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b9b23cce39f965fb5474de1fef810d339bf6dda2 109194 F20101208_AAAUPK li_y_Page_110.jpg db4b4cbc2b902e146d8d8124592eed25 c4c6f1c3d5cda6e1a052f40759627478f46dff89 SIDEIMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT BOUNDARY LAYER MEASUREMENT By YAWEl LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 O 2008 Yawei Li To my husband Zhongmin and my parents ACKNOWLEDGMENTS Financial support for the research project is provided by National Science Foundation (CTS04352835 and CMS0428593) and AFOSR grant (F4962003C0114). A doctoral dissertation is never the work of an individual, but instead a miracle that encompasses the efforts of many people. I would like to recognize a number of people who have helped me in various ways during my time in University of Florida. First and foremost, I extend my sincerest gratitude to my advisor, Dr. Mark Sheplak, who gave me the opportunity to work in MEMS research field. I sincerely appreciate his guidance, continuous encouragement and support in my research, tirelessly sharing with me his expertise and wisdom. His profound knowledge in MEMS, fluids, acoustics and so on is the invaluable source I always rely on. I also wish to extend gracious thanks to my committee members, Drs. Toshikazu Nishida, Louis N. Cattafesta, Bhavani V. Sankar and David Arnold for their instruction and assistance on this interdisciplinary project. They are always generous on their time and expertise, and I am grateful for their efforts. I would give special thanks to professors in Department of Electrical and Computer Engineering, Material Science Engineering and Mechanical and Aerospace Engineering at University of Florida, especially Dr. Mark Law and his student Ljubo Radic, Dr. Kevin Jones and Dr. Raphael Haftka for their invaluable suggestions on my device fabrication, process simulation and design optimization. I would especially like to thank Dr. Melih Pepila at Sabanchi University (Turkey) and Dr. Jaco F. Schutte for their suggestions in optimization design. My thanks go to Dr. Venketaraman Chandrasekaran at Sensata Technologies, Sean Knight in University of South Florida, Alvin A Barlian in Stanford University and Core Systems Company for their help in device fabrications, and Keck Pathammavong at Engent for his help in device packaging. I would also express my thanks to Al Ogden, Dr. Ivan Kravehenko and Bill Lewis at UFNF for the facility maintenance and help on the fabrication. I was fortunate enough to have great colleagues throughout my graduate school experience. My thanks go to IMG members, especially Hongwei Qu for his suggestions and discussions in device fabrication; Brandon Bertolucci, Alex Phipps, David Martin for their kind help and assistance in device package design, Vijay Chandrasekharan, Qi Song, Benjamin Griffin and John Griffin for their kind help in device characterization, Matt Williams, Benj amin Griffin, Brandon Bertolucci and Brian Homeijier for their great editing and suggestions in my dissertation writing. It has been a pleasure to have work with them, and I will carry these invaluable memories on rest of life. Finally, I reserve the special thanks to my families for their support and encouragement. I am always grateful to my husband, Zhongmin Liu for his endless love and support in my life. My parents always encouraged me to be the best and do my best on what I want to do. I would like to thank them for believing me every time I said I would graduate "next year". Without their love and support this dissertation would not be possible. TABLE OF CONTENTS page ACKNOWLEDGMENTS .............. ...............4..... LIST OF TABLES ................ ...............9............ .... LIST OF FIGURES .............. ...............10.... AB S TRAC T ............._. .......... ..............._ 14... CHAPTER 1 INTRODUCTION ................. ...............16.......... ...... Motivation for Wall Shear Stress Measurement............... ..............1 Wall Shear Stress............... ...............17. Turbulent Boundary Layer ................. ...............19................ Research Objectives............... ...............2 Dissertation Overview .............. ...............24.... 2 BACKGROUND .............. ...............29.... Techniques for Shear Stress Measurement............... ..............2 Conventional Techniques .............. ...............30.... MEMSBased Techniques............... ..............3 Floating Element Sensors .............. ...............32.... Sensor Modeling and Scaling ................. ...............32................ Error Analysis and Challenges .............. ...............34.... Effect of misalignment ........._..._... ...............34....._.. ..... Effect of pressure gradient ........._..._. ......_._ ..........._ ........ ..............35 Effect of crossaxis vibration and pressure fluctuations .............. .....................3 Previous MEMS Floating Element Shear Stress Sensors ................. ......... ................38 Capacitive Shear Stress Sensors ................. ...............38......___.... Optical Shear Stress Sensors .............. ...............40.... Piezoresistive Shear Stress Sensors ................. ... ........ ...............42..... A FullyBridge SideImplanted Piezoresistive Shear Stress Sensor ................... ...............43 3 SHEAR STRESS SENSOR MODELING .............. ...............53.... QuasiStatic Modeling ................. ...............54.......... ...... Structural Modeling ................. ...............54................. Small Deflection Theory .............. ...............55.... Large Deflection Theory .............. ...............56.... Energy method .............. ...............57.... Exact analytical model .............. ...............57.... Lumped Element Modeling .............. ...............58.... Finite Element Analy sis............... ...............60 Piezoresistive Transduction ................. ...............62........... .... Piezoresistive Coefficients .............. ...............64.... Piezoresistive Sensitivity ................. ...............66................. Electromechanical Sensitivity .............. ...............68.... Noise Model............... ...............69. Thermal Noise .............. ...............69.... 1/ f Noise............... ...............70. Device Specific Issues .............. ...............72.... Transverse Sensitivity .............. ...............72.... Temperature Compensation............... ..............7 Device Junction Isolation .............. ...............74.... Sum m ary ................. ...............78........ ...... 4 DEVICE OPTIMIZATION ................. ...............91.............. Problem Formulation ......__................. .........__..........9 Design Variables .............. ...............91.... Obj ective Function ................. ...............93................ Constraints ................. ...............94................. Candidate Flows .............. ...............95.... M ethodology ............... ... .... ........ ...............96....... Optimization Results and Discussion ................ ...............97................ Sensitivity Analysis .............. ...............98.... Sum m ary ................. ...............100......... ...... 5 FABRICATION AND PACKAGINTG ................ ...............105............... Fabrication Overview and Challenges ................. ...............105............... Fabrication Process ................. .......... .. .................105.... Sensor Packaging for Wind Tunnel Testing ................. ...............110.............. 6 EXPERIMENTAL CHARACTERIZATION ................ ...............118................ Experimental Characterization Issues ................. ...............118................ Experimental Setup............... ...............119. Electrical Characterization ................. ...............119......... ...... Dynamic Calibration .............. ...............120.... Noise Measurement ................. ...............121............. Experimental Results ................ ...............122................ Electrical Characterization .............. .. ...............122.. Dynamic Calibration Results and Discussion .............. ...............122.... Sum mary ................. ...............126......... ...... 7 CONCLUSION AND FUTURE WORK ................. ...............137........... ... Summary and Conclusions ................. ...............137............... Future Work............... ...... .............13 Temperature Compensation............... .............13 Static Characterization............... ...........14 Noise M easurement ................. ... ........ ...............142...... Recommendations for Future Sensor Designs ................. ...............142........... ... APPENDIX A MECHANICAL ANALYSIS ................. ...............145............... Small Deflection ................... ......... ... ...............145...... Large DeflectionEnergy Method ................. ...............147................ Large DeflectionAnalytical Method ................. ...............149................ Stress Analysis............... ... .. .. ...........15 Effective Mechanical Mass and Compliance .............. ...............153.... B NOISE FLOOR OF THE WHEATSTONE BRIDGE .............. ...............157.... C PROCE SS TRAVELER ............_...... ...............160... M asks ............ _. .... ...............160... Process Steps .............. ...............160.... D PROCESS SIMULATION ................. ...............166............... E MICROF ABRICATION RECIPE F OR RIE AND DRIE PRO CES S.............. ...... .........__16 9 F PACKAGING DRAWINGS .............. ...............170.... LIST OF REFERENCES ................. ...............173................ BIOGRAPHICAL SKETCH ................. ...............180......... ...... LIST OF TABLES Table page 11 Summary of typical skin friction contributions for various vehicles. ........._..... ..............25 12 Parameters in the turbulent boundary layer. ............. ...............25..... 31 Material properties and geometry parameters used for model validation. .......................79 32 Resonant frequency and effective mass predicted by LEM and FEA. ............. ................79 33 First 6 modes and effective mass predicted by FEA for the representative structure........79 34 Piezoresistive coefficients for ntype and ptype silicon. ............. .....................7 35 Piezoresistive coefficients for ntype and ptype silicon in the <110> direction. .............80 36 Space parameter dimensions for junction isolation. ............. ...............80..... 41 The candidate shear stress sensor specifications. ............. ...............102.... 42 Upper and lower bounds associated with the specifications in Table 41. ......................102 43 Optimization results for the cases specified in Table 41. ............... ..................10 61 LabVIEW settings for noise PSD measurement ................. ............_ ..... 128.__... 62 The optimal geometry of the shear stress sensor that was characterized. ................... .....128 63 Sensitivity at different bias voltage for the tested sensor. ............. ....................12 64 A comparison of the predicted versus realized performance of the sensor under test for a bias voltage of 1.5V. ................. ...............129......... . E1 Input parameters in the ASE on STS DRIE systems. ................... ............... 16 E2 Anisotropic oxide/nitride etch recipe on the Unaxis ICP Etcher system. ................... .....169 E3 Anisotropic aluminum etch recipe on the Unaxis ICP Etcher system. ............................169 LIST OF FIGURES Figure page 11 Schematic of wall shear stress in a laminar boundary layer on an airfoil section. ............26 12 Schematic representation of the boundary layer transition process for a flatplate flow at a ZPG ............. ...............26..... 13. Schematic of typical velocity profile for lowspeed laminar and turbulent boundary layers [ 9]. ............. ...............27..... 14 The structure of a typical turbulent boundary layer ................. ................ ........ .27 15 Estimates of Kolmogorov microscales of length and time as a function of Reynolds number based on a 1/7th powerlaw profile. ............. ...............28..... 21 Schematic crosssectional view of the floating element based sensor. ................... .........46 22 Schematic plan view and crosssection of a typical floating element sensor ..................46 23 Integrated shear force variation as a function of sensor resolution for different elem ent areas. ................. ...............47......... ..... 24 Schematic illustrating pressure gradient effects on the force balance of a floating elem ent. .............. ...............47.... 25 Schematic crosssectional view of the capacitive floating element sensor ..........._...........48 26 Planview of a horizontalelectrode capacitive floating element sensor .........................48 27 Schematic topview of a differential capacitive shear stress sensor ............... ...............49 28 A schematic crosssectional view of an optical differential shutterbased floating element shear stress sensor ............ ...............49..... 29 Schematic top and crosssectional view of a FebryPerot shear stress sensor ................50 210 Top and crosssectional view of Moire optical shear stress sensor ............ ..................50 211 A schematic top view of an axial piezoresistive floating element sensor .........................5 1 212 A schematic top view of a laterallyimplanted piezoresistive shear stress sensor ............51 213 A schematic 3D view of the sideimplanted piezoresistive floating element sensor.........52 31 Schematic top view of the structure of a piezoresistive floating element sensor. .............81 32 The simplified clampedclamped beam model of the floating element structure. .............81 33 Lumped element model of a floating element sensor: (a) springmassdashpot system (mechanical) and (b) equivalent electrical LCR circuit. .................. ................8 34 Representative results of displacement of tethers for the representative structure ............82 35 Representative loaddeflection characteristics of analytical models and FEA for the representative structure. ............. ...............82..... 36 Verifieation of the analytically predicted stress profie with FEA results for the representative structure. ............. ...............83..... 37 The mode shape for the representative structure. ............. ...............83..... 38 Geometry used in computation of Euler' s angles. ................ ...............84........... . 39 Polar dependence of piezoresistive coefficients for ptype silicon in the (100) plane. .....84 310 Polar dependence of piezoresistive coefficients for ntype silicon in the (100) plane. .....85 311 Piezoresistive factor as a function of impurity concentration for p type silicon at 300K ............ ...............85..... 312 Schematic illustrating the relevant geometric parameters for piezoresistor sensitivity calculations. ............. ...............86..... 313 Schematic representative of a deflected sideimplanted piezoresistive shear stress sensor and corresponding resistance changes in Wheatstone bridge. .............. .... ........._..86 314 Wheatstone bridge subj ected to crossaxis acceleration (a) and pressure (b). ................... 87 315 Schematic of the doublebridge temperature compensation configuration. ........._.._.........87 316 Top view schematic of the sideimplanted piezoresistor and p++ interconnect in an nwell (a) and equivalent electric circuit indicating that the sensor and leads are junction isolated (b). ............. ...............88..... 317 Doping profie of nwell, p++ interconnect, and piezoresistor using FLOOPS simulation ................. ...............88................. 318 Cross view of isolation width between p++ interconnects. ............. .....................8 319 Cross view of isolation width between p++ interconnect and piezoresistor. ................... ..89 320 Top view of the isolation widths on a sensor tether ................. ............... 90........... 321 Top view schematic of the sideimplanted piezoresistor with a metal line contact. ..........90 41 Flow chart of design optimization of the piezoresistive shear stress sensor. ................... 104 42 Logarithmic derivative of obj ective function rmn with respect to parameters. ...............104 51 Process flow of the sideimplanted piezoresistive shear stress sensor. ................... ........ 112 52 SEM side view of side wall trench after DRIE Si. ........... ..... ._ ........_ ....13 53 SEM side view of the notch at the interface of oxide and Si after DRIE. ....................1 13 54 SEM top view of the trench after DRIE oxide and Si. ......___ ..... ..._ ................1 14 55 SEM top views of the trench after DRIE oxide and Si with oxide overetch. ..................1 14 56 SEM top views of the trench with silicon grass through a micromasking effect due to oxide underetch. ................. ...............115.....__ ...... 57 SEM side view of the trench after DRIE oxide and Si. .......___......... ._. .............1 15 58 Photograph of the fabricated device. ....._.._................ ...............116 ... 59 A photograph of the device with a close up view of the sideimplanted piezoresistor. ..1 16 510 Photograph of the PCB embedded in Lucite package. ................ .........................1 17 511 Interface circuit board for offset compensation ................. ...............117........... .. 61 The bridge dc offset voltage as a function of bias voltages for the tested sensor............ 130 62 An electrical schematic of the interface circuit for offset compensation. ................... .....130 63 A schematic of the experimental setup for the dynamic calibration experiments. ........13 1 64 Forward and reverse bias characteristics of the p/n junction............._._ .........._._ ....13 1 65 Reverse bias breakdown voltage of the P/N junction. ......... ................ ...............132 67 The nonlinearity of the IV curve in Figure 66 at different sweeping voltages. ...........133 68 The output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 k 69 The normalized output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 k 610 Gain and phase factors of the frequency response function. ...........__.. .........__......134 611 The magnitude and phase angle of the reflection coefficient of the plane wave tube.....13 5 612 Outputreferred noise floor of the measurement system at a bias voltage of 1.5V.........136 71 Pressure drops versus length between taps in the flow cell. .............. .....................4 72 Experimental setup of static calibration ................. ...............144.............. A1 The clamped beam and free body diagram. a) Clampedclamped beam. b) Free body diagram of the beam. c) Free body diagram of part of the beam. ................. .................156 A2 Clampedclamped beam in large deflection. ............. ...............156.... A3 Clampedclamped beam in small deflection (a) and free body diagram of the clamped beam (b)............... ...............156.. B1 The Wheatstone brid ge. ............. ...............159.... B2 The thermal noise model of the Wheatstone bridge. ........._._. ........... .................159 B3 The 1/ f noise model of the Wheatstone bridge. ................. ....._.._............... ..15 E1 The drawing illustrating the Lucite packaging. ............. ...............170.... E2 The aluminum plate for the plane wave tube interface connection. ............. .................171 E3 Aluminum packaging for pressure sensitivity testing. ................ ...._.._ ...............172 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SIDEIMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT BOUNDARY LAYER MEASUREMENT By Yawei Li August 2008 Chair: Mark Sheplak Major: Aerospace Engineering In this dissertation, I discuss the device modeling, design optimization, fabrication, packaging and characterization of a micromachined floating element piezoresistive shear stress sensor for the timeresolved, direct measurement of fluctuating wall shear stress in a turbulent flow. This device impacts a broad range of applications from fundamental scientific research to industrial flow control and biomedical applications. The sensor structure integrates sideimplanted, diffused resistors into the silicon tethers for piezoresistive detection. Temperature compensation is enabled by integrating a fixed, dummy Wheatstone bridge adjacent to the active shearstress sensor. A theoretical nonlinear mechanical model is combined with a piezoresistive sensing model to determine the electromechanical sensitivity. Lumped element modeling (LEM) is used to estimate the resonant frequency. Finite element modeling is employed to verify the quasistatic and dynamic models. Two dominant electrical noise sources in the piezoresistive shear stress sensor, 1/ f noise and thermal noise, and amplifier noise were considered to determine the noise floor. These models were then leveraged to obtain optimal sensor designs for several sets of specifications. The cost function, minimum detectable shear stress (MDS) formulated in terms of sensitivity and noise floor, is minimized subj ect to nonlinear constraints of geometry, linearity, bandwidth, power, resistance, and manufacturing limitations. The optimization results indicate a predicted optimal device performance with a MDS of O(0.1 mPa) and a dynamic range greater than 75 dB. A sensitivity analysis indicates that the device performance is most responsive to variations in tether width. The sensors are fabricated using an 8mask, bulk micromachining process on a silicon wafer. An nwell layer is formed to control the spacecharge layer thickness of reversebiased p/n junctionisolated piezoresistors. The sensor geometry is realized using reactive ion etch (RIE) and deep reactive ion etch (DRIE). Hydrogen annealing is employed to smooth the sidewall scalloping caused by DRIE. The piezoresistors are achieved by sidewall boron implantation. The structure is finally released from the backside using the combination of DRIE and RIE. Electrical characterization indicates linear junctionisolated resistors, and a negligible leakage current (< 0. 12 CLA) for the junctionisolated diffused piezoresistors up to a reverse bias voltage of 10 V. Using a known acousticallyexcited wall shear stress for calibration, the sensor exhibited a sensitivity of 4.24 pIV/Pa, a noise floor of 11.4 mPa/JA at 1 kHz, a linear response up to the maximum testing range of 2 Pa, and a flat dynamic response up to the testing limit of 6.7 k transducer for turbulence measurements in lowspeed flows, a first for piezoresistive MEMS based direct shear stress sensors. CHAPTER 1 INTTRODUCTION This chapter provides an introduction to wall shear stress and motivation for its measurement. Then the scaling turbulent boundary layer is reviewed as it applies to dictating the requirements for wall shear stress sensors. The research objectives and contributions are presented. This chapter ends with the dissertation overview. Motivation for Wall Shear Stress Measurement The quantification of wall shear stress is important in a variety of engineering applications, specifically in the development of aerospace and naval vehicles. These vehicles span a wide range of Reynolds numbers (Re) from low Re (unmanned air vehicles for homeland security surveillance and detection) to a very high Re (hypersonic vehicles for rapid global and space access). Across the Re range, unsteady, complex flow phenomena associated with transitional, turbulent, and separating boundary layers play an important role in aerodynamics and propulsion efficiency of these vehicles [1, 2]. Furthermore, since shear stress is a vector field, it may provide advantages over pressure sensing in active flow control applications involving separated flows [3]. The accurate measurement of the wall shear stress is of vital importance for understanding the critical vehicle characteristics, such as lift, drag, and propulsion efficiency. Therefore, the ability to obtain quantitative, timeresolved shear stress measurements may elucidate complex physics and ultimately help engineers improve the performance of these vehicles [4]. Viscous drag or skin friction drag is formed due to shear stress in the boundary layer. The viscous loss is highly dependent on the physical aerodynamic/hydrodynamic system; typical viscous losses for different systems are listed in Table 11 [5]. For aircraft, reducing skin friction by 20% results in a 10% annual fuel savings, and for underwater vehicles, a reduction of skin friction drag of 20% would result in a 6.8% increase in speed [5]. Therefore, shear stress measurement attracts attention in sensoractuator systems for use in active control of the turbulent boundary layer with an aim of minimizing the skin friction [6]. Wall Shear Stress When a continuum viscous fluid flows over an obj ect, the no slip boundary condition at the surface results in a velocity gradient within a very thin boundary layer [7]; the streamwise velocity increases from zero at the wall to its freestream value at the edge of the boundary layer. The velocity profile is shown in Figure 11. The viscous effects are confined to the boundary layer, while outside of the boundary layer the flow is essentially inviscid [7]. Two classes of surface forces act on the aerodynamic body: the normal force per unit area (pressure) P and the tangential force per unit area (shear stress) zw For a Newtonian flow, the wall shear stress is proportional to the velocity gradient at the wall. The boundary layer is classified as laminar or turbulent depending on Reynolds number or flow structure [7]. A laminar boundary layer forms at low Reynolds numbers and is characterized by its smooth and orderly motion, where microscopic mixing of mass, momentum and energy occurs only between adj acent vertical fluid layers. A turbulent boundary layer forms at high Reynolds numbers and is characterized by random and chaotic motion [8]. The macroscopic mixing traverses several regions within the boundary layer. There is a transition range between laminar and turbulent boundary layers, partially laminar and partially turbulent, as shown in Figure 12. In the transition range, the flow is very sensitive to small disturbances [8]. Typical velocity profiles for low speed laminar and turbulent boundary layer are shown in Figure 13. Due to the intense mixing, the turbulent boundary layer has a fuller velocity profile; thus, the shear stress in the turbulent boundary layer is larger than in a laminar boundary layer. The boundary layer thickness, 6(x), is defined as the distance from the wall to the point at which the velocity is 99% of the freestream velocity [7]. The laminar boundary layer thickness in a zero pressure gradient flatplate flow is given by Blasius as [7] 3 5.0 (11) where Rex is the free stream Reynolds number and given by U x/v, x is the streamwise distance, Um is the free stream velocity, and v is the kinematic viscosity of the fluid. For turbulent flow, the boundary layer thickness is estimated by the 1/7th pOWeT laW VeoTcity profile is [7] 3 0.16 x Re (12) The shear stress is related to skin friction by the skinfriction coefficient C, = (13) pU 2 The wall shear stress z_ for a one dimensional laminar flow is given by Newton's law of viscosity [7], du zw = p , (14) dy I,=0 where pu is the dynamic viscosity of the fluid and u is the local streamwise velocity in the boundary layer. For turbulent flow, the shear stress is decomposed into mean shear stress r, and fluctuating shear stress r7, in terms of the Reynolds decomposition, zw = r, + r,~ (15) The mean skin friction for laminar and turbulent flow are given by [7] 27, 0.664 C (16) f,1la~te pU ~2 JK'_ 0.027 and C,,,, (17) respectively. Equation (12) and (17) are based on the assumption of the 1/7th pOWeT laW fOrm of the velocity profile proposed by Prandtl [7], i~ (18) These formulas are in reasonable agreement with turbulent flatplate data and are appropriate for a general scaling analysis [7]. Turbulent Boundary Layer To understand the temporal and spatial resolution requirements for the shear stress sensor, we need to understand the relevant time and length scales associated with a turbulent boundary layer. There are two regions in a turbulent boundary layer: the inner layer and outer layer [9] The semilog plot of the structure of a typical turbulent boundary layer is shown in Figure 14. The outer layer (wake region), is turbulent (eddy) sheardominated and the effect of the wall is communicated via shear stress. The inner 20% of the boundary layer is defined as the inner layer, where viscous shear dominates. The overlap layer smoothly connects the inner and outer layer. There are three regions within the inner layer: 0 < y' < 5 viscous sublayer (or linear) region ut = y 5 45 < y' < 0.23' log region u' = In y' + B where k is the Karman constant and B is the intercept. They are universal constants with k = 0.41 and B = 5.0 [7]. The nondimensional velocity u' is defined as u = u/u , (19) where ul is given by u = JZS, (110) if is the mean velocity, and p is the density of the fluid. The nondimensional distance y' is defined as y' = y/ll =yu'v, (111) where l' = v/u* is the characteristic viscous length scale. A turbulent flow possesses different length scales. The largest eddies are on the order of the boundary layer thickness, while the smallest eddies can approach the Kolmogorov length scales [8]. Kolmogorov's universal equilibrium theory states that the small scale motions are statistically independent of the slower largescale turbulent structures, but depend on the rate at which the energy is supplied by large scale motions and on the kinematic viscosity [8]. In addition, the rate at which energy is supplied is assumed to be equal to the rate of dissipation. Thus, the small eddies must have a smaller time scale and are assumed to be locally isotropic. Therefore, the dissipation rate and kinetic viscosity are parameters governing small scale motions. The scaling relationships between the small and large scale structures in a boundary layer flow are [4, 8, 10] r3/4 77 u, : = ( R es) 3 (112) Tu fu63 1/2 / andv = (Re,> (113) where r and T are the Kolmogorov length and time scales respectively, ue is the eddy velocity (typically u, ~ O(0.01U,~) [4]. Substitution of Equation (1 2) into Equation (1 12) and Equation (113) leads to estimates of the Kolmogorov microscales in terms of Re ,, r ~ 20x(Rex)11/14 (114) 400"x,) 4/71 and T ~ (e)(5 The relationship between the Kolmogorov microscales and Reynolds number is given in Figure 15 for a zero pressure gradient turbulent boundary layer with Um = 50 m/s, and at a distance x = 1 m downstream of the leading edge assuming a 1/7th pOwerlaw velocity profile. In order to detect the wall shear stress generated by the smallest eddies in a turbulent boundary layer, the sensor size must be of the same order of magnitude as the Kolmogorov length scale [10], and have a flat frequency range greater than the reciprocal of the Kolmogorov time scale [4]. These microscales are rough estimates, so some researchers used the viscous length scale l' and time scale, t* = v/u*2 to estimate the required sensor size and bandwidth [11, 12]. For example, Padmanabahn et al. [l l] used 41* in their sensor design, and Alfredsson et al.