior for each Ni ring structure. Then, the thermal and thermoelectric behaviors for each TEG module design were characterized using hot gas streams at various temperatures. The Seebeck coefficients were extracted from opencircuit voltage measurements. Power generation tests were also performed on individual modules and a stacked cylinder structure. The convective heat transfer coefficients were extracted for the stacked TEG structure. Where appropriate, the experimental measurements were compared against model predictions. 4.1 Electrical Characterization of Thin Films and Thermopile In this section, the room temperature metal thinfilm resistivities and as fabricated thermopile resistance were examined. First, the thinfilm electrical resistivities and contact resistivity of the sputter deposited Au and Ni were extracted using electrical test structures. Additionally, the metal thermal conductivities were estimated using the WiedemannFranz relationship. From the electrical resistivity measurements, the

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110 thermopile (or module) resistances were predicted and then compared to measured values. 4.1.1 ThinFilm Electrical Resistivity Measurements First, the electrical resistivities ( ) of the Au and Ni thin films were measured by using van der Pauw tests structures [51] Additionally, the specific contact resistivity ( c) of Au Ni films and the Ni resistivity were extracted by using the transfer length method (TLM) [51] Both van der Pauw crosses and TLM test structures were fabricated simultaneously on the same silicon wafer as the TEG modules as desc ribed in Chapter 3. Four point resistance measurements and a Keithley 2400 sourcemeter were used for all of the electrical resistance measurements. The measurements were all made at room temperature (25 C) using a semiconductor probe station. For the van der Pauw cross test structures, the electrical resistivity of the film under test is given by tR ( 4 1 ) where t is the film thickness, R is the measured resistance. This equation assumes that the metal film thickness is much less than the probe spacing. Since the probe spacing for all tests here was > 250 m and the film thicknesses were ~0.5 m, this assumption is validated. Electrical (four point probe) measurements were made on nine Au van der Pauw cross structures and eleven Ni van der Pauw cross structures. For resistance measurements, a current ( I =100 mA ) was set by the Keithley meter, and the internally measured V was used to display the resistance, R = V/I The manufacturer specified accuracy for a single resistance measurement was stated to be 0.003 This

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111 uncertainty (assumed to be 95% confidence interval) was considered a systematic measurement error, UR_Systematic. T he random uncertainty, UR _Random, of the mean resistance, R was determined from the set of N measurements given by [52] R RRandomS Ut N ( 4 2 ) where SR is the samp le population standard deviation, and t* is a factor determined from the degrees of freedom ( = N 1) and a confidence level (95% used in all cases here) [52] The random uncertainties of the thinfilm Au and Ni resistance measurements were estimated at 0.001 0.020 The systematic and random errors were combined to yield the final uncertainty in the mean measurement, UR_Total, given by __ _RSystematicRRandomRTotalUUU ( 4 3 ) The resulting estimates for the mean measured test structure resistances were 0.012 0.003 and 0.423 0.020 for the Au and Ni, respectively. Also, the thinfilm thicknesses for each metal were measured using a (Veeco Dektak 150) stylus surface profilometer on eleven different regions distributed across the wafer. The manufacturer specified accuracy for a single thickness measurement was stated to be 0.6 nm. Since this systematic measurement uncertainty was much smaller than the sample to sample variation (on the order of 10 nm ), the measurement uncertainty was neglected. Thus, the uncertainty, Ut, of the mean thickness, t for each metal was determined by t t S Ut N ( 4 4 )

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112 where t is the metal film thickness and St is the sampl e population standard deviation. Thus, the mean thickness of the Au layer was found to be 0.48 0.02 m, and for the Ni layer 0.57 0.03 m. The effective uncertainty in the measured resistance and film thickness determined the uncertainty in the calcul ated resistivity as follows. In the general case [52] where an experimental result, r is given as a function of k uncorrelated measured variables, Xk, i.e. (,,...,)k rfXXX ( 4 5 ) the uncertainty in r is given by ...krXXX krrr UUUU XXX ( 4 6 ) Equivalently, this can be rewritten as a relative uncertainty given by ...kX XX k r kkU UU X UX X rrr rrXXrXXrXX ( 4 7 ) Thus, by using Equation 47 and Equation 41 the uncertainty in resistivity ( U) can be written as t RU U U tR ( 4 8 ) where and t are the mean film resistivity and thickness, Ut is the uncertainty in the film thickness, and UR is the uncertainty in the resistance measurement of the test structures The raw data and calculations are shown in Appendix B. To complement the van der Pauw crosses, the film resistivity ( ) of Ni and the AuNi contact resistivity ( c) were measured using TLM test structures with the raw

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113 measurements and details shown in Appendix B. Four different TLM test structures were characterized. The TLM test structure consists of a striplike Ni mes a with multiple Au contacts as shown i n Figure 36. The total resistance, RT, between two adjacent contacts, assuming nonalloyed metal interface between Au and Ni thin films [51] is given by c TRd tss ( 4 9 ) where and t are the film resistivity and thickness of the film (Ni) mesa, s is the top metal (Au) contact length, d is the spacing between adjacent contacts, and c is the specific contact resistivity. The total resistance, RT, increases linearly with increasing spacing, d Thus, by plotting RT vs. d the thinfilm resistivity ( ) can be estimated from the slope of the linear fit. Similarly, the specific contact resistivity ( c) can be estimated from the y intercept. More details are given in [51] A summary of the thin film measurement results ( mean U _mean) is shown i n Table 4 1 with all of the data shown in Appendix B. From van der Pauw cross structures, the thin film resistivities for Au and Ni were estimated at 2.6 0.7 cm and 108.2 7.8 cm respectively. From the TLM test structure, the Ni fi lm resistivity was estimated at 81.5 6.4 cm (lower than the van der Pauw extracted resistivity). In addition to these characterizations of test structures, the film resistivity for Ni was also extracted from resistance measurements and physical dimens ions of the inner and outer resistive sensor Ni rings. An estimate of 87.3 7.5 c m was obtained, in better agreement with TLM test structures measurements.

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114 Table 4 1 Measurements of thin film Ni and Au electrical resistivity ( ) with van der Pauw crosses, TLM, and Ni ring structures at 25C. Film ( cm ) van der Pauw ( cm ) TLM ( cm ) from Ni rings ( cm ) Bulk [45] Ni 108.2 7.8 81.5 6.4 87.3 7.5 7.1 Au 2.6 0.7 --2.3 The resistivities of the thin films were then compared w ith known values for bulk metals. The experimentally extracted resistivity for the sputtereddeposited Au film showed reasonable agreement with the bulk Au resistivity at 25 C (~2.3 c m ) [45] In contrast, the sputter deposited Ni f ilm resistivity was up to 10 15X greater than bulk Ni at 25 C (7.1 cm ) [45] While the variance from bulk was not entirely unexpected, the results for the sputtered Ni films here also differed from other reported Ni thin films. For instance, the resistivity was higher than thinfilm Ni with thicknes s range of 6 70 nm and evaporated on glass (19 cm) [53] Moreover, the measured resistivity was also higher than sputtereddeposited Ni on polyimide up to 10 nm in thickness (21 cm) [54] The large resistivity differences may be attributed to differences in film thickness, deposition conditions, substrate, and film defects. 4.1.2 ThinFilm Thermal Conductivity Estimates From the electrical resistivity measurements, the thermal conductivities ( ) of the thin metal films were estimated by using the WiedemannFranz law, which states that the electronic component of the thermal conductivity ( e) is related to the electrical conductivity ( = 1/ ) as follows [10] : o eoLT LT ( 4 10)

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115 where the Lorentz number, Lo is given by Fermi Dirac statistics, T is the temperature (in Kel vin) and is the electrical resistivity ( m ) For metals, Lo is simplified to 2.45 x 108 V2K2 [10]. Also, the total thermal conductivity ( ) may be expressed as the sum of the electronic ( e) and the lattice ( L) component. In metals, the electronic contribution to the thermal conductivity is much larger than the lattice contribution [10] so that eLe ( 4 11) By using Equations 410 and 411, the thermal conductivity ( ) for the Au and Ni thin films were est imated at 285.2 73.4 W/mK and 6.8 0.5 W/mK, respectively, using resistivities from van der Pauw crosses. These values are summarized in Table 4 2 along with the estimated thermal conductivity values based on the different measured resistivities. The estimated thermal conductivity for the sputtereddeposited Au film was slightly lower than the bulk Au conductivity at 27 C (~ 317 W/mK ) [45] On the other hand, the sputtereddeposited Ni in this work showed a thermal conductivity ~10X lower than the bulk Ni value at 27 C (~91 W/mK ) [45] This is in line with the similarly lar ge discrepancies in the electrical resistivity measurements. Table 4 2 Estimated thermal conductivities ( ) for thin films Ni and Au based on measured resistivity ( ) values. Film (W/m K) from van der Pauw (W/m K) from TLM (W/m K) from Ni rings (W/m K) Bulk [45] Ni 6.8 0.5 9.0 0.7 8.4 0.7 91 Au 285.2 73.4 --317

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116 4.1.3 Module Thermopile Resistance Measurements Prior to heating tests, the TEG module electrical resistances were measured using a two point resistance probe and a dc current s ource of 0.1 mA (with a Keithley 2400 meter) at room temperature. To complement this measurement, the resistance of the module was also measured using a four point probe method using a semiconductor probe station and an ac current source of 0.2 mA (over a frequency of 40 Hz 10 KHz) with a precision impedance analyzer (HP 4294A). For instance, for a TEG module ( n =65), two point (dc) measurements showed a resistance of ~1.63 k with four point (ac) measurements of ~1.61 k Table 4 3 shows the measured twopoint dc thermopile resistance values for the three different TEG modules. Table 4 3 Two point probe dc current measurements and model estimates o f electrical resistance at room temperature for various TEG modules using AuNi thermoelement pairs. The percentages of the total thermopile resistance attributed to the legs and interconnects are indicated in parentheses. Leg Pairs ( n ) 18 65 90 Measured total resistance, RTotal 0.123 0.003 1.63 0.003 11.3 0.003 Estimated total resistance, RTotal 0.108 0.036 2.24 0.74 12.4 4.1 Estimated legs resistance, RLegs 0.065 (61%) 2.13 (95%) 12.3 (99%) Estimated interconnect resistanc e, RInterc 0.042 (39%) 0.101 (5%) 0.137 (1%)

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117 The module (total thermopile) electrical resistance was also calculated by using the extracted thin film resistivities in Table 4 1 and the derived Equation 223. In particular, by using the Au resistivity ( 2.6 cm ) and the Ni thin film resistivity ( 87.3 cm ), the expected total thermopile electrical resistance was calculated, including the contribution of the leg pairs (along the radial direction), the interconnects (along the circumferential direction), as well as the contact resistance between the different metal segments. The contact resistance of one individual contact, Rc, is given by ccRs ( 4 12) where s2 is the top contact surface area. From the TLM test structures, the AuNi specific contact resistivity, c, was estimated at ~15 15 cm2 by using the intercept as described in Chapter 3. Despite the large uncertainty, in all cases, the total estimated contact resistance 2* n Rc (since there are two contacts for every thermoelement pair), was <0.1% of the combined leg and interconnect resistance, and was thus neglected from future calculations. The estimated resistances are compared against the measured resistances in Table 4 3 For example, the expected TEG module ( n =65) resistan ce was estimated at 2.24 0.74 k compared with the measured 1.63 k Overall, by including the uncertainty in the estimated total resistance (from film properties and geometries), it is seen that the experimental ly measured resistances fell within the bounds of the estimated values. A lso included in Table 4 3 is an estimated breakdown of the total thermopile resistance (thermoelectrically active legs, versus inactive interconnects). For

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118 example, for the n =65 design, the leg pair and interconnects comprised ~95% and ~5%, respectively, of the total module resistance. Note, that the interconnections contributed only 1% of the total module resistance for the n =90 design, but 39% for the n =18 design. Since the inter connections do not generate voltage and only add resistance, their influence should be minimized. 4.1.4 Module Thermal Conductivity Estimates Using the estimated thermal conductivities discussed in Section 4.1.2, the thermopile thermal resistance was estimated from the extracted thinfilm thermal conductiv ities for Au ( Au = 285 K/W) and for Ni ( Ni = 8.4 K/W) and by using Equations 2 12 to 218 For this first analysis, room temperature values for the substrate thermal conductivities, e.g. polyimide ( Poly = 0.14 K/W ) and oxide ( Ox = 1.4 K/W ), and air ( A ir= 0.026 K/W ) were considered, as shown in Table 4 2 A summary of the estimated thermal resistances for the various TEG modules is shown i n Table 4 4 Even though the number of leg pairs increased from n = 18 to 90, the inner surface area of the legs decreased (from 71.3x1010 to 9.5x1010 m2). As a result, the total leg thermal resistance increased (from 0.9x103 to 6.8x103 K/W). Consequently, the total module radial thermal resistance also increased with increasing number of leg pairs. Also, the substrate thermal resistance, which included the polyimide/oxide membrane and air (independent of the thermopile design), was estimated at 4.5x103 K/W.

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119 Table 4 4 Estimate s of the thermopile thermal conduction resistance at 25 C based on estimated thermal conductivities from electrical resistivity measurements. Legs thermal resistance includes both Au and Ni thinfilm legs. Substrate thermal resistance includes polyimide/oxide membrane and air. Leg Pairs ( n ) 18 65 90 Legs inner surface area (x1010 m2) 71.3 32.4 9.5 Total Module Thermal Resistance, Conduction (x103 K/W) 0.7 1.3 2.7 Legs Thermal Resistance, Legs (x103 K/W) 0 .9 1.7 6.8 Substrate Thermal Resistance, Sub (x10 3 K/W) 4.5 4.5 4.5 4.2 Characterization of Integrated Resistive Temperature Sensors for Internal Temperature Measurements Accurate measurement of the thermopile junction temperature was important for quantification of the thermoelectric performance. Chapter 3 described the use of integrated thinfilm metal structures to enable direct measurement of the internal device temperatures [55] As described in Chapter 3, each TE G and dummy module had thinfilm resistive temperature sensors patterned on the inner and outer silicon rings. The resistors were Ni metal (~0.57 m in thickness, 100 m wide) with Au bond pads (~0.48 m in thickness). Also, because of the high thermal conductivity of the underlying silicon, the temperatures of the inner and outer rings were assumed to be the temperatures of the inner and outer thermoelement junctions.

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120 4.2.1 Experimental Methods First, electrical connections were made to the Au/Ni bond pads by soldering thin copper wires (gage 34 magnet wire from MWS Wire Industries) for stable, robust electrical connections. The resistance of the wire leads (< 1 was ignored, since it was small compared to the resistance of the patterned Ni resistors (> 300 Also, two point (as opposed to four point) electrical resistance measurements were made, again assuming that the resistance of the wire leads did not strongly affect the overall measured resistance. Thermal characterization of the Ni resistive sensor s was performed by measuring the resistance vs. temperature using an oven (Blue M Lindberg), with the goal of determining the linear temperature coefficient of resistance (TCR), TCR, for each Ni resistor. Each TEG module was placed inside the oven with the resistive sensor wire leads leading out to the Keithley 2400 source meters for resistance measurement. The temperature inside the oven was measured using a fine, barewire type K thermocouple from Omega positioned ~3 cm above the module. The thermocouple leads also extended outside of the oven and connected to a thermocouple data acquisition module (USB TC from Measurement Computing Corp.) used to read the temperature. A LabVIEW code was written to display in a computer the continuous temperature reading from the thermocouple. As recommended by the manufacturer, the USB TC module and thermocouple were connected and running for at least 1 hr. prior to taking measurements. This warm up time minimized thermal drift in order to achieve the rated accuracies f or measurement. Additionally, the USB TC module internally corrected for minor additional voltage error induced by connecting the type K thermocouples to its input pins.

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121 Specifically, high resolution temperature sensors, integrated on each side of the USB TC module, measure an average temperature of the USB TC module for estimation of the cold junction voltage. Then, this voltage was automatically subtracted from the inputs thermocouple voltage measurement. The integrated resistive temperature sensors were calibrated from ambient temperature up to ~200 C. Later tests with hot gas streams fell within this temperature range. The test procedure was as follows. First, the electrical resistances of the inner and outer ring were measured as the oven temperatur e was slowly increased (in steps of ~5 10 C) from ambient temperature up to ~200 C. Each temperature reading was allowed to settle for three minutes and then recorded. The temperature was then stepped down from the maximum temperature to room temperature, recording data as the device cooled to room temperature. Following th is first cycle, the temperature was once again increased to the maximum temperature and finally decreased to room temperature to complete a second cycle. Shown in Figure 4 1 is an example plot of the raw data of the resistance of the Ni resistors vs. temperature for a dummy module with no thermoelements. The inner Ni ring (with a smaller radius) exhibited a lower resistance than the outer Ni ring, as expected. On the first cycle (Rin up and Rin down for the inner Ni ring, and Rout up and Rout down for the outer Ni ring, shown in red), there is some variability in the resistances of the Ni ring. Most notably, the room temperature resistance decreased after the thermal cycle.

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122 0 20 40 60 80 100 120 140 160 180 200 300 320 340 360 380 400 420 440 460 Temperature (C)Resistance () Rin-upRin-downRin-up 2Rin-down 2 A 0 20 40 60 80 100 120 140 160 180 200 300 350 400 450 500 550 600 Temperature (C)Resistance () Rout-upRout-downRout-up 2Rout-down 2 B Figure 4 1 Characterization of the integrated (A) inner and (B) outer Ni resistive thermal sensors on a dummy module ( no thermoelements) for internal temperature measurements. Outer Ni Ring Inner Ni Ring

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123 How ever, in the second cycle (Rin up2 and Rin down2 for the inner Ni ring, and Rout up2 and Rout down2 for the outer Ni ring, shown in blue), the resistances on the up and down curves were more consistent, exhibiting a more linear and nonhysteretic behavior. Thus, after an initial burnin cycle, the resistors appeared reasonably suitable for temperature measurement. Following this methodology, six other resistancetemperature plots over various cycles were obtained for the other TEG modules (shown in Appen dix B). 4.2.2 Uncertainty Analysis Because much of the experimental results and conclusions of this dissertation hinge on these resistive temperature sensor measurements, quantification of the accuracy of the temperature measurements was critical. First, the uncertainties in the raw measurements of resistance and temperature were determined for the Ni resistive rings. From these uncertainties, statistical methods were used to derive the uncertainties in calculated values such as the TCR and silicon ring temperatures. The overall (expanded) uncertainty in the temperature measurement ( UT), was estimated from the uncertainties in the barewire thermocouple (TC) and in the USB TC module given by [52] TTCUSBTCUUU ( 4 13) where UTC and UUSB TC are the thermocouple and USB TC module effective compone nt uncertainties, respectively. Each uncertainty was evaluated from available information from the manufacturers specifications. From the manufacturers specification, the accuracy of the type K thermocouple (part no. CHAL010 from Omega) was 2.2 C or

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124 0.75% of the measured value in C, whichever was greater. For the temperature range tested in this work, the former value was the greater of the two accuracies, so UTC = 2.2 C. Also, according to the manufacturer, the USB TC module (part no. usb tc fro m Measurement Computing Inc.) had an estimated accuracy of UUSB TC = 1.19 C. Thus, the overall systematic uncertainty in the temperature measurements was calculated to be UT = 2.5 C. Similarly, the uncertainty in the Ni ring resistance measurements us ing the Keithley meters was estimated from the manufacturers user manual. Using a twopoint probe method resulted in an uncertainty in the resistance measurement of UR By using the experimental procedure describe above, oven temperature and el ectrical resistances of the inner and outer Ni rings were made to determine the corresponding TCR values. As an example, Figure 4 2 shows resistance temperature data for the dummy module (no thermoelements). The TCR for each resis tive temperature sensor was based on a linear least squared fit of the measured resistancetemperature data. For extraction of the TCR, only the data from the decreasing segment of the second temperature cycle was used (typically ~25 data points) the data from the first thermal cycle was ignored.

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125 0 20 40 60 80 100 120 140 160 180 200 300 320 340 360 380 400 420 440 460 480 500 ( )Temperature (C)Resistance () Figure 4 2 Least square fit of resistancetemperature data on a dummy module ( no thermoelements) using mean coefficients obtained from a Monte Carlo (MC) simula tion To quantify the uncertainty in the linear fit data, a Monte Carlo (MC) simulation technique was developed in MatLab for statistical assessment. The MC routine randomly perturbed each measured data point from the resistance temperature plot in Figure 4 2 by assuming each data point was from a parent population that is normally distributed. That is, for each data point, the measured value was assumed to be a mean value, and the uncertainty was assumed to be twice the standard deviation ( UR = 2* R and UT = 2* T) [52] Then using the randomn function in MatLab, on each data point, a new resistance temperature data set was generated, statistically varying both the resistance and temperature of each data point. A linear least square fit was then Inner Ring O uter Ring

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126 performed on the new data set to extract the corresponding coefficients of the slope ( m ) and intercept ( b ) for each Ni ring given by InnerInnerInner RmTb ( 4 14) OuterOuterOuterRmTb ( 4 15) Overall, the process was repeated 10,000 times, building up statistics for the fit m and b values. Figure 4 3 shows example results for the inner Ni ring on a dummy module (TEG n =0). The resulting distributions of the slopes and intercepts exhibited a Gaussian behavior (kurtosis = 3 and skew = 0), from which the net uncertainty in the TCR was determined. Thus, for the inner Ni ring example, the corresponding slope ( m ) and intercept ( b ) were 0.798 0.005 and 301.0 0. 5, respectively, with 95 % confidence bounds. Assuming a linear temperature dependency, the resistance should vary with temperature according to 1REFTCR REFRRTT ( 4 16) where TCR is TCR of the Ni ring (havi1]), TREF is the reference or ambient temperature, and RREF is the reference starting resistance of the Ni ring. The TCR for the Ni ring can be found by rearranging Equation 416 as follows: REF TCR REF REFRR TT R ( 4 17) TCR REFR T R ( 4 18) TCR REFREFRm TRR ( 4 19) Here m is the slope from the resistance temperature measurements.

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127 0.79 0.795 0.8 0.805 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]DTEG Inner RingNo. of Occurrences A 300.2 300.4 300.6 300.8 301 301.2 301.4 301.6 301.8 0 100 200 300 400 500 600 700 DTEG Inner RingRange of values of the intercept (b) []No. of Occurrences B Figure 4 3 Monte Carlo simulation distributions used to extract (A) slope ( m ), and (B) intercept ( b ) for least square fit, and thus, TCR of the inner resistive thermal sensors on a dummy module (no thermoelements).

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128 Since the TCR is calculated from the variables m and RREF, each having uncertainty, the net uncertainty in TCR must also be calculated. Assuming m and RREF are uncorrelated, and using Eq. 47 and 417, the uncertainty in TCR is REF TCRR m TCR REFU UU mR ( 4 20) where UR REF = UR = 3.3 m is the average slope obtained from MC simulations, and Um = 2* m is the uncertainty in m m is the standard deviation ( Figure 4 3 a). Finally, TCR U TCR is an estimate at the 95% confidence interval for the TCR. 4.2.3 Sum mary of Results A summary of the characterization of the inner and outer Ni resistive rings on all of the TEG modules is shown i n Table 4 5 The extracted TCR values for various Ni rings were fairly consistent with each other, with the mean of the 8 different rings estimated at 2.67x103 C1, and the upper and lower (95%) confidence intervals ranging from 2.55x103 C1 to 2.79x103 C1). The uncertainty in the TCR was dominated by the uncertainty in the initial r esistance measurement (second term under the square root of Equation 418), estimated at ~10X larger than the uncertainty in the resistancetemperature slope ( m ) estimate (the first term in Equation 420). Table 4 5 Extracted TCR parameters for the inner and outer Ni resistive ring s of TEG modules. Leg Pairs ( n ) 0 18 65 90 TCR_Inner Ring ( x103 C1) 2.48 0.03 2.87 0.04 2.69 0.03 2.51 0.03 TCR_Outer Ring ( x103 C1) 2.73 0.03 2.84 0.03 2.62 0.03 2.59 0.02

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129 These values were compared to known bulk values for Ni, and the experimentally extracted values were about onehalf the bulk TCR value for Ni at room temperature (5.9 x103 C1) [56] On the other hand, by comparing to other Ni thin films, reasonable agreement was found with the value ( TCR 2.3 x103 C1) obtained for Ni thinfilms (6 70 nm in thickness) vacuum evaporated on glass substrates [53] and with that ( TCR 1.8 x103 C1) for sputte red deposited Ni (10 nm in thickness) on Kapton polyimide (12.5 m) [54] The dissimilarity may be attributed to different film thickness (~400 nm in this work), different deposition methods (evaporated vs. sputtereddeposited), and/or different substrates (polyimide vs. glass vs. silicon dioxide/silicon) In this work, the Ni thin films were tested up to ~200 C, and the resistance varied linearly with temperature. Another study using Ni films (~20 m) as resistive heaters on alumina substrates also showed a linear increase of resistance with temperature up to ~300 C [57] Beyond this temperature (>300 C 500 C), a non linear increase in resistance with temperature was exhibited by the Ni films [57] Overall, for the temperature range in this work the thinfilm Ni resistance increased linearly with temperature (positive TCR) making them suitable as integrated temperature sensors [56] 4.3 Characterization of Single Radial TEG Modules Using a Hot Gas Stream In this section, the thermal and thermoelectric performances of individual TEG modules were examined. An experimental test stand was assembled to evaluate the performance of each TEG module using hot gas streams. Using the integrated Ni ring temperature sensors, the inner and outer silicon ring temperatures were determined for single TEG modules subjected to different ho t gas temperatures. Electrical measurements of the opencircuit thermoelectric voltage were made to extract the

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130 module Seebeck coefficient, and several resistive loads were connected to evaluate output power for the various TEG module designs. 4.3.1 Experiment al Setup The experimental setup for thermal and thermoelectric evaluation of the TEG modules is shown in Figure 4 4 In addition to the electrical contacts made to the inner and outer Ni rings, electrical contacts to the TEG outpu t voltage pads were made, one being on a Au/Ni pad, the other being on Au pad. A thin copper wire was soldered to one Au/Ni bond pad, while a miniature alligator clip was used for contact to the Au bond pad, since soldering a wire to the pad tended to pul l from the polyimide. The miniature alligator clip also mechanically supported the TEG module for alignment with the gas stream. Output voltage measurements were made using a highprecision digital voltage meter (SIM 970 module in a SIM 900 mainframe from SRS). The voltage meter was allowed to warm up for ~1 hr before taking measurements, as recommended by the manufacturer. The uncertainty in the voltage measurements was estimated at UV = 0.6 mV, which was determined from manufacturers specifications. Moreover, a heat gun (ProHeat Variair Model PH 1300) with an analog dial for temperature adjustments was used as the hot gas stream source A segment of a high temperatureresistant tubing (0.25 inch diameter) and a customed made aluminum fixture were coupled to the heat gun outlet to channel the hot gas to the 5 mm inner diameter of the TEG module A high temperature resistant (up to 370C), thermally conductive silicone paste (Supreme Copper Gasketing Silicone) was used to seal air gaps around the gun outl et and the aluminum fixture. For the singlemodule testing

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131 described in this section (i.e. not stacked cylinder), t he module was positioned within 2 mm of the aluminum fixture and aligned to the hot gas flow. The upstream and downstream hot gas temperat ures were simultaneously measured using two barewire type K thermocouples placed at the center of the gas stream which were also connected to a USB TC module. During testing, the upstream and downstream gas temperatures generally tracked each other within ~10 C, with the greatest difference at the highest gas temperature. In one particular case, though, the downstream gas temperature lagged by as much as 20 C. T he downstream thermocouplepositioned within 1 mm of the modulewas used as the gas temperature ( TGAS) for later analysis During operation, the gas temperature was slowly increased. At each step, the temperature was allowed to stabilize for ~3 minutes, and then the temperature, output voltage, and resistances of the inner and outer Ni rings were m easured. From the inner and outer Ni ring resistance readings, the inner and outer silicon ring temperatures were then calculated using the corresponding TCR values.

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132 Figure 4 4 Test setup for thermal and electrical characterization of single radial TEG modules using a heat gun as a source for a hot gas stream. 4.3.2 Thermal Performance The TCR values were previously extracted from measurements of the inner and outer Ni ring resistances (section 4.2.3). By rearranging Equation 416, the corresponding silicon ring temperatures are given by _1Inner REFInner Inner REF TCRInnerR R TT ( 4 21) USB TC ProHeat Heat gun control dials Downstream thermocouple TGasUpstream thermocouple Tubing Silicone sealant Hot Gas flow Aluminum fixture Radial Device Thermocouple Input Module Computer USB cable SRS SIM 970 digital voltmeter Keithley 2400 Sourcemeters + 10.0 mV + 0.00 mV + 0.00 mV 350.0 400.0 2 pt Resistance measurement Coaxial cable input < 2mm 5mm Magnetic thin wire Single TEG

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133 _1Outer REFOuter Outer REF TCROuterR R TT ( 4 22) where TREF is the starting reference room temperature, TCR_ Inner and TCR_Outer the inner and outer Ni TCR values, Rinner and Router the measured resistances for the inner and outer Ni rings, and RREF Inner and RREF Outer the starting resistance at room temperature for the inner and outer Ni rings. It is assumed that the inner and outer Ni ring temperatures are the same as the corresponding inner and outer silicon ring temperatures. The temperature difference T ) between inner and outer silicon ring is given by InnerOuterTTT ( 4 23) The thermal effectiveness (Thermal) of the TEG module can be defined as InnerOuter Thermal GASREFGASREFTT T TTTT ( 4 24) where TREF is the reference or ambient temperature. The thermal effectiveness is a measure of the temperature difference that can be sustained across the thermoelements with respect to the maximum temperature drop ( TGAS TREF). Ideally, perfect thermal effectiveness ( Thermal = 1) would mean that the inner silicon ring temperature is at the gas temperature, and that the outer silicon ring temperature is at ambient temperature. The propagated uncertainty of the calculated temperatures is determined from the individual uncertainties in various measured quantities. Following from Equations 46, 4 21, and 422, the corresponding uncertainties of the inner ( UT _i nner) and outer ( UT_outer) silicon rings are given by

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134 __ _1Inner Inner TCRInnerREFInner InnerREFInner T R REFInner T TCRInnerREFInner TCRInnerREFInner TCRInnerREFInnerR RR U U U UU RR R ( 4 25) __ _1Outer Outer TCROuterREFOuter OuterREFOuter T R REFOuter T TCROuterREFOuter TCROuterREFOuter TCROuterREFOuterR RR U U U UU RR R ( 4 26) where UR _inner UR _outer and UR EF are 3.3 UT_REF = 2.5 C. On each of the Equations 423 or 424, the first two terms in the square root (corresponding to uncertainties in the resistance measurement) were ~5X larger than the last two terms (corresponding to the uncertainties in temperature measurement and TCR estimates), and thus, dominated the uncertainty in UT_inner and UT_outer. Similarly, the uncertainty of the silicon ring temperature difference ( UT) is given by [52] InnerOuter TTTUUU ( 4 27) Consequently, the uncertainty in the thermal effectiveness ( U T hermal) is also given by _InnerOuterGASREFThermalTTTTUUUUU ( 4 28) As an example, consider the raw resistance vs. gas temperature data for a single TEG module with no thermoelements shown in Figure 4 5 Once the heat gun was turned on, the minimum stable sett ing corresponded to a temperature ( TGAS) around 100 C. Then the gas temperature was slowly increased to a maximum of ~215 C. As described previously, the measured inner and outer Ni ring resistances were converted to temperatures using the extracted TCRs ( TCR) shown in Table 4 5 The data in Figure 4 5 shows the inner and outer ring resistances with increasing gas temperature, with the corresponding silicon ring temperatures shown in Figure 4 6 The inner Ni ring

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135 resistance, although lower than the outer ring resistance at room temperature (because the resistor length is shorter), increased above the outer ring with increasing temp er ature (because it gets hotter). That is, the inner ring resistance increased to ~470 while the outer ring resistance increased to ~420 to maximum temperatures of ~200 C and 92 C for inner and outer silicon rings, respectively, for a hot gas at 215 C. 0 20 40 60 80 100 120 140 160 180 200 220 320 340 360 380 400 420 440 460 480 g ()Gas Temperature, TGAS (C)Resistance () Figure 4 5 I nner and outer resistive Ni ring resistances on a radial TEG (with no thermoelements) for internal temperature measurements. Inner Ring Outer Ring

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136 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 g p ()Gas Temperature, TGAS (C)Silicon Ring Temp. (C) Figure 4 6 I nner and outer silicon ring temperatures determin ed from integrated Ni ring resistances on a radial TEG (with no thermoelements ). Additionally, the temperature differential ( T TInner TOuter) between the inner and outer silicon ring against gas temperature is shown in Figure 4 7 At the maximum gas temperature of TGAS 215 C, the module sustained a temperature difference of ~ 108 C. This corresp onded to a maximum thermal effectiveness (Thermal) of ~0.57 0.1 1 Following the same measurement procedure for this module, other TEG modules were similarly tested with the results shown in Appendix B. A comparison of the T against gas temperature f or various TEG modules is shown in Figure 68. Four single TEG modules ( n = 0, 18, 65, 90) were tested independently using a hot gas stream up to ~215 C. Measurements on the fourth TEG module ( n =90) were only recorded up to a Inner Ring Outer Ring

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137 hot gas of 115 C since an electrical contact on one of the Ni rings and precluded further measurement. Also, for one TEG module ( n =65), additional data was recorded (below 100 C ) as the module cooled to room temperature to show that the resistance continued to decrease linearly wi th gas temperature below 100 C Overall, the TEG module with no thermoelements exhibited better thermal isolation between the silicon rings than those with thermoelements, as summarized in Table 4 6 From estimates shown in Table 4 4 in section 4.1.4, a TEG module with metal legs provided an additional conduction path for heat to flow from the hot to the cold side, thus lowering the module thermal resistance. This resulted in a lower T for a given gas temperature. For instance, for a gas temperature of 215 C a TEG module ( n =0) sustained up to a T of 108 C compared to only ~ 65 C for TEGs with thermoelements. Interestingly, the measured temperature data shows insignificant variation between the different TEG modules with legs. That is, the three different TEG modules showed similar T for a given gas temperature as shown in Figure 4 8 Even though the TEG module with n =90 leg pairs had a higher thermal resistance (2.7x103 K/W) compared to modules with n =18 (0.7x103 K/W) and n =65 (1.3x103 K/W) leg pairs, as shown i n Table 4 4 the uncertainty in the T resulted in comparable thermal isolation capability for TEG modules with ther moelements, and thus similar thermal effectiveness, ~36% (see Table 4 6 ). Also note that the heat transfer in the singlemodule testing here is likely not well approximated by the simple 1D thermal model. Since the top and bot tom surface of the module are exposed, there is likely significant additional convective heat transfer from these surfaces, which is not accounted for here.

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138 Later tests with a stacked module (Section 4.4) aim to better replicate the 1D heat transfer assu mptions. 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 g ()Gas Temperature, TGAS (C)Silicon Ring T (C) Figure 4 7 Silicon ring temperature difference as a function of gas temperature for a radial TEG (with no thermoelements ).

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139 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 g pGas Temperature, TGAS (C)Silicon Ring T (C) Single TEG n=0 Single TEG n=18 Single TEG n=65 Single TEG n=90 Figure 4 8 Silicon ri ng temperature difference as a function of gas temperature for various TEG modules. Table 4 6 Comparison between TEG modules with various TE leg pairs including TAMB C. Leg Pairs ( n ) 0 18 65 9 0 Max. T GAS (C) 215 2.5 215 2.5 200 2.5 115 2.5 Max. T (C) 108 10 65 9 65 9 34 9 T hermal effectiveness, (%) 57 11 34 11 36 10 37 9 4.3.3 Thermoelectric Performance In addition to the thermal characteristics, the thermoelectric behavi or of the TEG modules was also determined using the hot gas stream from the heat gun. Noload, opencircuit voltage measurements were made first, followed by measurements with

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140 various resistive electrical loads. The thermoelement pair Seebeck coefficient ( ) was determined from the opencircuit voltage measurements, and the power generation capability was evaluated from the resistive load tests. The opencircuit voltage ( Voc) as a function of gas temperature ( TGAS) and of T is shown in Figure 4 9 and Figure 4 10, respectively, for the four TEG modules. As described in 4.3.1, opencircuit voltage measurements were made having an estimated uncertainty of UV = 0.6 mV, which was determined from the manufact urers specifications. Also, as discussed in section 4.2.2, the uncertainty in the temperature measurements was estimated at UTGAS = 2.5 C. The opencircuit voltage in all cases increased linearly as gas temperature and T increased, as expected. For a given gas temperature, a module with the larger number of thermoelements is expected to generate a higher voltage as predicted from Equation 426. For instance, for a gas temperature at ~120 C, the n =90 TEG module generat ed an open circuit voltage of ~45 mV, exceeding the n =65 (30 mV), and n =18 (6 mV) modules. Further tests showed that the highest voltage generated by the n =65 TEG module was 60 mV for a gas temperature of 200 C, corresponding to a T of 65 C.

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141 0 20 40 60 80 100 120 140 160 180 200 220 0 10 20 30 40 50 60 Gas Temperature, TGAS (C)Open-Circuit Voltage (mV) Single TEG n=18 Single TEG n=65 Single TEG n=90 Figure 4 9 Open circuit voltage as a function of gas temperature for various TEG modules having small uncertainties in the voltage ( 0.6 mV) and TGAS ( 2.5 C).

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142 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 Silicon Ring T (C)Open-Circuit Voltage (mV) Single TEG n=18 Single TEG n=65 Single TEG n=90 Figure 4 10. Opencircuit voltage as a function of silicon ring temperature difference for various TEG modules. Using the slope ( m ) of the Voc and T curves shown i n Table 4 7 the overall Seebeck coefficient for the AuNi thermoelement pair ( Au Ni) was extracted according to the equation OC AuNi AuNiVnTnT ( 4 29) where the Seebeck coefficient or thermoelectric power is given by AuNim n ( 4 30) where n is the no. of thermoelement pairs. The uncertainty of the Seebeck coefficient ( U) can be estimated by using Equations 47 and 4 30 and is given by

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143 mnUU U mn ( 4 31) where = Au Ni. Since, there is no uncertainty in the number of leg pairs ( n ), then mmUU U mm ( 4 32) Following the same procedure used to extract the TCR from the slope of resistance temperature measurements, a Monte Carlo simulation was also used to obtain the statistical estimation of the Seebeck coefficient. After 10,000 generated curves using the experimental data and estimated error bounds, a Gaussian distribution of the slopes from least square curves was obtained. An example plot of the slope ( m ) distribution obtained from Monte Carlo simulations for the n =65 TEG module is shown in Figure 4 11. For this particular module, the extracted slope, m = 0.93 0.06 (mV/C). Using Equations 430 and 432, this corresponded to a Seebeck coefficient of 14.3 0.9 V/K. Using the procedures described above, the Seebeck coefficient was also extracted for TEG modules with n =18 and n =90 thermoelements, as summarized in Table 4 7 The extracted Seebeck coefficients ( Au Ni) for the three different TEG modules showed excellent agreement with each other, as expected, since all modules used AuNi thin films thermoelements. The extracted values are about onehalf of the bulk value ( Au Ni 26 V/K) estimated from Table 22 for a range of 100 C 200 C. However, in another study, in which thinfilm thermocouples of Au/Ni (0.2/0.1 m in thickness) were evaporated on SiO2/Si, Seebeck coefficients of up to 10 V/K were measured [58] The differences between these values may be due to metal thinfilm quality on different substrates (SiO2/Si vs. polymer/Si) and deposition methods (evaporated vs. sputtered)

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144 Also, Table 4 7 summarizes the overall thermal and thermoelectric performance of the various modules. 0.85 0.9 0.95 1 1.05 0 100 200 300 400 500 600 700 Range of values of the slope (m) [mV/C]No. of Occurrences oc Figure 4 11. Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from the slope of the opencircuit voltage and temperature difference for a radial TEG ( n =6 5 thermoelements). Table 4 7 Comparison between TEG modules with various TE leg pairs including Seebeck coef ficient estimates. TAMB C. Leg Pairs ( n ) 0 18 65 9 0 Max. T GAS (C) 215 2.5 215 2.5 200 2.5 115 2.5 Max. T (C) 108 10 65 9 65 9 34 9 T hermal effectiveness, (%) 57 11 34 11 36 10 37 9 Max. V oc (mV) 16 0. 6 60 0. 6 46 0. 6 Slope m (mV/C) 0.26 0.01 0.93 0.06 1.32 0.12 Seebeck coef. Au Ni (V/K) 14.4 0.7 14.3 0.9 14.7 1.3