[12] used 101*, 81* and 21* in their experiments. GadelHak and Bandyopadhyay [13] reported these viscous scales are on the same order of the Kolmogorov scales. If the sensor size is larger than the Kolmogorov length scale, the fluctuating component will be spatially averaged, which results in spectral attenuation and a corresponding underestimation of the turbulent parameters [14, 15]. It has been reported that the sensor smaller than 20 wall units were free from spatial averaging effects [16] while the sensor lager than 30 wall units suffered shear stress underestimation [17]. Equation (112) and (113) indicate that as the Reynolds number increases, the sensor size should decrease and the bandwidth of the sensor should increase. For example, at Rex = 107, the Kolmogorov length scale is 65 Cpm and the characteristic frequency is 3.7 k Lofdahl and GadelHak stated that a sensor size of 35 times of Kolmogorov length is reliable for accurate turbulence measurement [10]. A summary of parameters and their analytical expressions for a zero pressure gradient turbulent boundary layer are listed in Table 12 [7, 8]. In addition, roughness is another factor that may disturb the turbulent boundary layer. The roughness height due to the flatness of the device die in the package, misalignment in tunnel installation, and gap size is denoted by ks, and the characterized roughness is given by k = k ~(116) In turbulent flow if k' > 5 the roughness protrudes above the thin viscous layer, causing wall friction to increase significantly [7]. If k' < 4, the wall surface is deemed hydraulically smooth and the roughness does not significantly disturb the turbulent boundary layer [7]. Research Objectives The goal of this dissertation is to develop a robust, high resolution, and high bandwidth silicon micromachined piezoresistive floating element shear stress sensor for turbulent boundary layer measurement. The shear stress sensor should possess high spatial and temporal resolution and a low minimum detectable signal (MDS). To date, the quantitative, timeresolved, continuous, direct measurement of fluctuating shear stress has not yet been realized [4]. Further effort is required to developed standard, reliable MEMS shearstress sensors with quantifiable uncertainties. The detailed description of the choice of the piezoresistive sensing scheme is discussed in Chapter 2. Depending on the application, there are several challenges in the development of this device. An ideal shear stress sensor should have a large dynamic range (O(80 dB) ), large bandwidth (O(10 kctz)), and a spatial resolution of O(100 pLm) to capture the spectra of the fluctuating shear stress without spatial averaging. The resolvable shear stress would to be on the order of O(0.1 mPa), resulting in force resolution of O(10 pN) for the desired spatial resolution of O(100 ym) In addition, an ideal sensor should be packaged to allow for flushmounting on the measurement wall surface to avoid flow disturbances. Traditional intrusive instruments suffer from insufficient spatial and temporal resolution. Microelectromechanical systems (MEMS) technology offers the potential to meet these requirements by extending siliconbased integrated circuit manufacturing approaches to microfabrication of miniature structures [4]. From the perspective of measurement instrumentation, the small physical size and reduced inertia of microsensors vastly improves both the temporal and spatial measurement resolution relative to conventional macroscale sensors. Thus, MEMS shear stress sensors offer the possibility of satisfying transduction challenges associated with measuring very small forces while maintaining a large dynamic range and high bandwidth. The previous research in MEMS shear stress sensors [1825] is discussed in detail in Chapter 2. Three transduction schemes have been developed for direct measurement of shear stress: capacitive [18, 21, 24], optical [20, 22, 23] and piezoresistive [19, 25]. These previously developed sensors possess performance limitations and cannot be used for quantitative shear stress measurements. This research effort is the combination of multidisciplinary design and optimization, fabrication, packaging and calibration, which results in a truly flushmounted, MEMS direct wall shear stress sensor. The contributions to the above efforts are: Development of electromechanical modeling and nonlinear constrained design optimization to achieve good sensor performance for aerospace applications. Development and execution of a novel microfabrication process accounting for p/n junction isolation and highquality electrical and moisture passivation. Development of a sensor package that can be flushmounted on the wall surface. Realization and preliminary characterization of a functioning device. Dissertation Overview This dissertation is organized into seven chapters and Hyve appendices. Chapter 1 provides the motivation for the topic of this dissertation. Background information regarding previous shear stress measurement technology is discussed in Chapter 2. Sensor modeling is discussed in Chapter 3. This includes the electromechanical modeling, finite element analysis for model verification as well as specific design issues. Chapter 4 discusses device optimization subjected to manufacturing constraints and specifications. Chapter 5 describes the detailed fabrication process and device packaging. Experimental characterization setups and results are presented in Chapter 6. The conclusion and future work are presented in Chapter 7. Information supporting this dissertation is given in appendices. Appendix A provides detailed derivations of the quasistatic beam models and dynamic models. The detailed modeling of the noise floor of the fully active Wheatstone bridge is discussed in Appendix B. A fabrication process flow is presented in Appendix C. The process simulation using FLOOPS [26] is given in Appendix D. The recipes for plasma etching are given in Appendix E. Finally, packaging details, vendors, and engineering drawings are provided in Appendix F. Table 11. Summary of typical skin friction contributions for various vehicles [5]. Vehicles Typical viscous loss Supersonic fighter 2530 % Large transport aircraft 40 % Executive aircraft 50 % Underwater bodies 70 % Ships at low/high speed 9030 % Table 12. Parameters in the turbulent boundary layer. Parameters Free stream velocity U.n (m/s) Typical eddy velocity u, (m/s) Streamwise distance x (m) Kinematic viscosity Reynolds number based on streamwise distance Boundary layer thickness S(m) Momentum thickness B(m) Reynolds number based on momentum thickness Re, Reynolds number based on boundary layer thickness Skin friction coefficient C, Wall shear stress ir(Pa) Kolmogorov length scale 1 (m) Kolmogorov time scale T (s) Analytical expression ue ~ 0.01U. U~x Re 6= 0.16x(Rex~)' B 7 3 72 U.0B Re, = Re =u C, =0.027(Rexi r, = C, 1pU 2 9 ~ 3(Res)3/ 3 (Re, )0 T ~ u, i' __~~NoSlip Boundary Condition ....Boundary Layer t' Airfoil Figure 11. Schematic of wall shear stress in a laminar boundary layer on an airfoil section. Lamina I: Trasio I Trblt Rev Fiur 2 chmai rpesnttono teondr lae trasto proesfraftle flow~~n ata P [] Laminar / Turbulent Velocity Figure 13. Schematic of typical velocity profile for lowspeed laminar and turbulent boundary layers [9]. u' Inner Region Outer Region Wake Region ~2 10 Buffer Region Viscous Sublayer Region Log Region 10 5 30 104 Nondimensional Distance Figure 14. The structure of a typical turbulent boundary layer [8]. 3 '10 E 10~ '"F 2~' 10\ 3 9 S $~10 C Reynolds N~umber Rex Figure 15. Estimates of Kolmogorov microscales of length and time as a function of Reynolds number based on a 1/7th powerlaw profile. CHAPTER 2 BACKGROUND This chapter provides an overview of the techniques for shear stress sensor measurement with a focus on floating element sensors. Previous MEMS shear stress sensors are reviewed and their merits and limitations discussed. A sideimplanted piezoresistive shear stress sensor is then proposed to achieve high spatial and temporal resolution and quantifiable uncertainties. Techniques for Shear Stress Measurement The current techniques employed in shear stress measurement are grouped into two categories: direct and indirect [27]. Indirect techniques infer the shear stress from other measured flow parameters, such as Joulean heating rate for thermal sensors, velocity profile for curvefitting techniques or Doppler shift for optical sensors [27]. The uncertainty in these measurements is dominated by the validity of the model relating the flow parameter to wall shear stress [27]. The direct technique measures the integrated shear force generated by wall shear stress on surface [4]. This technique includes three areas: floatingelement skin friction balance techniques, thinoilfilm techniques and liquid crystal techniques. The floatingelement skin friction balance techniques are addressed in this dissertation. A floating element sensor directly measures the integrated shear force produced by shear stress on a flushmounted movable "floating" element [27]. Direct measurement techniques are more attractive since no assumptions must be made about the relationship between the wall shear stress and the measured quantity and/or fluid properties. In addition, direct sensors can be used to calibrate indirect devices. Conventional shear stress sensors and MEMSbased shear stress sensors are described in the following sections, with specific focus on the MEMS floating element technique. Conventional Techniques Many conventional techniques have been developed to measure the wall shear stress [28], including indirect measurement techniques such as surface obstacle devices and heat transfer/mass transferbased devices, and direct measurement techniques such as a floating element skin friction balance. Several review papers [2729] catalog the merits and drawbacks of these devices in various flow situations and a wide range of applications. The indirect conventional techniques are summarized in the following paragraph. Surface obstacle devices include the Preston tube, Stanton tube/razor blade and sublayer fence. These devices are easy to fabricate and favorable in thick turbulent boundary layers. However, they are sensitive to the size and geometry of the obstacle in the turbulent boundary layer. The device can only measure mean shear stress, and unable to measure the timeresolved fluctuating shear stress. In addition, they rely on an empirical correlation between a 2D turbulent boundary layer profile and property measured. Heat transfer/mass transferbased devices include hot films and hot wires. They have advantages of fast response, high sensitivity and simple structure. However, they are sensitive to temperature drift, have tedious calibration procedures, and suffer calibration repeatability problems due to heat loss to the substrate/air. In general, these devices are considered to be qualitative measurement tools [4]. The direct measurement techniques, known as "skin friction balance" or "floating element balance", have been widely used in wind tunnel measurements since the early 1950's [28]. These techniques measure the integrated shear force produced by the wall shear stress on a flush mounted laterallymovable floating element [29]. The typical device is shown in Figure 21. The floating element is attached to either a displacement transducer or to part of a feedback forcerebalance configuration. Winter [28] cataloged the limitations of this technique, which are summarized as follows: * Compromise between sensor spatial resolution and detectable shear force. * Measurement errors associated with misalignment, necessary gap and pressure gradient. * Crossaxis sensitivity to acceleration, pressure, thermal expansion and vibration. Some of these limitations can be significantly mitigated if the dimension of the device is reduced, which is a motivation for the development of MEMS floating element sensors. MEMSBased Techniques MEMS is a revolutionary new Hield that extends silicon integrated circuit (IC) micromachining technology for fabrication of miniature systems. The MEMSbased sensors possess small physical size and large usable bandwidth. The utilization of these devices broadens the spectrum of applications, which range from fundamental scientific research to industrial flow control [6] and biomedical applications [30]. From the fluid dynamics perspective, MEMSbased sensors provide a means of measuring fluctuating pressure and wall shear stress in turbulent boundary layers because the micromachined sensors can be fabricated on the same order of magnitude of the Kolmogorov microscale [10]. Lofdahl and GadelHak reviewed MEMSbased pressure sensors for turbulent flow diagnosis [10] including background, design criteria, and calibration procedures. Recently, Naughton and Sheplak reviewed modern skinfriction measurement techniques, such as MEMS based sensors, thinoil film interferometry and liquid crystal coatings. They summarized the theory, development, limitations, uncertainties and misconceptions surrounding these techniques [4]. Several microfabricated shear stress sensors of both direct and indirect types have been reported. The indirect MEMS wall shearstress sensors include thermal devices [3134], laser based sensors [35], micropillars [36, 37] and microfences [38]. Thermal shear stress sensors operate on heat transfer principles. Laser Doppler sensors operate on the measurement of Doppler shift of light scattered by particles passing through a diverging fringe pattern in the viscous sublayer of a turbulent boundary layer to yield the velocity gradient. Micropillars are based on a sensor film with micropillars arrays that are essentially vertical cantilever arrays within the viscous sublayer. These sensors employ optical techniques to detect the wall shear stress in the viscous sublayer via pillar tip deflection. Microfences employ a cantilever structure to detect the shear stress via piezoresistive transduction. Direct shear stress sensors include floatingelement devices [1825]. Three transduction schemes have been used in floating element sensors: capacitive [18, 21, 24], piezoresistive [19, 25] and optical [20, 22, 23]. Floating Element Sensors Sensor Modeling and Scaling The typical MEMS floating element shear stress sensor is shown in Figure 22. The floating element, with a length of Le, width of Weand thickness of 7(, is suspended over a recessed gap by four silicon tethers. These tethers act as restoring springs. The shear force induced displacement A of the floating element is determined by EulerBernoulli beam theory to be [l l] (the detailed derivation is given in Appendix A) r LR L~~ 2L,W 21 A = 1 21 4ET LW where L,, W, and 7( are tether length, width and thickness respectively, and E is the elastic modulus of tether material. The mechanical sensitivity of the sensor with respect to the applied shear force, F = r, eLe, is directly proportional to the mechanical compliance of the tethers 1/k [18] 1 A 1 L,2L,~ k F 4E7( i(i LW 22 The tradeoff associated with spatial resolution versus decreasing shear stress sensitivity is illustrated in Equation (21) and Figure 23. For example, a sensor with floating element area of 100 ym x100 Ctm, the integrated shear fore is O(10 pN) for a shear stress of O(1 mPa), which requires the tethers to have a high compliance to get an appreciable element detection. The compliance is limited by the maximum shear stress achievable before failure occurs or before nonlinearity in the forcedisplacement relationship [4] becomes substantial. The minimum detectable shear stress is determined by the sensitivity and the total sensor noise [39]. Assuming a perfectly damped or underdamped system, the bandwidth is proportional to the first resonant frequency, Jkhl, where M is the effective mass, M~ = pL,WE,7 (23) where p is the density of the floating element material and it is assumed that L e, >> L, . Therefore, the shear stress sensitivitybandwidth product is obtained as 1 1 L Jk2 4E pL,W,7' 24 The sensitivitybandwidth product is a parameter useful in investigations of the scaling of mechanical sensors. MEMS technology enables the fabrication of sensors with small thickness and low mass, in addition to large compliance and a superior sensitivitybandwidth product comparable to conventional techniques [4]. A MEMS floating element has lengths of L, = W = O(1000 pm) and 7J= O(10 ym), whereas conventional floating element lengths are L, = W = O(1 cm) Therefore, with the scaling of mass alone, MEMSbased sensors have a sensitivitybandwidth product at least threeorders of magnitude larger than conventional sensors. MEMSbased sensors also possess spatial resolution at least oneorder of magnitude higher than conventional sensors, which is vital for turbulence measurements to avoid spatial averaging [4]. Error Analysis and Challenges Compared to conventional techniques, MEMS shear stress sensors have a negligible misalignment error. This error is limited by the flatness of the device die [18] because the floating element, tethers and substrate are fabricated monolithically in the same wafer. Other sources of misalignment include packaging and tunnel installation, with packaging the dominant source [4]. Packaginginduced compressive or tensile force may drastically alter the device sensitivity [18]. The necessary gap between the wall and floating element is also reduced, with a typical gap size smaller than 5 Cpm [4]. Effect of misalignment Misalignment of the floating element results in the element not being perfectly flush mounted with the wall surface, which disturbs the flow field around the sensor. The effective shear stress is estimated by integrating the "stagnation pressure (pu?) over the floating element surface and dividing by the element area [39] to get TA 0r (25) where k~ is the height of protrusion or recession above or below the wall. Streamwise velocity u,~ is obtained via relationship between shear stress and velocity gradient in the sublayer, where p and pu are the density and dynamic viscosity of the fluid, respectively, and z is the distance from the wall. Substituting Equation (26) into Equation (25) to obtain the effective shear stress yields 1 pk 3z r~ (27) S3 pUL For a sensor with Le = 1000 Cpm, ks = 10 Cpm under the surface, and r, = 5 Pa in air, the misalignment error is about 0. 12% Therefore it may be neglected. Effect of pressure gradient Error due to a pressure gradient is also greatly decreased for MEMS sensors. As illustrated in Figure 24, there are two sources which introduce pressure gradient errors; one is the recessed gap beneath the floating element and the other is the net pressure force acting on the lip of the floating element [26]. The net force acting on the lip of the floating element is given as dP FU = (W AP = 7tW, L .(28) Sdy " The associated effective shear stress is obtained by dividing by the sensor area, W~L, dP r T (29) Sdy The pressure gradient also introduces a shear stress underneath the floating element that can be estimated to firstorder by assuming fullydeveloped Poiseuille flow, g dP r = (210) S2 dy ' where g is the height of the recessed gap beneath the floating element. The total effective shear stress acting on the floating element is zef/ = Zw + dP/ + =;.~( T 1+ + (211) 3' dP where p = is called Clauser's equilibrium parameter, which is employed to compare the r, dy external pressure gradient to wall friction in a turbulent boundary layer [7]. The displacement thickness 3' is a parameter quantifying the mass flux deficit due to viscous effects. As indicated in Equation (211i), the error is dependent on the gap size and thickness of the floating element and independent of the size of the floating element. The smaller gap and thickness of the MEMS sensors result in smaller errors compared to conventional floating element sensors; the MEMS sensors provide approximately a twoorder of magnitude improvement in lip force induced error. To get a more accurate estimate of these errors, direct numerical simulation of the flow around the sensor is required. Effect of crossaxis vibration and pressure fluctuations Errors due to streamwise acceleration scale favorably for low mass MEMS sensors [28]. The equivalent shear stress due to acceleration is approximated as F; Ma p L, La r, = == p~ta, (212) A, A, WL where a is the acceleration and A, is the surface area of the floating element, respectively. Equation (212) indicates that the effective shear stress due to streamwise acceleration is proportional to the tether thickness. Assuming the streamwise acceleration is 1 g for a proposed optimum sensor design with element dimensions of 1000 Cpm x 1000 Cpm x 50 pm and the tethers dimension of 1000 Cpm x 30 Cpm x 50 pm, the effective stress is found to be 1.14 Pa in the y direction. Depending on the aerodynamic body acceleration levels, local acceleration measurements in conjunction with coherent power data analysis may be used to mitigate acceleration effects [40]. The streamwise deflection is obtained from 3 ~MaC, (213) where ke and Cy are the streamwise stiffness and compliance of the tethers, respectively. Therefore, the streamwise acceleration sensitivity is proportional to Cy Assuming flow over the floating element in the y direction (Figure 24), the crossaxis compliances according to smalldeflection beam theory are C = (214) S4E~7 and C = (215) The ratios of transverse compliances to compliance in the flow direction are ` (216) and (217) If T, W, ~ O(50 ym) and L, ~ O(1 mm), the compliance in the x direction is four orders of magnitude less than the compliance in the flow direction ( y direction). Since the deflection is proportional to the compliance in the associated direction, the transverse deflection (x direction) is fourorders of magnitude smaller than in the flow direction ( y direction). Therefore, the transverse acceleration effect in x direction is negligible. However, the compliances in the z  and y directions are of the same order, and thus transverse acceleration effects in the z direction must be taken into account. This can be mitigated by using piezoresistive transduction scheme via a fullyactive Wheatstone bridge configuration. The transverse acceleration and pressure in the z direction supplies a common mode signal to the Wheatstone bridge, which can be rej ected by the differential voltage output. It is critical to minimize the pressure sensitivity as pressure fluctuations in wallbounded turbulent flows are much larger in magnitude than wall shear stress fluctuations [41]. Hu et al. [41] found that the wall pressure fluctuations is 7 20 dB (depending on frequency) higher than the fluctuations for the streamwise wall shear stress, and 15 20 dB higher than that for spanwise component. The detailed discussion is given in Chapter 3. Previous MEMS Floating Element Shear Stress Sensors Previous research in the floating element shear stress sensor is reviewed in this section. This review is divided into capacitive, optical and piezoresistive sensing in terms of transduction schemes. Their respective performance merits and drawbacks are discussed. Capacitive Shear Stress Sensors Realizing the merits of scaling shear stress sensors to the microscale, Schmidt et al. [18, 39] first reported the development of a micromachined floating element shear stress sensor with an integrated readout for applications in low speed turbulent boundary layers, As shown in Figure 25, the sensor was comprised a square floating element (500 Cpm x 500 Cpm x 32 Cpm) suspended by four tethers (1000 Cpm x 5 Cpm x 32 Cpm) and fabricated using polyimide/aluminum surface micromachining techniques. A differential capacitive scheme was employed to sense the deflection of the floating element. This differential capacitive scheme is insensitive to the transverse movement to first order. The sensor was calibrated in a laminar flow using dry compressed air up to a shear stress of 1 Pa The achieved minimum detectable shear stress was 0. 1 Pa with a bandwidth of 10 k model. However, the sensor was sensitive to electromagnetic interference (EMI) due to the high input impedance, and suffered from the sensitivity drift due to moistureinduced polyimide property variation. In addition, the capacitive sensing scheme was limited to nonconductive fluids. Pan et al. [21, 42] presented a forcefeedback capacitive design that monolithically integrated sensing, actuation and electronics control on a single chip using polysiliconsurface micromachining technology. The sensor has a comb finger structure with folded beam suspension. The folded beam provided higher sensitivity and internal stress relief. The floating element motion was measured by a differential capacitive sensing scheme while the folded beam served as mechanical springs (Figure 26). A linear measurement sensitivity of 1.02 V/Pa over a pressure range of 0.5 to 3.7 Pa was achieved in a 2D continuum laminar flow channel. No dynamic response, linearity and noise floor results were reported. In addition, the front wire bonds may disturb the flow in turbulent flow measurements. Zhe et al. [24] developed a floating element shear stress sensor using a differential capacitive sensing technique, with an optical technique as a selftest. The sensor was fabricated on an ultrathin (50 pm ) silicon wafer using wafer bonding and DRIE techniques. As shown in Figure 27, the sensor consisted of two sensor electrodes, two actuation electrodes, a floating element (200 Cpm in width and 500 Cpm in length) and a cantilever beam (3 mm in length). The shear stress was detected by a cantilever beam deflection, with a mechanical sensitivity of 1 Cpm/Pa This sensor was capable of measuring a shear force as small as 5 nN that corresponded to a shear stress of 50 mPa The static calibration in a rectangular channel shows a minimum detectable shear stress of 0.04 Pa with 8% uncertainty up to 0.2 Pa, which is the limit of the calibration technique. No frequency response results were reported. Optical Shear Stress Sensors Padmanabhan et al. [20] developed two generations of differential optical shutterbased floating element sensors for turbulent flow measurement. As shown in Figure 28, the floating element (120 Cpm x 120 Cpm x 7 Cpm and 500 Cpm x 500 Cpm x 7 Cpm ) is suspended 1.0 Cpm above the silicon substrate by four tethers. Two photodiodes were integrated into the substrate under the leading and trailing edges of the opaque floating element. The floating element motion induced by shear force causes the photodiodes shuttering. Under uniform illumination from above, the normalized differential photocurrent is proportional to the lateral displacement of the element and the wall shear stress. The sensor could measure a wall shear stress from 3 mPa up to 10 Pa, with a sensitivity of 0.4 V/mPa (without integration of detection electronics ). The dynamic response of the sensor was quantified up to the characterization limit of 4 kHz [43]. The measured shear stress was consistent with predicted theoretical values. The sensor showed very good repeatability, longterm stability, minimal drift, and EMI immunity. The main drawback to this sensor was that vibrations of the light source relative to the sensor resulted in erroneous signals. Tseng et al. [22] developed a novel FebryPerot shear stress sensor that employed optical fibers and a polymer MEMSbased structure. The sensor was micromachined using micromolding, UV lithography and RIE processes. As shown in Figure 29, a membrane was used to protect the inner sensing parts and support the floating element displacement measurement. The displacement of the floating element (400 Cpm high, 200 Cpm wide) induced by the wall shear stress on the membrane (1.5 mm x1.5 mm x 20 Cpm) was detected via an optical fiber using FabryPerot interferometer. The sensor was tested in a steady laminar flow between parallel plates and the results demonstrated a shear stress resolution of 0.65 Pa/nm The minimum detectable shear stress was 0.065 Pa. The fragile sensing parts were not exposed to the testing environment, making the sensor suitable for applications in harsh environments. This sensor was not tested in flows. The dynamic response and linearity of this sensor are questionable due to the potential buckling of diaphragm. Furthermore, crossaxis sensitivity due to vibration and pressure may be significant given the geometry of the sensing element. Horowitz et al. [23] developed a floatingelement shear stress sensor based on geometric Moire interferometer (Figure 210). The device structure consisted of a silicon floating element (1280 Cpm x 400 Cpm x10 pm ) suspended 2.0 Cpm above a Pyrex wafer by four tethers (545 Cpm x 6 Cpm x 10 Cpm). The sensor was fabricated via DRIE and a wafer bonding/thin back process. When the device was illuminated through the Pyrex, light was reflected by the top and bottom gratings, creating a translationdependent Moire fringe pattern. The shift of the Moire fringe was amplified with respect to the element displacement by the ratio of fringe pitch G to the movable grating pitch g2 The sensor die was flushmounted on a Lucite plug front side, and the imaging optics and a CCD camera was installed on the backside for the displacement measurement. Experimental characterization indicated a static sensitivity of 0.26 Cpm/Pa, a resonant frequency of 1.7 kHz, and a noise floor of 6.2 mPa/J Drawbacks to this sensor included an optical packaging scheme not feasible for wind tunnel measurement and limited bandwidth. Piezoresistive Shear Stress Sensors Shajii et al. [19] and Goldberg et al. [44] extended Schmidt's work to develop a piezoresistive based floating element sensor for polymer extrusion feedback control (Figure 2 11). The polyimide/aluminum composite floating element was replaced by single crystal silicon. These sensors were designed for operation in high shear stress 1 kPa 100 kPa), high static pressure (up to 40 1VPa) and high temperature (up to 300 OC) flow conditions. The floating element size was 120 Cpm x 140 Cpm in Ng' s design, and 500 Cpm x 500 Cpm in Goldberg' s design. The element motion was sensed by axial surface piezoresistors in the tethers via configuration these piezoresistors to a half Whitestone bridge. This sensor was not suitable for turbulent flow measurement due to low sensitivity as it was designed for maximum shearstress levels 5 orders ofmagnitude larger than those in a typical turbulent flow. However, Goldberg et al. [44] developed a backside contact structure to protect the wirebonds from the harsh external environment, which reduced the flow disturbance and associated measurement uncertainty for turbulence measurement. Barlian et al [25] developed a piezoresistive shear stress sensor for direct measurement of shear stress underwater. The sidewallimplanted piezoresistors measured the integrated shear force, and the topimplanted piezoresistors detected the pressure (Figure 212). The displacement of the floating element was detected using a Wheatstone bridge. The experimental measurements indicated the inplane force sensitivity ranged from 0.041 0.063 mV/Pa, while the predicted sensitivity was 0.068 mV/Pa The transverse sensitivity was 0.04 mV/Pa with a corresponding transverse resonant frequency of 18.4 k cantilever as an input. The dynamic analysis was performed using a laser Doppler vibrometer with a piezoelectric shaker to drive the inplane or outofplane motion. The inplane resonant frequency was experimentally found to be 19 k The integrated noise floor was 0. 