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145 For practical use as an energy harvesting system, the long term stability and repeatability of the TEG is of practical interest. As a first step towards evaluating this, tests were performed on the n =65 TEG module, 30 days and 33 days after the first test. Table 4 8 summarizes these results, showing that thermal performance and the Seebeck coefficient of the module remained fairly stable over this time span, even under repeated thermal cycles. For the last column in Table 4 8 the opencircuit voltage and T was recorded at five gas temperatures between 25 C and 200 C only. This resulted in a larger confidence interval for the Seebeck coefficient (14.6 1.4 V/K), yet still showed good agreement with the other measurements. Table 4 8 Seebeck coefficient (thermoelectric power) of AuNi thermoelement pair after ~1 month for a single radial TEG module ( n =65 leg pairs ). Time (days) 0 30 33 Slope m (mV/C) 0.97 0.05 0.93 0.06 0.95 0.09 Seebeck coef. Au Ni (V/K) 15.0 0.8 14.3 0.9 14.6 1.4 In addition to the opencircuit voltage measurements, the resistance of the TEG module was also measured against temperature using a twopoint probe method with a Keithley sourcemeter. A sample plot is shown i n Figure 4 12 for a TEG module ( n =65) during tests with a heat gun. The figure showed an increase in the resistance of a stacked TEG module ( n =65) as the hot gas temperature increased, due to TCR effects. In particular, the module resistance increased linearly and roughly doubled, from ~1.63 k square fit). Also, as the device cooled down to room temperature, the resistance also

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146 at 24 C, with some residual increase in resistance. Similar results for another TEG module are shown in Appendix B. 0 20 40 60 80 100 120 140 160 180 200 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 ()Module Resistance (k)Gas Temperature, TGAS (C) Stacked TEG n=65 Figure 4 12. Electrical resistance of a stacked TEG module ( n =65) as a function of gas t emperature during tests with a heat gun. In addition to the opencircuit voltages, the TEG modules were tested with resistive ( RL) loads, and the power output was also measured for the different TEG designs. Initially, matched resistive loads were used where the load resistance roughly equals the module resistance, for maximum power transfer. Specifically, load resistances of for the n =18, 65, and 90 designs, respectively. T he powe r output was calculated by measuring the voltage across the resistive load according to the equation

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147 L L LV P R ( 4 33) w here VL is the load voltage, and RL is the load resistance. From Equations 47 and 433, the uncertainty in the power delivered to a load ( UP _L) is given by LL LVR PL LLUU UP VR ( 4 34) where UR _L = 3.3 UV _L = UV = 0.6 mV since the same digital voltage meter (SIM 970) was used to measured the load voltage. As shown in Figure 4 13 the output power increased quadratically with gas temperature, as expected from Equation 433 (since the voltage increased linearly with gas temperature). T able 4 9 summarizes the performance between the various designs. The intermediate design ( n =65) showed higher output power compared to the other two designs ( n =18 and n =90). Also, TEG ( n =18) showed a larger uncertainty in the delivered power. Since this device had the lowest number of TE leg pairs, it generated the lowest voltage as depicted by Figure 4 9 and lowest electrical resistance compared to the other devices. As inferred from Equation 434, the combination of low output voltage and low device resistance resulted in higher uncertainty in the power output. Overall, at a gas temperature of 200 C, a maximum power output of ~0.45 W was measured for the n =65 design by using a 1.55 k load, which approximated the TEG

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148 0 20 40 60 80 100 120 140 160 180 200 220 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 pGas Temperature, TGAS (C)Delivered Power ( W) Single TEG n=18 Single TEG n=65 Single TEG n=90 Figure 4 13. Power output for single TEG modules as a function of gas temperature by using resistive loads matching the TEG device resi stance. Table 4 9 Thermoelectric performance of TEG modules with various TE leg pairs. TAMBC. Leg Pairs ( n ) 18 65 90 Max. TGA S (C) 215 2.5 200 2.5 115 2.5 Max T (C) 65 9 65 9 34 9 Max V L (mV ) 6.5 0.6 27 0.6 23 0.6 R L 0.120 0.003 1.550 0.003 11.50 0.003 RTEG ) 0.123 0.003 1.630 0.003 11.3 0.003 Max P L (W) 0.35 0.07 0.45 0.02 0.040 0.002 Additionally, one of the TEG modules ( n =65) was tested using various load resistor Figure 4 14 and Figure 4 15 show the load voltage and delivered power, respectively, against resistive

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149 loads for various temperatures. Note l oad resistors that exactly matched the module resistance were not available. With the exception of the curve at 171 C, overall, the load voltage and output power increased with gas temperature, and for large load resistances (>50 k ), the load voltage approximated the opencircuit voltage, as expected. Based on the anomalous behavior, it is believed the curve for the 171C degree test was corrupted. While it still remains unclear, as the gas temperature increased from 152 C to 171 C, an unexpected cooli ng of the outer silicon ring resulted in a larger than expected T resulting in an increase in load voltage and power (see Appendix B). This same TEG ( n =65) would be tested again within a stacked structure as described in the next section, and the device behaved as expected in those tests. Ignoring the data from the 171C test, a maximum power output of ~0.36 0.02 W was measured for 191 C gas flow using a 2 k load which was slightly higher than the room should occur when the load resistance matched the module resistance. Recall, however, that due to TCR effects, the overall module electrical resistance should increase as the temperature increased. Thus, the load resistance where maximum power is delivered should shift away from the room temper ature TEG resistance as the enough data points to be conclusive, Figure 615 seems to show this effect as the maximum power point appears to drift slightly to higher load resistances with increased gas temperatures

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150 Figure 4 14. Load voltage for various resistive loads over different gas temperatures for a single TEG module ( n =6 5 ). Figure 4 15. Power output for various resistive loads over different gas temperatures for a single TEG module ( n =65). 102 103 104 105 106 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Load Resistance ()Delivered Power ( Watts) 112C 118 C 152 C 171 C 191 C T GAS Single TEG ( n =65) 102 103 104 105 106 0 5 10 15 20 25 30 35 40 45 50 55 60 g Load Resistance ()Load Voltage (mV) 112C 118 C 152 C 171 C 191 C T GAS Single TEG ( n =65)

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151 4.4 Characterization of Stacked TEG Modules Using a Hot Gas Stream The stacke d cylinder structure described in Section 3.4 was also evaluated using the hot gas stream emanating from the same heat gun. The stacked structure comprises one active TEG module ( n =65) in between 15 dummy modules (no thermoelements). The characterization o f the stacked cylinder followed the same procedure as that for the single TEG modules. In addition, as shown in Figure 4 16 the stacked cylinder was directly attached to the end of the aluminum fixture using a hightemperaturere sistant silicone epoxy, thus focusing the gas stream flow within the inner channel formed by the stacked modules. Figure 4 16. Stacked cylinder structure composed of an active TEG ( n =65) between 15 dummy TEG modules ( n =0) for hot gas stream tests. 4.4.1 Thermal Performance As in the single module tests, the gas temperature was increased from ambient temperature (~22 C) to a maximum of ~200 C in steps of about 10 C. The heat gun temperature first stabilized around 80 C when it was turned on. Using the same methods described in Section 4.3.2, the inner and outer silicon ring temperatures were determined from the Ni ring resistance measurements and from previously extracted Active TEG mo dule stacked between dummy modules Aluminum fixture attached to heat gun Thermocouple at center of the channel

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152 TCR values. A fully developed temperature profile was assumed and the inner and outer silicon ring temperatures (resistances) were allowed to settle prior to making measurements. For instance, a sample plot of the raw resistances for the inner and outer Ni ring resistors comparing a single (Section 4.3 results) and a stacked TEG module ( n =65 leg pairs) are shown in Figure 4 17 The corresponding inner ( THot) and outer ring ( Tcold) temperatures are shown in Figure 4 18 The most marke d difference between the single device and the stacked device is that inner silicon ring was generally much hotter. For example, for TGAS 195 C the inner silicon ring of a single module lagged the gas temperature by 45 C while for the stacked module, the inner silicon ring differed from the gas temperature by only 3 C Thus, the channel formed by the inner finned array effectively co upled the hot gas, almost perfectly, at the highest tested temperature. In addition, the outer Ni ring temperature was also generally hotter in the stacked test due to additional heat flow through the TEG legs and substrate layers. The outer silicon ring temperature increased up to 90 C for a single module, and up to 105 C for a stacked module for a gas at ~195 C

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153 0 20 40 60 80 100 120 140 160 180 200 220 320 340 360 380 400 420 440 460 480 Gas Temperature, TGAS (C)Resistance () Stacked TEG n=65 Single TEG n=65 Figure 4 17. Inner and outer Ni ring resistances as a function of gas temperature for a single and a stacked TEG module (n= 65). Inner Ring s Outer Ring s

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154 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 g p pGas Temperature, TGAS (C)Silicon Ring Temp. (C) Stacked TEG n=65 Single TEG n=65 Figure 4 18. Inner and outer silicon ring temperature as a function of gas temperature for a single and a stacked TEG module (n= 65 ) including least squar e fit lines Figure 4 19 shows the module comparing the stacked structure to the single module. At a gas temperature of 195 C, the stacked cylinder sustained a corresponding to a thermal single TEG module (n=65) sustained a as summarized i n Table 4 7 This indicated an improveme nt of the stacked cylinder over the single TEG modules. Inner Ring s Outer Ring s

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155 0 20 40 60 80 100 120 140 160 180 200 220 0 10 20 30 40 50 60 70 80 90 100 Gas Temperature, TGAS (C)Silicon Ring T (C) Stacked TEG n=65 Single TEG n=65 Figure 4 19. Temperature difference between the i nner and outer silicon rings as a function of gas temperature for a single and a stacked TEG module ( n= 65). 4.4.2 Thermoelectric Performance In parallel with temperature measurements, voltage measurements were made using the voltage meter (SIM 970), in both opencircuit conditions and with resistive loads to characterize the thermoelectric performance. The opencircuit voltage data against gas temperature is shown in Figure 4 20 for the ( n =65) TEG module. For a gas temperature of 195 C the stacked TEG module ( n =65) generated an opencircuit voltage of ~80 mV, while the same TEG m odule generated only ~60 mV for the same gas temperature. The larger voltage in the stacked device is solely due to improved thermal effectiveness ( ). That is, for a given

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156 gas temperature, the stacked TEG sustained a higher T t han the single module as shown i n Figure 4 19. Thus, from Equation 4 27, the stacked module also generated a higher opencircuit voltage than the single module. 0 20 40 60 80 100 120 140 160 180 200 220 0 10 20 30 40 50 60 70 80 90 g pGas Temperature, TGAS (C)Open-Circuit Voltage (mV) Stacked TEG n=65 Single TEG n=65 Figure 4 20. Comparison of the opencircuit voltage vs. gas temperature for a single and a stacked TEG module ( n = 65 ) Moreover, the opencircuit voltage vs. T is shown in Figure 4 21. Here, the stacked TEG module and single TEG module show excellent agreement, as expected. The thermoelement pair Seebeck coefficient ( Au Ni) for the stacked module was estimated at 14.3 0.9 V/K, directly in line with the measurements from the single TEG modules summarized i n Table 4 7 It is evident that, the cylindrical structure

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1 57 formed by stacked TEG modules improves the T and thus improves the overall thermoelectric power generation, as compared to a s ingle unstacked TEG module. Figure 4 21. Comparison of the opencircuit voltage as a function of silicon ring temperature difference for a single and a stacked TEG module includi ng a least square fit line with slope, m = 0.93, and Au Ni =14.3 0.9 V/K Additionally, various resistors (50 to 50 k evaluate the maximum power output (or power delivered to a load) As an example, Figure 4 22 shows the power delivered to a 2 k test load as the gas temperature increased up to a maximum of ~195 C. Power output increased quadratically, and for the stacked TEG module ( n =65), a maximum of ~0. 8 W was obtained. This is 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 Silicon Ring T (C)Open-Circuit Voltage (mV) Stacked TEG n=65 Single TEG n=65 n slope Ni Au

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158 approximately twice the amount of power measured for the single module at the same temperature. 0 20 40 60 80 100 120 140 160 180 200 220 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Gas Temperature, TGAS (C)Delivered Power ( W) Stacked TEG n=65 Single TEG n=65 Figure 4 22. Power output to resistive loads vs. gas temperature for a single and a stacked TEG ( n =65) module including a least square (quadratic) fit lines. Additionally, the output power of the stacked cylinder (or power delivered to a load) was evaluated by using various resistive loads (50 to 50 k ) for different gas temperatures. Figure 4 23 shows the load voltage as a function of the resistive load. For instance, at a gas temperature of ~195 C the load voltage increased for higher load resistances and is expected to approach the opencircuit voltage of ~80 mV for larger loads (>50 k Figure 4 24 shows the corresponding load power. At a gas

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159 temperature of ~195 C, a maximum power output of ~0.8 W was measured for a 2 k r esistive load. As before (see discussion of Figure 4 15), the data may indicate a slight increase in the matched load resistance with increasing gas temperatures, due to increase module resistance at elevated temperatures. Figure 4 23. Load voltage for various resistive loads over different gas temperatures for a stacked TEG ( n =65) module. 101 102 103 104 105 0 10 20 30 40 50 60 70 80 Load Resistance ()Load Voltage (mV) Stacked TEG ( n =65) 93 C T GAS 113 C 128 C 150 C 170 C 195 C

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160 Figure 4 24. Power output for various resistive loads over different gas temperatures for a stacked TEG ( n =65) module. 4.5 Summary of Results Electrical resistivity measurements were made on the Au and Ni thin films using van der Pauw crosses, TLM structures, and the integrated Ni rings on the TEG modules. Also, from resistivity measurements, thermal conductivities were estimated using the WiedemannFranz law. While, the electrical resistivity and thermal conductivity of Au thin films were in agreement with expected values, the Ni thin films, on the other hand, showed significantly higher resistivity and lower thermal conductivity than expected. 101 102 103 104 105 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Load Resistance ()Delivered Power ( Watts) Stacked TEG ( n =65) 93 C T GAS 113 C 128 C 150 C 170 C 195 C

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161 Radial TEG modules with various number of AuNi thermoelement pairs ( n =0, 18, 65, 90) were then c haracterized using a heat gun as heat source to examine the thermoelectric performance. The module with no thermoelements sustained a larger T at the highest gas temperature. Also, modules with more thermoelements generated larger opencircuit voltage for a given gas temperature (or a given T). The Seebeck coefficients (~14.3 V/K) for all modules were determined and were in agreement with each other, as expected. The maximum power output obtained for the stacked TEG module ( n =65) was ~0.8 W, corresponding to a power density of ~17 W/cm3 (48 mm3 module volume). This is approximately twice the amount of power measured for the single module at the same temperature (~195C) A summary comparison of the thermoelectric performance for the single and stacked TEG is shown in Table 4 10 Additional discussion of performance is included at the end of Chapter 5. Table 4 10. Thermoelectric performance between a single and a stacked TEG module ( n =65 metal leg pairs). TAMB2.5 C. Leg Pairs ( n =65 ) Single TEG Stacked TEG Max. T GAS (C) 200 2.5 195 2.5 V oc (mV) 60 0.6 80 0 .6 Max. T (C) 65 9 90 10 Thermal effectiveness (%) 36 10 52 10 Slope m (mV/C) 0.93 0.06 0.93 0.06 Seebeck Coeff. Au Ni (V/K) 14.3 0.9 14.3 0.9 R TEG k 1.630 0.003 1.630 0.003 R L 1.550 0.003 2.00 0.003 V L (mV) 27 0.6 40 0.6 PL (W) 0.45 0.02 0.80 0.02 PD (W/cm 3 ) 9.4 0.4 16.7 0.4

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162 CHAPTER 5 MODEL VALIDATION This chapter focuses on using the experimental r esults from the stacked TEG cylinder (Chapter 4) to determine relevant heat transfer characteristics and to compare the measured thermoelectric results with model predictions. First, with knowledge of the material thermal conductivities and geometries the thermal resistance of the stacked TEG structure was estimated. With this estimation, and the temperature measurements, the heat flow rates through the module were then estimated. Furthermore, the convective heat transfer coefficients on the hot side ( hH ot) and cold side ( hCold) of the finned stacked TEG module were then estimated. Using all of these extracted parameters, the overall thermal and thermoelectric performance of the TEG structure is then modeled and compared against the experimentally measured values from Chapter 6. While there are many simplifying assumptions, the results will show that the 1 D thermal model reasonably predicts the overall module performance. 5.1 Thermal Model of Stacked Structure The 1 D heat transfer model developed in Chapter 2 was extended and applied to the experimental measurements of the stacked TEG structure. Note that the stacked cylinder consisted of 16 total modules one active TEG module sandwiched between 15 dummy modules (no thermoelements) Convection from the e nds of the stack was ignored, radiation was ignored, and good thermal contact between the modules was assumed. The thermal resistances of the inner and outer silicon rings were also negligible and ignored. With these assumptions, 1D radial heat transfer w as assumed. Figure 5 1 shows the equivalent thermal and electrical models for the stacked structure.

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163 Figure 5 1 Thermal and electrical model of a stacked TEG with one active TEG module sandwiched between dummy modules (no thermoelements) to form a cylindrical structure for hot gas stream tests. The inner ring and outer ring temperatures were assumed to be constant along the length (axis ) of the stacked cylinder, i.e., uniform along the cylinder length. The thermal resistance between stacked modules (along the cylinder length) was estimated to be fairly low (20 K/W), calculated from the contact area and thermal conductivity of the hightemperature thermally conductive epoxy used to bond the modules. On the other hand, the thermal resistance (along the radial direction) was estimated at ~103 K/W. This indicated comparatively good thermal contact between the stacked modules. As a result, the temperature gradient along the length of the cylinder was expected to be small compared to the radial gradient. In terms of the thermal model, this permitted R TEG V OC = n( Au Ni )(T Hot T Cold ) q Legs T Hot T Cold T AMB T GAS Sub ConvHot ConvCold Legs Sub Sub q S tack qSub qTEG

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164 all of the module conduction resistances to be connected in parallel, as depicted in Figure 5 1 The estimated room temperature thermal conductivities from the thin film test structures Au ( Au =285 W/m K ) and Ni ( Ni =8. 4 W/m K ) from Table 4 2 were used to determine the radial conductive heat transfer parameters of the m etal legs. Additionally, room temperature estimates of the thermal conductivities for polyimide ( Poly =0.14 W/m K ), SiO2 ( Ox =1.4 W/m K ), silicon ( Si =148 W/m K ), and air ( Air =0.026 W/m K ) from Table 2 2 were also used. Using these values and the appropriate geometries in Equations 212 to 216, the estimated thermal resistances of the legs and supporting substrate were Legs =1.73x103 K/W and Sub=4.5x103 K/W, respectively The net thermal resistance of the stacked cylinder, Stack was estimated as 1 16 1Stack LegsSub ( 5 1 ) The resulting net thermal resistance of the stack was Stack = 0.24x103 K/W. The total heat flow rate, qStack, into the stacked cylinder is given by Stack Stack T q ( 5 2 ) where T = TH ot TC old is the temperature difference between the inner and outer silicon rings for the stacked cylinder. Similarly, the individual heat flow rates through the TE legs, qLegs, and the supporting substrate of a module, qSub, are given by Legs Legs T q ( 5 3 ) Sub SubT q ( 5 4 )

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165 Thus, the total heat flow rate, qTEG into the active TEG module is given by TEGLegsSubqqq ( 5 5 ) For instance, the stacked cylinder sustained a maximum T 90 C, corresponding to qLegs 52 mW and qSub 20 mW. Thus, the total heat flow through the active TEG was qTEG 72 mW, and the total heat flow through the entire stack was qStack 370 mW. Note that under the assumptions of the model, qStack = qHot = qCold. By using the measured t emperatures, the thermal resistances associated with convection, ConvHot and ConvCold can be determined as follows: GASHot ConvHot HotTT q ( 5 6 ) ColdAMB ConvCold ColdTT q ( 5 7 ) Similarly, the conv ective heat transfer coefficients, hHot and hCold, are given by ,1 16Hot InnerConvHoth A ( 5 8 ) ,1 16Cold OuterConvColdh A ( 5 9 ) where AInner = 2 ritsi = 5.4x106 m2 and AOuter = 2 rotsi = 9.8x106 m2 were estimates of the inner and outer surface areas of a single module. Figure 5 2 shows the heat transfer rate, qStack, into the s tacked cylinder linearly increased as the gas temperature increased, reaching a maximum of ~370 mW at a gas temperature of 195 C. Additionally, plots of the convective thermal resistance, ConvCold and ConvHot calcu lated at different input gas temperatures are shown in Figure 5 3 These values for the cold side appear fairly stable over the tested