16 CLV over bandwidth of 1 Hz 100 k the piezoresistors to changes in temperature was investigated in a deionized (DI) water bath, and the temperature coefficient of sensitivity was found to be 0.0081 kOZ/ C No electrical characteristics of p/n junction isolation and flow characterization are reported and no fluid mechanics characterization was performed. A FullBridge SideImplanted Piezoresistive Shear Stress Sensor According the above discussion, the most successful 1VEMS floating element sensor to date used integrated photodiodes to detect the lateral displacement via a differential optical shutter [20]. This sensor can detect the shear stress as low as 1.4 mPa However, it is not suitable for wind tunnel testing because the sensing system is sensitive to tunnel shock and vibration. The capacitive transduction technique integrated the mechanical sensor and electronics on one chip to eliminate the parasitic capacitance [45], and has the capability to measure small signals. Unfortunately, the sensitivity drifted due to the charge accumulation in the electrodes [18], which can be mitigated by hermetic sealing [46] or by employing metal electrodes. However, the shear stress sensor must be exposed to the flow for shear stress measurement and wind tunnels are typically not humidity controlled environments. The piezoresistive transduction scheme is widely used in commercial pressure sensors and microphones due to its low cost, simple fabrication, and higher reliability than capacitive transduction. In addition, piezoresistive technology can resolve sufficiently small forces up to O(10 "N) [47]. Shajii et al. [19] proposed a backsidecontact, piezoresistive sensor to measure very high shear stress in a polymer extruder. Axial mode piezoresistive transducers [19, 25] for highshear industrial applications have been fabricated using standard ionimplantation techniques, but more sensitive bendingmode transducers require that the piezoresistors be located on the tether sidewall. This concept has been proposed by Sheplak et al.[48] and applied by Barlian et al. who presented an integrated pressure/shear stress sensors for underwater applications [25]. The authors did not present a comprehensive fluidinduced shear stress characterization of their sensor. Rather, the sensor was statically characterized using a mechanical cantilever and dynamically characterized using an acceleration input. In a conference paper, the authors presented some water flow results possessing a large uncertainty and an unexplained sensitivity that was larger than the value predicted by beam mechanics [49]. None of these devices have successfully transitioned to wind tunnel measurement tools because of performance limitations and/or packaging impracticalities [2]. For use in a wind tunnel, the sensor package must be flush mounted in an aerodynamic model, robust enough to tolerate humidity variations and immune to electromagnetic interference (EMI). We have attempted to address these limitations via the development of a fullyactive Wheatstone bridge sideimplanted piezoresistive sensor. This approach was motivated by the following two side implanted piezoresistive transducer concepts. Chui et al. [50] first presented a dualaxis piezoresistive cantilever using a novel oblique ion implantation technique. Later, Partridge et al. [51] leveraged the sideimplant process to fabricate a high performance lateral accelerometer. The device structure developed in this dissertation is illustrated in Figure 213 which shows an isometric view of the floating element, sidewall implanted ptype silicon piezoresistors, heavily doped endcap region, and bond pads. In this transduction scheme, the integrated force produced by the wall shear stress on the floating element causes the tethers to deform and thus induces a mechanical stress field. The piezoresistors respond to the stress field with a change in resistance from its nominal, unstressed value due to a change in the mobility (or number of charge carriers) within the piezoresistor [52]. The conversion of the shear stress induced resistance change into an electrical voltage is accomplished via configuration of the piezoresistors into a fullyactive Wheatstone bridge to increase the sensitivity of the circuit compared to half bridge configuration. This bridge requires the presence of a bias current through the piezoresistors, typically, it is driven by constant voltage excitation. This sensor is designed to measure shear stress only and to mitigate pressure sensitivity. An onchip dummy bridge located next to the sensor is used for temperature corrections. Ideally, common mode disturbances do not have any effect while differential disturbances are linearly converted into the bridge output. To achieve a differential signal, the piezoresistors are oriented such that the resistance modulation in each resistor of a given leg is equal in magnitude but opposite in sign. These conditions are achieved by placing the side implanted resistors facing one another such that when one resistor is in tension, the other is in compression. This results in equal mean resistance but opposite perturbation. Once the transduction scheme is selected, the mechanical models and transduction sensing models need to be developed to get sensor performance, such as sensitivity, linearity, bandwidth, noise floor, dynamic range, MDS. The detailed discussion of the electromechanical modeling is given in Chapter 3. u(z) Floating Element Restoring Springs Figure 21. Schematic crosssectional view of the floating element based sensor. Tether AFloating Element Flow Figure 22. Schematic plan view and crosssection of a typical floating element sensor [4]. Flow u(z) 10 10  l6 10 10 03 2 0 2 13 10 10 10 10 1 Shear Stress w (Pa) Figure 23. Integrated shear force variation as a function of sensor resolution for different element areas. U.0 u~) 1 We zY 3/ P1 Z P2x y Wall Floating Element Figure 24. Schematic illustrating pressure gradient effects on the force balance of a floating element. Embeded Floating Element Sense Capacitor Dnive Capacitor Sense Capacitor on chip off chip Figure 25. Schematic crosssectional view of the capacitive floating element sensor developed by Schmidt et al. [18]. Tether Floating Element Release Holes Expanded View of Comb Finger Structures Cl V+ C2 Figure 26. Planview of a horizontalelectrode capacitive floating element sensor [21]. Photodiodes Sense Electrode Actuation Electrode Pads r Figure 27. Schematic topview of a differential capacitive shear stress sensor [24]. Incident Light from a Laser Source Flow 1 1 ,, ,, Floating 1Element~ute I I ntype Si Oxide Passivation ptype Si Figure 28. A schematic crosssectional view of an optical differential shutterbased floating element shear stress sensor [l l]. F tn Flow n2 t~I Tethers  II Incoherent Light )l Frinee Pyrex _XXI Reflection Mirror (Floating Element) AA' CrossSection Input(Output) Fiber d R1 R MRTV1 Membrane Air or Liquid Flow Figure 29. Schematic top and crosssectional view of a FebryPerot shear stress sensor [22]. Aluminum Gratings (Floating Element & Base Gratmngs) Incident Reflected Moire Laminar Flow Cell Ti Lr Floating. Element Figure 210. Top and crosssectional view of Moire optical shear stress sensor [23]. "I I Floating Element Figure 211. A schematic top view of an axial piezoresistive floating element sensor [19]. TopImplanted Piezoresistor for Pressure Measurement Tether Floating Element SideImplanted P~iezoresistor for ShearStress Measurement Figure 212. A schematic top view of a laterallyimplanted piezoresistive shear stress sensor [25]. R+M~ Sidewall Implanted Plezoresistor ,n a Cr ~R+M\ ~ RM Bond Pads Silicon Tether nwell Figure 213. A schematic 3D view of the sideimplanted piezoresistive floating element sensor. CHAPTER 3 SHEAR STRESS SENSOR MODELING This chapter presents the electromechanical modeling of the MEMS sideimplanted piezoresistive shear stress sensor. These models are leveraged for use in finding an optimal sensor design (detailed discussion in Chapter 4). Formulation of the objective function for performance optimization begins with structural and electronic device models of the shear stress sensors. The structural response directly determines the mechanical sensitivity, bandwidth, and linearity of the dynamic response. The piezoresistor design determines the overall sensitivity and contributes to the electronic noise floor of the device. The organization of this chapter is as follows. First, the mechanical modeling is discussed, including quasistatic modeling and dynamic response analysis. Linear and nonlinear quasistatic behaviors are presented. Lumped element modeling is employed to find the dynamic behavior of the sensor. These analytical models were verified using finite element analysis (FEA) in CoventorWare". Second, the piezoresistive sensing electromechanical model is developed, where the resistance and piezoresistive sensitivity for nonuniform doping are derived via stress averaging and a conductanceweighted piezoresistance coefficient. Two dominant electrical noise sources in the piezoresistive shear stress sensor, 1/ f noise and thermal noise, as well as amplifier noise are considered to determine the noise floor. Finally, some device specific issues are addressed, including transverse sensitivity, acceleration sensitivity, pressure sensitivity, junction isolation issues and temperature compensation via a dummy bridge. QuasiStatic Modeling In this section, the sensor structure is discussed and modeled. Quasistatic models for small and large floating element deflections that make use of EulerBernoulli beam theory and the von Karman stain assumption, respectively, are presented. Two methods are used in large deflection analysis, an energy method and an exact analytical method. Structural Modeling Floating element sensors are composed of four tethers and a square floating element. A schematic of the piezoresistive shear stress sensor is shown in Figure 31. The floating element is suspended above the surface of the silicon wafer by tethers, each of which is attached at its end to the substrate. Sideimplanted boron in the sidewalls of the tethers forms the four piezoresistors. These resistors are aligned in the <110> direction and located near the edge zone of the tethers to achieve the maximum sensitivity. Two resistors are oriented along opposite sides of each tether. When the fluid flows over the floating element, the integrated shear force causes the tethers to deform and induces a bending stress. For the mechanical analysis, the floating elements and tethers are assumed to be homogeneous, linearly elastic, and symmetric. In practice, this is not strictly valid as the beam is partially covered by thin silicon dioxide and silicon nitride layers. The floating element is assumed to move rigidly under the applied shear stress, and the motion is permitted inplane only. The tethers are assumed to be perfectly clamped on the edge. The effects of pressure gradient and gap errors are ignored. Furthermore, the Young's modulus and Poisson ratio are assumed to be constant and do not change with processing. Small Deflection Theory Assuming that L, >> W,, T,, the tethers can be modeled as a pair of clampedclamped beams with a length of 2L,, subj ected to a uniform distributed load Q (per unit length) and a central point load P [39], as shown in Figure 32. The distributed load is due to the shear stress acting on the tethers and is given as Q = r,W,. (31) The point load, P is the effect of the resultant shear force on the floating element and is given by P = r,W,Le/2, (3 2) where the factor of 1/2 comes from the symmetry of the problem. The maximum deflection and bending stress distribution is obtained using Euler Bernoulli beam theory. The detailed derivation is given in Appendix A. The lateral displacement of the beam is given by w~x) [ (IYL,L, +8(~L, x (2WY,L, +8WL,)x' +2(xy (0<;x where E = 168 GPa is the Young's modulus of silicon in the (110) direction [53]. The maximum deflection occurs at the center of the beam and is obtained by substituting x = L, into Equation (33) to get r,W,LBI L,r ]II+2WL, 34 A12 34 4E7E W W,L, This corresponds to the floating element displacement. The second term in the brackets of Equation (34) is a correction for the distributed wall shear stress on the tethers. Equation (34) indicates that the important parameters affecting the scaling of the device are the area of the floating element, W,L,, ratio of the tether length to the tether width, L,/R,, and ratio of the area of a tether to that of the floating element, WL,/RL, If the tether surface area WL, << WL,, the stiffness is approximated as 1 A 1 L k w~~e.Et (35) This indicates that the stiffness is proportional to the tether thickness and ratio of the tether width and length. The bending stress distribution through the width and length of the tether is given by 7,e~~e 2y 3 2WL, W~ x 3WL, x 0xL 02(x, y)= 1 ~ + + ~ + (36 W, Te W 4 WeLe 2 WeL L, WeL L, 0 where x = 0 is at the end of the beam, and y = 0 is on the side wall surface. Equation (36) indicates that the maximum shear stress is located at the end of the beam and on the side wall surface ( x, y = 0 in Figure 32). Linear EulerBernoulli beam theory [54] fails for sufficiently large wall shear stresses because the midplane of the beam is strained [46]. The beam grows stiffer as the deflection becomes large. Furthermore, the nonlinear motion generates undesired harmonic distortion in the frequency domain. The sensor is required to maintain a linear relationship between shear stress and displacement in order to preserve spectral fidelity for time resolved measurement. This requirement places a nonlinear constraint in the sensor design optimization (discussed in Chapter 4). A large deflection mechanical model was therefore developed for use in determining this constraint. Large Deflection Theory Large deflection theory provides a measure of the maximum shear stress that may be measured while maintaining mechanical linearity. Two analysis techniques are pursued to determine the nonlinear mechanical behavior of the sensor: the strain energy method [46] and an exact analytical method. The detailed derivations are given in Appendix A. Energy method The deflection predicted by the strain energy method [46] is obtained by assuming a trial function which meets both the clamped boundary condition and symmetry condition of the beam, w(x) = ^1+ cos (37 82 iL, ) : 37 where A, is the floating element deflection. The trial function is substituted into the expression for strain energy in the beam and the principle of minimum potential energy is applied. The result is 3 z w,~ L, WL Az :1+ Ltr = , 1+2 .:L (38) Comparing this result to Equation (34), one can see that cubic nonlinearity term has been added. The mechanical response of the floating element sensor will be linear provided that the non linear term is small with respect to unity; that is, if the displacement of the sensor is small in comparison to the tether width, (Az /W,) << 1. The nonlinear term is cubic and therefore represents a Duffing spring behavior, or stiffening of the beam as deflections become large. This means that the nonlinear deflection is smaller than the ideal linear deflection for large shear stresses. Exact analytical model In the large deflection model, the neutral axis tension force Fa is taken into account. The average axial tension force is obtained by integrating the neutral axis strain along the length of the beam. It then serves as a constitutive equation between axial force and strain. The detailed model development procedure is given in Appendix A. The maximum deflection predicted by the exact analytical method is obtained using von Karman strain assumption, P .cosh(ALl,)1 n +P oP QL PL 2AFE F A sinh(AL, ) ~~Y 2 2 2Fa 2F; where the axial force Fa is given by F = dxay(( (310) and Ai is given by A= 12,/EW (311) There are five variables, four boundary conditions and one constitutive equation. But the equation is indeterminate, so the final solution is obtained using an iterative technique to find Ai, and therefore obtain the maximum deflection. Lumped Element Modeling Lumped element modeling is used to represent the fluidic to mechanical transduction of the shear stress sensor and facilitates the prediction of the dynamic response. The main assumption of LEM is that the length scale of the physical phenomena of interest is be much larger than the characteristic length scale of the device [55]. For the shear stress sensor, this means that the bending wavelength of the beam must be much larger than the length of the tethers. The LEM provides a simple way to estimate the dynamic response of a system for low frequencies, up to just beyond the first resonant frequency, which is appropriate for design purposes [56]. There are several types of elements in the lumped element model. For example, in a lumped mechanical system, mass represents the storage of kinetic energy, compliance of a spring (inverse of stiffness) represents the storage of potential energy, and a damper represents the loss of energy through dissipation. Similarly, in lumped electrical systems, generalized potential energy is stored in a capacitor, generalized kinetic energy is stored in an inductor, and energy is dissipated via a resistor. From a LEM perspective, the two sets of tethers are modeled as a spring possessing an effective compliance C_,, In an impedance analogy, this compliance shares a common displacement with the effective mass IM,,, of the tethers and floating element as well as the damper, R,, of the system. The main source of damping is the viscous damping underneath the element, and thermoelastic damping, compliant boundaries and vibration radiation to the structure boundaries are neglected in this research. Therefore, the sensor is modeled as a spring massdashpot system, as schematically shown in Figure 33. In the equivalent circuit, the voltage and current are analogous to force and velocity, respectively. The motion of the mass springdashpot system is described by the classic secondorder differential equation, F (t) = M,,, + R, + 1/C,,, A (3 12) medt2 dt Therefore, the frequency response function of the device is found to be A (jei) 1 H( je) =(313) F( jm) ( jeS)2 M,,l,, + jC(R, + 1 C,,,e where the angular frequency m = 27r f f. is the cyclic frequency, and j = Jl. Assuming a lightly damped system, the first resonant frequency f, is f = (314) The detailed derivation of the lumped elements is given in Appendix A. The effective mechanical compliance is determined by equating the potential energy stored in the beam to that of an equivalent lumped system and is C = 1+2 1+4 + (315) 2E7E ( W,L, 1 L, 15 ,L The effective mass is obtained by equating the kinetic energy of the sensor to that of a lumped system and is 1494 ,L, 223 8 W,, 1024 (,( M = psWL,( 1+ '+ ~ + 12 (16 ;se315 WL 315 L 315 WL WL, where p,, = 2331 kg/m3 is the density of silicon [53]. Finite Element Analysis To verify the analytical models, a finite element analysis with a clamped boundary condition on the edge of the tethers is performed. The material properties of silicon and the geometry of a representative structure are given in Table 31. Finite element analysis is performed in CoventorWare" using the multimesh model by partitioning the continuum solid model into plate and tether volumes. A fine mesh is used in the tethers because of the large stress gradients with respect to those found in the plate. These volumes are j oined to form one volume via RigidLink after meshing. The mesh is composed of parabolic Manhattan brick elements. A mesh refinement study revealed sufficient elements dimensions are 3 Cpm,0.5 Cpm and 1 Cpm in length, width and thickness within the tethers, respectively, and 10 Cpm,10 Cpm,1 Cm within the plate. Since the device is symmetric, only half of the structure is analyzed in the model, with 6600 elements in the analysis. A representative displacement field of the tethers at r, = 5 Pa is shown in Figure 34. The comparison in Figure 34 indicates that the nonlinear analytical model is in agreement with FEA simulation results. Figure 35 shows the maximum displacement of the floating element as a function of applied shear stress for analytical linear and nonlinear models, nonlinear energy method model and FEA model. This comparison in Figure 35 indicates that all results are in agreement in the linear range (50 Pa approximately), while the nonlinear analytical model, nonlinear energy method model and FEA models agree in this nonlinear deflection region. Figure 36 shows the stress distribution using analytical linear model (Equation (36)) and FEA results along the tether length on the sidewall surface ( y = 0) for the representative structure. Figure 36 demonstrates that the analytical model is in agreement with the FEA model. The bending stress varies from tensile to compressive in a parabolic distribution along the tether length. Figure 36 shows that the maximum stress occurs on the edge zone ( x, y = 0 ) of the tether. The resonant frequency obtained from LEM (12.44 k well, as shown in Table 32. The next 5 modes were also found using FEA and are given in Table 33. The first six mode shapes are shown in Figure 37. The inplane resonant frequency (second mode) is 17.08 k because the tether width is greater than the tether thickness for the verification studies (Table 3 1). Clearly, the representative dimensions used for model verification are not a preferred design, let alone an optimized design. Piezoresistive Transduction In 1954, Smith [52] discovered the piezoresistance effect in silicon and germanium. The piezoresistance effect is defined as the change of semiconductor resistivity due to a change in carrier mobility that results from an applied mechanical stress. In piezoresistive transduction, the resistance modulation is a function of the applied stress and piezoresistive coefficients (xjz [57]. For the cubic crystal structure of silicon under small strain, the correlation of normalized piezoresistivity (Ap/ p) and stress for reduced tensor notation reduces to < > =3 (317) pI~2 A 0 0 0 O4 Ap 0 0 O r4 0 9 Ap1 0 0 0 0 0 z4 1,, where Ap is the change in resistivity, a, are normal stresses along the cubic crystal < 100 > axes, and 5, are shear stresses. For a given resistor geometry, there are two piezoresistive coefficients used for piezoresistive sensing analysis in terms of stress orientation with respect to the current. The longitudinal piezoresistive coefficient captures the effect of an applied stress in the same direction as the current, and the transverse piezoresistance coefficient captures the effect of an applied stress in the direction perpendicular to the current. The longitudinal and transverse piezoresistive coefficients in terms of the fundamental piezoresistive coefficients and direction cosines are given by, respectively [58], a =x, +2 %4 2 1 2 12 1Z2 l2 12\l (318) and 4 = n,2 (%4 + 2 1~)(l 1 2 12n1 nZ13Z) (319) where (ly,ng,n ) is the set of direction cosines between the longitudinal direction and the crystal axis, and 13,,m, n,n is the set of direction cosines between the transverse direction and the crystal axis. The direction cosines are given in terms of Euler' s angles [59] 1, m, n, c~c~cry s~sry s~c~cry + c~sy s~cry 1, m, n, = c~c~sry s~cry s~c~sy + c~cy s~sry ,(320) 13m, n, c~s8 s~s8 cB where c# = cos (#), sf = sin (#), and etc. The geometry of the Euler' s angle i s shown in Figure 38. In this research, a (100) wafer is used, thus B = 0, y/ = 0 and # sweeps from 0 to 180 degree in Figure 38. Therefore, the matrix (320) reduces to, 1, m, n, c# s# 0 1, m, n, I= s# c# 0 (321) 13 m, n, O 0 1 The piezoresistive coefficients, 4z;, 4i, and try are given in Table 34 for both ptype and ntype piezoresistors at room temperature for low doping concentrations. For this piezoresistive device, the floating element sensor features integrated side implanted diffused resistors [25, 50, 51] in the element tethers for piezoresistive detection. In this transduction scheme, the integrated force produced by the wall shear stress on the floating element causes the tethers to deform and thus creates a mechanical stress field in the tethers. The piezoresistors respond to the mechanical stress field with a change in resistance from its nominal unstressed value [46] as indicated by AR Ap = gr + 4r, ,(3 22) R p where p and R are the resistivity and resistance of the piezoresistor, respectively, A signifies the perturbation in the resistance and resistivity due to the piezoresistive effect, a, is the bending stress along the beam, and o, is the transverse stress. For a beam subjected to pure bending, Equation (322) simplifies to S= zzG:,. (323) Piezoresistive Coefficients The piezoresistive coefficients depend on crystal orientation, doping type and level, and temperature. This dependence is typically expressed as a product of the coefficient' s lowdoped room temperature value so~ and a piezoresistive factor P(N, T) [59] ~z(N, T) = ~zoP(N, T), (324) where Ni is the doping concentration and T is the temperature. For a (100) wafer, the dependence of the piezoresistive coefficient on the crystal direction is given in Figure 39 and Figure 310 for ptype and ntype piezoresistors, respectively. This indicates that the maximum piezoresistive coefficient for ptype silicon is in the (110) direction, while for ntype silicon the maximum is in the (100) direction. Also note that ntype silicon has a larger achievable piezoresistive coefficient than ptype silicon. The longitudinal and transverse piezoresistive coefficients zz, and z, in the (110) direction for ntype and ptype silicon are given in Table 35 [52]. As shown in Table 35, piezoresistors in ptype silicon are more sensitive than for ntype in the (110) direction, which is parallel or perpendicular to the flat of a (100) wafer. In this design, the ptype piezoresistors are chosen due to its high sensitivity in the (110) direction and because of the lower temperature sensitivity at higher doping concentrations compared to ntype piezoresistors [60]. Many theoretical [59] and experimental [6163] studies have reported the dependence of the piezoresistive factor P(N, T) on doping concentration at room temperature. Kanda' s model [59] is most popular and is accurate for low concentrations. However, when compared to experimental data [6163], Kanda' s model under predicts the rolloff of P(N, T) for concentrations above 10'7 cm For doping concentration above 10 cm the fundamental piezoresistive coefficient is expressed as a product of its lightlydoped room temperature value 4,~ and the experimentally fitted piezoresistive factor P(N, T) [47], Fr (N, T) = 4P(N, T) = 4, log .312 1004 (325) The piezoresistive factor is plotted in Figure 311 versus concentration at room temperature. The piezoresistive coefficient is also temperature dependent. At higher doping concentrations, there will be a reduction in both thermal noise and 1/ f noise compared to lower doping concentrations [47]. In addition, the temperature dependence of the piezoresistance coefficient is reduced significantly as the concentration increases at low doping concentration. For doping concentrations above 10" cm3, the piezoresistance coefficient is almost independent of temperature variation [61]. However, the sensitivity degrades due to the reduced piezoresistive coefficient at a high doping level [62]. Thus, there is a tradeoff between sensitivity and noise floor. This tradeoff suggests optimization is necessary to obtain the best performance, as will be discussed in chapter 4. Piezoresistive Sensitivity For the structure shown in Figure 312, the sideimplanted piezoresistors are fabricated by first implanting ptype impurities (boron) into the sidewall, followed by a diffusion step to drive in and to electronically activate the impurities. The impurities diffuse laterally, and the resulting impurity concentration profie decreases from the surface of the side wall to the junction depth. If the unstrained impurity profile as a function of depth, N:(y), is known, the piezoresistive coefficient profie tr(y) can be determined. As shown in Equation (36), the stress varies along the beam, and varies across the junction depth, y, as well. Therefore, the product of the stress and the piezoresistive coefficient distributions need to be integrated in the electromechanical model . Several models have been developed for piezoresistive sensitivity. Tortonese [64] and Harley [65] built a twostep model for nonuniform doping concentration and formulated an efficiency factor to be inserted into the numerator of the surface sensitivity equation. In integrating across the beam, their model does not account for the junction isolation of diffused resi stores. Senturia [46] presents the piezoresistive coefficient dependence of the doping concentration, but does not account for stress variation as a function of depth. Sze's model [57] addresses stress variations across the resistors (y direction) and incorporates a conductance weighted piezoresistance coefficient. Sze, however, did not account for the stress variation along the piezoresistor (x direction). Based on Harley's work, a new model was developed by involving stress averaging along the tether length and across the depth of piezoresistor, and using a conductanceweighted piezoresistive coefficient. Two issues need to be considered in calculating the piezoresistive response. One is that the piezoresistors are typically formed by diffusion, thus have a nonuniform doping profile with respect to junction depth. The second issue is that piezoresistors also span a finite area on the device, and hence have nonuniform stress with respect to length and depth. The derivation of the resistance of the piezoresistor begins with the nonuniform doping concentration that varies from the sidewall surface to the junction depth ( y direction). The stress varies in this direction as well. As shown in Figure 312, the resistor can be considered as a stack of slices, where each slice has a slightly different doping concentration and stress. The current flow is in x direction, so the slices ( dy ) are connected electrically in parallel because they share the same potential. The stress also varies along the length of the resistor (x direction). Thus, the resistor is also segmented along its length. These segments (dx) are connected in series due to the same current flow. The mechanical model assumes that L, >> W and 72, thus the differential resistance of a unit cell for a small segment dx and a small slice dy with width of W, is given by 1 p, ( x, y) dx dRunlt, (x, y) (3 26) dG,,,,,, (x, y) W dy where it is assumed that y = 0 at the surface and y = W,/2 at the neutral axis. In Equation (326), o, (x, y) is the stressed resistivity determined by [46] Pe~x y)= Po~y)1+7z (~o2x, )),(3 27) where peo (y) is the unstressed resistivity and 0t(x, y) is given in Equation (36). For non uniform doping, peo(y) is given by [66] peo (y) = ,(3 28) p, (y)qN, (y) where q = 1.602 x 101 C is the electronic charge of an electron and up (y) is the boron mobility. In this research, the mobility is obtained from [67]. To simply the calculation process, we use conductance G = 1/R rather than resistance in the derivation. The total conductance for segment dx is obtained by summing the conductance of each unit dG,I, = CdG 1Wd .