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166 temperature range, but the hot side convective thermal resistance seemed to decrease from 80 K/ W at 90 C to 5 K/W at 195 C. This indicated an apparent improvement in convective heat transfer with increasing temperature. Whether or not this is an actual physical phenomena is unclear, because of the numerous assumptions made in the thermal modeling Additionally, large uncertainties in the thermal resistances were obtained due to the propagated uncertainty estimates from material properties and dimensions. 0 20 40 60 80 100 120 140 160 180 200 0 50 100 150 200 250 300 350 400 450 500 q pGas Temperature (C)Heat Transfer Rate (mW) Figure 5 2 Estimate of the heat transfer rate, qStack, coupled into the stacked cylinder

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167 0 20 40 60 80 100 120 140 160 180 200 0 50 100 150 200 250 300 350 400 450 500 pGas Temperature (C)Conv. Thermal Resistance (K/W) Figure 5 3 Estimate of the convective thermal resistances, ConvColdand ConvHoton the cold and hot side, respec tively of a stacked cylinder Also, Figure 5 4 and Figure 5 5 show the corresponding convective heat transfer coefficients. The value at the cold side seems fairly stable, while that at the hot side incr eased (~10X at 195 C) due to a decrease of the convective thermal resistance. By considering the temperature range in which the convective coefficients appear stable, the mean values were estimated to be hHot 220 200 W/m2 K and hCold = 27 10 W/m2 K including propagated uncertainties in the thinfilm properties and dimensions (Appendix B). These heat transfer coefficients estimates were inline with typical (gas) values for forced convection ( generally 25 250 W/m2K) and natural convection ( generally 2 25 W/m2 K ) [44] Outer Cold Side Inner Hot Side

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168 80 100 120 140 160 180 200 0 10 20 30 40 50 60 70 80 90 100 Gas Temperature (C)Conv. Coeff. Cold Side (W/m2*K) Figure 5 4 Estimate of the convective heat transfer coefficient, hCold, on the cold side of a stacked cylinder 80 100 120 140 160 180 200 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Gas Temperature (C)Conv. Coeff. Hot Side (W/m2*K) Figure 5 5 Estimate of the convective heat transfer coefficient, hHot, on the hot side of a stacked cylinder

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169 The inner and outer ring temperatures (and consequently T ) increase in proportion, as shown in Figure 5 6 and Figure 5 7 The solid lines represent the theoretically predicted temperatures by using the estimated material properties and other extracted thermal parameters. The calculated temperatures predict well the experimental inner and outer silicon ring temperatures across the tested temperature range. The model does not predict, though, the apparent temperature rise at the higher temperatures. 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 Gas Temperature, TGAS (C)Silicon Ring Temp. (C) Figure 5 6 Experimental data (points) and model predictions (solid lines) for the inner and outer silicon ring temperatures for the stacked TEG. Inner Ring Outer Ring Predicted temperature using extracted thinfilm properties

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170 0 20 40 60 80 100 120 140 160 180 200 220 0 10 20 30 40 50 60 70 80 90 100 110 g Gas Temperature, TGAS (C)Silicon Ring T (C) Figure 5 7 Experimental data (points) and model predi ctions (solid line) for the between inner and outer silicon rings radially through the stacked TEG. 5.2 Thermoelectric Performance The model predictions for thermoelectric voltage and power were also compared against the experimental data. The load voltage and power delivered to a 2 k test load were estimated using thin film electrical resistivity values (from Section 4.1.3 and 4.1.4) and Equation 433. Figure 5 8 shows the load voltage experimental data compared against the model predictions. The solid lines represent two different theoretical predictions using two different values for the TEG electrical resistance. For the first line, the stacked TEG (n=65) electrical resistance (2.24 k ) was estimated by using the thinPredicted extracted thinfilm properties

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171 film resistivity fr om test structures. The second line is the load voltage predicted by using the measured TEG resistance (1.63 k Both model predictions generally match the measured load voltage. Higher load voltages were predicted by using the measured TEG module resis tance of while lower load voltages were obtained by using the estimated module resistance of 2.24 k slightly overpredicted, and using the larger module resistance, the power delivered was slightly underpredicted as shown in Figure 5 9 As the gas temperature increased, the TEG resistance also increased due to TCR effects, which likely affected of the load voltage and power to shi ft from predicted values at elevated gas temperatures (~200 C). Note, the model assumes a constant module resistance. Additionally, Figure 5 10 shows the corresponding predicted delivered power by using the measur ed TEG resistance of 1.63 k The predicted power output showed good agreement with experimental data (points), although, the measured peak power seemed to occur at a higher resistance compared to the predicted curve. Similar results were obtained by using the estimated TEG resistance (Appendix B).

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172 0 10 20 30 40 50 60 70 80 90 100 110 0 10 20 30 40 50 60 g () Silicon Ring T (C)Load Voltage (mV) Figure 5 8 Experimental data (points) and model predictions (solid lines) of load voltage Mode l prediction using the estimated TEG resistance Model prediction using the measured TEG

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173 0 20 40 60 80 100 120 140 160 180 200 220 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Gas Temperature, TGAS (C)Delivered Power ( Watts) Figure 5 9 Experimental data (points) and m odel predictions (solid lines) of power versus gas temperature for the stacked TEG. Model prediction using the estimated TEG Model prediction using the measured TEG

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174 101 102 103 104 105 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Load Resistance ()Delivered Power ( Watts) 23 C 93 C 113 C 128 C 150 C 170 C 195 C Figure 5 10. Model estimates of power delivered to various loads using extracted thin film resistivity and measured TEG resistance (1.63 k ). Better approximation to the data is obtained at lower than at higher temperatures. As discussed in Section 2.2, when a resistive load is connected to the active TEG module shown in Figure 5 1 current will flow and electrical power is delivered to the load. Thus, the contributions by the Peltier heat transport (second terms) and Joule heating (third terms) to overall heat flow rate were estimated by using the appropriate terms in Equations 21 and 2 2, repeated here for the readers convenience. The heat flow rate into the hot side of the TEG, qHot, is given by 1 Hot AuNiHot TEG TEGT qnTIIR ( 5 10) Similarly, the heat flow rate out of the cold side of the TEG, qC old, is given by

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175 1 Cold AuNiCold TEG TEGT qnTIIR ( 5 11) From Figure 5 7 at 195 C the maximum measured voltage across a 2 k load was VL = 40 mV, corresponding to an electrical current ( I = VL/RL) of 0.02 mA. Thus, the second terms of Equations 510 and 511 are n Au NiTHotI = 8.71 W and n Au NiTColdI = 7.02 W, respect ively. The third term, considering the measured TEG resistance ( RTEG = RLegs=1.63 k ), for instance, yielded I2 RTEG/2 = 0.33 W. All of these terms were negligible (three orders of magnitude smaller) compared to the first term (heat conduction term), T /TEG= 72 mW, of Equations 510 and 511. This indicates that for the TEG with metal leg pairs, the electrically and thermoelectrically generated heating/cooling within the active TEG module, are not expected to affect the inner and o uter ring temperatures or overall heat transfer characteristics, validating the assumptions made for the model development. Moreover, the conversion efficiency, Module, of the stacked TEG module, discussed in Section 1.2.7, was estimated at Module = 0.8 W / 72mW = 1.1 x105 (or 0.001%). Additionally, the heat exchanger efficiency, ex, can be defined as the capability of the cylindrical structure to couple energy from the hot gas flow into its inner surface. Thus, ex can be estimated from the heat flow rate coupled into the stacked structure, qStack, and the available thermal power content of the hot gas stream, qGas _Available, given by Stack ex GasAvailableq q ( 5 12) For instance, by considering a hot gas stream at 200 C (assuming air with mass flow r ate of 0.1 g/s as shown in Figure 1 1 ) the available thermal power content was

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176 estimated at ~1 8 W. Thus, the stacked structure efficiency is then estimated at ex = 370 mW / 18 W = 0.021 (or 2.1%). Also, the t hermocouple figure of merit, ZTC, from Equation 2 37, was estimated at 9.2x107 K1 (with ZTC TAVG = 4.5x104) for the metal thinfilms Thus the thermal to electrical efficiency, Material, using thinf ilm metals was estimated at 4.5x103 % On the other hand, as shown i n Table 29 for 200 C, the originally predicted performance was ZTC = 8.1x106 K1 and ZTC TAVG = 3.1x103, which corresponded to Material = 36x103 % ( for a TEG with n =65 leg pairs) Th e experimental results were <10X of the values shown in Table 29 mainly due to a combination of low er than expected extracted Seebeck coefficient, Au Ni, (<2X), as discussed in section 4.3.3, and higher than expected electrical resistance (~3X) compared to that shown i n Table 28. The reader is reminded that these results are based on the experiments of the TEG with thin film metals, a nd that improved performance can be obtained with semiconductors, as discussed in Chapter 2. Also, in the absence of the TEG module (or any other energy scavenger), the exhaust hot gas stream would simply be dissipated into ambient as waste heat energy. Nonetheless, the TEG structure showed that some electrical power can be generated from the wasted heat using thinfilm m etals, and that more power is possible by using semiconductor alloys. 5.3 Summary of Results By using the experimentally extracted thinfilm resistivity, thermal conductivity, Seebeck coefficients, and heat transfer coefficients in the thermal and electrical models, the thermoelectric performance of the stacked module was well modeled by basic theory. For the all metal design, the internal heating/cooling effects due to Peltier heat transport

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177 and Joule heating were negligible compared to heat conduction. The stacked module demonstrated 0.8 W of power generation using a hot gas stream at 195 C. Also, the efficiency for the stacked heat exchanger structure, defined as the ratio of thermal power coupled to the TEG to the thermal power available i n the flow, was estimated at 2.1 %. A thin film metal figure of merit, ZTC, determined from measured properties and geometries, was estimated at 9.2x107 K1. Al though low values were obtained and expected for thin film metals, however, better performance is estimated by using semiconductor materials.

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178 CHAPTER 6 CONCLUSIONS AND FUTURE WORK 6.1 Conclusions This chapter reviews the research w ork and provides guidelines and recommendations for future work. 6.1.1 Research Summary This dissertation described the design, fabrication processes and characterization of thin film based radial thermoelectric (TE) generators for hot gas streams. In Chapter 1, various previously investigated thinfilm TE devices were discussed and compared. In contrast to the typical parallel p late structure, a micromachined radial TE generator design was introduced as an alternative structure for thermal energy harvesting using hot gas streams. The radial TE generator module can be designed and fabricated to more effectively harness energy from hot gas sources. Chapter 2 presented the concept and radial TEG design, as well as the foundational thermal and electrical analytic models. These models were then used to estimate the thermoelectric performance of various concept designs using various combinations of semiconductor and metal thin films on silicon substrates. Additionally, design guidelines were provided for the fabrication of TEG modules based on metal thin films and the expected performance. Chapter 3 presented the microfabrication of multiple radial TE generator modules using thinfilm metals thermoelements. The development of a process flow for the fabrication of TEG modules and test structures on silicon substrates was discussed, as well the fabrication of a stacked cylinder structur e.

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179 Chapter 4 described the thermal and electrical characterization of single TEG modules using a hot gas stream. Also, relevant thinfilm metal parameters including electrical resistivity were estimated from various test structures Additionally, a stack ed TEG module was used to further demonstrate thermoelectric power generation from a hot gas stream. Chapter 5 further explored the heat transfer characteristics of the stacked TEG module. The radial heat conduction through the various layers was analyzed, along with the convective heat transfer on the hot and cold sides of the structure. The estimated thermal and electrical parameters were then used to compar e the analytic models and with the actual measurements. Also, the TEG efficiency, power output, and module figure of merit were estimated and showed agreement with expected performance for thin film metal TEG modules. 6.1.2 Summary of Device Performance The thinfilm metal (Au Ni) TEG module explored in this dissertation (~47 mm3) showed power output of up to 0.8 W (17 W/cm3) using a hot gas stream at 195 C. Moreover, at this gas temperature, a temperature difference of 90 C was sustained across the thermoelements, generating up to 80 mV. While the power output of the prototype device here was quite l ow, thermal and electrical models showed that by using p and ntype semiconductors much high er power of 1.3 mW (27 mW/cm3) may be possible with a similar structure using hot gas streams at 400 C Additionally, stacking multiple modules, could potential ly generate tens of milliwatts of power for in line, heat powered sources.

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180 In practice, the voltage and power generated by the TEG may change due to thermal variations from the heat source, thus, a power management circuit or converter would be required to properly power a device. Typically, a power management syste m may consist of a charge pump, for instance, followed by a dc/dc converter with a variable conversion factor, and some feedback circuit [59] as shown in Figure 61. Simple step up (boost) circuits are commonly employed, but alternative configurations for dc/dc conversions with switching capacitors have been published including the Fibonacci type converter [60] and the Dickson charge pump [61] For ener gy harvesting applications, a power management system converts the generated energy from the TEG and can then store it in a storag e capacitor for later use or re charge a microbattery. For instance, a TEG output voltage in the range of ~300 mV can activate the charge pump and dc/dc stepup circuit [62] which would then increase the voltage (~1 Volts range) to a suitable level for microelectronics. In ultra low power wireless sensor applications, the required power is typically within a range of 50 W 100 W [59] One of the main concerns is the power consumption by the stepup control/converter system which can be up to 70 W [63] As a result, n ew power management circuits with integrated dc/dc converter have been implemented as more appropriate for micromac hined TEG modules. For instance, a (Dickson) charge pump dc/dc converter implemented in CMOS technology [59] exhibited a total power (current) consumption of the control circuit as low as 2.1 W (corresponding to a current consumption of 1.4 A) This type of converter demonstrated system efficiencies of up to ~58%, but can vary depending on converter components and operating conditions [59]

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181 Furthermore more active TEG modules can be stacked and connected in series for higher voltage (and power) from a hot gas stream. Thus, when the output voltage of th e TEG modules rises above a certain set value, e.g. hundreds of milliVolts, then the dc dc step up system can be activated. The converter system would then stepup the voltage and an output current would be supplied to a suitable storage capacitor. The pro cess of recovering waste heat energy from a hot gas stream, for instance, can proceed autonomously. Ultimately, sufficient electrical energy would be generated and become available for low power wireless sensor applications. F igure 6 1 Diagram of power converter system consisting of a dc/dc converter and feedback/control circuit. TEG energy at the input is converted at the output, which can then be stored in a capacitor or delivered to a load through a dc regulator Table 6 1 summarizes the device performance compared to other reported small scale TEGs. One of the attractive features of the radial TEG module was the thermal isolation between the inner and outer silicon rings discussed in Section 6.4.1. For the Buffer or Storage Capacitor I in Step Up Output Step Up Input VIn V Out I Out R TEG RL Voc ~ Charge Pump and dc/dc Converter Feedb ack / Control Circuit Power Converter System

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182 TEG module, high module thermal resistance ( ~1250 K/W for single module) was obtained by using thin supporting polyimide/oxide membranes extending 1 mm between concentric silicon rings. Other simi lar miniature TEG designs fabricated on silicon substrates showed much lower overall thermal resistances (~2 27 K/W). Thus, the radial design explored here is fundamentally expected to provide a larger T and hence larger output power for a given hot side temperature. Table 6 1 Comparison of the thermal isolation and electrical performance between the proposed radial TEG and a few of the other miniature TEG designs fabricated on silicon substrates Refs. Materials TE Element Fabrication Method Device Size ( mm 2 ) Thermal Resistance (K/W) DPF ( W/cm2K2) Notes [30] p and n Bi Sb Te (300 m) Micropacking alloy powders 100 for the device: 2 -High density:10000 thermocouples [19] n poly Si (0.7 m) Al (0.25 m) CVD and sputtered 100 for the device: 2 0.016, but with p/n BiSbTe: 0.81 P=0.014W Max. =0.95K [35] n dopedSi with Al ( 1 m) CVD 16.5 supporting (10 m) Si layer : 27 0.091 P=1.5W Max. =10K This work Au (0.5 m ) Ni (0.6 m ) Sputtered 132.7 for single device: ~1250 Supporting poly/ox membrane/air : ~4500 0.001 at mid radius, rmid P=0.8 W, V =80mV, Max. T=90K at 195 C gas From the test results however, the device power factor ( DPF ) a metric for normalizing the output power by area and T was fairly low, only 0.001 W/cm2 K2. The primary reason this power metric was so low (10 100X smal ler than other comparable devices ) was because of the use of low performing Au Ni thermoelement

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183 leg pairs. As expected, other TE devices using hybrid thermoelement pairs of semiconductor and metal exhibited greater DPF values than an all metal design. Con sequently, combining the thermal isolation and direct gas coupling advantages of the radial design with higher performing pand n type TE legs, can arguably improve the overall performance. 6.1.3 Research Contributions A summary of the research contributions of this dissertation is included here: Proposed, desi gned and modeled (to first order) a radial TEG system with integrat ed hot and cold heat exchangers for convective coupling to hot gas streams Developed a process flow for the microfabrication of radial T EG modules using thin film metals on micromachined polymer and silicon substrates. Batch fabricated functional radial TEG modules using thinfilm metals on micromachined polymer and silicon substrates. Experimentally characterized the thermoelectric perfor mance of radial TEG modules and a stacked TEG structure using hot gas streams. 6.2 Recommendations and Future Work 6.2.1 Obstacles Throughout the course of the research work, many unforeseen obstacles arose, particularly in the microfabrication. For instance, the challenge of patterning thin film metals on polyimide was not easy due to microcracking on the polymer and metal. At first, to simplify the fabrication process flow, a photodefinable positivetone polyimide (HD 8820 from HD Microsystems) was used to patter n the annular polyimide rings (~ 5 10 m in thickness) on the SiO2/Si substrate. Careful steps measures were taken to

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184 ensure that the film was cured to high temperatures (>300 C) and cooled slowly to room temperature to reduce residual stress according to the recommended recipe from the manufacturer [39] Also an adhesion promoter (VM 651), diluted in deionized wat er (DI water) 200:1 was also used to prevent delamination from the substrate. Nonetheless, microcracking would appear on the polyimide after deposition and patterning of the thin film metal. As a result, the patterned thin film metal exhibited microcracks in random pattern. These defects were observed with various deposition methods including by sputtering and electron beam evaporation, and on different metals such as Ni, Cr, Cu, Ti, and Auwith severe cracking and striations on Ni and Cr than on Au for ins tance. Consequently, after many attempts and tests, it was determined that the photodefinable polyimide was not suitable and thus a nonphotodefinable polyimide (PI 2611 from HD Microsystems) was explored. According to specifications, this particular poly imide had a lower residual stress after cured and lower thermal coefficient of expansion than the previous photodefinable polyimide. As a result, no microcracking or striations were evident on the film after deposition on the substrate, nor on the thinfilm metals on the polyimide. The challenge was then to determine a method (recipe) to pattern the nonphotodefinable PI2611, which added extra steps in the process flow. As described in Chapter 3, a recipe based on a dry etch using an O2 plasma in a reactiv e ion etcher (RIE) was explored, and which worked well in patterning the annular rings. It was also observed that after O2 plasma etching, residue would be left on the substrate, not easily removed with solvents and DI water. This residue was then removed immersing the substrate in an acetone bath and stirring with an ultrasonic cleaner for ~1

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185 minute. Also, during the patterning of SiO2 by using hydrofluoric acid (HF) or buffered oxide etch (BOE), the polyimide residue would also be removed, thus leaving a clean silicon surface. Moreover, unexpected high thermopile resistance (>100 k ) was measured after patterning the second set of TE legs (Au) on the first set (Ni). It was then determined that a combination of oxidation on the Ni surface and photoresist residue on the contact areas yielded high electrical resistance. Thus, a more thorough cleaning procedure consisted of a brief ultrasonic clean in solvents after patterning the first set of TE legs, Also, the substrate was immersed in diluted hydrochloric (HCL) acid followed by an in situ brief Ar plasma clean prior to sputtering of the second set of TE legs. As a result, lower thermopile resistances were then obtained, as described in Section 6.1. Another critical step was singulating and releasing the TEG modules from the substrate by using deepreactive ion etching (DRIE) of sil icon (~345 m thick). Ideally, the silicon etch or removal would stop on the silicon dioxide (SiO2) (~0.4 m thick), but extended etching time to ensure release of all TEG modules would, in some cases, etch through the silicon dioxide and polyimide membrane. Thus, the DRIE was performed in steps or cycles for a more controlled and uniform silicon removal, up to a depth before complete removal. Then smaller DRIE times or cycles were carried out until silicon was removed from the backside, thus, avoiding over etching into the supporting membrane. Once the TEG modules (9 mm and 13 mm in diameter) were released, the yield of functional TEG modules was about <50%, while the yield for the Ni ring test structures was essentially ~100%. The defective TEG modules had some of the Au legs missing, which occurred when the modules were released from the supporting substrate during

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186 the DRIE step. For the functional TEG modules, electrical contacts were made by soldering thin Cu wires (gage 34) to the five Au/Ni pads on pol yimide. These contacts were stable and durable. The sixth pad (Au on polyimide), from the third mask design, showed weaker adhesion to polyimide than Au/Ni pads, even though, the polyimide surface was exposed to O2 plasma to roughen the surface for impro ved adhesion [39] Overall, all contacts were stable but soldering a wire to Au would, at times, pull the pad fro m the polyimide. Instead of a thin wire, a miniature alligator type clip was used to make the final electrical interconnect (for voltage measurement), which favorably also served to hold the TEG module inline with the hot gas flow. Prior to soldering thi n wires, the electrical resistance of the modules and of the inner and outer Ni ring structures were measured using a two point probe method with a Keithley (2400) sourcemeter. The electrical resistance of two inner Ni rings on different modules was measur ed using a source dc current ( > 1mA). When the resistance was measured again, a dark spot emerged on a portion of the Ni ring where it transitioned from the inner silicon ring onto the suspended polyimide membrane. The result was a larger resistance (~M ), which indicated a damaged portion of the inner Ni ring. On the other hand, no failure occurred on the outer Ni ring, which was patterned completely on polyimide/oxide/silicon. Overall, considering that several measurements would be made during the course o f testing of the modules, a source current <10X was used for measurements of the Ni ring a current level that showed no damage on the Ni rings. Also, the van der Pauw crosses (Au and Ni) and TLM structures (Au/Ni) on polyimide showed no damage when repeate d resistance measurements were made using a four probe method with a dc current of 100 mA.