(329 aceL~ "" d Peo(y) (1+ zzl(y)01 (x, y)) The total resistance is determined by summing the resistance of the small dx segments, LR +L,. LR +L, R +AR / dGstice = 1 dx ,v (330) LR LR W dy a, Pe(y)(1+ ;z,(y)o, (x, y)) where LR = 10 Cpm is the overlap end cap and it does not change the resistance value. The total unstressed resistance is similarly found by integrating along the length of the resistor using the unstressed resistivity, LR +L,. LR +L, R = [1/d~ticedx .(33 1) LR R W dy Then the resistance modulation is obtained by arranging Equation (330) and (331), AR R+AR R peo(F LR+L R R o dxyL R+ ,1. (332) R R L LR Tdy Electromechanical Sensitivity The four sidewall implanted piezoresistors form a full Wheatstone bridge circuit that provides sensitivity enhancement for a small change in resistance. As illustrated in Figure 313, when the tether deflects in the y direction, piezoresistors 1 and 3 experience a compressive stress while 2 and 4 experience a tensile stress. These resistors experience a change in resistance of MR and MR, respectively. For an ideal bridge, R, = R, = R MR and R, = R4 = R + MR, so that the output voltage, Vo, for a given bias voltage V,, is V R4 R' V,= (333) ii : R,+R4 R,+R, R The sensitivity of the piezoresistive sensor is defined as the change of output voltage per unit of applied shear stress and for a linear sensor is expressed as aV, V Sm<= (334) Substituting in Equation (333), the electromechanical sensitivity is rewritten as Sm, = (3 3 5) RT, Noise Model The key sources of the electrical noise in piezoresistive sensors are thermal noise, low frequency 1/ f noise, and amplifier noise [65]. Physical fluctuations of the floating element at an equilibrium temperature, T, can result in random motion of the device; however, the contribution of thermomechanical displacement noise has been found to be much smaller than the electronic noise sources except at mechanical resonance [47]. For an ideally balanced Wheatstone bridge, the bias source noise will be common mode rej ected. Thermal Noise Thermal noise, also known as "Nyquist" or "Johnson noise", is produced when electrons are scattered by thermal vibration of the lattice structure [68]. Since higher temperatures lead to increased vibrational motion, thermal noise power spectral density (PSD) is directly proportional to temperature. Moreover, thermal noise is present in thermodynamic equilibrium, and its PSD is independent of frequency since random thermal vibrations are not characterized by discrete time constants. The thermal noise PSD (S,, ) is modeled by Nyquist [68], which was experimentally verified by Johnson [69], as S,, = 4kTR (3 3 6) where kg = 1.38e23 J/K is the Boltzmann constant, R is the total resistance in the resistor, and T is the temperature in Kelvin. In a piezoresistor, the rms noise voltage, V,, due to thermal noise is obtained by taking the square root of the thermal noise PSD integrated over the bin width of interest Af = f2 J; [68], Vm S, Vdf = J4kg TR f ,(337 1/J Noise The dominant noise source for most ionimplanted piezoresistors is 1/ f noise. Hooge [70] first reported that the 1/ f noise PSD of a piezoresistor is inversely proportional to the total number of carriers in the resistor when an external dc bias voltage is applied, and is given by S,/ HV2,f (338) where VR is the voltage across the resistor, N, is the total number of ionized carriers in the resistor, f is frequency, and aH is Hooge parameter, with the experimental values ranging from 5 x106 to 2x103 [71]. Hooge' s parameter is sensitive to bulk crystalline silicon imperfections and the interface quality. Low frequency noise occurs under nonequilibrium conditions and its spectra is proportional to the square of the applied voltage. Two physical mechanisms have been proposed to account for the low frequency noise: random trapping/detrapping of carriers at the surface and bulk electronic traps, and random mobility fluctuations [72]. The noise power of 1/ f noise is obtained by integrating Equation (33 8) over a frequency range of operation aR =In (339) The total number of ionized carriers in the resistors for the piezoresistor geometry in Figure 312 is given as No = Lj,i*.W N(dy (340) where N, (y) is the p type doping concentration. As indicated in Equation (339), 1/ f noise increases for small volumes and highly resistive piezoresistors. In this dissertation, the typical input noise of a low noise amplifier at 1 kHz , 4 nV/JA [73], is used in the noise floor model. For an ideally balanced Wheatstone bridge assuming a unity gain amplifier, the total rms output noise voltage I is I =1 aH B2N 4.~, 7 4,TR, f (4e9 Af (341) where the first, second and third terms in Equation (341) are the contribution of 1/ f noise, thermal noise, and the amplifier noise, respectively. The detailed derivation of Equation (341) is given in Appendix B. Since narrow bin turbulence spectra are desired, a figure of merit bin width of Af = 1 Hz centered at 1 kHz is used in this dissertation; therefore, J = 999.5 Hz and f2 =1000.5 Hz. The minimum detectable shear stress (MDS) or input noise, Zminn is the minimum shear stress that the shear stress sensor can resolve in the presence of noise, and is defined as r =" (3 42) mm, S The dynamic range (DR) is then given by DR = 201og zmax (343) Device Specific Issues In this section, a few specific design issues are addressed, including transverse sensitivity, acceleration sensitivity, pressure sensitivity, temperature compensation and device junction isolation issues. Transverse Sensitivity Transverse sensitivity was discussed in Chapter 2 (Equation (216)), and restated here briefly. Recall that the transverse mechanical sensitivity in the x direction can be neglected due to the large differences in bending versus axial stiffness, while transverse mechanical sensitivity in the z direction is of the same order as in the flow direction. The x direction also possesses electromechanical rej section for an ideally balanced bridge. Assuming the flow is in the y direction, when the sensor is subj ected to an xaxis acceleration, piezoresistors 1 and 2 experience a tensile stress while 3 and 4 experience a compressive stress. These resistors experience a change in resistance of MR (piezoresistors 1 and 2 and MR (piezoresistors 3 and 4), respectively (Figure 314 (a)). The resistances in the bridge become R, = R, = R + MR, R, = R4 = R MR The output voltage, Vo, for a given bias voltage V,, is given by R, R R+MR RMR V =0 (3 44) oR, +R, R, + R4 2R +2MR 2R 2M When the fluctuating pressure load acts in the z direction, the stress distribution in all four tethers is the same, leading to equal resistance perturbations (AR) in all four piezoresistors. The reaction of the Wheatstone bridge due to pressure is shown in Figure 314 (b). The total pressure effect is to supply a common mode signal into this differential sensing scheme, which does not affect the voltage output. Therefore, the ideal electromechanical sensitivity due to the xaxis load and pressure disturbance is ideally equal to zero. In reality, there will still be transverse sensitivity due to bridge mismatch. Temperature Compensation The output voltage of a piezoresistive sensor is dependent on temperature due to the thermal sensitivity of the resistance, strain and piezoresistive coefficient [46]. In this dissertation, it is assumed that the thermal coefficient of resistance will dominate over thermal strain effects and changes in the piezoresistive coefficient. The typical temperature coefficient of resistance for a laterally implanted sensor is reported to be 0.0081 kOZ/oC, which is much larger than the shear stress sensitivity [25]. Since it is impossible in practice to have absolute temperature control in a wind tunnel, temperature compensation of the output signal must be employed. In it important that the temperature is measure as close as possible to the sensing element to avoid compensation errors due to temperature gradients in the flow. In this thesis, the temperature compensation of the resistors are achieved using a double bridge configuration [74]. As shown in Figure 315, two Wheatstone bridges are used on one chip; one is the active Wheatstone bridge with output that is a function of shear stress and temperature, while the other is a dummy compensation Wheatstone bridge with output that acts as a thermometer and only depends on temperature. The dimension of the compensation bridge resistors is identical to the active bridge and is kept as close as possible to the active bridge (safe distance of 100 Cpm suggested for the peripheral circuits [75] ). The detailed temperature compensation procedure for the nonideal case of a statically unbalanced bridge is discussed in Chapter 6. For ideally balanced Wheatstone bridge, the power supply noise is just a common mode signal to the bridge and would not affect the bridge voltage output. In most physically realized devices, the bridge is not exactly balanced. Therefore, the power supply noise contribution to the noise scales with the bridge offset voltage output normalized by the bias voltage. Device Junction Isolation One design issue is the difficulty of realizing a junctionisolated, laterally diffused resistor in the sidewall of a tether. As shown in Figure 316, the ptype piezoresistor (with resistance Rs), the p++ interconnects (with resistance R,) and the ntype substrate form a p/n diode. For an ideal p/n diode, the leakage current is negligible in the reverse bias region [76]. When the reverse voltage exceeds a certain value, the reverse current will increase rapidly and the diode will breakdown. To ensure the current flows exclusively through the ptype regions, the p/n junction must be reversebiased for all possible bias voltages along the entire length of the piezoresistor and interconnect. This section addressed design issues associated with this design constramnt. Two issues must be taken into account in the design: (1) maintaining junction isolation and (2) avoiding p/n junction breakdown while achieving the desired piezoresistor sensitivity. When a voltage is applied between the two p++ interconnects, the p/n junction voltage varies linearly with position due to a linear voltage drop across a distributed resistance. For junction isolation, the p/n junction must be reversebiased at all spatial locations. Under reverse bias, a p/n junction develops a space charge layer due to the depletion of carriers [76]. In order to maintain electrical isolation, it is necessary to ensure that the space charge layers for adjacent ptype regions extending into the ntype substrate do not overlap or 'punchthrough'. The space charge layers punchthrough will cause the corresponding p regions to become shorted, resulting in a nonfunctional device. Assuming uniform doping, the acceptor concentration in the p region is assumed to be N and the donor concentration in the n region is assumed to be ND The space charge layer widths on the pside (x,) and nside (x,,) are given as a function of the junction voltage V~ [76], xE, ((() = t i, ) (3 45) ql N (N +ND) and x, (P)= St, A Fi, ), (346) ql ND 4+ND ) where E,1 = 1.045 x 10' F/cm is the silicon permittivity, and the intrinsic number of electrons is n, = 10'0 /cm3 in Silicon at room temperature. The builtin voltage is given as k In N~N(347) In order to electrically isolate the p++ regions, the entire length of the p/n junction must be reversebiased (~ < 0) The space charge layer width in the p and n region, x, and x~,, respectively, increases with reverse bias. The total space charge width on the n side is given by W(y) = x, (()+ x, ((? +? )) (348) If the total space charge layer width on the n side, W (V increases to the width between the piezoresistor and the p++ interconnect, L,, or to the width between the p++ interconnects, L, , the space charge layers will punchthrough, causing the corresponding p regions to be shorted. To avoid punchthrough, W V ) < Additionally, lateral diffusion that occurs during high temperature process steps, leading to an increase in the actual width of the ptype region compared to the designed width, must be taken into account. Therefore, the total isolation width is approximated by V12L=z,+x V1)+x (r V+V1 (349) where Ld is the lateral diffusion width estimated from the net effect of high temperature process time on the diffusion length (thermal budget) [77]. The total thermal budget (Dt)mt is equal to the sum of the diffusion x time, Dt products for all high temperature cycles affecting the lateral diffusion, (Dt),, = D~t where D, and t, are the diffusion coefficient and time associated with each processing step. In this design, the doping profie is nonuniform, and the acceptor concentration in the p region N ,(y) and the donor concentration in the n region ND f) Vary with depth, as shown in Figure 317. The nonuniform doping profies are obtained by FLOOPS" simulation [78], where sidewall boron implantation in amorphosized silicon is simulated by SRIM [79] and then imported to FLOOPS ". The crosssectional view of the isolation width for a doping profile at a bias voltage of 10 V is shown in Figure 318 and Figure 319, which are associated with the AA and BB cuts shown in Figure 320. The dimensions of the tether width W the sidewall implanted piezoresistor depth L4, the p++ interconnect width L3, and the space parameters, L,, L2 and L, are listed in Table 36 for the actual device. There is a tradeoff between the p++ interconnect widths, L3 and L4 and the punch through width L,. A large value of L3 and L4 is desired to reduce the lead resistance. The resulting narrow gap, L,, may cause p/n junction punchthrough. On the edge of the tethers, the p++ interconnects are tilted 24 degrees from the tether centerline to increase the isolation gap spacing. For the worst case, V, = 10 V at left and 0 V on the right, as shown in Figure 320, there is about 9 Cpm between adjacent p++ interconnects assuming a lateral diffusion of ~ 1.1 pm Meanwhile, a crossover between the piezoresistor and p++ interconnects must be avoided. As shown in Figure 319, the space charge layer of the piezoresistor in the nwell increases as the depth increases. If the space between the piezoresistor and the p++ interconnect is too close, there will be crossover and the pregion will punch through. A top view of the isolation width is shown in Figure 320. The blue region is the tether, the cyan region is the p++ interconnects, the green region is the piezoresistor, and the pink line is the final isolation width considering lateral diffusion and space charge diffusion to the nwell at V, = 10 V (worst case). In order to minimize the space charge width in the nwell, one can increase the doping concentration of the nwell, ND There is, however, a tradeoff between increased nwell doping concentration and reduced reverse breakdown voltage. With increasing doping, the internal electric field increases and the reverse junction breakdown voltage decreases [80, 81]. The breakdown voltage decreases from ~ 50 V to ~ 10 V when the impurity concentration increases from 1.0 x1016 3" to 1.0 x10 cm3 The curvature of the tether corner and the curvature of the junction regions must also be considered. A sharp corner dramatically increases the mechanical stress, which could lead to possible failure of the materials [82]. Additionally, a sharp corner in the p/n junction may increase the local electric field and decrease the breakdown voltage [83]. Thus, the corner is rounded. The stress concentration factor, K, depends on the fillet radius for a given thickness [82] and is relatively high when the ratio of the fillet radius and tether width is less than 0.5. In this design, K is chosen as 0.9. In addition, 4 slots in the substrate near the edge of each tether are designed to relieve stress concentrations that arise during fabrication [51]. In order to avoid these issues, a metal contact design is employed, where the metal lines run on the top of the tethers to connect either side of the laterally implanted piezoresistors, as shown in Figure 321. Because there are two 50 Cpm deep trenches on both sides of the tether for tether release, the fabrication process of this design is very challenging and is discussed in detail in Chapter 5. Summary Electromechanical modeling of a sideimplanted piezoresistive floating element shear stress sensor has been developed for aerospace applications. Two Wheatstone bridges are employed, an active bridge for shear stress sensing and a dummy bridge for temperature compensation. The predicted sensitivity, noise floor, dynamic range and MDS have been modeled and verified by FEA. To accurately resolve the fluctuating shear stress in a turbulent boundary layer, the shear stress sensor is desired to possess a small size, large usable bandwidth and a low MDS. MDS depends on the geometry of sensors and piezoresistors, dopant profile, process parameters, and sensor excitation. To achieve a low MDS, it is favorable to maximize sensitivity and minimize noise. However, there are tradeoffs between sensitivity and noise floor. It is necessary to perform design optimization to balance these conflicting requirements. Additionally, the sensor design is constrained by temporal and spatial resolution requirements as well as structural limits. The detailed optimization is discussed in Chapter 4. Table 31. Material properties [53] and geometry parameters used for model validation. Density of silicon ps dkg/m3) 2330 Young's modulus in [110] orientation E(GPa) 168 Poisson ratio v 0.27 Lemooungth of ehesLm 400 Thickness of the tethers 7(Clm) 3 Width of the tethers W (pmn) 4 Length of the square floating element Le (pm) 150 Table 32. Resonant frequency and effective mass predicted by LEM and FEA for the representative structure given in Table 31. Frequency (k FEA 12.47 1.72e10 Table 33. First 6 modes and effective mass predicted by FEA for the representative structure given in Table 31. Mode Domain Frequency~ (kd~z) Effective Mass (kg) 1 12.47 translationall in z direction) 1.72e10 2 17.08 translationall in y direction) 1.74e10 3 34.95 (rocking mode about x axis) 6.82e10 4 162.33 (rocking mode about y axis) 18e1 5 170.11 (rocking mode about z axis) 1.84e11 6 219.50 translationall in x direction) 1.70e11 Table 34. Piezoresistive coefficients for ntype and ptype silicon [53]. 4i, (10"Pa ') 42~ (10"Pa ') F4 1P ntype 102.2 53.4 13.6 ptype 6.6 1.1 138.1 Table 35. Piezoresistive coefficients for ntype and ptype silicon in the <110> direction [53]. gil(* 10"Pa') (0P) ntype 31.2 17.6 ptype 71.8 66.3 Table 36. Space parameter dimensions for junction isolation. W L, L2 L3 L4 L, 30 Cpm 9 Cpm 13.6 Cpm 15 Cpm 1 Cpm 33 Cpm Figure 31. Schematic top view of the structure of a piezoresistive floating element sensor. ,i Lt C Le Lt Tether Floating Element y~ PQ 0 xWt ~Tt a 2Lt Figure 32. The simplified clampedclamped beam model of the floating element structure. k=1/Cme Mme Rd Cme F U rF (a) (b) Figure 33. Lumped element model of a floating element sensor: (a) springmassdashpot system (mechanical) and (b) equivalent electrical LCR circuit. 0.07 0.0 0.5 0.03 0.02 0.01 9 FEA No~riiear Aralytical O.4 0.6 I~Nortlized Tethe~r Lengthx/Lt Figure 34. Representative results of displacement of tethers for the representative structure given in Table 31 at r, = 5 Pa . 40 60 Wall Shear~ Stress w (Pa) Figure 35. Representative loaddeflection characteristics of analytical models and FEA for the representative structure given in Table 31 and r = 5 Pa . El FEA 0.5 ' Linear Analytical 0.5 1 0 0.2 0.4 0.6 0.8 1 Normaolized Tether Isngth x/Lt Figure 36. Verification of the analytically predicted stress profile (Equation (36)) with FEA results for the representative structure of Table 31 and r, = 5 Pa . Translational in z direction Translational in y direction Rocking mode about x axis Rocking mode about y axis Rocking mode about z axis Translational in x direction Figure 37. The mode shape for the representative structure of Table 31 and r, = 5 Pa . Figure 38. Geometry used in computation of Euler' s angles [59]. 88010 <110> 1 240 300 270 Figure 39. Polar dependence of piezoresistive coefficients for ptype silicon in the (100) plane. S1.58009 60 0 300 Figure 310. Polar dependence of piezoresistive coefficients for ntype silicon in the (100) plane.  Ian~da  fHnrley 0.9 0.8 0 0.75 0.65 17 18 10 10 Boron Cbnlcentation (cm 3) 20 10 Figure 311. Piezoresistive factor as 300K [47]. a function of impurity concentration for p type silicon at 996 Tether iezoresistor End Cap Td dxj Wt Figure 312. Schematic illustrating the relevant geometric parameters for piezoresistor sensitivity calculations. Flow Tether Floating Element J R4 Compression Tension R2~~  Tension Compression Figure 313. Schematic representative of a deflected sideimplanted piezoresistive shear stress sensor and corresponding resistance changes in Wheatstone bridge. /I, (a) (b) Figure 314. Wheatstone bridge subjected to crossaxis acceleration (a) and pressure (b). ~Circuit for Offset Comp. SR560 Pre Amp Piezoresistive Iv tIH~O Bridge VBH390 Circuit for Offset Comp. SR560 Compensation Pre Amp Bridge 1V8 ;, HP34970ADM Figure 315. Schematic of the doublebridge temperature compensation configuration. End Cap Piezoresistor (p ) Figure 316. Top view schematic of the sideimplanted piezoresistor and p++ interconnect in an nwell (a) and equivalent electric circuit indicating that the sensor and leads are junction isolated (b). 25 * Pf interconnect  piezoresistor ,c~ t1 15,, 10  10t 10l 0.5 1 1.5 2 Deptl~um) Figure 317. Doping profile ofnwell, simulation. p++ interconnect, and piezoresistor using FLOOPS 0.8 1.6 O 5 10 15 20 Isolation Width (Cun) Figure 318. Cross view of isolation width between p++ interconnects (AA cutinFeiguore 320). in igre3O ) Figure 320. Top view of the isolation widths on a sensor tether. p++\ Piezotirei stor 4 Tether nwell Bond Pads AlSi( 1%) Figure 321. Top view schematic of the sideimplanted piezoresistor with a metal line contact. CHAPTER 4 DEVICE OPTIMIZATION This chapter presents the nonlinearly constrained design optimization of a micromachined floating element piezoresistive shear stress sensor. First, the problem formulation is discussed, including the objective function and constraints based on flow conditions. Next, the optimization methodology is outlined. The optimization results are then presented and discussed. Finally, a postoptimization sensitivity analysis of the objective function is performed. Problem Formulation The objective function is selected based on tradeoffs identified between the sensitivity and noise floor of the shear stress sensor. The constraints are formed due to physical bounds, manufacturing limits and operational requirements [84], and are dependent on the flow conditions of the desired applications. The obj ective function and constraints are functions of the design variables, including the geometry of the floating element structure and the piezoresistors, the surface doping concentration, and sensor excitation. The detailed discussion of the design variables chosen is presented in next subsection. Design Variables The obj ective function and constraints depend on geometry of sensors structures and piezoresistors, process related parameters, and sensor operational parameters. The geometry parameters include tether length L,, tether width W, tether thickness, 7(, floating element length Le, and piezoresistor lengthLr, piezoresistor width W The process related parameters include piezoresistor surface concentration Ns and junction depth yJ (assuming a uniform doping profile). The sensor operational parameter is the supplied bias voltage. The geometry parameters of the sensor structure determine the mechanical characteristics of the sensor, such as sensitivity, linearity and bandwidth. Design issues related to the tether width ( and tether thickness 7( are addressed here. As discussed in Chapter 3, the minimum tether width W, is set to 30 Cpm to avoid p/n junction punch through. The tether thickness must be larger than the tether width to ensure that the crossaxis resonant frequency is larger than the inplane resonant frequency. As shown in the representative structure in Table 31, the first mode is out of plane due to the tether thickness larger than the tether width. The increases in tether thickness results in bending stress decreases (Equation (36)), and thus sensitivity decreases (Equation (323)). On the other hand, the piezoresistor related parameters, such as piezoresistor length Ly piezoresistor width W,, and p/n junction depth y, and surface concentration Ns, are related to noise floor and sensitivity. For each design optimization, different tether thickness, junction depth and tether width may be achieved, but all designs are fabricated in one wafer due to economic constraints. Thus these parameters for each design must be set to the same value. In this research, the tether thickness is set to 50 Cpm considering the sensitivity of the shear stress sensor and SOI wafer availability. Due to the rough sidewall surface near the buried oxide layer after DRIE process and no passivation on the bottom of the tethers after final release, the high 1/ f noise and current leakage became issues in the piezoresistor design [85]. Partridge et al.[51] investigated the accelerators with piezoresistors implanted in the top 15 Cpm (total thickness), 5 Cpm, 3 Cpm of the flexures, and found that 3 Cpm case has large sensitivity and low 1/ f noise. In this research, piezoresistor width W,= 5 Cpm is chosen to avoid current leakage while maintaining high performance. A junction depth of y, = 1 Cpm is chosen taking account the piezoresistor and p++ interconnection and the manufacturing constraint. In summary, six design variables are included in the optimization design, and they are tether length L,, tether width W, floating element length Le, and piezoresistor length L , piezoresistor surface doping concentration Ns and bias voltage V, . Objective Function As stated in Chapter 1, to accurately recognize the fluctuating wall shear stress in the turbulent boundary layer, the measurement device must possess sufficiently high spatial and temporal resolution as well as a low MDS, which is defined as the ratio of noise floor to the sensitivity. Therefore, lowering the noise floor and increasing sensitivity are favorable in shear stress sensor design to achieve a low MDS [84]. Some parameters, such as junction depth, surface doping concentration and bias voltage, affect both sensitivity and noise floor creating tradeoffs between these performance parameters. The following discusses the tradeoffs in sensitivity and noise floor and the arrival at the MDS as the obj ective function of the optimization. Junction depth, y, and surface doping concentration, Ns, are two major factors involved in processing that affect sensitivity and noise floor. As discussed in chapter 3, changes in Ns while keeping y, constant invoke tradeoffs between noise and sensitivity. If Ns increases, the resistivity of the piezoresistor decreases and the total carrier number increases. This leads to the reduction of thermal noise and 1/ f noise. Conversely, sensitivity decreases due to the reduction of the piezoresistive coefficient Fr, from high doping concentration (Equation (323)). The bias voltage V, also affects both sensitivity and noise floor. As V, increases, the sensitivity increases (Equation (335)) because the output voltage is directly proportional to the bias voltage. The voltage noise contribution from 1/ f noise also increases squarely as indicated by Equation (33 8). By establishing the MDS as the obj ective function, a balance between noise floor and sensitivity is achieved. Previous researchers have investigated the potential and methods in piezoresistive sensor optimization. Harley and Kenny [47] presented an informal graphical design optimization guidelines in the form of design charts by varying the dimensions of the cantilever, the geometry of the piezoresistor, doping level, and process issues related to sensitivity and noise floor. Papila et al. [84] performed a piezoresistive microphone Pareto design optimization, in which the tradeoff between pressure sensitivity and electronic noise is investigated. The Pareto curve indicated that the MDS in units of pressure is the appropriate parameter for performance optimization. Constraints The constraints are determined by physical bounds, fabrication limits and performance requirements [84]. The constraints used in this optimization and their associated physical explanations are listed below: * Piezoresistor geometry: Ly /Lt <0.4, as discussed in Chapter 3, stress changes sign at the longitudinal center of the tether (shown in Figure 36). Thus, the sensitivity will be reduced if the length of the piezoresistor is larger than L,/2. As a result, the maximum piezoresistor length is limited to 40% of the tether length * Resistance: R,/4 > 3, represents a balance between the sensor resistance R, being 3 times larger than the interconnect resistance R, but small enough to minimize electromagnetic interference (EMI). * Frequency: f, > f ,, puts a bandwidth constraint in the design. The constraint changes with flow conditions. * Power consumption: Pgh <; 0.1, where P,. = V/2/(Rs + RL ) When P,.M increases to a large value, the temperature of the piezoresistor will increase due to Joule heating resulting in voltage drift and eventually electromigration. * Nonlinearity: A, AL /A, <3%, device linearity is required to keep spectral fidelity for timeresolved measurements. * Inplane resonant frequency: 7( > W To avoid disturbing the flow at the sensor resonance, the tether thickness T, is required to be larger than tether width W, to ensure the onset of the inplane resonant frequency occurs before the out of plane. In this dissertation, the minimum tether width is 30 p~m and its upper bound is set to 40 p~m ,thus the tether thickness is set to 50 p~m. * Lower bounds (LB) and upper bounds (UB): LBR t (L,,, W W ;, LN, V,~) I UB, present the limitation of the design variables. LB and UB are given in Table 42 based on the candidate shear stress design specifications and design issues related to fabrication. In summary, both the obj ective function and constraints are nonlinear. Therefore, the optimal performance design deals with solving the constrained nonlinear optimization problem. Candidate Flows Several sensor specifications associated with various flow phenomena, ranging from low speed flow to supersonic and hypersonic flow, are listed in Table 41. Here rmax is the maximum shear stress to be measured and constrained by nonlinearity, fmin is the minimum resonant frequency to provide adequate temporal resolution and Lemax is the maximum floating element size that determines the lowest tolerable spatial resolution, Wmin is the minimum tether width that is limited by the junction isolation, and 7( is the minimum thickness that is constrained by the inplane resonant frequency. The temporal and spatial resolution fmm, and Lemax are chosen to approach the Kolmogorov time and length scales, but are sufficiently conservative to yield a proof of concept device. Methodology The design problem is formulated to find the optimum dimensions of the floating element and tethers, geometry and surface doping concentration of piezoresistors, and bias voltage for each candidate flow. Mathematically, the optimization seeks to minimize the MDS subj ect to constraints. The key points regarding the optimization of the minimum detectable shear stress, rmn, are summarized below: Design variables: L,, Wt, We, Lr, V, and Ns Objective function: minimize F(X)= Zrmn, where X is the design variable vector. Constraints : g, = L,/(0.4L,)1<0 O; g2 nu r~f 1<; 0; g3 = 1Rs,/3RL~ <; g4 =10V,2/(R + RL) 1<0; g, = 16, 6L/0.036, 1<~0; g = LB /x, 1<0, i =6,8,...,11; g =x,/ UB 1< 0,j= 12, 13...17. where xl = L,, W,, W, L,, Ns and V, Since the magnitudes of design variables differ by several order of magnitude (Table 42), all variables are nondimensionalized to avoid singularities in the program. This nonlinear constrained optimization is implemented using the function fmincon in MATLAB" (2006b) [86] optimization Toolbox, which employs sequential quadratic programming (SQP) for nonlinear constrained problems and calculates the gradients by finite difference method. The optimum value of Ns for different designs might be different. All designs, however, are fabricated on one wafer. Therefore, surface concentration, Ns, for all designs must be set to the same value. In this dissertation, the optimal Ns for first three cases were the same and is Ns=7.7 x1019 3". This value was chosen as the surface concentration for all designs. The optimization was reimplemented using this fixed concentration following the same steps described above. The SQP method is a local optimizer and is highly dependent on the initial value. The initial designs are selected randomly, and a number of local optimum solutions from different initial designs were obtained. The solution identifies one best design points as the optimal solution. A global optimization algorithm using particle swarms [87] is also employed to investigate the possibility of improving the optimum solutions. It is found that global optimization solution is very similar to the optimization results obtained by fmincon function. The global optimization results have a large computational cost. Optimization Results and Discussion In the optimization, the doping profile is assumed to be uniform to simplify the modeling. The Gaussian profile is more accurate than a uniform profile, but it is not employed in this research to avoid computational cost. The doping concentration for p++ interconnect is achieved as 2.0x1020 3, With a junction depth of 1 Cpm for all designs. In this research, the material properties of silicon is fixed. The resulting optimization design is shown in Table 43. The highlights are active constraints. Since the low resistance results in low thermal noise, but the power dissipation increases. Therefore, the power constraint is always active (close for case 9). For each device, the dynamic range from the optimum design is in excess of 75 dB. KuhnTucker conditions [88] are conducted to check the optimality and active constraints, which are stated as follows: *Lagrange multipliers 1, are nonnegative, and satisfy equation (41) dF n = i=1,2...m, (41) where ng is the total number of constraints, and m is the total number of design variables. Lagrange multipliers S are obtained by the fmincon M~ATLAB function. * The corresponding 1, is zero if a constraint is not active. The active constraints for each case are indicated in bold font in Table 43. Once the optimum design for uniform doping is obtained, nonuniform doping profies are applied to achieve the Einal performance of the sensor. The optimization flow chart is shown in Figure 41. The nonuniform doping profies are obtained by FLOOPS simulation [26], where sidewall boron implantation to amorphous silicon is simulated by SRIM simulation [79] and imported to FLOOPS. The surface concentration of the piezoresistor, the piezoresistive interconnection, and nwell are achieved to 7.7 x1019 3 2.0 x1020 cm and 7 x1016 3" respectively, as shown in Figure 317. The results indicate that nonuniform doping profies yield approximately a 5 dB decrease in dynamic range. Therefore, implementing a Gaussian profile as part of the optimization would result in a more accurate model and thus optimal design. Sensitivity Analysis Due to parameter uncertainty caused by process, ra~n may achieve different values than theoretical optimization. The sensitivity analysis is implemented to understand sensitivity of MDS to the variations of the design variables, constraints, and Eixed parameters at the optimum design. Therefore, sensitivity analysis is a postoptimization step, which involves two parts: * Sensitivity of the obj ective function to design variables at the optimum design. * Sensitivity of the obj ective functions to the Eixed parameters at the optimum design, where the effect of a change in the active constraints on the obj ective function is taken into account. For the sensitivity analysis with respect to the design variables, logarithmic derivative [88] is employed to measure the sensitivity of MDS to uncertainty of design parameters at the optimum design, 8 log (zrs., r,, x (42) dlog(xl) Dx~ Zrm where x = L,,W, We,L,, and N, . For the sensitivity analysis with respect to the fixed parameters, equation (42) is invalid if the nonlinear inequality constraints are active. Lagrange multipliers based on the KuhnTucker conditions [88] is employed to calculate the sensitivity of the optimal solution to the fixed parameters. Assuming that the objective function and the constraints depend on a fixed parameter p, so that the optimization problem is defines as, minimize F (X, p) (43) such that g, (X, p?) > 0 j=1,2... 17. The gradient of F with respect to p is given as [88], dF F; dg, Ar a (44) dp dp dp where go denotes the active constraint functions and go = 0 from KuhnTucker conditions. The equation (44) indicates that the Lagrange multipliers are a measure of the effect of a change of the constraints to the objective function. Lagrange multipliers Ai = 0 for active constraints, otherwise it is obtained by A = N'N IN' VF (45) where N and VF are defined as dg~ N= ,j=1,2...17, i=1,2...6 (46) drx' 8F and VF i=1,2...6 (47) The sensitivity of rmin to uncertainty of the fixed parameters is given as 8% in % ril P (48) dp/ p dp dp rm ii can be obtained from the output of fmnincon function directly. The fixed parameters are p = yJ,Wr,T,, Ns For case 1, power is the active inequality constraint, and the associated Lagrange multiplier, Ai = 0.0026179, is obtained from MATLAB calculation. Therefore, Equation (42) is employed to calculate the sensitivity of MDS to uncertainty of design parameters (L,, W,, We, Lr and V,) at the optimum design. Equation (48) is employed for the fixed parameters (y ,, Wr, 7( and Ns). Figure 41 shows the sensitivity of ran to uncertainty of the design variables and fixed parameters for case 1, i.e., 10% change of the tether width causes 19% change of the minimum detectable shear stress. It is illustrated that r, is sensitive to variation of tether width, W,, tether length, L,, floating element width, We, and junction depth, yJ The MDS is less sensitive to variation of piezoresistor length Lr. In summary, rmin is very sensitive to uncertainties of tether and element dimensions, junction depth and width of the piezoresistors, and less sensitive to uncertainties of piezoresistor length. Summary This section described the choice of objective function and associated constraints. The optimization has been implemented for nine designs, from low Reynolds number flow to supersonic and hypersonic flow. The optimization results indicate that the dynamic range exceeds 75 dB for all designs based on a uniform doping profile. Accounting for nonuniform doping profile results in a 5 dB decrease in dynamic range. The sensitivity analysis indicates that the MDS is very sensitive to uncertainties of tether and element dimensions, junction depth and width of the piezoresistors, and less sensitivity to uncertainties of piezoresistor length. Table 41. The candidate shear stress sensor specifications. Low Speed Supersonic, High Re Hypersonic, Underwater Deic 1 2 3 4 5 6 7 8 9 tmax (Pa) 5 5 5 50 50 100 100 500 500 .fmn (k~Hz) 5 5 10 10 50 50 100 100 200 Lema (pLm) 1000 1500 1000 1000 1000 1000 500 500 500 Wan(p) 30 30 30 30 30 30 30 30 30 7;(pm) 50 50 50 50 50 50 50 50 50 Table 42. Upper and lower bounds associated with the specifications in Table 41. Design Variables and LB UB Flow Description L (gmn) W, (gm) L (gmn) L, (gmt) Vi, (V) Ns (cm3 min (Pa) fmin(kHz) 1100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 5 5 2 100 1000 30 40 100 1500 50 400 5 10 5e+18 2e+20 5 5 3 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 5 10 4 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 50 10 5 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 50 50 6 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 100 50 7 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 100 100 8 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 500 100 9 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 500 200 Table 43. Optimization results for the cases specified in Table 41 (bold for active constraints). Parameter Casel1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 max (Pa) L, (p~m) 0' (pm) w' (p~m) L, (p~m) VB (V) f (kHz) Rs (R) RL (2) 5 1000 30 1000 228.5 10 0.1 9.8 851 149 5 1000 30 1500 228.5 10 0.1 6.60 851 149 5 1000 30 983.5 228.5 10 0.1 10 851 149 50 991.2 30 996.1 228.5 10 0.1 10 851 149 3.58e5 21.1 0.33 103.7 50 100 100 500 500 343.6 348.7 308.8 500.4 500 30 30.7 30 30 30 1000 993.3 499.1 250.2 100 98.8 99.9 88.6 126.8 117.7 6.8 6.8 6.5 7.6 6.0 0.1 0.1 0.1 0.1 0.07 50.53 50.01 130.15 104.07 231.11 368 372 330 470 438 94 94 89 105 102 6.64e6 6.40e6 1.47e6 1.13e6 4.20e7 11.0 10.97 10.95 11.19 9.54 1.66 1.72 7.44 9.88 2.28e2 89.6 95.3 82.6 94.1 86.8 S,, (V/Pa) 3.65e5 7.92e5 3.54e5 V, (nV) 21.1 21.1 21.1 rmn (mPa) 0.58 0.27 0.60 DR (dB) 78.7 85.4 78.5 Figure 41. Flow chart of design optimization of the piezoresistive shear stress sensor. Lt Wt We Tt VB Ns yj Wr Lr Figure 42. Logarithmic derivative of objective function r, with respect to parameters (Casel). MDS (Uniform Doping) FLOOPS Simulation (nonuniform doping) Final MDS CHAPTER 5 FABRICATION AND PACKAGINTG The fabrication process and packaging of the sideimplanted piezoresistive shear stress sensor are presented in this chapter, with the aid of masks and schematic cross section drawings. A detailed process flow is given in Appendix C, which lists all the process parameters, equipment and labs for each step. The detailed packaging approach for wind tunnel testing is also presented. Fabrication Overview and Challenges The first generation of the shear stress sensor is fabricated in an 8mask, silicon bulk micromachining process. All the masks are generated using AutoCAD" 2002 and manufactured in Photo Sciences, Inc (PSI). It is described in detail in the following sections. Some challenges in this process are addressed before starting the process flow: * Sideimplanted piezoresistors: boron is side implanted into the silicon tethers to form the piezoresistors with an oblique angle of 54o normal to the top surface. The traditional piezoresistor is formed by top implantation. The doping profile for sideimplantation is simulated via FLOOPS, and the accuracy of the profile needs to be judged only after device testing. * Trench filling: 50Cpmdeep trenches were etched on the top surface to define the tethers. Trench filling is required to obtain good photoresist coverage before subsequent deposition and patterning of the metallization layer. * Junction isolation: the space between piezoresistors and p++ interconnects should be larger than the isolation width to avoid p/n punch through, as discussed in chapter 3. Fabrication Process The fabrication process starts with a 100mm (100) silicononinsulator (SOI) wafer with a 50Cpmthick 1~5 Rcm ntype silicon device layer above a 1.5Cpmthick buried silicon dioxide (BOX) layer. The corresponding background doping concentration is from 2.5 x10 cm3 to 5 x 1014 3" The total wafer thickness is 450 Cpm A brief overview of the process is as follows. The four sideimplanted piezoresistors are first formed by boron oblique implantation. The structure of the sensor is then defined by DRIE Si etch. Thermal dry oxide is grown for high quality passivation. AlSi (1%) is deposited and patterned to form the bond pads. PECVD nitride is deposited as a moisture barrier layer. Finally, the structure is released from the backside via DRIE Si and RIE of the oxide and nitride. The process flow is broken down into 8 maj or steps as follows: a. The nwell formation: the fabrication begins with the formation of the nwell by a phosphorus blanket implantation (Figure 51 (2)). An energy of 150 keV and a dose of 4.0 x10' cm2 are used to achieve a surface concentration of 6.5 x10 cm3 to control the space charge layer thickness of the reversebiased p/n junctionisolated piezoresistors. b. Reverse bias contact: a 100 nm thin oxide layer is then deposited via plasmaenhanced chemical vapor deposition (PECVD) and patterned, then etched via buffered oxide etch (BOE) in preparation of the reversebias contact implant. This step also creates alignment marks on the top surface. Phosphorus is then implanted with energy of 80 keV and dose of 9.0 x1013 m2 to achieve a n++ region with a surface concentration of 1.8 x10 cm3 (Figure 51 (4)). The device is then annealed at 1000 oC for 450 minutes to drivein the inpurities. c. Piezoresistor interconnects: the oxide is selectively removed by BOE. Then, a twostep Ge preamorphization implant is performed to minimize the effect of random channeling tail caused by the subsequent highdose boron implantation [66], which provides a heavily doped Ohmic body contact. The preamorphization implant energies are 160 keV and 50 keV, respectively, and a dose of 10 cm 2. This preamorphization is to ensure no more than 2% of the implanted boron dose penetrates into the substrate [89]. Then boron is implanted into the silicon with a dose of 1.2 x 10' cm2 and an energy of 50 keV to provide Ohmic contacts (Figure 51 (5)). The resulting surface concentration and junction depth, xJ while taking into account the thermal budget of the entire process, are simulated by FLOOPS to be 1.96 x 1020 3" and 1 pm , respectively. The interconnect region begins from the edge of the tether and distributes symmetrically along the centerline of the tethers to minimize the sensitivity error, with a larger width on the end cap to decrease the resistance. The FLOOPS simulation file is given in Appendix D. d. "Nested" mask release: a 1 Cpm oxide layer is deposited via PECVD and patterned via reactive ion etch (RIE) [90] to serve as a nested mask for the deep reactive ion etch (DRIE) [91] that defines the tethers and floating element (Figure 51 (7)). New alignment marks are also created in this step. e. Side wall etch and side wall implantation: the wafers are then patterned using the mask SIM (Figure 51 (8)). To ensure good contact between the piezoresistor and the p++ interconnect, the SIM mask has a 4 Cpm overlap with the p++ interconnect on the edge of the tether, 10 Cpm overlap with the p++ interconnect on the end cap, and 4 Cpm overlap with sidewall. Prior to DRIE, the native oxide or oxide residues are etched via BOE about one minute. The Si is then etched vertically to approximately 8 Cpm deep by DRIE to form the trenches for the sidewall oblique implant, as shown in Figure 52 (scanning electron microscope (SEM) top view). The trench width is set to (5 +1.1 Clm) x tan (54' )=8.5 pm to achieve a 5 pLm implant, where 54" is the implant tilt angle from the normal axis, and 1.1 Cpm is the thickness of the oxide layer. The sidewall implantation is restricted on the top 5 Cpm to ensure the silicon surface on which the boron implanted is smooth and avoid forming the current leakage path on the bottom [85]. This can reduce the 1/ f noise at low frequency [85]. The basic recipes on STS DRIE system and Unaxis RIE systems are shown in Appendix E. The extruded oxide resulting from the DRIE is etched via BOE (6:1) for one minute, as shown via the scanning electron microscope image in Figure 53. This avoids the protruded oxide blocking the implant dosage to the side wall. Hydrogen annealing (1000"C, 10 mTorr for 5 minutes) [92] is performed to smooth the scallops on the sidewalls that arise from the DRIE process, which will improve the noise floor [25]. A 0. 1 Cpm oxide layer is thermally grown as a thin implant oxide layer on the sidewall, which must be accounted for in the thermal budget. After a twostep Germanium preamorphization implant, boron is then implanted with an energy of 50 keV, a dose of 2x 1016 m2 (two times of the simulation dose to compensate the solubility loss at high dosage) and an oblique angle of 54o to achieve a 5 Cpm shadow side wall implantation (shown in Figure 51 (9)). f. Tether definition: the oxide on the trench bottom is then etched via DRIE while the oxide on the sidewall is left to protect the doped sidewall, as shown in Figure 54. This is a time controlled process: an overetch will expose silicon on the edge of the sidewall of the tether (Figure 55), while an underetch will create a "silicon grass" effect [93] after the subsequent DRIE silicon etch due to the oxide residues that acts as a micromask (Figure 56). The channels/trenches are then etched via DRIE with the BOX as an etch stop, as shown in Figure 5 7 (note the rough surface is caused by the dicing saw). The tether sidewall oxide is then etched for two minutes by BOE (6:1). Subsequently, the wafers are annealed at 1000" C for 60 min to drive in the boron to form the piezoresistors. A 0. 1 Cpm thin dry oxide layer was thermally grown at 975" C as an electrical passivation layer. The temperature 975" C is selected to avoid excessive diffusion and excessive compressive stress when the temperature is below 950" C [94]. Meanwhile, the boron is segregated into the oxide from the silicon. g. Metallization and nitride passivation: since there are 50Cpmdeep trenches on the wafer for tether release, it is necessary to fill the trench to achieve good photoresist coverage before subsequent wafer patterning. A twostep trench filling process is performed as follows: first, a thin layer of photoresist AZ 1512 is coated and soft baked, then a thick photoresist AZ9260 is coated and soft baked; second, the wafer is flood exposed for 300 seconds and developed using developer AZ400 until the surface is clear. Thus, the trench can be reduced from 50 Cpm to only 5~6 Cpm deep if following the above process once or twice. After filling the trenches with photoresist, the oxide is patterned and then etched via BOE (6: 1) to open contact vias for Al sputtering. This step is very critical for the quality of the metal contact. Since the boron laden silicon dioxide etches much slower than the standard oxide etching (1000 A min ), an over etch is required to remove all oxide to ensure an Ohmic contact. Any residual oxide left over will result in Schottky diode effect. A 1ymthick layer of AlSi (1%) is sputtered and patterned via RIE to form the metal interconnects (Figure 51 (12)). A 200nmthick, lowstress silicon nitride layer is deposited via PECVD to from a protective moisture barrier. The bond pads are exposed by patterning and plasma etching the silicon nitride via RIE. h. Backside release: to protect the device, the front side of the wafer is coated with a 10 Cpmthick photoresist layer. The wafers are then patterned from the backside using fronttoback alignment. The structure is released from the backside using DRIE up to the BOX layer (Figure 51 (14)), along with an oxide and nitride etch using RIE (Figure 51 (15)). Finally, a post metallization anneal is performed in forming gas (4% H2, 96% N2 ) at 450"C for 1 hour [95]. This annealing allows the aluminum to react with the native oxide to remove the tunneling oxide, and allow the hydrogen to passivate the interface traps. This improves the contact resistance and reduces the electrical noise floor [25]. The fabricated device is shown in Figure 58 and the close view of the piezoresistors is shown in Figure 59. The trenches between each device were patterned and created during back side release, thus the die can be easily separated by tweezers. Sensor Packaging for Wind Tunnel Testing After fabrication, the individual die (6.2 mmx6.2 mm) were then packaged in a custom printed circuit board (PCB) (20 mmx20 mm) designed for modularity. The PCB layout was performed using Protel and was manufactured by a commercial vendor, Sierra Proto Express. The MEMS device die and PCB were then packaged by Engent Inc. The MEMS die are flush mounted into a machined cavity in the PCB and sealed with epoxy at the perimeter. The aluminum bond pads are then bonded to gold pads on the PCB. Subsequent to the bonding process, the wire bonds are covered by nonconductive epoxy to protect the wire bonds from the gas flow in the calibration wind tunnel or flow cell. The roughness of the epoxy is less than 300 Cpm and is located (3.2 mm ) downstream of the sensing element to mitigate flow disturbances. The PCB package is then flushmounted into a Lucite package, which in turn is flush mounted in an aluminum plate to minimize flow disturbance. Figure 510 shows the PCB embedded in the Lucite package. Copper wires (gauge 26) pass from underneath up through the vias in the PCB and are soldered to PCB via rings. The wire is reinforced by the glue on the backside of the Lucite package. An interface circuit board was designed for offset compensation and signal amplification, as shown in Figure 511. This board includes two sets of compensation circuitry: one for active bridge, another for dummy bridge. Each circuit has two amplifying stages: the first stage is used to null the amplified offset, and the second stage is to amplify the compensated signal. The detailed description of the interface circuit for offset compensation is given in Chapter 6. This board is attached on the backside of the device package and supported by two screws that connect it to the Lucite packaging. The copper wires for the signal output and voltage supply from the Lucite plug are soldered to this board. There are eight BNC connectors for the amplified signal outputs and power supplies. (1) Starting with SOI wafer with 50um top Si layer (2) Blanket P implantation to create nwell nSi (3) PECVD oxide (0.1um). Pattern & BOE etch oxide (4) Reverse bias implantation: P implantation followed by N2 annealing it++ p nSi (5) Pattern & wet etch oxide followed by "piezo" contact implantation AlSi(l%)(l1pm ) ptt Ohmic Contact (Ilm) nSi (13) PECVD silicon nitride then pattern it to expose the bond pads (14) Backside Si DRIE etch AA nSi (9) Thermal oxidation followed by side wall B implantation BB nSi (10) Remove top oxide(0.1um) & DRIE Si (50um) to define tethers nSi (11) Wet etch oxide(0.1um), thermal diffusion and thermal oxidation (1)Trench filling, Wet etch oxide to open contact vias followed by AlSi(1%) sputtering and Al etch via RIE IA O (6) PECVD oxide (1um) (7) Pattern & dry etch oxide (8) Pattern & DRIE trench ~10um for side wall implantation followed by H2 annealing I Tether Centerline B B Figure 51. Process flow of the sideimplanted piezoresistive shear stress sensor. A 1 A (15) RIE etch oxide and nitride to release the structure (16) Forming gas anneal at 450 degree for 1 hour SiO2 P++ I PR Al (%1 SI) Silicon Nitride Piezoresistor Inwell Oxide Mask Figure 52. SEM side view of side wall trench after DRIE Si. Extrude Oxide Silicon Figure 53. SEM side view of the notch at the interface of oxide and Si after DRIE. Oxide Figure 54. SEM top view of the trench after DRIE oxide and Si. Oxide Exposed Silicon due to Oxide Overetch Figure 55. SEM top views of the trench after DRIE oxide and Si with oxide overetch. Figure 56. SEM top views of the trench with silicon grass through a micromasking effect due to oxide underetch. Figure 57. SEM side view of the trench after DRIE oxide and Si. Active Wheatstone Bridge Dummy Wheatstone Bridge for Temperature Compensation Bonds Pads Figure 58. Photograph of the fabricated device. SideImplanted Piezoresistor Trench for Tether Release Slots for Stress Release p++ Interconnect Figure 59. A photograph of the device with a close up view of the sideimplanted piezoresistor. c\ Solder Connections Holes for PCB Epoxy SCovered Wirebonds P) Lucile Package Holes for Offset CompCens Board Installation MDEi/S Figure 510. Photograph of the PCB embedded in Lucite package. AD624 AD711 Figure 511. Interface circuit board for offset compensation. ation CHAPTER 6 EXPERIMENTAL CHARACTERIZATION Preliminary electrical and fluidic characterization were performed to determine the performance of the shear stress sensor and to partially compare to the analytical models discussed in Chapter 3. The experimental setup for sensor characterization is described and then the results are presented. The experiments include measurement of characteristics of p/n diode, system noise, sensor sensitivity and linearity, and frequency response. Experimental Characterization Issues There are two complicating issues in characterizing the sensors: the initial offset voltage output without shear stress applied and the temperature sensitivity of the bridge output. These two issues directly affect the measurement resolution and static sensitivity. Therefore, offset compensation and temperature compensation must be employed for the static calibration experiments. The motivation and methodology for offset compensation is discussed in the following paragraphs. The temperature compensation was not performed and will be discussed in Chapter 7. For a balanced Wheatstone bridge, the differential voltage output of the sensor is directly proportional to the applied shear stress. In reality, the Wheatstone bridge is not perfectly balanced due to uncertainty in the fabrication process. As shown in Figure 61, the dc offset exists without applied shear stress, and is directly proportional to the bias voltage. The offset is typically O(10 mV/V), or even larger in