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187 There were also numerous challenges encountered during the testing phase. The use of a simple heat gun, while beneficial as a hot gas source, was not ideal. The hea t gun had a minimum stable temperature of ~80 C and maximum of <300 C, thus limiting the testing range. Moreover, the gas temperature was adjusted by using a dial type control, so uniform increments in temperature remained difficult. Accurately positioni ng the single modules in line with the hot gas flow was also difficult. The inner channel diameter of the modules was ~5 mm, and aligning the module took a considerable amount of time. Another challenge in measurements of the gas temperature included plac ing the barewire thermocouple as close to the center of the channel without touching the inner silicon ring. Moreover, for the power testing measurements of load voltages were made by using several discrete resistors, which provided a limited number of data points when plotting power against load resistance over several gas temperatures. As a result, shift of the peak power was not clearly visible. Furthermore, interpretation of the data was limited by large uncertainties in the measurements. The temperature measurement uncertainty was relatively large ( 2.5 C) by using a thermocouple connected to an electronic USB TC module. Also, resistance measurements using a twopoint probe method yielded an uncertainty of ~ 3.3 6.2.2 Potential Improvements Certainly, there are a number of steps that can be implemented in the fabrication of the TEG modules. First, more aggressive fabrication (smaller features, higher packing densities, thicker films, etc.) could be performed to ac hieve higher performing

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188 devices. Additionally, low resistance thinfilm metals may be obtained by using other deposition methods other than the lift off method. For example, depositing the metals first and wet etching to form the thermopile, as oppose to patterning by lift off method which can leave behind photoresist residue on the contact regions. Also, deposition of thin film metals by evaporating in a high vacuum chamber may improve the quality of the deposited metal and yield low resistance TE leg pai rs. Moreover, investigating new low stress, polymer films that may be more compatible with thinfilm metal or semiconductor structures can potentially minimize film cracking and striations. There are also many improvements to the overall design of the TEG module. In this work, design of the heat exchanger structure was largely ignored. Only five free parameters were explored for design of the thermopile layouts. The design space could be expanded to include more variables, and perhaps other design method ologies may be explored to design for maximum power. Also in the design and model of the TEG module, many simplifying assumptions were made, including constant thermal properties for the substrate, 1D radial heat transfer through the stacked devices, small internal heat currents (Peltier heat transport and Joule heating) within the device compared to heat conduction (decoupled thermal and electrical models), etc. For the thin film metal stacked TEG module, the model reasonably predicted, to a first order estimate, the expected performance. After evaluating the experimental results, improvements can be made to the thermal model to better capture the device performance at higher temperatures, in which the additional thermoelectric heat sources/sinks may not be negligible. Under these conditions, nonlinear variations of the inner and outer silicon ring temperatures may become more pronounced, which affect

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189 the generated voltage and power for instance. These effects may be more apparent for fabricated TEG modul es using semiconductor materials, which have larger Seebeck coefficients than metals. A fully coupled thermal electrical TE model would provide more insight into these current generated heat sources, and the extent of their impact on miniature thinfilm TE G modules. Experimentally, there is also room for improvement. For measurements of load voltage and delivered power, rather than using a bank of test resistors, a dial type or electronic potentiometer may provide a more continuous experimental data set of measured voltage and power, and also, simplify measurements. In addition, the analog dial simpler heat gun may be replaced with a heat source with digital temperature controls for uniform temperature steps. Also, to reduce uncertainties, resistance esti mates of the TEG module and Ni resistive rings can be improved by four point method measurements and temperature measurements may be improved by using more precise temperature measurement meters other than the USB TC data acquisition system. Micromachined TEG modules, although mainly for low power generation and cooling, will continue to benefit as better performing materials are developed. The silicon micromachined radial TEG modules, demonstrated here by using thinfilm metals in hot gas streams, show promise of considerable improvement in performance with new TE materials.

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190 APPENDIX A THERMAL ENERGY ( POWER ) FROM A GAS STREAM Consider a hot gas flowing through the inner finned array, the first law of thermodynamics states that the rate of change of energy of a material region (MR) is equal to the rate that energy is recovered by heat and work transfers, given by [44, 64] deqw (A 1) For an infinitesimal (v olume) element dV, the total energy is given by u edV (A 2) where is density, e is internal energy/unit mass, and u2/2 is kinetic energy/unit mass. Using Reynolds transport theorem, MR AR CSduuu edVedVeudA dt t (A 3) with the ri ght side of the equation equal to Into OutwQ By assuming steady state, ideal gas, and incompressible fluid, then the power flux or heat transfer rate (in Watts), qGas _Available, is given by GasAvailable VOutletInletqmcT (A 4) which can be s implified to GasAvailableVOutletInletqmcTT (A 5) where m is the mass flux (or mass flow rate [g/s]), cV is the specific heat [J/g K], and TInlet and TOutlet are the cylinder (or tube) inlet and outlet temperatures [K], respectively, (Figure 2 1B). To estimate the available power in a hot gas stream, assuming room -

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191 temperature ambient conditions the ambient temperature is assumed TO utlet = 298 K and the specific heat for air is assumed cV 1.1 J/g K in Equation A 5.

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192 APPENDIX B CHAPTER 7 EXPERIMENTAL RESULTS OF RADIAL TEG MODULE S Sample plot for TLM structures. Resistance between adjacent pads for increasing spacing, d. More details are given in [51] .: Raw data is given below (note: that the pad size is given as s in section 3.4 and as z in the MatLab code below ) Section 3.4: 0 50 100 150 200 250 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Au on NiContact Spacing, d (m)Resistance () z=400m z=400m z=300m z=275m Figure B 1 Resistance (R) vs. contact spacing (d) between Au/Ni pads for estimates of film resistivity and contact resist ivity using the TLM method.

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193 %Israel Boniche %01/26/10 %TLM raw data to get resistivity and contact resistivity clear all close all clc %format compact d1 = [35 45 55 104 155 204] % spacing between pads in (um) for largest cells d2 = [35 45 55 104 155 204 250] % spacing between pads (um) for middle and smallest cells d3 = [35 45 55 104 155 204 250] % spacing between pads (um) for middle and smallest %cells z1 = 400e6; % in meters size of largest contact z2 = 300e6; z3 = 275e6; A1 = z2.^2; tAu = 0.48e6; % thickness tNi = 0.57e-6; %1st mesa, largest pads R1a = [0.157 0.186 0.218 0.429 0.581 0.739]; %in Ohms R1b = [0.100 0.187 0.263 0.428 0.592 0.778]; R2 = [0.170 0.213 0.259 0.488 0.716 0.926 1.135]; R3 = [0.205 0.323 0.293 0.543 0.799 1.295 1.256]; %R3 = [0.205 0.323 0.293 0.543 0.799 1.256]; %determine the slope m and intercept b options=optimset('Display','on'); x0 =[1 0.5]; f = inline('x(1)*d1 +x(2)','x','d1'); [coef_R1a, resnorm] = lsqcurvefit(f,x0,d1,R1a,[],[], options) %store m and b f = inline('x(1)*d1 +x(2)','x','d1'); [coef_R1b, resnorm] = lsqcurvefit(f,x0,d1,R1b,[],[], options) %store m and b f = inline('x(1)*d2 +x(2)','x','d2'); [coef_R2, resnorm] = lsqcurvefit(f,x0,d2,R2,[],[], options) %store m and b % f = inline('x(1)*d2 +x (2)','x','d2'); % [coef_R3, resnorm] = lsqcurvefit(f,x0,d2,R3,[],[], options) %store m and b f = inline('x(1)*d3 +x(2)','x','d3'); [coef_R3, resnorm] = lsqcurvefit(f,x0,d3,R3,[],[], options) %store m and b % -----%electrical resistivity % divided by 1e 6 because R vs. d plot, d is in micrometers rho1a = coef_R1a(1).*tNi.*z1./1e-6 % resistivity of the Ni film (Ohm -m) rho1b = coef_R1b(1).*tNi.*z1./1e-6 rho2 = coef_R2(1).*tNi.*z2./1e -6 rho3 = coef_R3(1).*tNi.*z3./1e -6 rho_avg_Ni = mean([rho1a rho1b rho2 rho3]) % mean of resistivities std_rho_avg_Ni = std([rho1a rho1b rho2 rho3]) %std of the avg. %confidence_rho_avg_Ni = rho_avg_Ni %N=4, v=N -1=3, t=3.18 (t distribution: at th 95% confidence level) confidence_rho_avg_Ni = 3.18*std_rho_avg_Ni/sqrt(4) %95 % level %thermal conductivity Lo = 2.45e8; %V^2/K^2

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194 To = 298; % in K or 25C kth1a = Lo.*To./rho1a kth1b = Lo.*To./rho1b kth2 = Lo.*To./rho2 kth3 = Lo.*To./rho3 kth_avg_Ni = mean([kth1a kth1b kth2 kth3]) % mean of conductivities std_kth_avg_Ni = st d([kth1a kth1b kth2 kth3]) %2*std of the avg. confidence_kth_avg_Ni = 3.18*std_kth_avg_Ni/sqrt(4) %95 % level % ------co_rho1a = coef_R1a(2).*(z1^2)/2 % contact resisitivity of Au-Ni co_rho1b = coef_R1b(2).*(z1^2)/2 co_rho2 = coef_R2(2).*(z2^2)/2 co_rho3 = coef_R3(2).*(z3^2)/2 co_rho_avg_Ni = mean([co_rho1a co_rho1b co_rho2 co_rho3]) std_co_rho_avg_Ni = std([co_rho1a co_rho1b co_rho2 co_rho3]) confidence_co_rho_avg_Ni = 3.18*std_co_rho_avg_Ni/sqrt(4) %95 % level figure(1) plot(d1, R1a, 'k*'), hold on plot(d1, R1b,'b^'), hold on plot(d2, R2,'ro') hold on plot(d3,R3, 'gs') hold on plot([0 d1], coef_R1a(1).*[0 d1] + coef_R1a(2), 'k') hold on plot([0 d1], coef_R1b(1).*[0 d1] + coef_R1b(2), 'b') hold on plot([0 d2], coef_R2(1).*[0 d2] + coef_R2(2), 'r' ) hold on plot([0 d2], coef_R3(1).*[0 d2] + coef_R3(2), 'g') hold off grid on title('Au on Ni'); xlabel('Contact Spacing, d ( \ mum)','fontWeight', 'bold', 'fontSize', 12); ylabel('Resistance ( \ Omega)','fontWeight', 'bold', 'fontSize', 12); legend('z=400\ mum ','z=400 \ mum', 'z=300\ mum', 'z=275 \ mum')

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195 Measurements of sputter e d film thickness using a Veeco profilometer Section 4.1.1. Film thickness of sputter Au and Ni tAu (m) tNi (m) 4.50E-07 6.20E-07 5.30E-07 5.30E-07 4.80E-07 5.30E-07 4.60E-07 5.50E-07 4.90E-07 6.00E-07 4.80E-07 6.70E-07 4.80E-07 5.60E-07 4.90E-07 5.50E-07 5.00E-07 5.40E-07 5.00E-07 5.30E-07 4.60E-07 5.30E-07 Average: 4.84E-07 5.65E-07 Std: 2.25E-08 4.61E-08 95% conf. level 1.51E-08 3.10E-08 t distribution N=11,v= 10,t=2.23 N=of samples, v=N-1 deg. of freedon, t= value at 95%confidence Table B 1 Thin Film thickness of sputtered deposited Au and Ni on various regions of the van der Pauw crosses.

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196 Resistance measurements using van der Pauw crosses. Section 4.1.1. Keithley Is = 100mA, 4-pt U_resistance: 0.003 Ohms of the Ni and Au vdp resistance. Measured at room temperature! Au: rho = pi*t*(V/I)/ln(2) chip R ( rho=pi*t*R/ln(2) ( k_e= Lo*T/rho vdp cross1 smallest1 0.0112 2.46E-08 2.97E+02 middle1 0.0112 2.46E-08 2.97E+02 middle2 0.0108 2.37E-08 3.08E+02 largest1 0.0115 2.52E-08 2.90E+02 vdp cross2 largest1 0.011 2.41E-08 3.03E+02 largest2 0.011 2.41E-08 3.03E+02 vdp cross3 larget1 0.013 2.85E-08 2.56E+02 middle1 0.013 2.85E-08 2.56E+02 middle2 0.013 2.85E-08 2.56E+02 Average: 0.0117 2.57E-08 2.852E+02 Std: 9.61E-04 2.11E-09 2.23E+01 95% Conf 1.81E-09 2.02E+01 t distribution N=9,v= 8,t=2.31: 0.000739672 1.62E-09 Uncertainty 1.72E+01 N=of samples, v=N-1 deg. of freedon, t= value at 95%confidence level A Ni R ( rho=pi*t*R/ln(2) ( vdp cross1 smallest1 0.449 1.15E-06 6.35E+00 middle1 0.425 1.09E-06 6.71E+00 vdp cross2 largest1 0.43 1.10E-06 6.64E+00 middle1 0.38 9.72E-07 7.51E+00 middle2 0.39 9.98E-07 7.32E+00 smallest1 0.37 9.47E-07 7.71E+00 vdp cross3 largest1 0.446 1.14E-06 6.40E+00 middle1 0.44 1.13E-06 6.48E+00 middle2 0.45 1.15E-06 6.34E+00 smallest1 0.42 1.07E-06 6.79E+00 smallest2 0.45 1.15E-06 6.34E+00 Average: 0.423 1.082E-06 6.78E+00 Std: 2.96E-02 7.57E-08 5.01E-01 95% Conf 7.83E-08 4.94E-01 t distribution N=11,v= 10,t=2.23 1.99E-02 5.09E-08 3.37E-01 B Table B 2 A B) Resistance of various van der Pauw crosses to determine electrical resistivity. Thermal conductivity is estimated from the WiedemannFranz law.

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197 Resistance measurements using Ni resistive rings Section 4.1.1. Using the inner and outer Ni resistive rings to extract the resistivity (See lab not Uncertainty in R of 22.1 was used in this case (rather than 3.3 Ohms, since 0.1mA source) starting R rho (ohm-m) k (W/mK) R_REF_inner TEG(n=0) 326.3 8.347E-07 8.718E+00 TEG(n=20) 298.7 7.791E-07 9.340E+00 TEG(n=68) 321.8 8.393E-07 8.670E+00 TEG(n=94) 346.9 9.048E-07 8.042E+00 R_REF_outer TEG(n=0) 349.6 9.158E-07 7.946E+00 TEG(n=20) 316 8.178E-07 8.897E+00 TEG(n=68) 345.3 8.937E-07 8.142E+00 TEG(n=94) 384.8 9.959E-07 7.306E+00 Average: 336.175 8.726E-07 8.383E+00 Std: 26.34516762 6.84981E-08 6.436E-01 95% Conf 7.47E-08 7.21E-01 t distribution N=8,v= 7,t=2.37 2.21E+01 5.74E-08 0.539 N=of samples, v=N-1 deg. of freedon, t= value at 95%confidence level Table B 3 Resistance measurements of the inner and outer Ni ring resistances to determine electrical resis tivity. Thermal conductivity is estimated from the WiedemannFranz law. Module thermal conductance estimates. Section 4.1.4. Leg Pairs ( n ) 18 65 90 Legs inner surface area (x1010 m2) 71.3 32.4 9.5 Total Module Thermal Resistance (x103 K/W) 0.7 1 .3 2.7 Legs Thermal Resistance (x103 K/W) 0.9 1.7 6.8 Substrate Resistance (x103 K/W) 4.5 4.5 4.5 Membrane Resistance (x103 K/W) 36.3 36.3 36.3 Air Resistance (x103 K/W) 5.1 5.1 5.1 Table B 4 .T hermopile thermal conduction resistance at 25 C based on estimated thermal conductivities from electrical resistivity measurements. Legs thermal resistance includes both Au and Ni thinfilm legs. Substrate includes polyimide/oxide membrane and air gap.

PAGE 198

198 Heating cycles in the oven f or indiv idual TE modules to extract TCR. Section 4.2.1. Leg Pairs ( n ) 0 18 65 90 Slope mInner Ring 0.798 0.005 0.856 0.006 0.855 0.005 0.871 0.005 Intercept bInner Ring 301.0 0.5 271.5 0.7 291.2 0.5 322.9 0.6 TCR Inner Ri ng ( x103 C1) 2.48 0.03 2.87 0.04 2.69 0.03 2.51 0.03 Slope mOuter Ring 0.942 0.004 0.897 0.006 0.900 0.004 0.995 0.004 Intercept bOuter Ring 321.3 0.4 287.6 0.7 315.9 0.5 355.6 0.5 TCR Outer Ring ( x103 C1) 2 .73 0.03 2.84 0.03 2.62 0.03 2.59 0.02 Table B 5 Extracted parameters for the inner and outer Ni ring of radial TEG modules. Uncertainty in the mean value of all 8 TCR. Section 4.2.1. Average and uncertainty of all 8 Ni rings TCR values N=8, v=7, t=2.37 2.48E-03 2.73E-03 2.87E-03 2.84E-03 2.69E-03 2.62E-03 2.51E-03 2.59E-03 Average 2.67E-03 std: 1.43E-04 95% confi: 1.20E-04 lower limit: 2.55E-03 Upper limit: 2.79E-03 Table B 6 Resistance measurements of the inner and outer Ni ring resistances to determine the temperature coefficient of resistance, TCR.

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199 Section 4.2.2 0.936 0.938 0.94 0.942 0.944 0.946 0.948 0.95 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]No. of Occurrences A 320.8 321 321.2 321.4 321.6 321.8 322 0 100 200 300 400 500 600 700 Range of values of the slope (b) []No. of OccurrencesDTEG Outer Ring B Figure B 2 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on a dummy radial TEG (no thermoelements).

PAGE 200

200 For TEG n =65. Section 4.2.2 and 4.2.2. 0 20 40 60 80 100 120 140 160 180 200 300 320 340 360 380 400 420 440 460 480 500 TEG1: Resistors Temperature (C)Resistance () Rin-upRin-downRout-upRout-down A 0 20 40 60 80 100 120 140 160 180 200 300 320 340 360 380 400 420 440 460 480 500 TEG1: Resistors (down) Temperature (C)Resistance () B Figure B 3 Characterization of the inner and outer resistive thermal sensors on radial TEG ( n =65 thermoelements) for internal temperature measurements. Outer Ring Inner Ring Outer Ring Inner Ring

PAGE 201

201 0.846 0.848 0.85 0.852 0.854 0.856 0.858 0.86 0.862 0.864 0.866 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]No. of OccurrencesTEG1: Inner Ring A 290.2 290.4 290.6 290.8 291 291.2 291.4 291.6 291.8 292 292.2 0 100 200 300 400 500 600 Range of values of the slope (b) []No. of OccurrencesTEG1: Inner Ring B Figure B 4 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for le ast square fit, and thus, TCR of the inner resistive thermal sensors on radial TEG (n=65 thermoelements) for internal temperature measurements.