some device die. The optimization results in Chapter 4 indicate that the normalized sensitivity of the sensor designs is O(1 CIV/V/Pa). Such a small sensitivity requires high gain amplification prior to being sampled by data acquisition board. However, a dc offset will cause amplifier saturation even at a relatively low gain. Therefore, it is imperative to minimize or eliminate the offset to maximize the dynamic range of the measurement system. An approach for the interface circuit readout is discussed as follows for dc offset compensation. The interface circuit consists of a precision programmable instrumentation amplifier AD625 and a high speed precision Op Amp AD 711 from Analog Devices [73], as shown in Figure 62. The gain of the AD625 is set by adjusting external resistors RF and RG and is given by 4RF /RG +1. The AD711 acts as a unity buffer. The initial offset voltage goes through the amplifier AD625 with a set gain of 21. Then the amplified offset voltage is precisely controlled by adjusting the input of the AD71 1, which is provided by a Stanford Research Systems SIM928 isolated voltage source [96]. SIM928 is an ultra low noise voltage source (10 CLVrms at 1 kHz bandwidth) that provides a stable lownoise voltage reference with mV resolution. Unfortunately, there was an error in the second amplifier stage of the PCB and a decision was made to just proceed with AC shear stress calibrations to demonstrate "proof of concept" functionality. Experimental Setup In this section, the experimental setup for the shear stress sensor characterization is discussed. A probe station is used to measure the currentvoltage (IV) characteristics of the sensor. A plane wave tube (PWT) is then used to determine the sensor linearity, sensitivity and frequency response. Then sensor system noise is measured with dynamic calibration setup in the plane wave tube with speaker amplifier off. Electrical Characterization Electrical characterization includes measurement of the bridge impedance and leakage current of the junctionisolated devices, as well as the breakdown voltage. All measurements were made using an Agilent 4155C semiconductor parameter analyzer and a wafer level probe station. As discussed in Chapter 5, the p/n junctions are formed by the ptype piezoresistor and the p++ interconnects with the nwell. To ensure that the current flows entirely through the ptype regions, the p/n junction must be reverse biased and the leakage current should be negligible. In this experiment, the reverse bias characteristics of the p/n junction were measured to determine the leakage current from the piezoresistors to the ntype substrate. The resistance is extracted from the IV characteristics of the piezoresistors in the p/n forward bias region. Dynamic Calibration The frequency response and linearity were deduced using Stokes' layer excitation of shear stress in a planewave tube (PWT). This technique utilizes acoustic plane waves in a duct to generate known oscillating wall shear stresses [97]. This technique relies on the fact that the particle velocity of the acoustic waves is zero at the wall due to the noslip boundary condition. This leads to the generation of a frequencydependent boundary layer thickness and a corresponding wall shear stress. Therefore, at a given location, the relationship between the fluctuating shear stress and acoustic pressure is theoretically known. The acousticallygenerated wall shear stress for the frequency range of excitation in this paper is approximated by [97] r'zze an 9 ) (61) where p' is the amplitude of the acoustic perturbation, j = Jl, v is the kinematic viscosity, m is the angular frequency, k = /cil is the acoustic wave number, 17 = J is the non dimensional Stokes number and b is the half height of the duct. A conceptual schematic of the dynamical calibration setup is shown in Figure 63. The plane wave is generated by a BMS 4590P compression driver (speaker) that is mounted at one end of the PWT. The PWT consists of a rigidwall 1"xl" duct with an anechoic termination (a 30.7" long fiberglass wedge), which is responsible for supporting acoustic plane progressive waves propagation along the duct [97]. The sensor and a reference microphone (B&K 4138) are flushmounted at the same axial position from the driver. The usable bandwidth for plane waves in the PWT is defined by the cuton frequency of the first higher order mode which is 6.7 k output voltage from the AD625 interface circuit is accoupled and amplified 46 dB by the SR560 low noise preamplifier. A B&K PULSE MultiAnalyzer System (Type 3109) is used as the microphone power supply, data acquisition unit, and signal generator for the source signal in the plane wave tube. Noise Measurement A noise measurement is necessary to determine the minimum detectable signal (MDS). The sensor is mounted on the sidewall of the plane wave tube and the speaker amplifier is turned off. This provides a reasonable estimate of the entire sensor system noise floor as installed in a calibration chamber. The compensated voltage output is amplified by the AD625 and the SR560 low noise preamplifier (ac coupled), and then fed into the SRS785 spectrum analyzer [98]. The spectrum analyzer measures the noise power spectral density (PSD), using a Hanning window to minimize PSD leakage. The measured noise PSD includes the sensor noise and the setup noise, including noise from sources such as EMI, the amplifier, the spectrum analyzer, and the power supply. LabVIEW is used for data acquisition and manipulation. The noise PSD is measured in three overlapping frequency spans from 10 Hz to 1024 Hz The settings for three frequency ranges are listed in Table 61. Experimental Results Electrical Characterization As shown in Figure 64, IV characterization results indicate a negligible leakage current (< 0.12 CLA) up to a reverse bias voltage of 10 V. The reverse bias breakdown voltage for the P/N junction is around 20 V or greater (Figure 65). IV measurements of the diffused resistors across the Wheatstone bridge are shown in Figure 66 for a representative design in Table 62. One curve is for the resistors across the bias voltage port and ground, another is for the resistors across the output ports V, and V2 The nonlinearity of the IV curve is obtained subtracting the actual voltage in the VBGND curve (or V1V2) from a linear curve fit (fit between 0.5 V to 0.5 V and extended to +10 V ), then normalizing by the linear curve and multiplying by 100. The nonlinearity is shown in Figure 6 7. The linear variation of current with voltage below 5 V (3% nonlinearity in Figure 67) indicates Ohmic behavior of the piezoresistors and p++ interconnects. The average resistances across the bridge are 397 0Z and 411 R respectively, while the predicted value for the individual resistor is 1 kO The smaller than predicted resistances may due to the high implant dosage (double of the simulation value to avoid solubility loss). The asymmetry of V1V2 curve may be due to the Schottky effect. The asymmetry may also be due to residual heating as the voltage was swept from 10 V to 10 V instead of performing two tests sweeping the voltage from 0 to 10V and 0 to 10 V. The root cause of this asymmetry requires further study. Dynamic Calibration Results and Discussion The dynamic sensitivity and linearity of the sensor were tested with a single tone of 2.088 k 2.088 k of the static sensitivity. In this measurement, the frequency span was 0.26.4 k frequency resolution of 32 Hz 3000 linear averages with 0% overlap were taken to minimize the random error. The sensor was operated at bias voltages of 1.0 V, 1.25 V and 1.5 V This is substantially lower than the optimized bias voltage of 10 V because electronic testing indicated nonlinearities in the currentvoltage relationship at excitation voltages above 4.5 V from resistor selfheating. Any resistor selfheating will lead to temperatureresistive voltage fluctuations due to unsteady convective cooling [38]. In other words, the direct sensor will behave somewhat like an indirect sensor. To avoid this phenomenon, testing was limited to bias voltages of 1.5 V and below. The dynamic sensitivity is the ratio of the differential sensor output voltage to the input wall shear stress. Ideally, the lateral displacement of the floating element will be solely a function of the acoustically generated wall shear stress. In practice, however, it is known that there will be an additional displacement due to the local pressure gradient forces generated by traveling acoustic waves across the floating element [43]. The magnitude of the effective shear stress including pressuregradient effects for a purelytraveling acoustic wave in a duct is [43] r (I)= f b = 1+ + t razz .p: (62) The second and third terms of Equation (62) represent the error due to the fluctuating flow beneath the element and the net fluctuating pressure force acting on the lip (assuming a square element). Accounting for the fact that the actual shear stress is proportional to JJ, the magnitude of the error terms is proportional to f The second term of Equation (62) assumes that Le >> g so that the flow underneath the element can be approximated by fullydeveloped pressuredriven flow in a slot. For the current sensor, g = 400 Cpm and Le = 1000 pm Clearly, this approximation is invalid and the flow beneath the element is sufficiently complex and must be evaluated using computational techniques. Therefore, only an estimate for the pressure gradient force acting on the thickness can be provided. The maximum error for this term is 7.5 dB (2.4r 7,,) at the highest frequency tested, 6.7 k phase with the actual shear stress. By adjusting the SPL from 123 dB to 157 dB, the induced shear stress varies from 0.04 Pa to 2.0 Pa Figure 68 shows output voltages response to the shear stress variation at different bias voltages. The slopes of the plots shown in Figure 68 indicate the dynamic sensitivity of the sensor at different bias voltages. For all bias conditions, the sensors respond linearly up to 2.0 Pa and the sensitivities are 2.905 CLV/Pa, 3.602CLV/Pa and 4.242CLV/Pa at bias voltages of 1.0 V, 1.25 V and 1.5 V, respectively. The normalized sensitivity is defined as the ratio of sensitivity to applied bias voltage. For a Wheatstone bridge without resistor selfheating, the normalized sensitivity is a constant. If resistor selfheating is occurring, a powerlaw dependence on the power dissipation is expected. The slopes of Figure 69 are the normalized sensitivities at bias voltages of 1.0 V, 1.25 V and 1.5 V, respectively, which are 2.905 CLV.V/Pa, 2.882 pV V/Pa and 2.828pV. V/Pa The predicted normalized sensitivity is 3.65 CLV V/Pa Note that for Figure 69, the initial offset voltages were subtracted for normalized slope comparison purposes. The close match in normalized sensitivities (<3% variation) indicates that the sensor is responding solely to the piezoresistive effects and not unsteady convective cooling. This piezoresistive effect is a combination of shear stress sensitivity, pressure gradient sensitivity and normal pressure sensitivity . The frequency response at a bias voltage of 1.5 V was also investigated in this experiment. For this test, the generator is set to a random signal with a span of 6.4 k frequency of 3.4 kHz to ensure that all harmonics up to 6 kHz are captured. A 200 line FFT is used corresponding to frequency resolution of 32 Hz At each measurement frequency, 2000 linear averages are taken with 0% overlap. The input shear stress is desired to be 0.3 Pa The theoretical SPL for each measurement frequency obtained via Equation (61). By adjusting the SPL at specific frequency, the target shear stress is then achieved. The normalized frequency res ponse function of the shear stress sensor is given as [43] H ( f )= "' ,(63) TwZlll( f ) dV where Vou, ( f ) is the sensor output with a known input, Twazz ( f) is obtained via Eqluation (61), and Br/BV is the flat band sensitivity. For this experiment, the sensitivity at 2.088 k the linearity test was used for normalization. Figure 610 demonstrates the magnitude and phase of the actual frequency response function of the shear stress sensor for a nominal input shear stress magnitude of 0.3 Pa. The gain factor is flat and is between 3.01 dB to 0.09 dB for this test. The phase is flat up to 4.552 kHz. It is noted that the gain factor at frequency of 2.088 k measurements. These results are not corrected for nonidealities in the anechoic termination which results in a finite reflected wave [97]. In addition, there is some suspicion that the results above 4.552 k Regardless, there is no apparent resonance in this sensor up to 6.7 k To check the wave reflection effect on the measurement, the twomicrophone method [99] is used to measure the reflection coefficient, as shown in Figure 611. The frequency spans from 0.2 Hz to 6.4 k linear averages with 0% overlap are taken. The results indicated that the magnitude of the reflection coefficient is comparatively large when the frequency is below 1 kHz Therefore, the frequency in the measurement for both linearity and frequency response are above 1 kHz to minimize the uncertainty. The lower end of the dynamic range of the sensor is ultimately limited by the device noise floor. The outputreferred noise floor of the sensor and measurement system is shown in Figure 612 for a bias voltage of 1.5 V As expected, the noise spectrum is dominated by 1/ f noise indicating that the signaltonoise ratio for this sensor is a strong function of frequency. At 1 kHz (with 1 Hz bin) the outputreferred noise floor of the sensor and measurement system is 48.2 nV/JH which corresponds to the minimum detectable shear stress of 11.4 mPa. Summary Preliminary electrical and dynamic characterization and the noise determination are presented to demonstrate device functionality. At a bias voltage of 1.5 V, the dynamic characterization of the device revealed a linear response up to at least 2.0 Pa and a flat response up to the frequency testing limit of 6. 7 kHz The theoretically predicted resonant frequency is 9.8 k detectable shear stress at 1 kHz is 11.4 mPa Therefore, the experimentally verified dynamic range is 11 mPa2 Pa The theoretically predicted upper end of the dynamic range at 3% static nonlinearity is 5 Pa. The upper ends of the dynamic range and bandwidth, however, could not be verified due to constraints in the calibration apparatus. A summary of the experimental results compared to the predicted results for a bias voltage of 1.5 V are listed in Table 64. The normalized sensitivity is close to the predicted design value, but resistor heating precluded using higher bias voltages, thus lowering the maximum allowable sensitivity by 16.5 dB. Furthermore, the noise floor is roughly a factor of 7 higher than predicted. This may be due to the noise floor measured is the total system noise, which includes setup noise and sensor noise, whereas the predicted value is just due to the sensor and the AD 625 circuit. There are also substantial differences in the predicted versus realized bridge impedance which means that the voltage noise of the resistors may also be higher than predicted. Table 61. LabVIEW settings for noise PSD measurement Frequency Range (Hz) Bin Width (Hz ) Number of Averages 10200 0.25 2300 2001600 2 4000 1600102400 128 30000 Table 62. The optimal geometry of the shear stress sensor that was characterized. Parameters Design Values Target Shear Stress r t(Pa) 5 Tether Length L, (pm) 1000 Tether Width W, (ym) 30 Tether Thickness 7((pm) 50 Floating Element Width W (pm) 1000 Piezoresistor Length L, ~(Cm) 228.5 Piezoresistor Width W (ym) 5 Piezoresistor Depth y,; (ym) 1 Table 63. Sensitivity at different bias voltage for the tested sensor. Bias Voltage (V) Sensitivity (mV/Pa) 1.5 0.27 2.95 0.71 3.1 0.93 4.8 3.0 Table 64. A comparison of the predicted versus realized performance of the sensor under test for a bias voltage of 1.5V. Parameters Theoretical Value Experimental Result Normalized Sensitivity (CIV/V/Pa) 3.65 2.83 Noise Floor (nV) 6.5 48.2 MI/DS (mPa) 1.2 11.4 Bandwidth (kH~z) 9.8 >6.7 Resistance (02) 1000 397 rmax (Pa) 5 >2 ) .02   0.03   * O .04  0.06 O 1 2 3 4 s Bias Voltage( V) Figure 61. The bridge dc offset voltage as a function of bias voltages for the tested sensor. V1 1 RF I 10 ~Output CVA RG ~i 5AD625 Rv 7 S16 WheatstoneVBig AD7111 Offset Null SIM 928 Figure 62. An electrical schematic of the interface circuit for offset compensation. 4 2 n I 10 8 6 4 2 O 2 Bias Voltage ( V) PC Techron 7540 Power B&K Pulse Supply Amplifier Analyzer System Anechoic Acoustic Plane Wave Mirpoe Termination Speaker Shear Stress Sensor Offset Null & Amplification Circuit Figure 63. A schematic of the experimental setup for the dynamic calibration experiments. Bias Forward Bias Figure 64. Forward and reverse bias characteristics of the p/n junction. )))ii 10 20 15 10 5 Bias Voltage ( V) Figure 65. Reverse bias breakdown voltage of the P/N junction. 30 20   10~ ~ V2~C'Fti y = 2.43*x +~ 0.273 10   V GND Linear FittingI V GhD Linear FittingI y= 2.52*x 0.01 R2= 0.9992 Bias Voltage( V) Figure 66. IV characteristics of the input and output terminals of the Wheatstone bridge. 2 0 2 10 0 Voltage (Volts) Figure 67. The nonlinearity of the IV curve in Figure 66 at different sweeping voltages. O 8 7 4 2 1 0 y = 3.6Q2*x +0.01884 y = 2.9b5*x + 0.004148j a V =1 V o V =1.25 V V =1.5 V 0.5 1 Shear Stress (Pa) Figure 68. The output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 k y= 2.905*xt 0.3113 for V 1.OV 5  Sy= 2.882* 0.2964 for 1.V 1.25 Sy= 2.828*x 0.2914 for B.V 15 ~2 V =1.0 V I./.o V =1.25 V o4 VB=1 .5 V Z 1   Linear Fittin~g O 'F O 0.5 1 1.5 2 Shear Stres (Pa) Figure 69. The normalized output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 k 10 10 1 2 3 4 5 6 Frequency (k~z 50 0 1 2 3 4 5 6 Frequency (k~z Figure 610. Gain and phase factors of the frequency response function. 0.8 0.6 S0.4 0.2 O 200 100 0 .c100 1 2 3 4 5 6 Freq [kH 1 2 3 4 5 6 Freq [kH Figure 611i. The magnitude and phase angle of the reflection coefficient of the plane wave tube. S10 System Noisp S1 Systemn"hemrmal Noise" 1 2 3 4 5 10 10 10 10 10 Frequency (Hi Figure 612. Outputreferred noise floor of the measurement system at a bias voltage of 1.5V. CHAPTER 7 CONCLUSION AND FUTURE WORK Summary and Conclusions A proofofconcept micromachined, floating element shearstress sensor was developed that employs laterallyimplanted piezoresistors for the direct measurement of fluctuating wall shear stress. The shear force on the element induces a mechanical stress field in the tethers and thus a resistance change. The piezoresistors are arranged in a fullyactive Wheatstone bridge to provide rej section to common mode disturbances, such as pressure fluctuations. A dummy bridge located next to the sensor is used for temperature corrections. The device modeling, optimal design, fabrication process, packaging and comprehensive calibration were presented. Mechanical models for small and large deflection of the floating element have been developed. These models are combined with a piezoresistive model to determine the sensitivity. The dynamic response of the shear stress sensor was explored by combining the above fundamental mechanical analysis with a lumpedelement model. Finite element analysis is employed to verify the mechanical models and lumpedelement model results. Dominant electrical noise sources in the piezoresistive shear stress sensor, 1/ f noise and thermal noise, together with amplifier noise, are considered to determine the noise floor. These models are then leveraged to obtain optimal sensor designs for measuring shear stress in several flow regimes. The cost function, minimum detectable signal (MDS) formulated in terms of sensitivity and noise floor, is minimized subj ect to nonlinear constraints on geometric dimensions, linearity, bandwidth, power, resistance, and manufacturing constraints. The optimization results indicate that the predicted optimal device performance is improved with respect to existing shear stress sensors, with a MDS of O(0.1 mPa) and dynamic range greater than 75 dB. A sensitivity analysis indicates that the device performance is most responsive to variations in tether geometry. The process flow used an 8mask bulk micromachining process, involving PECVD, thermal oxidation, wet etch, sputtering, DRIE and RIE fabrication techniques. After fabrication, the die was packaged for wind tunnel testing in a custom printed circuit board for modularity. An interface circuit board was designed for amplification and offset compensation. Then the sensor was calibrated electrically and dynamically. Electrical characterization indicates linear junctionisolated resistors, and a negligible leakage current (<0.12 CLA) for the junctionisolated diffused piezoresistors up to a reverse bias voltage of 10 V. Using a known acousticallyexcited wall shear stress for calibration at a bias voltage of 1.5 V, the sensor exhibited a sensitivity of 4.24 pV/Pa, a noise floor of 11.4 mPa/A~ at 1 kHz a linear response up to the maximum testing range of 2 Pa, and a flat dynamic response up to the testing limit of6.7 kHz These results coupled with a windhtnnel suitable package are a significant first step towards the development of an instrument for turbulence measurements in lowspeed flows. The system noise is 48.2 nV/JH at 1 kHz (with 1 Hz bin), and is roughly 7 times higher than predicted. Static heating limitations limited the maximum bias voltage to 1.5 V instead of 10 V . Suggestions for Future Work Future work should focus on the comprehensive characterization of the sensor to determine absolute performance and to compare against all of the theoretical predictions. An uncertainty analysis of all experiments and accurate measurement of the sensor geometry are required to enable this comparison. Specifically, a temperature compensation approach must be realized that will enable the static calibration of the sensor as well as any dc measurement application. The resonant frequency of the sensors must be determined. Sensitivity to vibration and pressure fluctuations must also be determined. Detailed noise measurements that isolate the contribution from the piezoresistor should be carried out. Finally, the flow around the floating element will be investigated via numerical simulations to provide an improved estimate of pressure gradient induced errors. In the following subsection, several suggestions for carrying out these measurements are discussed below. Temperature Compensation The sensitivity of the shear stress sensor changes with temperature due to the variation of the piezoresistive coefficient with temperature, as indicated in Equation (323) and (324). In sensor static calibration in a 2D laminar cell, the sensitivity is defined as the slope of the curve of voltage output versus shear stress. However, due to the temperature effect, the output voltage is a function of shear stress and temperature. Thus the temperature induced voltage output should be subtracted from the active bridge voltage output. For the identical active and dummy Wheatstone bridge, the temperature effect on them should be same. Therefore, the temperature effect on the active bridge in the static calibration can be removed by subtracting the voltage output of the dummy bridge. Unfortunately, the active bridge and dummy bridge are not identical due to Wheatstone mismatch. So the voltage output dependence of the temperature need to be measured for both active bridge and dummy bridge. The output voltage of the active bridge is a function of shear stress and temperature variations, while the dummy bridge depends on temperature variation only. The measured output voltages in the laminar flow are Iin (r~,,T) for the active bridge and I, (T) for the dummy bridge, respectively. The slope of the voltage vs. temperature curve is S,, for active bridge and S~d for dummy bridge. In the static calibration, the output voltage dependence of shear stress is given as l(w>= l (4wT)~ (T) (71) Assuming that the slope of the Vo vs. T curve remains constant and they are given as, (7 2) Vid(T) d TO S~d Substituting V (T) from Equation (71) into (72) and rearranging it, the shear stress dependent output voltage is obtained as V,(r)= V,(rT)V (o)) (Vd(T)d T)),(73) T~d where V~ (To) is the initial voltage value at room temperature. The Equation (73) indicates that S,, and S~d must be obtained in order to get V (r.). Preliminary experiments prior to employing dc offset nulling were performed to determine the temperature sensitivity. Unfortunately, the large dc offset limited the quality of the results. The experimental set up is as follows. The voltage output dependence of temperature variation is conducted in two bath settings. Both bathes are filled with DI water. The outer bath is the chamber of Isotemp refrigerated circulator, and the inner bath is glass beaker. The packaged sensor is sitting on the top of the beaker. The beaker is used to protect the sensor from flow circulation disturbance. The compensated voltage output is connected to a HP34970A data acquisition unit and DAQ card. A HP34970A digital voltage meter is used to minimize the 60 Hz noise. LabVIEW is used for data acquisition. Static Characterization Initially, we attempted to statically characterize the sensor, but the temperature sensitivity and dc offset issues prevented any meaningful results. The goal of the static characterization is to verify the sensor design and characterize the sensitivity and linearity. After temperature compensation and dc nulling have been achieved, a static calibration can be performed. The flow cell design is such that an ideal onedimensional fully developed incompressible laminar flow exists between two semiinfinite parallel plates (Poiseuille flow between two parallel plates). For this case, the pressure drop is constant and the wall shear stress is given by the theoretical relation [7] h dP r (74) S2 dxC where h is the height of the channel in meters and P is pressure in Pascals. Detailed setup information can be found in [34]. The incompressible flow is first verified before the sensor static calibration. The incompressible flow exhibits a linear pressure drop versus length for wall shear stress up to 2 Pa, which is a necessary assumption for Equation (74). The pressure measurements are carried out using the Scannivalve pressure measurement system. This multiplexing valve system allows the pressure taps to be reached sequentially to measure pressure drop between the first pressure tap and other taps downstream. The inlet flow rate is regulated using a mass flow controller (GFC4715). A linear pressure drop versus length is displayed in Figure 71. Figure 72 shows the experimental setup for the static calibration of the wall shear stress sensor. The sensor is flushmounted on one wall of the laminar flow cell and oriented for measuring wall shear stress in the flow direction. The corresponding pressure drops across two pressure taps 1F and P, is measured using a differential pressure gauge, Heise pressure meter. The voltage output is first fed into the compensation circuit. The compensated signal is then supplied to a HP34970A precision digital voltage meter to eliminate 60Hz noise from the power supply by averaging. The mass flow rates are controlled automatically by LabVIEW to obtain different pressure drops and correspondingly wall shear stress. LabVIEW is also used for data acquisition and manipulation. Noise Measurement In order to determine the isolated resistor noise characteristics, the sensor is placed in a doublenested Faraday Cages to improve the electromagnetic interference (EMI) reduction [98]. The compensated voltage output is amplified by a SR560 preamplifier, and then fed into the spectrum analyzer (SRS785). The spectrum analyzer (ac coupled) measures the noise power spectral density (PSD), using a Hanning window to avoid PSD leakage. The noise PSD of the sensor is obtained by subtracting the setup noise PSD from the total measurement noise PSD. The setup noise sources include EMI and noise from the amplifier, spectra analyzer, and power source. Recommendations for Future Sensor Designs Based on lessons learned during the first generation shear stress sensor fabrication and characterization, there are several issues that need to be addressed in future designs. Specifically, issues regarding resistor selfheating and pressure sensitivity need to be addressed. In the sensor calibration, piezoresistor selfheating was clearly present when the dissipated power was greater than 10 mW A study of the normalized sensitivities indicated that self heating could be avoided all together for a power dissipation limit of 5.7 mW Therefore, the power dissipation limit in the design optimization should be decreased from 100 mW down to 10 mW to avoid resistor self heating. The power limit will be a function of the tether geometry, but the order of magnitude in power reduction will provide a better estimate of appropriate biasing conditions for design purposes. A detailed numerical study of the resistor heating may also provide insight into this phenomenon, but this may be challenging due to the complexity of the convective boundary conditions at the tether surface. For a balanced Wheatstone bridge, pressure fluctuations should not affect the voltage output. Preliminary pressure calibrations, however, indicate that the pressure sensitivity is only O(10 dB) lower than the shear stress sensitivity. In addition to achieving better control of the resistor implant process to balance the bridge, this can be mitigated by extending the side implanted resistor all the way down tether thickness. The fabrication process should change correspondingly to protect the bottom of the piezoresistor with a high quality passivation. In current sensor design, the piezoresistor is implanted on the top 5 Cpm of the tether thickness to avoid resistor current leakage. So in the final backside release step, the BOX layer was removed to release the structure and the tether bottom is exposed to the flow without any protection. This will cause sensitivity drifting if the piezoresistor is implanted on the whole tether thickness. A process flow must be designed to realize an electrically passivated resistor that extends to the bottom of the resistor thickness. In general, improved test structures are needed to provide additional information about the sideplanted resistors. Specifically, a test structure must be added into the mask design to enable the measurement resistor doping profile via secondary ion mass spectroscopy (SIMS). In addition, providing additional bond pads for each resistor will permit a resistor trim based approach to bridge balancing and temperature compensation [60]. *Testing Data linear Fitting~ S100 60 1 2 3 4 5 6 7 Length (Inch) Figure 71. Pressure drops versus length between taps in the flow cell. Figure 72. Experimental setup of static calibration. APPENDIX A MECHANICAL ANALYSIS A clampedclamped beam with a central point force and a distributed pressure load is shown in Figure A1 (a). This is a second order statically indeterminate problem. Euler Bernoulli beam theory is used to predict the linear, small deflection behavior and Von Karman strain is included in the nonlinear, large deflection models. Two methods, an energy method and an exact analytical method, are used to solve the large deflection problem. Using Euler Bernoulli beam theory, the stress distribution is also derived. Small Deflection Equilibrium equations may be written based on the free body diagram of the symmetric structure, Figure A1(b). The relationships between the resultant forces, RA and R,, point load P, and distributed load Q are thus RA = R, = P/2 + QL,, (A1) where P = zw Le, 2 = zW, and z is the wall shear stress. The nonlinear differential equation governing the beam deflection caused by bending is given as [82] d2 (~~~2 El = M~ (A2) 1+ (dw/dxh)iU where w(x) is the deflection in the z direction, E is the Young's Modulus, I is the area moment of inertia given as I = (T43/12, and Mx is the resisting moment in cross of x Writing the equation for moment equilibrium, C1MD = 0, yields Mx = M~A RAX e2/2 (A3) where M~ is the resisting moment, and M~ = M, due to the symmetry of the structure. Assuming the rotation d~w/dx is very small, Equation (A2) is simplified to d2w(x) Ml (A4) dx~C El Integrating Equation (A4) yields the rotation and deflection of the beam along its length, Av(x)LC E1 (Mx 1 1 ~X +Mx + Rx4 Ox 1, (A5) and w(x)= + 3 Ox A6 El 2 6 24 where c, and c, are constants. There are three unknown quantities in Equations (A5) and (A6) n~, M1 ,nd c, Therefore, three boundary conditions should be employed, w ,(0) = (clamped), (A7) = 0 (clamped), (A8) and = 0 (symmety) (A9) Substituting the above boundary conditions and R, from (A1) into (A6), one obtains c1 = c, = 0, (A10) 1 1 and M=4PL, + 3 L, (A11) The displacement wu(x) is then obtained by substituting Eqluation(A10)(A 11) and momentum of inertia I = (7~3 /12 into (A6) w(x) = [3 L;5WL,+8(L,) (2 L,+8WL,)x3+ 2Wx4 ], (0 The maximum deflection at the center of the beam is given as 7w W L L 2W L AL = w(L,)= 1+7 .I W (A13) Large DeflectionEnergy Method In a large lateral deflection, the beam experiences bending and stretching. The total strain is composed of bending and stretching strain [42] t beding strnchig ,(A14) d2W where sbending 2 y is the position upward. The axial strain at y = W/2 is given as [100] du 1 dwY\ E + l (A15) dx 2 dx~C The total change in beam length is given by /dL =\~I f eS dx + (A16) J 0 a dx 2 dx( The integration of the first term is zero due to the clampedclamped boundary condition. The axial stain is the total change in beam length divided by the total length of the beam strentchin 2L, 4L, dxS~ rI~) ~ il The total strain is obtained as E = y + Wc4 JO ~\a~l d (A1 8) For large deflection, a trial function in the form of a cosine is assumed, as it automatically satisfies the doubly clamped boundary condition and is a maximum at the center of the beam. The trial function is thus w 8x=^ 1+ cos '(1 ,1 (A19) where A, is the maximum deflection at the center of the beam. Substituting this model into (A18) yields dw~ Awarsi z(L, x) (0 d2 8 sm2~ ~ 1 (A20) dx~C 2 L, L, E = y co z(A22) '2 L,2 L, 1 6L,2 The strain energy density is given as U = rds= Ee E y cos ^z(A23) o a2 2 2L, L, 16L, The strain energy is then obtained U = UodV= 00L dxy (A24) The total strain energy is obtained by integrating Equation (A24) to yield U = E7( ^z6L3 4rrr .~ (A25) Based on the principle of virtual work, the total potential energy W is equal to the stored strain energy minus the work done by the external forceK , W= UK, (A26) where K is given by K= P3+Q "L 1+ cos =(~ A,(+QL) (A27) The equilibrium configuration is that in which the potential energy is minimized. The minimum is obtained when dW Ag43  = E;7t +~~~4: a'i"w r WL r WL, =0. (A28) d6 48L 3 64L,3 2 " Rearranging Equation (A28) yields x 4 4 rW L 2 ,L, L As+ = 1+ (A29) 96 128W 4E(t WL, Simplifying the above equation, ~21 and~ , yields an approximate large deflection 96 128 4~ solution, 3( A L 2 WL, L A,~E7 1+ 1 (A30) Large DeflectionAnalytical Method For large deflection, axial force in the beam is not zero as in the small deflection model, and serves as a constitutive equation in the modeling analysis. Since the beam is symmetric, only half of the beam is analyzed, as shown in Figure A3. For large deflections, taking axial force Fb into account, the differential equation governing the beam deflection caused by bending is given as d2WX El = M~(x), (A31) dx~C where the slope of beam caused by large deflection is assumed d~w/dx <<1i, and therefore (dw/~dx)2 is negligible. The moment M(x) is given by 1 P M~(x) = Q x2 + x Mo0 Fa (w(0) w(x)) (A32) 2 2 where w(0) is an unknown constant. Substituting Eqluation (A32) into Eqluation (A31) yields d2w(x) 1 P El 2 Fw(x)= Qx2 + xMoF,w(0). (A33) dx~C 2 2 The above equation can be solved as a superposition of one general solution wn and a particular solution ws w(x) = wn (x) + ws(x), (A34) where w, (xC) = C, sinh(ilx) + C2 COsh(ilx) and w, (x) = axc2 + bx + c, assuming ii=l . Substituting ws into Equation (A33), a, b, and c are obtained as Q P MQ a b= and c = w(0)+ 2F a F Fi A2 Equation (A34) can be rewritten as Q! P MQ w(x) = C, sinh(ilx) +C2 COsh(ilx) x2 ~x +w(0)+ o, 2F; 2F; F F122 (A35) for which the boundary conditions are: dwY (0) =0, dw (L,) w,(L,)= 0.  W/2 is nonlinear and is given as 2d oE EA'F (A36) (A37) (A38) and For large deflection, the axial strain at y I du E 0 (A39) where A = 7(W Integrating the above equation yields EA du d F = l oN, ~1 + (A40) "L dx 2 dx~C The first term in the integration is zero due to the doubly clamped boundary condition. Axial force Fa in the neutral axis y = W/2 is then obtained as F:~EA dw ~\2LC FI = dx (A41) There are five unknown variables: C,, C2, F ,Mo, and w(0), thus five boundary conditions are needed to solve for these unknown variables. However, only three boundary conditions (A36) (A38) and one constitutive equation (A41) are available. Another condition is w1(0) = wI(0). The problem is indeterminate and an iterative technique must be used to find the final result. First, we applied boundary conditions (A36)(A3 8) and the constitutive equation (A41) into Equation (A3 5) and solve it to get the maximum deflection as a function of the axial force in the neutral axis, F~ The detailed procedure for solving this problem is given in the following. Substituting (A35) into boundary conditions (A36) and (A37) yields P 1 PP C,=E an C2 Q+ coh(L,) (A42) Substituting C, and C2 into (A35) and setting x = 0 yields Q! 1 PP Mo QL +cosh(L).(3 22 2 Sinh(AL, 2 243 Substituting Mo from (A43) and C, and C2 fTOm (A42) into (A35) yields P cosh(ilx) 1 w~x)= sn(A) QL +cosh( AL. ) I x2 ~x +w(0) (A44) 2ilF FAsn(L) 2 2 2F 2F Substituting (A3 8) into (A44) yields deflection at the center, P cosh(3L, )1/, P _P Q~li~T j+tL'2 PL, w(0) = sinh(ALl,) QL,`""' +F ohAL)+ + ' 2ilF FA lsinh(AlL ) 2 2 2 Derivative Equation (A44) to obtain dw (x) 1c P ohix sinh(Ax) /1~ P P~o \ ) P dx F 2sinh(AL, )\Y 2 22. (A45) (A46) Secondly, we solve the maximum deflection equation (A45) by iterating Fa An initial value Fa =104 Pa is selected randomly and the following steps are performed to obtain the maximum deflection, w (0) . dwy a 1) Substitute Fb into (A46) to get where ii = . dre El 2) Substitute into (A41) to obtain new F . 3) Repeat 1), 2) until the relative error IFa"' Fa" /Fa"' < le 6 . 4) Substitute F into (A45) to find the maximum deflection w,(0). Stress Analysis The bending stress along a beam (shown in (A3)) is given as [82] F; 2f y cr =+ =, A I (A47) where IZ is the moments of inertia for the z axis, and IZ = 7,'W3/12. In small deflection, the axial force Fb = 0 A free body diagram of the clamped beam is shown based on the discussion in the small deflections section, where R, and MA are obtained from Equation (A1) and (A11i), respectively. The moment for a certain length from the edge of the beam is obtained as, 11 1 1 M= PL, QL2 PQ xx2. (A48) 4 322 Substituting Equation (A48) into (A47) and simplifying the equation to obtain the bending stress along the beam (0 <; x < L,) at y = 0, 3 2~L2 r, LL, 3 2(L, 3 6(L, x 3(L, x ~27t 4 WL, 2 LL, WL L Effective Mechanical Mass and Compliance In this section, the mechanical lumped parameters for a clampedclamped beam are found. These parameters include lumped compliance obtained via the storage of potential energy and lumped mass obtained via the storage of kinetic energy. These results are used in Chapter 3 to develop the lumped element model of a laterally diffused piezoresistive shear stress sensor. Recall that the lateral displacement and maximum displacement of the clampedclamped beam in small deflection given in Chapter 2, w(x) = [ 3 LL, + 8(Lt2 2 (2 L + 8 L,)x 3 + 2 (x4 (0 <;x Tw LL [~;12L, A and w(L,)= 2 .(1 The kinetic coenergy W, of a rectilinear system with a total effective mass m moving with velocity u is given as, 1 W, = mu2 (A52) For a simple harmonic motion, the velocity and displacement of the beam are related by u(x)= jcuw(x), (A53) where m is the frequency and uI (L,) = jew l(L,) uI (x) is then expressed as w (x) u(x)= u (L,) (A54) For an infinitesimal element on the beam with a mass of psW~dx, the kinetic coenergy dW,' is calculated using Equations (A52) and (A54) to be S1 p,,W7tu2 (L,) dW, psI,7,W'(u2 __2 (x)dx ~ (A55) 2 2w2 (L,) where psl is the density of silicon. Integrating Equation (A55) over the beam gives the total kinetic coenergy of the system, r s t (L,)T( 1 2 Ly W, = 2 dW, w2(x~dx (A56) o W2(L,) o The reference point is x = Lt, which corresponds to the maximum deflection of the beam wi(Lt). The distributed deflection of the beam can be lumped into a rectilinear piston by equating the kinetic energy obtained in Equation (A56) to the kinetic energy of the rectilinear piston of mass W = (A57) Equating Equation (A57) and (A56) yields effective mechanical mass as M,,, =2 I" w2(x)dx (A.58) Since the velocity of the plate is u = ~jmw(L,) the effective mechanical mass of the device is the sum of the mass of the plate and the effective mechanical mass of the beam, M2, M Z~ + MZh = p,,L WT, + M . (A59) The strain energy stored in the beam due to its deflection can be expressed as The strain energy of an equivalent spring is given by WE=1 1 w(2,( 2 C, where C,,, is the mechanical compliance of the beam. Equating Equation (A61) and (A60) yields w(L,)2 Ziod2W()LC Substituting wu(x) and w(Lt) in Equation (A50) and (A51) into (A_59) and(A62) yields L60) L61) L62) 1+1494 WL, 315 WL nM,,, pW,WL,7t (A63) (A64) 1+4 WL 2238WL,1024 W L, 315 WL, 315 WL +2tVL, W liiL) 1 L, C = 7\~ 641 WL, 2L P W 2Le Rx x=0 Ax=0l M, f "'B /I Figure A1. The clamped beam and free body diagram. a) Clampedclamped beam. b) Free body diagram of the beam. c) Free body diagram of part of the beam. x Figure A2. Clampedclamped beam in large deflection. VM R" x Figure A3. Clampedclamped beam in small deflection (a) clamped beam (b). and free body diagram of the ?~ : APPENDIX B NOISE FLOOR OF THE WHEATSTONE BRIDGE For a Wheatstone bridge shown in Figure B1, assuming R, = R, = R, = R, = R we get I, = V,/2, therefore the voltage across each resistor is VR B B/2Yla= V,/2 (B1) The current through the resistor is IR B (B2) 2R Assuming the noise sources are uncorrelated, the mean square noise can be solved as a superposition of the mean square thermal noise, the 1/ f noise, and the amplifier noise. For thermal noise, the equivalent noise model is given in Figure B2. The rms thermal voltage is given as ;aen,a, E + ==ii~ 4k~,iiiT (RR Af +kT ( R ) A = 4k,TRAf (B3) For 1/ f noise, the equivalent noise model is given in Figure B3. The mean square current noise is I = RIn .(B4) The mean square voltage noise E, is obtained as Substituting Equation (B4) and (B2) into (B5) to obtain E,=aHR 2 HR2 7 R (B6) Nc4R / Nc4R /41( 157 Rearrange the above equation to get (B 7) (B8) The rms 1/ f voltage is obtained as The total noise floor is obtained via the superposition of the mean square noises 2~ +4khTRAf +(e/p9)2 , (B9) where the last term in the above equation is the low amplifier noise. E 2 H ," 2~ 2 . 8No 4N V = HV,2 Figure B1. The Wheatstone bridge. R, V, R2 R E Rf, E2 VI ~ cx V2 Figure B2. The thermal noise model of the Wheatstone bridge. R, V, R R R2 R3 E' R //R, R 4//R3 E, VItx V, Figure B3. The 1/ f noise model of the Wheatstone bridge. APPENDIX C PROCESS TRAVELER Wafer: ntype <100> 15 ohmcm, SOI wafer Start with SOI wafer (nSi (100) 15 O2cm) with 50Clm silicon on 1.5um buried oxide (BOX). DI rinse Masks Reversed biased maskRBM Piezo contact maskPCM Nested maskNM Side implant maskSIM Bond pad cuts maskBPCM Metal maskMM Bond pad maskBPM Process Steps 1. nwell Implant * Ion implant dopant = phosphorus, energy = 150 keV, dose = 4el2 cm2. 7 degree tilt, blanket implantation. This forms the nwell. This needs to be simulated first. * Piranha clean 2. PECVD oxide: deposit oxide 0.1pum via PECVD 3. Reverse Bias Contact * Coat and pattern photoresist/oxide on front side 0 HMDS evaporation for 5min 0 Spin AZ 1529 at 4000rpm for 50sec & softbake at 90"C oven for 30min 0 Pattern by mask RBM Exposure 60sec at 8.8mJ/cm2 Develop at AZ300MIF for 50sec Hard bake at 90"C oven for 60min * BOE(7:1) : ~80sec to etch 0.1um oxide. This step puts alignment marks on the wafer * Ion implant dopant phosphorus, energy = 80 keV, dose = 9el3 cm2. 7 degree tilt * Ash strip photoresist * RCA clean * Thermal annealing at T = 10000 C, time=420sec in nitrogen 4. Inplant Interconnection Contact * Coat and pattern photoresist/oxide on front side 0 HMDS evaporation for 5min 0 Spin AZ 1529 at 4000rpm for 50sec & softbake at 90"C oven for 30min 0 Pattern by mask PCM, align to the alignment marks created via RBM Exposure 60sec at 8.8mJ/cm2 Develop at AZ300MIF for 50sec Hard bake at 90" C oven for 60min * BOE(7:1) : 90sec to etch 0.1um oxide. This step puts alignment marks on the wafer * Preamorphization Implant lon implant dopant = Ge, energy = 160 keV, dose = lel5 cm2 .7 degree tilt lon implant dopant = Ge, energy = 50 keV, dose = lel5 cm2 .7 degree tilt * Ion implant dopant = boron, energy = 50 keV, dose = 1.2el6 cm2 7 degree tilt * Ash strip photoresist * Piranha clean 5. Nested Mask Release * Deposit PECVD oxide l Cym * Coat and pattern photoresist on front side 0 HMDS evaporation for 5min 0 Spin AZ 1529 at 2000rpm for 50sec & softbake at 95"C convection oven for 25min 0 Pattern by mask NM, align to the alignment marks created via PCM Exposure 85sec at 7.9 mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90"C oven for 60min * Plasma dry oxide etch. This step puts new alignment marks on the wafer * BOE(6:1) oxide etch to remove the oxide residues 6. Etch Sidewalls * Coat and pattern photoresist on front side 0 HMDS evaporation for 5min 0 Spin AZ 1512 at 2000rpm for 40sec & softbake at 95"C hotplate for 50sec o Pattern by side implantion mask(SIM), align to the alignment marks created via NM Exposure 19sec at 4.5mJ/cm2 Develop at AZ300MIF for 70sec Hard bake at 90"C oven for 60min * BOE(6:1) oxide for 2min * DRIE silicon to ~8Cpm deep * BOE(6:1) oxide for 60sec to avoid Piezoresistor and Piezo contact disconnection due to DRIE undercut * Ash strip photoresist * Piranha clean 7. Hydrogen Annealing * T = 10000C P=5mTorr for 5min in pure hydrogen for surface roughness reduction 8. Oxidation: thermal grown wet oxide 1000A at T=1 000oC 9. Side Wall Implantation * Preamorphization implant lon implant dopant = Ge, energy = 160 keV, dose = lel5 cm2 54 degree tilt lon implant dopant = Ge, energy = 50 keV, dose = lel5 cm2 54 degree tilt * Ion implant dopant = boron, energy = 50 keV, dose = lel6 cm2 54 degree tilt * Piranha clean 10. Beam Definition * Etch oxide by reactive ion etch via dielectric setting in STS * DRIE silicon to BOX * BOE(6:1) 2min to remove oxide (ensure to remove 0.1um oxide on sidewall) 162 11. Oxidation * Piranha clean * Annealing at T=1000oC for 60min in nitrogen * Thermal dry oxide grown at T=975oC: for 235min (0.1Cpm) 12. Bond Pad Cuts * Trench filling o Spin AZ 1512 at 800rpm for 40sec & softbake at 95"C hotplate for 50sec o Spin AZ9260 at 800rpm for 50sec & softbake at 90"C oven for 30min 0 Flood exposure Exposure 300sec at 7.9mJ/cm2 Develop at AZ400MIF till clear * Coat and pattern photoresist on front side 0 HMDS evaporation for 5min 0 Spin AZ 1512 at 0.5k/2k for 5/40sec & softbake at 95"C hotplate for 50sec o Pattern by bond pad cuts mask(BPCM), align to the alignment marks created via PCM Exposure 45sec at 4.5mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90"C oven for 60min * BOE(6:1) oxide for 15min * Remove photoresist 13. Metalization * Trench filling * Desccum in oxygen plasma * Deposit lum AlSi(1%) to avoid spiking via sputtering * Coat and pattern photoresist on front side 0 HMDS evaporation for 5min 0 Spin AZ 1529 at 0.2k rpm and stay for 2min. Then spin at 0.2k/2k rpm for 10/50sec with ramp rate of 100/500 rmp/s o Softbake at 90"C oven for 30min 0 Pattern by metal mask (MM), align to the alignment marks created via BPCM Exposure 100sec at 7.9mJ/cm2 Develop at AZ300MIF for 1min 30sec Hard bake at 90"C oven for 60min * Etch Al by RIE * Remove photoresist 14. Nitride Passivation * Deposit 2000A PECVD silicon nitride * Trench filling * Coat and pattern photoresist on front side 0 HMDS evaporation for 5min 0 Spin AZ 1512 at 4000rpm for 40sec & softbake at 95"C hotplate for 50sec o Pattern by bond pad mask(BPM), align to the alignment marks created via MM Exposure 18sec at 4.5mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90"C oven for 60min * Etch nitride by RIE * Remove photoresist 15. Final Release (a) Device wafer * Spin AZ9260 on front side of the device wafer o Spin speed 200rpm, ramp rate 100rpm/s for 10s, wait for 1min. Run this recipe twice 0 Spin speed 4000rpm, ramp rate 1000rpm/s for 50s o Soft bake at 90"C oven for 30min * HMDS on the backside * Spin AZ9260 on backside of the device wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s o Soft bake in 90"C oven for 30min * Pattern by back release mask(BRM), align to the alignment marks created via NM o Exposure 25 sec in EVG520 mask aligner o Develop at AZ300MIF for 3min 40sec o Hard bake at 90' C oven for 60min (b) Carrier wafer * Spin PR AZ9260 on a carrier wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s * Soft bake at 90"C oven for 2030min * Put some cool grease on the edge of the carrier wafer * Bake on hotplate, 60"C for 5min * Put the device wafer face down on the carrier wafer. * Put on the hotplate, apply pressure using swab (c) DRIE * Run DRIE, stopped until 50um silicon left * Put the wafer on the hotplate 60"C for 5min, separate from the carrier wafer * Separate the wafer into individual dies (d) Process on individual dies * Spin AZ9260 on a carrier wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s o Put the device die on the top of the carrier wafer, apply pressure using swab o Soft bake in 90"C oven for 30min * DRIE to BOX layer * RIE BOX layer for 15min, run BOE 510min to remove the residues * RIE nitride for 6min * Remove the device die using tweezers * Put the device die in AZ400 PR stripper * Plasma clean in Asher for 10min APPENDIX D PROCESS SIMULATION This chapter includes the FLOOPS process simulation of the piezoresistor, p++ interconnects and nwell, as well as the reverser bias connections. (a). Piezoresistor This program simulates the doping profile of piezoresistor in the silicon layer after ion implantation, anneal and thermal oxidation. The boron is implanted into preamorphization Si layer with oxide as a screen layer. Its initial doping profile is simulated by SRIM, and then imported to FLOOPS file for subsequent process simulation. line xloc=0.1 spa=0.005 tag= SiO2top line x loc=0 spa=0.005 tagtop line x loc=1.5 spa=0.01 tag=bot region oxide xlo=SiO2top xhi=top region silicon xlo=top xhi=bot imit #profile name=B_SRIM inf/home/yawei/Floops~new/SRIM B 50keV_0.1umSiO2 Si_only.txt sel z=B SRIM*5 name=Boron sel z=log(Boron) layer etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=23 5 puts "### Oxide thickness after thermal oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." sel z=logl0(Boron) plot.1Id bound !cle label=PZR set cout [open /home/yawei/Floops~new/pzrdata w] puts $cout [print.1Id] close $cout sel z=logl0(5.0el4) plot.1Id !cle labelbackground sel z = Boron5el4 puts "The Junction Depth is [interpolate silicon z=0.0]" set z=Boron layer (b). P++ interconnection and nwell #p++ surface concentration is ~1e+21 and nwell Ns~1e+16 # generate grid line x loc=0 spa=0.001 tagtop line x loc=1.0 spa=0.01 line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot imit sel z=5el4 name=Phosphorus implant phosph dose=4.0el2 energy=150 tilt=7 #deposit 0.1lum PECVD oxide deposit time=4 rate =0.030 oxide grid=10 puts "Oxide thickness after PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." diffuse temp=1000 time=450 strip oxide implant boron dose=1.2el6 energy=50 tilt=7 #strip oxide #deposit lum PECVD oxide deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." diffuse temp=1000 wet time=9.2 # oxide thickness is 1000A etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=23 5 sel z=logl0O(Phosphorus+1) plot.1id bound !cle colorblue label=nwell set cout [open /home/yawei/Floops~new/nwelldata w] puts $cout [print.1id] close $cout sel z=logl0(5el4) plot.1id !cle colorpink labelbackground sel z=logl0(Boron+1) plot.1id bound !cle colorred label=p++ set cout [open /home/yawei/Floops~new/ohmicdata w] puts $cout [print.1id] close $cout sel z = Boron Phosphorus layer puts "The Junction Depth is [interpolate silicon z=0.0]" (c). Reverse biased contact line x loc=0 spa=0.005 tagtop line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot imit sel z=5.0el4 name=Phosphorus implant phosph dose=4.0el2 energy=150 #deposit 0.1lum PECVD oxide deposit time=4. 19 rate =0.0239 oxide grid=10 puts "Oxide thickness after PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." strip oxide smooth set t [open temp.P w+] sel z=Phosphorus puts $t [print.1id] close $t # start with a new grid ... since strip oxide removes the nodes near the surface where the new phosphorus profile is about to go set former~interface [interface gas /silicon] line x loc=$former~interface spa=0.0001 tagtop line x loc=0.1 spa=0.001 line x loc=1.0 spa=0.01 line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot imit profile name=Phosphorus inftemp.P # inplant phosphorus for reverse bias contact implant phosph dose=9.0el3 energy=80 tilt=7 sel z=logl0(Phosphorus) plot.1id bound !cle colorred label=Profile~ini #Thermal Annealing 450min at T=1000 deg diffuse temp=1000 time=450 #deposit lum PECVD oxide deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." # thermal grown oxide 1000A at T=975 deg diffuse temp=1000 dry time=9.2 etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=23 5 puts "### Oxide thickness after thermal oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." sel z=logl0(5.0e+14) plot.1id bound !cle colorblack labelbackground sel z=logl0O(Phosphorus+1) plot.1id bound !cle colorblue label=reverse~bias set cout [open /home/yawei/Floops~new/reversedata w] puts $cout [print.1d] close $cout layers Table E2. Anisotropic oxide/nitride etch recipe on the Unaxis ICP Etcher system. Parameters Oxide Nitride CHF, flow (sccm) 45  SF6 flOW (Sccm)  15 O, flow (sccm) 3 5 RF2 power (W) 600 300 RF1 power (W) 100 100 Chamber pressure (mTorr) 15 20 Helium flow (sccm) 20 10 Table E3. Anisotropic aluminum etch recipe on the Unaxis ICP Etcher system. Parameters Settings Ar flow (secm) 5 Cl, flow (sccm) 30 BC1, flow (sccm) 15 RF2 power (W) 500 RF1 power (W) 100 Chamber pressure (mTorr) 5 Helium flow (sccm) 20 APPENDIX E MICROFABRICATION RECIPE FOR RIE AND DRIE PROCESS .Input parameters in the ASE on STS DRIE systems. Parameters 50 Cpm Si etch 8 Cpm Si etch SiO, etch Coil power 600 W 600 W 800 W Platen power 12 W 12 W 130 APC (mTorr) 28 (fixed) 28 (fixed) 50 (auto) Etching process 11 6 Passivation process 6.5 4 SF, flow (sccm) 130 130 O, flow (sccm) 13 13 C4F, flow (sccm) 85 85 Table E1. 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Reddy, Theory and Analysis ofla~stic Plates: Taylor and Francis, 1999, pp. 25. BIOGRAPHICAL SKETCH Yawei Li received her BS and MS degree in Aerospace Engineering at Beijing University of Aeronautics and Astronautics, China. She worked with China Aerospace Corporation before she joined University of Florida. She also received MS (2003) in Aerospace Engineering and ME (2006) in Electrical Engineering from University of Florida, respectively. She is currently a Ph.D student in the Department of Mechanical and Aerospace Engineering at the University of Florida. Her current research focuses on the sensor modeling, design optimization, fabrication, and characterization of MEMSbased piezoresistive sensors that enable the measurement and control of wall shear stress in turbulent flow. PAGE 1 SIDEIMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT BOUNDARY LAYER MEASUREMENT By YAWEI LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 1 PAGE 2 2008 Yawei Li 2 PAGE 3 To my husband Zhongmin and my parents 3 PAGE 4 ACKNOWLEDGMENTS Financial support for the research project is provided by National Science Foundation (CTS04352835 and CMS0428593) and AFOSR gr ant (F4962003C0114). A doctoral dissertation is never the work of an individual, but instead a mira cle that encompasses the efforts of many people. I would like to recognize a numbe r of people who have helped me in various ways during my time in University of Florida. First and foremost, I extend my sincerest gratitude to my advisor, Dr. Mark Sheplak, who gave me the opportunity to work in MEMS resear ch field. I sincerely appreciate his guidance, continuous encouragement and support in my resear ch, tirelessly sharing with me his expertise and wisdom. His profound knowledge in MEMS, fl uids, acoustics and so on is the invaluable source I always rely on. I also wish to extend gracious thanks to my committee members, Drs. Toshikazu Nishida, Louis N. Cattafesta, Bhavani V. Sankar and Davi d Arnold for their instru ction and assistance on this interdisciplinary project. They are always generous on their time and expertise, and I am grateful for their efforts. I would give special thanks to professors in Department of Electrical and Computer Engineering, Material Science Engineering a nd Mechanical and Aerospace Engineering at University of Florida, especi ally Dr. Mark Law and his stude nt Ljubo Radic, Dr. Kevin Jones and Dr. Raphael Haftka for th eir invaluable suggestions on my device fabrication, process simulation and design optimization. I would espe cially like to thank Dr. Melih Pepila at Sabanchi University (Turkey) and Dr. Jaco F. Schutte for th eir suggestions in optimization design. My thanks go to Dr. Venketaraman Chandrasek aran at Sensata Technologies, Sean Knight in University of South Florida, Alvin A Bar lian in Stanford University and Core Systems 4 PAGE 5 Company for their help in device fabrications, and Keck Pathamma vong at Engent for his help in device packaging. I would also express my tha nks to Al Ogden, Dr. Ivan Kravchenko and Bill Lewis at UFNF for the facility maintenance and help on the fabrication. I was fortunate enough to have great co lleagues throughout my graduate school experience. My thanks go to IMG members, especially Hongwei Qu for his suggestions and discussions in device fabricatio n; Brandon Bertolucci, Alex Phi pps, David Martin for their kind help and assistance in device package design, Vijay Chandr asekharan, Qi Song, Benjamin Griffin and John Griffin for their kind help in device characterization, Matt Williams, Benjamin Griffin, Brandon Bertolucci and Brian Homeijier for their great editing and suggestions in my dissertation writing. It has been a pleasure to have work with them, and I will carry these invaluable memories on rest of life. Finally, I reserve the special thanks to my fa milies for their support and encouragement. I am always grateful to my husband, Zhongmin Liu for his endless love and support in my life. My parents always encouraged me to be the best and do my best on what I want to do. I would like to thank them for believing me every time I said I would graduate next year. Without their love and support this dissert ation would not be possible. 5 PAGE 6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES.......................................................................................................................10 ABSTRACT...................................................................................................................................14 CHAPTER 1 INTRODUCTION................................................................................................................. .16 Motivation for Wall Shear Stress Measurement.....................................................................16 Wall Shear Stress.............................................................................................................1 7 Turbulent Boundary Layer..............................................................................................19 Research Objectives............................................................................................................ ....22 Dissertation Overview.......................................................................................................... ..24 2 BACKGROUND................................................................................................................... .29 Techniques for Shear Stress Measurement.............................................................................29 Conventional Techniques................................................................................................30 MEMSBased Techniques...............................................................................................31 Floating Element Sensors....................................................................................................... 