PAGE 202

202 0.892 0.894 0.896 0.898 0.9 0.902 0.904 0.906 0.908 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]No. of OccurrencesTEG1: Outer Ring A 315 315.2 315.4 315.6 315.8 316 316.2 316.4 316.6 316.8 0 100 200 300 400 500 600 700 Range of values of the slope (b) []No. of OccurrencesTEG1: Outer Ring B Figure B 5 Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on radial TEG ( n =65 thermoelements) for internal temperature measurements.

PAGE 203

203 For TEG n=18. Sections 4.2.1 and 4.2.2. 0 20 40 60 80 100 120 140 160 180 200 220 280 300 320 340 360 380 400 420 440 460 480 500 TEG7: Resistors (down)Temperature (C)Resistance () Figure B 6 Cha racterization of the inner and outer resistive thermal sensors on radial TEG ( n =18 thermoelements) for internal temperature measurements. Outer Ring Inner R ing

PAGE 204

204 0.845 0.85 0.855 0.86 0.865 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]No. of Occurrences A 270.5 271 271.5 272 272.5 0 100 200 300 400 500 600 700 Range of values of the slope (b) []No. of Occurrences g B Figure B 7 Monte Carlo simulations used to extract (A) slope (m), and (B) inte rcept (b) for least square fit, and thus, TCR of the inner resistive thermal sensors on radial TEG ( n =18 thermoelements) for internal temperature measurements.

PAGE 205

205 0.89 0.895 0.9 0.905 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]No. of OccurrencesTEG7 Outer Ring A 286.5 287 287.5 288 288.5 0 100 200 300 400 500 600 700 Range of values of the slope (b) []No. of OccurrencesTEG7 Outer Ring B Figure B 8 Monte Carlo simulations used to extract (A) slop e (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on radial TEG ( n =18 thermoelements) for internal temperature measurements.

PAGE 206

206 For TEG n=90. Sections 4.2.1 and 4.2.2. 0 20 40 60 80 100 120 140 160 180 200 220 340 360 380 400 420 440 460 480 500 520 540 560 580 TEG11: Resistors (down)Temperature (C)Resistance () Figure B 9 Characterization of the inner and outer resistive thermal sensors on radial TEG ( n =90 thermoelements) for internal temperature measurements. Outer Ring Inner Ring

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207 0.862 0.864 0.866 0.868 0.87 0.872 0.874 0.876 0.878 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]No. of Occurrences A 322 322.5 323 323.5 324 0 100 200 300 400 500 600 700 Range of values of the slope (b) []No. of Occurrences B Figure B 10. Monte Carlo simulations used to extract (A) slope ( m), and (B) intercept (b) for least square fit, and thus, TCR of the inner resistive thermal sensors on radial TEG ( n =90 thermoelements) for internal temperature measurements.

PAGE 208

208 0.988 0.99 0.992 0.994 0.996 0.998 1 1.002 0 100 200 300 400 500 600 700 Range of values of the slope (m) [/C]No. of OccurrencesTEG11 Outer Ring A 355 355.5 356 0 100 200 300 400 500 600 700 Range of values of the slope (b) []No. of OccurrencesTEG11 Outer Ring B Figure B 11. Monte Carlo simulations used to extract (A) slope (m), and (B) intercept (b) for least square fit, and thus, TCR of the outer resistive thermal sensors on radial TEG ( n =90 thermoelements) for internal temperature measurements.

PAGE 209

209 Thermal and Electrical Characterization Using a Hot Gas S tream Next, the TEG modules are tested us ing a heat gun. Section 4.3.2. 0 20 40 60 80 100 120 140 160 180 200 220 320 340 360 380 400 420 440 460 480 DTEG18: Ni ring Resistance. vs. Gas Temp.Gas Temperature (C)Resistance () Rin-upRin-downRout-upRout-down Figure B 12. I nner and outer resistive Ni ring resistances (as gas temperature increases and decreases) on a radial dummy TEG ( no thermoelements) for i nternal temperature measurements.

PAGE 210

210 0 20 40 60 80 100 120 140 160 180 200 220 280 300 320 340 360 380 400 420 440 460 Gas Temperature, TGAS (C)Resistance () Figure B 13. I nner and outer resistive Ni ring resistances on a radial TEG ( n = 18 thermoelements) for internal temperature measurements. 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 Gas Temperature, TGAS (C)Silicon Ring Temp. (C) Figure B 14. I n ner and outer silicon ring temperatures determined from integrated Ni ring resistances on a radial TEG ( n =18 thermoelements ). Inner Ring Outer Ring Inner Ring Outer Ring

PAGE 211

211 Section 4.3.3. 0.24 0.25 0.26 0.27 0.28 0 100 200 300 400 500 600 700 Range of values of the slope (m) [mV/C]No. of Occurrences oc Figure B 15. Monte Carlo simulations used to determine the thermoelement pair Seeb eck coefficient ( Au Ni) from the open circuit voltage and temperature difference for a radial TEG ( n = 18 thermoelements). 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 G 0 oad otageSilicon Ring T (C)Load Voltage (mV) Figure B 16. Load voltage vs. T for TEG with n=18 leg pairs. V oc = 0.26*

PAGE 212

212 0 10 20 30 40 50 60 70 80 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 g Temperature Difference (C)Delivered Power ( Watts) Figure B 17. Delivered power for TEG module with n=18 leg pairs using matched load. Resistance increase against gas temperature due to TCR effects. Section 4.3. 0 20 40 60 80 100 120 140 160 180 200 220 100 120 140 160 180 200 220 240 260 280 300 320 340 g () Gas Temperature, TGAS (C)Module Resistance () Single TEG (n=18) Figure B 18. Module electrical resistance vs. gas temperature for TEG with n=18 leg pairs. P= (6.0x10 5 ) 2 + (1.8x10 3 )

PAGE 213

213 0 20 40 60 80 100 120 140 160 180 200 300 320 340 360 380 400 420 440 TEG1: Ni RingsGas Temperature, TGAS (C)Resistance () Figure B 19. Measurement of the inner and outer resistive Ni ring resistances on radial TEG ( n =65 thermoelements) for internal temperature measurements. 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 TEG1: Si Ring Temp.Gas Temperature, TGAS (C)Silicon Ring Temp. (C) Figure B 20. I nner and outer silicon ring temperatures determined from integrated Ni ring resistances on radial TEG ( n =6 5 thermoelements). Inner Ring Outer Ring Inner Ring Outer Ring

PAGE 214

214 0 10 20 30 40 50 60 70 0 5 10 15 20 25 30 TEG1: Load VoltageSilicon Ring T (C)Load Voltage (mV) Figure B 21. 0 10 20 30 40 50 60 70 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 g Temperature Difference (C)Delivered Power ( Watts) Figure B 22. Quadratic fit in a least square sense. P= ( 8.6 x10 5 ) 2 + ( 1.5 x10 3 ) V Load = 0.4 3

PAGE 215

215 To demonstrate functionality of the TEG module over time, TEG ( n =65) was tested 30 days later. 0 20 40 60 80 100 120 140 160 180 200 220 300 320 340 360 380 400 420 440 460 TEG1: Ni Ring Resistance vs. Gas Temp.Gas Temperature (C)Ring Resistance () Figure B 23. Re test 30 days later of the inner and outer resistive Ni ring resistances on a radial TEG ( n =65 thermoelements) for internal temperature measurements and for functionality over time Inner Ring Outer Ring

PAGE 216

216 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 TEG1: Silicon Ring Temp. vs. Gas Temp.Gas Temperature (C)Silicon Ring Temp. (C) Figure B 24. Re test of the i nner and outer silicon ring temperatures determined from integrated Ni ring resistances on a radial TEG ( n =65 thermoelements ) for functionality over time. 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 TEG1: Voc vs. Ring TSilicon Ring T (C)Open Circuit Voltage (mV) Figure B 25. Re test of the thermoelement pair Seebeck coefficient ( Au Ni) from the opencircuit voltage and t emperature difference for a radial TEG ( n =65 thermoelements) for functionality over time. Inner Ring Outer Ring V oc = 0.93*

PAGE 217

217 0.85 0.9 0.95 1 1.05 0 100 200 300 400 500 600 700 Range of values of the slope (m) [mV/C]No. of OccurrencesTEG1: Slope of Voc vs. T Figure B 26. Re test Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from the open circuit voltage and temperature difference for a radial TEG ( n =65 leg pairs ). 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 TEG1: Load Voltage vs. Ring TSilicon Ring T (C)Load Voltage (mV) Figure B 27. Re functionality over t ime. V oc = 0.42*

PAGE 218

218 0 10 20 30 40 50 60 70 80 0 0.1 0.2 0.3 0.4 0.5 TEG1: Power vs. Ring TSilicon Ring T (C)Delivered Power ( Watts) Figure B 28. Re test of the power functionality over time. 0 20 40 60 80 100 120 140 160 180 200 320 340 360 380 400 420 440 TEG1: Ni RingsGas Temperature, TGAS (C)Ring Resistance () Figure B 29. Third test of the inner and outer resistive Ni ring resistances on a radial TEG ( n =65 leg pairs ) for internal temperature measurements. Inner Ring Outer Ring P= (9.0x10 5 ) 2 + (1.0x10 3 )

PAGE 219

219 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 TEG1: Si Ring Temp. vs. Gas Temp. at no LoadGas Temperature (C)Silicon Ring Temp. (C) Figure B 30. Third test of the i nner and outer silicon ring temperatures de termined from integrated Ni ring resistances on a radial TEG ( n =65 leg pairs ). 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 pSilicon Ring T (C)Open-Circuit Voltage (mV) Figure B 31. Third test of the thermoelement pair Seebeck coefficient ( Au Ni) from the opencircuit voltage and temperature difference for a radial TEG ( n =65 leg pairs ). Inner Ring Outer Ring V oc = 0.9 5

PAGE 220

220 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 0 100 200 300 400 500 600 700 Range of values of the slope (m) [mV/C]No. of OccurrencesTEG1: Slope of Voc vs. T Figure B 32. Third test Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from t he open circuit voltage and temperature difference for a radial TEG ( n =65 leg pairs ). T he TEG (n=65) module was again tested with various resistive loads. 102 103 104 105 106 370 380 390 400 410 420 430 440 TEG1: Inner Ni Ring Resistance vs. Load ResistanceLoad Resistance ()Inner Ni Resistance () Figure B 33. Inner Ni ring resistance vs. load resistance at var ious temperatures. Error bar is +/ 3.3 Ohms. 112C 118 C 152 C 171 C 191 C

PAGE 221

221 102 103 104 105 106 375 380 385 390 395 400 405 410 415 TEG1: Outer Ni Ring Resistance vs. Load ResistanceLoad Resistance ()Outer Ni Resistance () Figure B 34. Outer Ni ring resistance vs. load resistance at various temperatures. Error bar is +/ 3.3 Ohms. 102 103 104 105 106 80 90 100 110 120 130 140 150 160 TEG1: Inner Si Ring Temp. vs. Load ResistanceLoad Resistance ()Inner Si Ring Temperature (C) Figure B 35. Inner Ni ri ng resistance vs. load resistance at various temperatures. Error bar is +/ 3.3 Ohms, and Ring temperatue is ~ 6.5 C 112C 1 18 C 152 C 171 C 191 C 112C 118 C 152 C 171 C 191 C

PAGE 222

222 102 103 104 105 106 55 60 65 70 75 80 85 90 95 TEG1: Outer Si Ring Temp. vs. Load ResistanceLoad Resistance ()Outer Si Ring Temperature (C) Figure B 36. Outer Ni ring resistance vs. load resistance at various temperatures. Error bar is +/ 3.3 Ohms, and Ring temperatue is ~ 6.0 C. 102 103 104 105 106 25 30 35 40 45 50 55 60 65 TEG1: T vs. Load ResistanceLoad Resistance ()Silicon Ring T (C) Figure B 37. Temperature difference vs. load resistance at various temperatures. Error bar is +/ 3.3 Ohms, and Ring temperatue is ~ 8.5 C. 112C 118 C 152 C 171 C 191 C 112C 118 C 152 C 171 C 191 C

PAGE 223

223 0 20 40 60 80 100 120 340 350 360 370 380 390 400 410 420 430 Gas Temperature, TGAS (C)Resistance () Figure B 38. I nner and outer resistive Ni ring resistances on a radial TEG ( n =90 thermoelements) for internal temperature measurements. 0 10 20 30 40 50 60 70 80 90 100 110 120 0 10 20 30 40 50 60 70 80 90 100 110 G 9 S g epGas Temperature, TGAS (C)Silicon Ring Temp. (C) Figure B 39. I nner and outer silicon ring temperatures determined from integrated Ni r ing resistances on a radial TEG ( n =90 thermoelements ). Inner Ring Outer Ring Inner Ring Outer Ring

PAGE 224

224 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 50 Silicon Ring T (C)Open-Circuit Voltage (mV) Figure B 40. T hermoelement pair Seebeck coefficient ( Au Ni) from the opencircuit voltage and temperature difference for a radial TEG ( n =90 thermoelements). 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 0 100 200 300 400 500 600 700 Range of values of the slope (m) [mV/C]No. of Occurrences oc Figure B 41. Monte Carlo simulations used to determine the thermoelement pair Seebeck coefficient ( Au Ni) from the ope n circuit voltage and temperature difference for a radial TEG ( n =90 thermoelements). V oc = 1.32

PAGE 225

225 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 gSilicon Ring T (C)Load Voltage (mV) Figure B 42. Load voltage of resistive load (1.55 k ) as a function of temperature difference for a radial TEG ( n =90 thermoelements). 0 5 10 15 20 25 30 35 40 45 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 TEG11 n94: Power vs. Ring TTemperature Difference (C)Delivered Power ( Watts) Fi gure B 43. Electrical power delivered to a test resistive load (1.55 k ) as function of temperature difference for a radial TEG ( n =90 thermoelements). V Load = 0.65

PAGE 226

226 Section 4.4: Tests with a stacked TEG (n= 65) with other 15 dummy modules. 0.85 0.9 0.95 1 1.05 0 100 200 300 400 500 600 700 Range of values of the slope (m) [mV/C]No. of Occurrences Figure B 44. Monte Carlo simulations of the slope to determine the Seebeck coefficient of the stacked TEG ( n =65 leg pairs). 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 30 35 40 45 Stacked TEG1: Load Voltage vs. Gas Temp. at Load R=2kGas Temperature, TGAS (C)Load Voltage (mV) Figure B 45. Sample load voltage vs. gas temperature for a stacked T EG (n=65).

PAGE 227

227 Section 5.2: Sample plots for a stacked TEG (n=65) 20 40 60 80 100 120 140 160 180 200 -10 0 10 20 30 40 50 60 70 80 90 Stacked TEG1: VoltageGas Temperature, TGAS (C)Open-Circuit Voltage (mV) Figure B 46. Opencircuit voltage vs. gas temperature for a stacked TEG (n=65).

PAGE 228

228 Experimental data of the ring temperatures vs. load: 101 102 103 104 105 380 390 400 410 420 430 440 450 460 470 480 490 Stacked TEG1: Inner Ni Ring Resistance vs. Load ResistanceLoad Resistance ()Inner Ni Resistance () Figure B 47. Inner Ni ring resistance for various loads and temperatures for a stacked TEG (n=65). 81C 9 4 C 109 C 128 C 146 C 187 C

PAGE 229

229 101 102 103 104 105 375 380 385 390 395 400 405 410 415 420 425 Stacked TEG1: Outer Ni Ring Resistance vs. Load ResistanceLoad Resistance ()Outer Ni Resistance () Figure B 48. Outer Ni ring resistance for various loads and temperatures for a stacked TEG (n=65). 81 C 94 C 109 C 128 C 146 C 187 C

PAGE 230

230 101 102 103 104 105 80 90 100 110 120 130 140 150 160 170 180 190 200 Stacked TEG1: Inner Si Ring Temp. vs. Load ResistanceLoad Resistance ()Inner Si Ring Temperature (C) Figure B 49. Inner silicon temperature for various loads and temperatures for a stacked TEG (n=65). 81 C 94 C 109 C 128 C 146 C 187 C

PAGE 231

231 101 102 103 104 105 50 60 70 80 90 100 110 Stacked TEG1: Outer Si Ring Temp. vs. Load ResistanceLoad Resistance ()Outer Si Ring Temperature (C) Figure B 50. Outer silicon temperature for various loads and temperatures for a stacked TEG (n=65). 81 C 94 C 109 C 128 C 146 C 187 C

PAGE 232

232 101 102 103 104 105 20 30 40 50 60 70 80 90 100 Stacked TEG1: T vs. Load ResistanceLoad Resistance ()T (C) Figure B 51. Silicon rings temperature difference for various loads and temperatures for a stacked TEG (n=65). Section 5.2: Opencircuit voltage for the stacked TEG (n=65). Using thin film extrac ted properties to predict performance (solid lines) and compare to experiments (data points): using measured TEG resistance (1.63kOhm ) and estimate resistance ( 2.24 kOhm ) at 25 C 81 C 94 C 109 C 128 C 146 C 187 C

PAGE 233

233 0 20 40 60 80 100 120 140 160 180 200 220 0 10 20 30 40 50 60 70 80 90 100 Stacked TEG1: VoltageGas Temperature, TGAS (C)Open-Circuit Voltage (mV) Figure B 52. Experimental data (points) and model predictions (solid lines) of opencircuit voltage versus gas temperature for the stacked TEG. 0 20 40 60 80 100 120 140 160 180 200 220 0 10 20 30 40 50 60 Stacked TEG1: Load Voltage (2kOhm) vs. Gas Temp.Gas Temperature, TGAS (C)Load Voltage (mV) Figure B 53. Experimental data (points) and model predictions (solid lines) of load or the stacked TEG.

PAGE 234

234 0 10 20 30 40 50 60 70 80 90 100 110 0 10 20 30 40 50 60 70 80 90 100 Stacked TEG1: VoltageSilicon Ring T (C)Open-Circuit Voltage (mV) Figure B 54. Experimental data (points) and model pr edictions (solid lines) of opencircuit voltage versus 0 10 20 30 40 50 60 70 80 90 100 110 0 0.2 0.4 0.6 0.8 1 1.2 1.4 g Silicon Ring T (C)Delivered Power ( Watts) Figure B 55. Experimental data (points) and model predictions (solid lines) of delivered power to

PAGE 235

235 Section 5.2: Tests with a stacked device (n=65) and comparison to the model. 101 102 103 104 105 0 10 20 30 40 50 60 70 80 Stacked TEG1: Load Voltage vs. Load ResistanceLoad Resistance ()Load Voltage (mV) 23 C 93 C 113 C 128 C 150 C 170 C 195 C Figure B 56. Model estimates of voltage acros s various loads using extracted thin film resistivity and measured TEG resistance (1.63 k ). Better approximation to the data is obtained at lower than at higher temperatures.

PAGE 236

236 101 102 103 104 105 0 10 20 30 40 50 60 70 80 Stacked TEG1: Load Voltage vs. Load ResistanceLoad Resistance ()Load Voltage (mV) 23 C 93 C 113 C 128 C 150 C 170 C 195 C Figure B 57. Model estimates of voltage across various loads using extracted thin film resistivity and estimated TEG resistance (2.24 k ). Better approximation to the data is obtained at lower than at higher temperatures.

PAGE 237

237 101 102 103 104 105 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Stacked TEG1 n=65: Power vs. LoadLoad Resistance ()Delivered Power ( Watts) 23 C 93 C 113 C 128 C 150 C 170 C 195 C Figure B 58. Model estimates of power delivered to various load s using extracted thin film resistivity estimated TEG resistance of (2.24 k ). Better approximation to the data is obtained at lower than at higher temperatures.

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238 APPENDIX C MATLAB FUNCTIONS The following code is used to ex tract the optimized parameters (n, FP, FN, tP, tN) of the radial TE generator based on material properties and system level constraints. Calls a function to compute optimized parameters as described in Chapter 2. % radial TEG chip with pieshaped thermocouple % optimPIE_v20.m close all; clear all; clc; global lbFtp ubFtp lbFtn ubFtn lbFFp ubFFp lbFFn ubFFn lbnn ubnn r1 r2 ri ro rf tsi tox tpoly; global Tgas Tamb an ap rn rp kn kp ka kpoly kox hh hc w1 w2; format compact % --------------------MP = load( 'CrNi200.txt') %p_n_temp. Tgas= MP(1); % gas temp. Tamb= MP(2); % ambient temp.: 22 C ap = MP(3); % Cr=20e-6, p -BiTe=185, PbTe=125 (for p and n) an = MP(4); % Ni= -20e -6, n -BiTe= -205 rp= MP(5); % of p type film rn= MP(6); %electrical resistivity of n-type film (Ohm -m) kp= MP(7); % of chromium=94 (metal 2) kn= MP(8); % of nickel=91 (metal 1), BiTe=~ 1.9 or 2 W/mK, PbTe=2 ka= MP(9); % thermal conductivity of air (0.03 at room temp.) kpoly= MP(10); % for polyimide kox= MP(11); % for oxide % --------------------hh=100; % convective heat transfer coef. in the hot side from experiment hc=100; % in the cold side (free convection) from experiment w1 = 100e-6; % width of metal interconnects (even if it's 25, 100 or 200um does not influence results) w2 = w1; % make equal for now %Substrate thickness is the sum of these 3 layers tpoly=5e6; % thickness of polyimide tox=0.4e-6; % thickness of oxide tsi = 345e-6; % silicon thickness (m) ri=2.5e -3; %radius of inner surface of inside Si ring (m) r1=3e-3; % radius of outer surface on inside Si ring r2=4e-3; % radius of inner surface of outer Si ring ro=4.5e-3; % radius of outer surface of outer Si ring of active die rf=6.5e 3; % radius of outer surface of outer Si ring of fins min_width = 10e-6; %min. TE width: 10um % for the design that we are fabricating

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239 min_d = 10e-6; %min. feature size and/or gap: 10um % film thickness, Ft, is i n microns. Ftp=0.5e-6; % normalize thickness to Ftp= (Ftp-lb)/(ub lb) (initial guess: 0.5 um) lbFtp=0.1e6; % lower bound of Ftp ubFtp=10e6; % upper bound of Ftp limitation on metal evaporation/sputtering (used to be 0.08) Ftn=1e 6; % normalize thi ckness to Ftn= (Ftn -lb)/(ub-lb) (initial guess: 1um) lbFtn=0.1e6; % lower bound of Ftn ubFtn=10e6; % upper bound of Ftn limitation on metal evaporation/sputtering (used to be 0.08) FFp=0.05; %fraction of total angle/or surface area of pmetal ( initial guess: 0.24) lbFFp=0; ubFFp=1; % before it was set to 0.45 FFn=0.95; %fraction of total angle/or surface are of n-metal (initial guess: 0.35) lbFFn=0; ubFFn=1; nn=10; %guess of no. of TE pairs (initial guess: 10) lbnn=1; % lower bound of n (1) ubnn=500; %upper bound of n (500) %format short eng; X0 = [(Ftp -lbFtp)./(ubFtp lbFtp) (FFp -lbFFp)./(ubFFp -lbFFp) (FFn -lbFFn)./(ubFFn-lbFFn) (nn -lbnn)./(ubnn-lbnn) (FtnlbFtn)./(ubFtn-lbFtn)]' %column vector of initial guess at the solution lb=[0 0 0 0 0]'; % normalized bounds ub=[1 1 1 1 1]'; %inequality constraints modified to account for normalized inputs : Ax <= b %X(1)=tp, X(2)=Fp, X(3)=Fn, X(4)=n, X(5)=tn % ------Only considers the lower bound on gap and spacing of TE legs A=[0 pi*r1*(ubFFp-lbFFp) pi*r1*(ubFFn-lbFFn) min_d*(ubnnlbnn) 0; 0 ( -1)*2*pi*r1*(ubFFp -lbFFp) 0 min_width*(ubnn-lbnn) 0; 0 0 ( 1)*2*pi*r1*(ubFFnlbFFn) min_width*(ubnn-lbnn) 0]; b=[pi*r1*(1-lbFFp -lbFFn) min_d*lbnn; 2*pi *r1*lbFFp min_width*lbnn; 2*pi*r1*lbFFnmin_width*lbnn]; % ---------------options=optimset('LargeScale','off','Display','iter','MaxFunEvals',500000,'MaxIter',50000,'TolFun',1e-15,'TolCon',1e15); [X,fval,exitflag,output]=fmincon(@opt_radial_math_v20,X 0,A,b,[],[],lb,ub,[],options); fval=fval*1e-6; %format short eng; Powerdel = ( -1).*fval*1000; % power density (units of mW) %format short eng; X % normalized values Ftp %initial guesses not normalized Ftn FFp FFn % in SI units (not normalized) n_guess=(1-FFp -FFn).*2*pi*r1/2/min_d Ftpopt= X(1).*(ubFtp lbFtp) + lbFtp % t back to SI units (not normalized) Ftnopt= X(5).*(ubFtn lbFtn) + lbFtn % t back to SI units (not normalized)

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240 Fpo pt=X(2).*(ubFFp lbFFp) + lbFFp % fraction of phip,phin to phi_net Fnopt=X(3).*(ubFFn lbFFn) + lbFFn nopt=X(4).*(ubnn lbnn) + lbnn % no. of TE pairs gap=(1Fpopt -Fnopt).*2*pi.*r1/2/nopt %arc length spacing between TEs at r1 %nopt=floor((1Fpopt -Fnopt).*2*pi*r1/2/min_d) % no. of TC that fit Wp_in=Fpopt*2*pi*r1/nopt % inner width of single p-type leg Wn_in=Fnopt*2*pi*r1/nopt % inner width of single n-type leg Ws_in=(1 -Fpopt Fnopt)*2*pi*r1/nopt/2 % inner width of space between legs Adie=pi*(rf*100)^2 % area of single die in cm squared % total device thickness: film + silicon + oxide + polyimide tmax =max(Ftpopt,Ftnopt) % thicker of the p an n type film L = (tmax + tsi + tox + tpoly)*100 % in cm %delivered power to the load Powerdel % power (mW) % power density in mW/cm^3 PowerDensity = Powerdel/L/Adie % (mW/cm^3) % power per area PperA = Powerdel/Adie % (mW/cm^2) % --------------------------------------------------------------------------This function is called by the code above which then returns the optimized parameters. % opt_radial_math_v20 function [npowergen] = opt_radial_math_v20(X) global lbFtp ubFtp lbFtn ubFtn lbFFp ubFFp lbFFn ubFFn ubnn lbnn r1 r2 ri r o rf tsi tox tpoly; global Tgas Tamb an ap rn rp kn kp ka kpoly kox hh hc w1 w2; Ftp= X(1).*(ubFtp lbFtp) + lbFtp; % tp of thermocouples back to SI units (not normalized) Ftn= X(5).*(ubFtn lbFtn) + lbFtn; % tn factorp=X(2).*(ubFFp lbFFp) + lbFFp; factorn=X(3).*(ubFFn lbFFn) + lbFFn; % fraction of phip,phin to phi_net n=X(4).*(ubnn lbnn) + lbnn; % no. of TE pairs phi_net= 2.*pi./n; % net angle width of thermocouple phip=factorp.*phi_net; % angle width of p leg; phin=factorn.*phi_net; % angle width of nleg; % phip + phin + phispace = phi % temperature difference between Si rings: DeltaT = (Tgas -Tamb)./(((factorp.*kp).*Ftp/tsi +(factorn.*kn).*Ftn/tsi + ka + kpoly*tpoly/ tsi + kox*tox/tsi).*(1/hh./ri + 1/hc./ro)./log(r2./r1) + 1); %in Celsius % open circuit voltage of series -connected couple pairs (silicon thermal resistance is negligible), added oxide layer V = n.*(ap an).*DeltaT; % in Volts

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241 % elec. resistance including interconnects (not considering contact resistance) A = (n.^2); B = (log(r2./r1)).*(rp./factorp./Ftp + rn./factorn./Ftn)/2/pi; % pie legs term C = pi.*(1 -factorp factorn).*(rp.*r2./w2./Ftp + rn.*r1./w1./Ftn)./n.^2; % divided by 2 because of two gaps: interconnects term R_total = A.*(B + C); % electrical resistance (in Ohms) of TEG P = (V.^2)./4./R_total; % power (W) delivered to a matched load npowergen = ( 1)*P*1e6; % optimizing for power % -------------------------------------------------------------For Chapter 2 design: This function uses the optimized values or the extracted values of thin film parameters into the model to predict performance: %Israel Boniche % updated: 03/04/09 % radial TEG chip with pies haped thermocouple % optimPIE_check_v20.m % Optimized for power, P clc clear all close all format compact % ---MP = load('CrNi400.txt') %p_n_temp. Tgas= MP(1); % gas temp. Tamb= MP(2); % ambient temp.: 22 C ap = MP(3); % Au=2.8, Cr=20e-6, p -BiTe=185, PbTe=125 (for p and n) an = MP(4); % Ni= -20e -6, n -BiTe= -205 rp= MP(5); % of p type film rn= MP(6); %electrical resistivity of n-type film (Ohm -m) kp= MP(7); % of chromium=94 (metal 2) kn= MP(8); % of nickel=91 (metal 1), BiTe=~ 1.9 or 2 W/mK, PbTe=2 ka= MP(9); % thermal conductivity of air (0.03 at room temp.) kpoly=MP(10); % for polyimide kox= MP(11); % for oxide ksi=148; % for Silicon (148 at room temp.) Ftpopt Ftnopt Fpopt Fnopt nopt gap

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242 % ------------hh=100; % from TEG7 test hh, convective heat transfer coef. in the hot side from Sivam's experiment hc=100; % hc= in the cold side (free convection) from Sivam's experiment (100) w1 = 100e-6; % width of metal interconnects (even if it's 25, 100 or 200um does not influence results) w2 = w1; % make equal for now %Substrate thickness is the sum of these 3 layers tpoly = 5e-6; % thickness of polyimide tox = 0.4e-6; % thickness of oxide (0.4 um) tsi = 345e-6; % silicon thickness (345 um) esi=0.5; % Si emissivity (assuming avg of 0.12 to 1) bolt=5.67e-8; % W/m^2*K^4 boltzmann constant ri=2.5e -3; % inner radius of inside Si ring r1=3e-3; % inner radius of TE legs r2=4e-3; % outer radius of TE legs %r2=linspace(r1,10.*r1); ro=4.5e-3; % outer radius of outside Si ring rf =6.5e -3; % fin radius % ---%gap=90e6; %gap b/w TE pair (90um), min. gap 10um Ftp = Ftpopt; % P leg thickness: Au Ftn = Ftnopt; % N leg thickness: Ni (um) factorp = Fpopt; %0.1973 P -Type factorn = Fnopt; %0.1491 % N -type %n=linspace(1,500,500); n=(1 -factorp factorn).*2*pi.*r1/2/gap % checking no. of TE pairs that fit n=floor(nopt) %TEG7: n=20, Fp=Fn=0.40; TEG1: n=68, Fp=0.1973, Fn=0.1491; % ZT dimensionless figure of merit for a pair of materials subject to p/n width/length matching ratio % Tavg=mean([Tgas Tamb]) + 273 %Kelvin % Z=((ap an)^2)/(sqrt(kp*rp) + sqrt(kn*rn))^2 % % ZT= Z*Tavg %for pair of materials phi_net= 2.*pi./n; % net angle width of thermocouple phip=factorp*phi_net % angle width of p-leg; degp=phip*180/pi phin=factorn*phi_net % angle width of n-leg; degn=phin*180/pi % phip + phin + phispace = phi arc_ p=phip.*r1 % arc length of p-leg arc_n=phin.*r1 % arc length of n-leg %t= 100e-6; % thickness of thermocouples %FT=linspace(0.001,0.5,500); %T= 3500e6; % thickness of silicon, same as that for air %T=linspace(200e-6,4000e-6)

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243 % temperature difference between Si rings: % if testing a single device then convective term should use rf, if using stack of small/large dies then ro? DeltaT = (Tgas -Tamb)./(((factorp.*kp).*Ft p/tsi +(factorn.*kn).*Ftn/tsi + ka + kpoly*tpoly/tsi + kox*tox/tsi).*(1/hh./ri + 1/hc./ro)./log(r2./r1) + 1); %in Celsius % Test DeltaT % open circuit voltage (silicon thermal resistance is negligible), added oxide layer V = n.*(ap an).*DeltaT; % in V olts %from experiments: %V = n.*(apn).*DeltaT; % in Volts % thermal resistance due to convection % for single devide, rf is used not ro Rth_hot= 1/hh./ri./2./pi./tsi Rth_cold= 1/hc./ro./2./pi./tsi % thermal resistance Rth_p= (log(r2/r1))/2/pi/factorp/ Ftp/kp % for all p-type lumped Rth_n= (log(r2/r1))/2/pi/factorn/Ftn/kn % for all ntype lumped Rth_ox=(log(r2/r1))/2/pi/tox/kox % oxide resistance Rth_poly=(log(r2/r1))/2/pi/tpoly/kpoly % polyimide resistance Rth_air=(log(r2/r1))/2/pi/ts i/ka % air resistance Ri_si=(log(r1/ri))/2/pi/tsi/ksi % inner Si ring thermal resistance %if single device is used, rf is used for outer Si ring Ro_si=(log(rf/r2))/2/pi/tsi/ksi % outer Si ring resistance %Rteg_sub= log(r2./r1)./((factorp.*kp + factorn.*kn).*t./T + ka)./2/pi./N./T; Rth_legs = 1/( 1/Rth_p + 1/Rth_n) Rcond_layers = 1/( 1/Rth_p + 1/Rth_n + 1/Rth_poly + 1/Rth_ox + 1/Rth_air) % thermal conduction resistance only %Rcond = 1/(1/Rth_poly + 1/Rth_air) % thermal conduction resistance only qcond= DeltaT./(Rcond_layers + Ri_si + Ro_si) % assuming constant heat flow rate thru device (only conduction) qnet= qcond; %h coef. extraction %qcond=(Tgas -Thot)/(Rth_hot + Ri_si) % R1Si= (log(r1/ri))/2/pi/ksi/TT % [K/W] conduction thermal resistance of inside Si ring % % R2Si= (log(ro/r2))/2/pi/ksi/TT % [K/W] conduction thermal resistance of outside Si ring T1= Tgas qnet*Rth_hot % inner surface temp. of inside Si ring T2= T1 qnet*Ri_si % hot side of TE T3= T2 Delt aT % cool side of TE T4= T3 qnet*Ro_si % outer surface temp. of Si ring %radiation exchange b/w Si surfaces qrad1=bolt*2*pi*r1*tsi*((T2 +273)^4 (T3 +273)^4)/ (1/esi + (1-esi)*r1/esi/r2) qradenv=esi*bolt*2*pi*r1*tsi*((T2 +273)^4 (T3 +273)^4) ratio_qrad1_to_qcond=qrad1/qcond %importance of Si rings radiation exchange % elec. resistance including interconnects (not considering contact resistance) A = (n.^2);

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244 B = (log(r2./r1)).*(rp./factorp./Ftp + rn./factorn./Ftn)/2/p i; % pie legs term (corrected 04/13/08) C = pi.*(1 -factorp factorn).*(rp.*r2./w2./Ftp + rn.*r1./w1./Ftn)./n.^2; % divide by 2 because of two gaps: interconnects term R_total = A.*(B + C); % total electrical resistance (in Ohms) of TEG Rlegs_only= A.*B % elect. resis. of p/n legs Rinter = A.*C % elect. resist. of inner and outer interconnects P = (V.^2)./4./R_total; % power in Watts delivered to a matched load Adie=pi*(rf*100)^2 % area of single die in cm^ 2 (includes central hot channerl and outer annular fins) % total device thickness: film + silicon + oxide + polyimide tmax =max(Ftp,Ftn) % thicker of the p an n type film L = (tmax + tsi + tox + tpoly)*100; % in cm % power density Pcm3= P*1000/Adie/L % power density in mW/cm^3 V DeltaT R_total powerdel=P*1000 % in mW % Device power factor rmid = mean([ri rf]) % mid section radius Amid = 2*pi*rmid*100*tsi*100; % mid-section surface area of single module in cm^2 DPFmid=(P*1e6)/Amid/(DeltaT^2) %units of microWatts/(cm^2 K^2) Ainner = 2*pi*ri*100*tsi*100; % inner Si surface area of single module in cm^2 DPFinner=(P*1e6)/Ainner/(DeltaT^2) %units of microWatts/(cm^2 K^2) Aouter = 2*pi*rf*100*tsi*100; % outer Si surface area (annular fi ns) of single module in cm^2 DPFouter=(P*1e6)/Aouter/(DeltaT^2) %units of microWatts/(cm^2 K^2) % power density (to compare to solar cells) PperA= P*1000/Adie % power density in mW/cm^2 %Peltier terms I=P./(V./2) % [A] assuming match load, the voltage splits evenly I= sqrt(P/R_total) Qp_hot=n*(ap-an)*(T2 +273)*I %peltier heat source at hot side for n TE couples (W) Qp_cold=n*(ap-an)*(T3 +273)*I %peltier heat source at hot side for n TE couples % Joule heating Qjoule=R_total*I ^2 % total joule heating of device (W) Zpn_module = (n.*(apan)).^2.*Rcond_layers./R_total % for the module Tavg = (T2 +T3)./2 %avg. b/w hot temp. and cold side temp. ZTavg_module = Zpn_module.*(Tavg +273) % zpn_single_pair = (n.^2).*((ap-an).^2).*Rth_legs./R_total % for the specific TE leg pairs % zT_single_pair = zpn_single_pair.*(Tgas +273) efficiency1 = (P./qcond) % thermodynamic efficiency

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245 carnot_efficiency = DeltaT./(T2+273) % Temperature in Kelvin: deltaT/ Thot Tgas qcond % -----------------------------------------Code to extract h values (convect. Transfer coef.) %Israel Boniche %01/20/10 %Radial TEG parameter extraction for the stacked struture % stacked device TEG1: n=65 with other dummy devices clear all close all clc f ormat compact MP = load('AuNi100.txt') %p_n_temp. Tgas= MP(1); % gas temp. Tamb= MP(2); % ambient temp.: 22 C ap = MP(3); % Au=2.8, Cr=20e-6, p -BiTe=185, PbTe=125 (for p and n) an = MP(4); % Ni= -20e -6, n -BiTe= -205 rp= MP(5); % of p type film rn= MP(6); %electrical resistivity of n-type film (Ohm -m) kp= MP(7); % of chromium=94 (metal 2) kn= MP(8); % of nickel=91 (metal 1), BiTe=~ 1.9 or 2 W/mK, PbTe=2 ka= MP(9); % thermal conductivity of air (0.03 at room temp.) kpoly=MP(10) % for polyimide kox= MP(11) % for oxide %bulk at 25C % kp= 317 %Au 25C: 317, from vdp: 345 % kn= 91 %Ni 25C: from Ni rings: 11.8 % ka = 0.026 %air (stagnant) at 100C; 0.032, at 25C: 0.026 % ksi=148; % for Silicon (148 at room temp.), at 200: 80 % kpoly = 0.14 % kox =1.4 % % rp=2.3e-8; %Au 25C:2.26e8, from v.d.p crosses: 2.13e -8 % rn=7.1e-8; % Ni 25C: 7.12e -8, from vdp: 76.6e8, from TLM: 57.2e-8, from Ni rings: 61.8e -8 % -----------------% %bulk at 200C % kp= 306 %Au 25C: 317, from vdp: 345 % kn= 75 %Ni 25C: from Ni rings: 11.8 % ka = 0.039 %air (stagnant) at 100C; 0.032, at 25C: 0.026 % ksi=80; % for Silicon (148 at room temp.), at 200: 80 % kpoly = 0.14 % kox =1.4 % % rp=3.8e-8; %Au 25C:2.26e8, from v.d.p crosses: 2.13e -8 % rn=17e-8; % Ni 25C: 7.12e8, from vdp: 76.6e8, from TLM: 57.2e-8, from Ni rings: 61.8e -8 % ---------------%Estimated thin film (Au and Ni) properties at 25C kp= 285 %Au 25C: 317, from vdp: 345 kn= 8.4 %Ni 25C: from Ni rings: 11.8 ka = 0.026 %ai r (stagnant) at 100C; 0.032, at 25C: 0.026 ksi=148; % for Silicon (148 at room temp.), at 200: 80 kpoly = 0.14 kox =1.4

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246 rp=2.6e-8; %Au 25C:2.26e-8, from v.d.p crosses: 2.13e-8 rn=87.3e-8; % Ni 25C: 7.12e8, from vdp: 76.6e -8, from TLM: 57.2e8, from N i rings: 61.8e 8 % ------------------------%Substrate thickness is the sum of these 3 layers tpoly = 5e-6; % thickness of polyimide tox = 0.4e-6; % thickness of oxide (0.4 um) tsi = 345e-6; % silicon thickness (350um) ri=2.5e -3; %radi us of inner surface of inside Si ring r1=3e-3; % radius of outer surface on inside Si ring r2=4e-3; % radius of inner surface of outer Si ring ro=4.5e-3; % radius of outer surface of outer Si ring of active die rf=6.5e 3; % radius of outer surface of outer Si ring of fins % Ain=pi.*(r1.^2 ri.^2) % Aout = pi.*(rf.^2 r2.^2) Ain = 2*pi*ri*tsi % inner Si surface area of single module in m^2 Aout = 2*pi*ro*tsi % inner Si surface area of single module in m^2 z= 16 % no. of devic es stacked stacked_Ain = 2*pi*ri*tsi*z % inner Si surface area of single module in m^2 stacked_Aout = 2*pi*ro*tsi*z % inner Si surface area of single module in m^2 % Ain= 5.42e-6; %at ri=2.5mm inner surface % Aout= 14.1e-6; %at rf=6.5mm outer surface % ---gap=90e-6; %gap b/w TE pair (90um), min. gap 10um Ftp = 0.48e6; % P leg thickness: Au Ftn = 0.57e6; % N leg thickness: Ni (um) factorp = 0.1886; %teg(n=65):0.1886, teg(n=18):0.36, teg(n=90):0.048 factorn = 0.1425; %teg(n =65):0.1425, teg(n=18):0.36, teg(n=90):0.048 % N -type n=(1 -factorp factorn).*2*pi.*r1/2/gap % checking no. of TE pairs that fit n=65 %TEG7: n=20, Fp=Fn=0.40; TEG1: n=68, Fp=0.1973, Fn=0.1491; % -----------Stack TEG (n=65) data Tamb= 22.7 % Cels ius: previous room temp. Rtegi= 1630; % initial value (ohms): previous initial value: 1590 Ohms Rloadi = 2000; %TEG1 (n=65) test Rini = 327.0; % initial values (ohms): previous initial value: Routi = 347.2; % previous initial value: Tinleti = 22. 7; % Celsius % Toutleti = 22.4; % Voc_i = 0; % Vloadi = 0; Rin_up = [327 378.6 391.5 395.2 403 404 407.9 416.7 417 423.3 428.3 432.4 433.4 441 448 462 471.5 472.1 477.1 477.4 478]; % Ohms Rin_down = [478 466 465 425.8 399.5 340 336 329.3 328.5]; % Rout_up = [347.2 374.8 381.4 382.9 387 386.5 390 393.7 394 397.9 399.5 401.2 401.6 405.4 408 414.2 420 419.8 421.9 422.2 422.8]; % Ohms Rout_down =[422.8 416 416.1 398.9 385.1 355 353 348.2 347.6];

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247 Tinlet_up =[22.7 91.2 106.8 111.7 121 121.1 126.1 137 137.2 144 148.8 155 154.9 163 170 183 190 190.8 194.6 195 196]; Tinlet_down=[196.3 185 185 143 116 48 38 25.7 24.1]; %Toutlet_up = [22.4 78.2 89 92.3 102 102.1 107.1 116 116.1 122 127.1 133 132 140 145 163 181 181.1 185.8 186.5]; % Gas temp., thermocouple Celsius (ch 1) %Toutlet_down =[187 175 175.1 133 98.2 27 26.4 23.2 22.5]; Voc_up = [0 27.3 34.2 36.3 40.3 40.9 43.5 48.8 49.1 52.5 55.1 57.8 57.7 62.5 66.9 74.2 77.5 78.5 81.3 81.5 81.5]; %open circuit voltage vs. gas temp. Voc_down =[81.5 75 74.7 48.1 38 4 2.8 0.4 0]; Vload_up =[0 14 17.9 18.8 20.6 20.6 22.3 25 24.4 26.2 28.1 26.5 26.4 30.1 31.8 35.7 37.2 37.5 38.2 38.5 39.9]; Vload_down = [39.9 36.2 36 25.6 18.9 2.4 1.7 0.2 0]; % Rload = 2000; % Ohms % Pload_up =(1e6).*((Vload_up./1000).^2)./Rload; % power in microWatts % Pload_down =(1e6).*((Vload_down./1000).^2)./Rload; % power in microWatts Tinlet = [Tinlet_up]; %Toutlet = Toutlet_up; Rin_oc = [Rin_up]; Rout_oc = [Rout_up]; Voc = [Voc_up]; Vload = [Vload_up]; % -------------%Based on Ni TCR found (updated from v.4: MC simulations): TCRinner = 0.002685; %numbers from TEG1_NiAu_102005_v5 TCRouter = 0.002620; % resistance/temperature taken at opencircuit condition Tinner_oc = (((Rin_oc./Rini) 1)./TCRinner) + Tinleti; Touter_oc = (((Rout_oc./Routi) 1)./TCRouter) + Tinleti; DeltaT_oc = Tinner_oc Touter_oc; % temp. difference of Si rings as temp. is increased % --------% thermal resistance Rth_p= (log(r2/r1))/2/pi/factorp/Ftp/kp % for all p-type lumped Rth_n= (log(r2/r1))/2/pi/factorn/Ftn/kn % for all ntype lumped Rth_ox= (log(r2/r1))/2/pi/tox/kox % oxide resistance Rth_poly= (log(r2/r1))/2/pi/tpoly/kpoly % polyimide resistance Rth_air= (log(r2/r1))/2/pi/tsi/ka % air resistance stack_Rth_poly = Rth_poly./z stack_Rth_ox = Rt h_ox./z stack_Rth_air = Rth_air./z Ri_si=(log(r1/ri))/2/pi/tsi/ksi/z % inner Si ring thermal resistance %if single device is used, rf is used for outer Si ring Ro_si=(log(ro/r2))/2/pi/tsi/ksi/z % outer Si ring resistance Rth_legs = 1/(1/Rth_p + 1/ Rth_n) single_Rth_sub = 1/(1./Rth_poly + 1./Rth_ox + 1./Rth_air) stack16_Rth_sub = 1/(z./Rth_poly + z./Rth_ox + z./Rth_air) %for the cylinder Rcond_layers = 1/( 1/Rth_p + 1/Rth_n + z./Rth_poly + z./Rth_ox + z./Rth_air) % thermal conduction resistan ce only Rth_TEG = 1/( 1/Rth_p + 1/Rth_n + 1./Rth_poly + 1./Rth_ox + 1./Rth_air) %for a single TEG module %Rcond = 1/(1/Rth_poly + 1/Rth_air) % thermal conduction resistance only

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248 p_legs_wall_surface = r1*factorp*2*pi*Ftp % for all plegs n_legs_wall_surface = r1*factorn*2*pi*Ftn % for all nlegs Tinlet Tinner_oc Touter_oc DeltaT_oc %qcond= max(DeltaT_oc)./(Rcond_layers + Ri_si + Ro_si) % assuming constant heat flow rate thru device (only conduction) %qcond= max(DeltaT_oc)./Rcond_layers qcond_mat rix = DeltaT_oc./Rcond_layers % in Watts, see how q changes over the measured points %Uq_est = sqrt((7./Rcond_layers).^2 + (6./Rcond_layers).^2 + (DeltaT_oc.*0.19./Rcond_layers).^2); %absolute uncertainty in q [W], (from 02/07/10 notes) esi=0.5; % Si emissivity (assuming avg of 0.12 to 1) bolt=5.67e-8; % W/m^2*K^4 boltzmann constant %radiation exchange b/w Si surfaces qrad1= z.*bolt*2*pi*r1*tsi.*((Tinner_oc +273).^4 (Touter_oc +273).^4)./ (1/esi + (1esi).*r1/esi/r2) qradenv=z.*esi*bolt *2*pi*r1*tsi.*((Tinner_oc +273).^4 (Touter_oc +273).^4) ratio_qrad1_to_qcond=qrad1./qcond_matrix; %importance of Si rings radiation exchange %get convective coef. %Rthconv_h = (max(Tinlet) max(Tinner_oc))./qcond Rthconv_h_matrix = (Tinlet Tinn er_oc)./qcond_matrix % %hh = 1./Rthconv_h./Ain./z hh_matrix = 1./Rthconv_h_matrix./Ain./z; %Rthconv_c = (max(Touter_oc) Tamb)./qcond Rthconv_c_matrix = (Touter_oc Tamb)./qcond_matrix %hc = 1./Rthconv_c./Aout./z hc_matrix = 1./Rthconv_c_matrix./ Aout./z; hh_matrix hc_matrix % hh_avg=mean(hh_matrix(1,2:length(hh_matrix))) % entire range, affected by large values % hc_avg=mean(hc_matrix(1,2:length(hc_matrix))) hh_avg=mean(hh_matrix(1,2:15)) % range of Tgas: 90 to 170 C (for bulk), 90 to 180C (for thin film) %N=14, v=13, t=2.15 std_hh_avg =std(hh_matrix(1,2:15)) confidence_hh_avg = (2.16).* std_hh_avg./sqrt(14) hc_avg=mean(hc_matrix(1,2:length(hc_matrix))) std_hc_avg =std(hc_matrix(1,2:length(hc_matrix))) %N=20, v=19, t=2.09 confidence_hc_avg = (2 .09).*std_hc_avg./sqrt(20) % ----error bars %simulations ET = 2.5; % accuracy on temp. measured (95% confidence = 2*std = 2.5): x -axis ER = 3.3; % accuracy on Resistance measured (Ein_down2 vary between 3.2 and 3.3): y axis uVoc = 0.6; % in mVolts, calc ulated for the Sim970 module 12/18/09

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249 le = length(Rin_oc); % le = 30 data observations %plot both x and y error bars dx=ET.*ones(1,le); dy=ER.*ones(1,le); dy_Voc= uVoc.*ones(1,le); %****Calculate uncertainty for the Tinner******* not dx,dy. %from the l abnotebook and equ. 3-3 m_inner =0.8553; %value of m for inner ring from MC simulations: TEG1 on 12/18/09 um_inner = 0.0050; %uncertainty in m for the inner ring m_outer = 0.9004; um_outer = 0.0044; uTCRinner = TCRinner*(sqrt((um_inner/m_inner)^2 + (E R/Rini)^2)) uTCRouter = TCRouter*(sqrt((um_outer/m_outer)^2 + (ER/Routi)^2)) Ainner = 1./Rini./TCRinner; Binner = -Rin_oc./TCRinner./(Rini^2); Cinner = -((Rin_oc./Rini) 1)./(TCRinner^2); %uncertainty of inner Si ring temperature uTinner = sqrt((Ainner.^2)*ER^2 + (Binner.^2).*ER.^2 + (Cinner.^2).*uTCRinner.^2 + ET^2); %***** uncertainty in Touter ****** Aouter = 1./Routi./TCRouter; Bouter = -Rout_oc./TCRouter./(Routi^2); Couter = -((Rout_oc./Routi) 1)./(TCRouter^2); %uncertainty of outer Si ring temperature uTouter = sqrt((Aouter.^2)*ER^2 + (Bouter.^2).*ER.^2 + (Couter.^2).*uTCRouter.^2 + ET^2); U_q_cond_est = sqrt((uTinner./Rcond_layers).^2 + (uTouter./Rcond_layers).^2 + (DeltaT_oc.*0.19./Rcond_layers).^2) %absolute uncertainty in q [W], (from 02/07/10 notes) %on the hot side U_Rthconv_h_est = sqrt((ET./qcond_matrix).^2 + (uTinner./qcond_matrix).^2 + ((Tinlet Tinner_oc).*U_q_cond_est./(qcond_matrix.^2)).^2) %absolute uncertainty in R_thermal_conve [K/W], U_hh_est = hh_matrix.*sqrt((U_Rthconv_h_est./Rthconv_h_matrix).^2 + (0.07).^2) %on the cold side U_Rthconv_c_est = sqrt((uTouter./qcond_matrix).^2 + (ET./qcond_matrix).^2 + ((Touter_oc Tamb).*U_q_cond_est./(qcond_matrix.^2)).^2) %absolute uncertainty in R_thermal_conve [K/W], U_hc_est = hc_matrix.*sqrt((U_Rthconv_c_est./Rthconv_c_matrix).^2 + (0.07).^2) figure(1) %errorbarxy(x,y,lx,ly,ux,uy,linecol,errorcol) %old version being used here errorbarxy(Tinlet, Rin_oc,dx,dy,dx,dy,'*r','r') hold on errorbarxy(Tinlet, Rout_oc,dx,dy,dx,dy,'ob','b') h old off grid on title('Stacked TEG1: Ni Ring Resistance at no Load'); xlabel('Gas Temperature, T_{GAS} ( \ circC)', 'fontWeight', 'bold', 'fontSize', 12); ylabel('Resistance ( \ Omega)', 'fontWeight', 'bold', 'fontSize', 12); %legend('R_{in}', 'R_{out}') figu re(2) errorbarxy(Tinlet, Tinner_oc,dx,uTinner,dx,uTinner,'*r','r') hold on errorbarxy(Tinlet, Touter_oc,dx,uTouter,dx,uTouter,'ob','b') hold off grid on

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250 title('Stacked TEG1: Si Ring Temp. at no Load'); xlabel('Gas Temperature, T_{GAS} ( \ circC)','fontWeight ', 'bold', 'fontSize', 12); ylabel('Silicon Ring Temp. ( \ circC)','fontWeight', 'bold', 'fontSize', 12); %legend('T_{inner}', 'T_{outer}') %****error in DeltaT **** See pg. 91 Coleman book udeltaT = sqrt((uTinner.^2) + (uTouter.^2)); figure(3) errorbarxy( Tinlet, DeltaT_oc,dx,udeltaT,dx,udeltaT,'*b','b') grid on title('Stacked TEG1: Si Ring \ DeltaT at no Load'); xlabel('Gas Temperature, T_{GAS} ( \ circC)','fontWeight', 'bold', 'fontSize', 12); ylabel('Silicon Ring \ DeltaT ( \ circC)','fontWeight', 'bold', 'fon tSize', 12); figure(4) errorbarxy(DeltaT_oc,Voc,udeltaT,dy_Voc,udeltaT,dy_Voc,'*b','b') grid on title('Stacked TEG1: Voltage'); xlabel('Silicon Ring \ DeltaT ( \ circC)','fontWeight', 'bold', 'fontSize', 12); ylabel('Open-Circuit Voltage (mV)','fontWeight', 'bold', 'fontSize', 12); %determine the slope: m = options=optimset('Display','on'); x0 =[0.3]; f = inline('x(1)*DeltaT_oc','x','DeltaT_oc'); [m_s, resnorm] = lsqcurvefit(f,x0,DeltaT_oc,Voc,[],[], options) %store m Seebeck = m_s.*1000./65 figure(5) %pl ot(Tinlet, qcond_matrix.*1000, '*b'), errorbarxy(Tinlet, qcond_matrix.*1000,dx,U_q_cond_est.*1000 ,dx,U_q_cond_est.*1000 ,'*b','b') grid on title('Stacked TEG1: q vs. Gas Temp.'); xlabel('Gas Temperature ( \ circC)','fontWeight', 'bold', 'fontSize', 12); yl abel('Heat Transfer Rate (mW)','fontWeight', 'bold', 'fontSize', 12); % hold on % errorbarxy(Tinlet, Rout_oc,dx,dy,dx,dy,'ob','b') hold off grid on figure(6) %plot(Tinlet, Rthconv_h_matrix, '*b'), errorbarxy(Tinlet, Rthconv_h_matrix,dx,U_Rthconv_h_est dx,U_Rthconv_h_est ,'*b','b') grid on title('Stacked TEG1: Hot Side Thermal Resist. vs. Gas Temp.'); xlabel('Gas Temperature ( \ circC)','fontWeight', 'bold', 'fontSize', 12); ylabel('Conv. Thermal Resistance Hot Side (K/W)','fontWeight', 'bold', 'fontSize', 12); figure(7) %plot(Tinlet, hh_matrix, '*b'), errorbarxy(Tinlet, hh_matrix,dx,U_hh_est ,dx,U_hh_est ,'*b','b') %plot(Tinlet(1,2:7), hh_matrix(1,2:7), '*b'), grid on title('Stacked TEG1: h_h vs. Gas Temp.'); xlabel('Gas Temperature ( \ circC)','fontWeigh t', 'bold', 'fontSize', 12); ylabel('Conv. Coeff. Hot Side (W/m^{2}*K)','fontWeight', 'bold', 'fontSize', 12); figure(8) %plot(Tinlet, Rthconv_c_matrix, '*b'),

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251 errorbarxy(Tinlet, Rthconv_c_matrix,dx,U_Rthconv_c_est ,dx,U_Rthconv_c_est ,'*b','b') grid on title('Stacked TEG1: Cold Side Thermal Resist. vs. Gas Temp.'); xlabel('Gas Temperature ( \ circC)','fontWeight', 'bold', 'fontSize', 12); ylabel('Conv. Thermal Resistance Cold Side(K/W)','fontWeight', 'bold', 'fontSize', 12); figure(9) %plot(Tinlet, hc_mat rix, '*b'), errorbarxy(Tinlet, hc_matrix,dx,U_hc_est ,dx,U_hc_est ,'*b','b') %plot(Tinlet(1,2:7), hc_matrix(1,2:7), '*b'), grid on title('Stacked TEG1: h_c vs. Gas Temp.'); xlabel('Gas Temperature ( \ circC)','fontWeight', 'bold', 'fontSize', 12); ylabel('C onv. Coeff. Cold Side (W/m^{2}*K)','fontWeight', 'bold', 'fontSize', 12); figure(10) %plot(Tinlet, Rthconv_h_matrix, '*b'), errorbarxy(Tinlet, Rthconv_h_matrix,dx,U_Rthconv_h_est ,dx,U_Rthconv_h_est ,'*r','r') hold on errorbarxy(Tinlet, Rthconv_c_matri x,dx,U_Rthconv_c_est ,dx,U_Rthconv_c_est ,'ob','b') hold off grid on title('Stacked TEG1: Hot and Cold Side Thermal Resist. vs. Gas Temp.'); xlabel('Gas Temperature ( \ circC)','fontWeight', 'bold', 'fontSize', 12); ylabel('Conv. Thermal Resistance K/W)','fontWeight', 'bold', 'fontSize', 12); figure(11) %plot(Tinlet, hh_matrix, '*b'), errorbarxy(Tinlet, hh_matrix,dx,U_hh_est ,dx,U_hh_est ,'*r','r') hold on errorbarxy(Tinlet, hc_matrix,dx,U_hc_est ,dx,U_hc_est ,'ob','b') hold off %plot(Tinlet(1,2:7), hh_matr ix(1,2:7), '*b'), grid on title('Stacked TEG1: Conv. Coef. vs. Gas Temp.'); xlabel('Gas Temperature ( \ circC)','fontWeight', 'bold', 'fontSize', 12); ylabel('Conv. Coeff. (W/m^{2}*K)','fontWeight', 'bold', 'fontSize', 12);

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258 BIOGRAPHICAL SKETCH Israel Boniche was born in Managua, Nicaragua. After graduati ng from high school in Miami, Florida in 1 999, he attended the University of Florida (UF) in Gainesville where he graduated with a Bachelor of Science in electrical and computer engineering (with honors) in the s pring of 2003. He continued his studies at UF working on circuit design, and earned a Master of Science in electrical and computer engi neering in the spring of 2005. Shortly thereafter, Israel earned a National Science Foundation South East Alliance for Graduate Education and the Professoriate ( NSF SEAGEP) fellowship and joined the Interdisciplinary Microsystems Group (IMG) at UF under the supervision of Dr. David P. Arnold, where he focused his doctoral research on microfabrication and microsystems (MEMS). During his graduate research in 2008, Israel joined the Army Research Laboratory (ARL) as an electronics engineer for a oneyear internship, where he worked with Power Components Branch in MEMS. His research interests include process engineering, analog digital circuit design, micro electrical mechanical systems (MEMS), power MEMS, magnetics, and microelectronics manufacturing and assembly.