32 Sensor Modeling and Scaling..........................................................................................32 Error Analysis and Challenges........................................................................................34 Effect of misalignment.............................................................................................34 Effect of pressure gradient.......................................................................................35 Effect of crossaxis vibration and pressure fluctuations..........................................36 Previous MEMS Floating Element Shear Stress Sensors.......................................................38 Capacitive Shear Stress Sensors......................................................................................38 Optical Shear Stress Sensors...........................................................................................40 Piezoresistive Shear Stress Sensors.................................................................................42 A FullyBridge SideImplanted Piez oresistive Shear Stress Sensor......................................43 3 SHEAR STRESS SE NSOR MODELING.............................................................................53 QuasiStatic Modeling.......................................................................................................... ..54 Structural Modeling.........................................................................................................54 Small Deflection Theory.................................................................................................55 Large Deflection Theory.................................................................................................56 Energy method.........................................................................................................57 Exact analytical model.............................................................................................57 Lumped Elemen t Modeling....................................................................................................58 6 PAGE 7 Finite Element Analysis........................................................................................................ ..60 Piezoresistive Transduction....................................................................................................62 Piezoresistive Coefficients..............................................................................................64 Piezoresistive Sensitivity.................................................................................................66 Electromechanical Sensitivity.........................................................................................68 Noise Model............................................................................................................................69 Thermal Noise.................................................................................................................6 9 1 f Noise........................................................................................................................70 Device Specific Issues............................................................................................................72 Transverse Sensitivity.....................................................................................................72 Temperature Compensation.............................................................................................73 Device Junction Isolation................................................................................................74 Summary.................................................................................................................................78 4 DEVICE OPTIMIZATION....................................................................................................91 Problem Formulation............................................................................................................ ..91 Design Variables.............................................................................................................91 Objective Function..........................................................................................................93 Constraints.......................................................................................................................94 Candidate Flows.....................................................................................................................95 Methodology...........................................................................................................................96 Optimization Results and Discussion.....................................................................................97 Sensitivity Analysis........................................................................................................... .....98 Summary...............................................................................................................................100 5 FABRICATION AND PACKAGING.................................................................................105 Fabrication Overview and Challenges..................................................................................105 Fabrication Process............................................................................................................ ...105 Sensor Packaging for Wind Tunnel Testing.........................................................................110 6 EXPERIMENTAL CHARACTERIZATION......................................................................118 Experimental Characterization Issues...................................................................................118 Experimental Setup............................................................................................................. ..119 Electrical Characterization............................................................................................119 Dynamic Calibration.....................................................................................................120 Noise Measurement.......................................................................................................121 Experimental Results............................................................................................................122 Electrical Characterization............................................................................................122 Dynamic Calibration Results and Discussion...............................................................122 Summary...............................................................................................................................126 7 PAGE 8 7 CONCLUSION AND FUTURE WORK.............................................................................137 Summary and Conclusions...................................................................................................137 Future Work..........................................................................................................................138 Temperature Compensation...........................................................................................139 Static Characterization...................................................................................................141 Noise Measurement.......................................................................................................142 Recommendations for Fu ture Sensor Designs......................................................................142 APPENDIX A MECHANICAL ANALYSIS...............................................................................................145 Small Deflection............................................................................................................... ....145 Large DeflectionEnergy Method.........................................................................................147 Large DeflectionAnalytical Method....................................................................................149 Stress Analysis................................................................................................................ ......152 Effective Mechanical Mass and Compliance.......................................................................153 B NOISE FLOOR OF THE WHEATSTONE BRIDGE.........................................................157 C PROCESS TRAVELER.......................................................................................................160 Masks....................................................................................................................................160 Process Steps........................................................................................................................160 D PROCESS SIMULATION...................................................................................................166 E MICROFABRICATION RECIPE FO R RIE AND DRIE PROCESS.................................169 F PACKAGING DRAWINGS................................................................................................170 LIST OF REFERENCES.............................................................................................................173 BIOGRAPHICAL SKETCH.......................................................................................................180 8 PAGE 9 LIST OF TABLES Table page 11 Summary of typical skin friction contributions for various vehicles.................................25 12 Parameters in the turbulent boundary layer.......................................................................25 31 Material properties and geometry parameters used for model validation..........................79 32 Resonant frequency and effec tive mass predicted by LEM and FEA...............................79 33 First 6 modes and effective mass predicte d by FEA for the representative structure........79 34 Piezoresistive coefficients fo r ntype and ptype silicon...................................................79 35 Piezoresistive coefficients for ntype and ptype sili con in the <110> direction..............80 36 Space parameter dimensions for junction isolation...........................................................80 41 The candidate shear stre ss sensor specifications.............................................................102 42 Upper and lower bounds associated with the specifications in Table 41.......................102 43 Optimization results for the cases specified in Table 41................................................103 61 LabVIEW settings for noise PSD measurement..............................................................128 62 The optimal geometry of the shear stress sensor that was characterized.........................128 63 Sensitivity at different bias voltage for the tested sensor................................................128 64 A comparison of the predicted versus real ized performance of the sensor under test for a bias voltage of 1.5V.................................................................................................129 E1 Input parameters in th e ASE on STS DRIE systems.......................................................169 E2 Anisotropic oxide/nitride etch recipe on the Unaxis ICP Etcher system.........................169 E3 Anisotropic aluminum etch recipe on the Unaxis ICP Etcher system.............................169 9 PAGE 10 LIST OF FIGURES Figure page 11 Schematic of wall shear stress in a la minar boundary layer on an airfoil section.............26 12 Schematic representation of the boundary layer transition process for a flatplate flow at a ZPG ....................................................................................................................26 13 Schematic of typical velocity profile fo r lowspeed laminar and turbulent boundary layers [9]............................................................................................................................27 14 The structure of a t ypical turbulent boundary layer.........................................................27 15 Estimates of Kolmogorov microscales of length and time as a function of Reynolds number based on a 1/7th powerlaw profile.......................................................................28 21 Schematic crosssectional view of the floating element based sensor.............................46 22 Schematic plan view and crosssection of a typical floating element sensor ...................46 23 Integrated shear force variation as a function of sensor resolution for different element areas.................................................................................................................. ....47 24 Schematic illustrating pressure gradient effects on the force balance of a floating element........................................................................................................................ .......47 25 Schematic crosssectional view of the capacitive floating element sensor .......................48 26 Planview of a horizontalelectrode capacitive floating element sensor ..........................48 27 Schematic topview of a differen tial capacitive shear stress sensor .................................49 28 A schematic crosssectional view of an optical differential shutterbased floating element shear stress sensor ...............................................................................................49 29 Schematic top and crosssectional view of a FebryPerot shear stress sensor ..................50 210 Top and crosssectiona l view of Moir optical shear stress sensor ..................................50 211 A schematic top view of an axial piezoresistive floating element sensor .........................51 212 A schematic top view of a laterallyimpla nted piezoresistive shear stress sensor ............51 213 A schematic 3D view of the sideimplant ed piezoresistive floating element sensor.........52 31 Schematic top view of the structure of a piezoresistive floating element sensor..............81 32 The simplified clampedclamped beam m odel of the floating element structure..............81 10 PAGE 11 33 Lumped element model of a floating elem ent sensor: (a) springmassdashpot system (mechanical) and (b) equivalent electrical LCR circuit.....................................................81 34 Representative results of displacement of tethers for the representative structure............82 35 Representative loaddeflection characteri stics of analytical models and FEA for the representative structure......................................................................................................82 36 Verification of the analyt ically predicted stress profile with FEA results for the representative structure......................................................................................................83 37 The mode shape for the representative structure...............................................................83 38 Geometry used in computation of Eulers angles..............................................................84 39 Polar dependence of piezoresistive coeffici ents for ptype silic on in the (100) plane......84 310 Polar dependence of piezoresistive coeffici ents for ntype silic on in the (100) plane......85 311 Piezoresistive factor as a function of impurity concentra tion for ptype silicon at .................................................................................................................................85 300K 312 Schematic illustrating the relevant geomet ric parameters for piez oresistor sensitivity calculations........................................................................................................................86 313 Schematic representative of a deflected sideimplanted piezoresistive shear stress sensor and corresponding resistance changes in Wheatstone bridge.................................86 314 Wheatstone bridge subjec ted to crossaxis accelera tion (a) and pressure (b)....................87 315 Schematic of the doublebridge temp erature compensation configuration.......................87 316 Top view schematic of the sideimplanted piezoresistor and p++ interconnect in an nwell (a) and equivalent electric circuit indicating that the sensor and leads are junction isolated (b)...........................................................................................................88 317 Doping profile of nwell, p++ interconnect, and piezoresistor using FLOOPS simulation..................................................................................................................... ......88 318 Cross view of isolation wi dth between p++ interconnects................................................89 319 Cross view of isolat ion width between p++ inte rconnect and piezoresistor......................89 320 Top view of the isolatio n widths on a sensor tether...........................................................90 321 Top view schematic of the sideimplanted piezoresistor with a metal line contact...........90 41 Flow chart of design optimization of the piezoresistive sh ear stress sensor....................104 11 PAGE 12 42 Logarithmic derivative of objective function min with respect to parameters................104 51 Process flow of the sideimplanted piezoresistive shear stress sensor............................112 52 SEM side view of side wall trench after DRIE Si...........................................................113 53 SEM side view of the notch at the interface of oxide and Si after DRIE........................113 54 SEM top view of the trench after DRIE oxide and Si......................................................114 55 SEM top views of the trench after DR IE oxide and Si with oxide overetch...................114 56 SEM top views of the trench with silic on grass through a micromasking effect due to oxide underetch................................................................................................................115 57 SEM side view of the trench after DRIE oxide and Si....................................................115 58 Photograph of the fabricated device................................................................................116 59 A photograph of the device with a close up view of the sideimplanted piezoresistor...116 510 Photograph of the PCB embedded in Lucite package.....................................................117 511 Interface circuit board for offset compensation...............................................................117 61 The bridge dc offset voltage as a functi on of bias voltages for the tested sensor............130 62 An electrical schematic of the inte rface circuit for offset compensation.........................130 63 A schematic of the experimental setup for the dynamic calibration experiements.........131 64 Forward and reverse bias char acteristics of the p/n junction...........................................131 65 Reverse bias breakdown voltage of the P/N junction......................................................132 67 The nonlinearity of the IV curve in Figure 66 at different sweeping voltages.............133 68 The output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 kHz as a function bias voltage..........................................................133 69 The normalized output voltage as a functi on of shear stress magnitude of the sensor at a forcing frequency of 2.088 kH z for several bias voltages.........................................134 610 Gain and phase factors of the frequency response function............................................134 611 The magnitude and phase angle of the refl ection coefficient of the plane wave tube.....135 612 Outputreferred noise floor of the measur ement system at a bias voltage of 1.5V.........136 12 PAGE 13 71 Pressure drops versus length between taps in the flow cell.............................................144 72 Experimental setup of static calibration...........................................................................144 A1 The clamped beam and free body diagram. a) Clampedclamped beam. b) Free body diagram of the beam. c) Free body diagram of part of the beam.....................................156 A2 Clampedclamped beam in large deflection....................................................................156 A3 Clampedclamped beam in small de flection (a) and free body diagram of the clamped beam (b).............................................................................................................15 6 B1 The Wheatstone bridge....................................................................................................15 9 B2 The thermal noise model of the Wheatstone bridge........................................................159 B3 The 1 f noise model of the Wheatstone bridge..............................................................159 E1 The drawing illustrating the Lucite packaging................................................................170 E2 The aluminum plate for the plane wave tube interface connection.................................171 E3 Aluminum packaging for pr essure sensitivity testing......................................................172 13 PAGE 14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SIDEIMPLANTED PIEZORESISTIVE SHEAR STRESS SENSOR FOR TURBULENT BOUNDARY LAYER MEASUREMENT By Yawei Li August 2008 Chair: Mark Sheplak Major: Aerospace Engineering In this dissertation, I discuss the devi ce modeling, design optimization, fabrication, packaging and characterization of a micromachin ed floating element piezoresistive shear stress sensor for the timeresolved, direct measurement of fluctuating wall shea r stress in a turbulent flow. This device impacts a broad range of appli cations from fundamental scientific research to industrial flow control and biomedical applications. The sensor structure integrates sideimplanted, diffused resistors into the silicon tethers for piezoresistive detection. Temperature compensa tion is enabled by integrating a fixed, dummy Wheatstone bridge adjacent to the active shearstr ess sensor. A theoretical nonlinear mechanical model is combined with a piezoresistive sens ing model to determine the electromechanical sensitivity. Lumped element modeling (LEM) is used to estimate the resonant frequency. Finite element modeling is employed to verify the qua sistatic and dynamic models. Two dominant electrical noise sources in the piezoresistive shear stress sensor, 1 f noise and thermal noise, and amplifier noise were considered to determ ine the noise floor. These models were then leveraged to obtain optimal sensor designs for se veral sets of specificatio ns. The cost function, minimum detectable shear stress (MDS) formulated in terms of sensitivity and noise floor, is 14 PAGE 15 minimized subject to nonlinear constraints of geometry, lineari ty, bandwidth, power, resistance, and manufacturing limitations. The optimization results indicate a predicted optimal device performance with a MDS of and a dynamic range greater than 75 dB. A sensitivity analysis indicates that the device performance is mo st responsive to varia tions in tether width. 0.1 mPa O The sensors are fabricated using an 8ma sk, bulk micromachining process on a silicon wafer. An nwell layer is formed to control th e spacecharge layer thickness of reversebiased p/n junctionisolated piezoresisto rs. The sensor geometry is r ealized using reactive ion etch (RIE) and deep reactive ion etch (DRIE). H ydrogen annealing is employed to smooth the sidewall scalloping caused by DRIE. The piezoresistors are achieved by sidewall boron implantation. The structure is finally released from the backside using the combination of DRIE and RIE. Electrical characterization indica tes linear junctionisolated resistors, and a negligible leakage current (< ) for the junctionisolated diffused piezoresistors up to a reverse bias voltage of 10 V. Using a known acousticallyexc ited wall shear stress for calibration, the sensor exhibited a sensitivity of a noise floor of 0.12 A 4.24 V/Pa 11.4 mPa/Hz at 1 kHz, a linear response up to the maximum testing range of and a flat dynamic response up to the testing limit of These results, coupled with a windtunnel suitable pack age, result in a suitable transducer for turbulence measurements in lo wspeed flows, a first for piezoresistive MEMSbased direct shear stress sensors. 2 Pa 6.7 kHz 15 PAGE 16 CHAPTER 1 INTRODUCTION This chapter provides an introduction to wall shear stress and motivation for its measurement. Then the scaling tu rbulent boundary layer is reviewed as it applies to dictating the requirements for wall shear stress sensors. Th e research objectives and contributions are presented. This chapter ends with the dissertation overview. Motivation for Wall Shear Stress Measurement The quantification of wall shear stress is importa nt in a variety of engineering applications, specifically in the development of aerospace and naval vehicles. These vehicles span a wide range of Reynolds numbers Re from low (unmanned air vehicles for homeland security surveillance and detec tion) to a very high (hypersonic vehicles for rapid global and space access). Across the range, unsteady, complex flow phenomena associated with transitional, turbulent, and separating boundary layers play an important role in aerodynamics and propulsion efficiency of these vehicles [1, 2]. Furthermor e, since shear stress is a vector field, it may provide advantages over pressure sensing in active flow control applications involving separated flows [3]. Re Re Re The accurate measurement of the wall shear st ress is of vital impor tance for understanding the critical vehicle characteristics, such as lift, drag, and propulsion efficiency. Therefore, the ability to obtain quantitative, timeresolved sh ear stress measurements may elucidate complex physics and ultimately help engineers improve the performance of these vehicles [4]. Viscous drag or skin friction drag is formed due to shea r stress in the boundary layer. The viscous loss is highly dependent on the physical aerodynamic/hydr odynamic system; typical viscous losses for different systems are listed in Table 11 [5]. For aircraft, reducing skin friction by 20% results in a 10% annual fuel savings, and for underwater ve hicles, a reduction of skin friction drag of 20% 16 PAGE 17 would result in a 6.8% increase in speed [5]. Therefore, shear stress measurement attracts attention in sensoractuator syst ems for use in active control of the turbulent boundary layer with an aim of minimizing the skin friction [6]. Wall Shear Stress When a continuum viscous fluid flows over an object, the no slip boundary condition at the surface results in a velocity gradient within a very thin boundary layer [7]; the streamwise velocity increases from zero at the wall to its free stream value at the edge of the boundary layer. The velocity profile is shown in Figure 11 The viscous effects are confined to the boundary layer, while outside of the boundary layer the flow is essentially inviscid [7]. Two classes of surface forces act on the aerodynamic body: th e normal force per unit area (pressure) and the tangential force per un it area (shear stress) For a Newtonian flow, the wall shear stress is proportional to the velocity gradient at the wall. P w The boundary layer is classified as laminar or turbulent depending on Reynolds number or flow structure [7]. A laminar boundary la yer forms at low Reynolds numbers and is characterized by its smooth and orderly motion, where microscopic mixing of mass, momentum and energy occurs only between ad jacent vertical fluid layers. A turbulent boundary layer forms at high Reynolds numbers and is characteri zed by random and chaotic motion [8]. The macroscopic mixing traverses seve ral regions within the boundary layer. There is a transition range between laminar and turbulen t boundary layers, partially lamina r and partially turbulent, as shown in Figure 12 In the transition range, the flow is very sensitive to small disturbances [8]. Typical velocity profiles for low speed lamina r and turbulent boundary layer are shown in Figure 13 Due to the intense mixing, the turbulent boundary layer has a fuller velocity profile; thus, the shear stress in the turb ulent boundary layer is larger than in a laminar boundary layer. 17 PAGE 18 The boundary layer thickness, x is defined as the distance fr om the wall to the point at which the velocity is 99% of the freestream ve locity [7]. The laminar boundary layer thickness in a zero pressure grad ient flatplate flow is given by Blasius as [7] 5.0 x x R e (11) where x R e is the free stream Reynolds number and given by Ux x is the streamwise distance, U is the free stream velocity, and is the kinematic viscosity of the fluid. For turbulent flow, the boundary layer thickness is estimated by the 1/7th power law velocity profile is [7] v 170.16xx Re (12) The shear stress is related to skin friction by the skinfriction coefficient 21 2w fC U (13) The wall shear stress w for a one dimensional laminar fl ow is given by Newtons law of viscosity [7], 0 w y du dy (14) where is the dynamic viscosity of the fluid and is the local streamwise velocity in the boundary layer. For turbulent flow, the shear stress is decompos ed into mean shear stress u w and fluctuating shear stress w in terms of the Reynolds decomposition, www (15) The mean skin friction for laminar and turbulent flow are given by [7] 18 PAGE 19 , 22 0.664w flplate x C U R e (16) and ,0.027ftplate xC Re 1 7 (17) respectively. Equation (12) and (17) are based on the assumption of the 1/7th power law form of the velocity profile proposed by Prandtl [7], 1 7uy U (18) These formulas are in reasonable agreement with tu rbulent flatplate data and are appropriate for a general scaling analysis [7]. Turbulent Boundary Layer To understand the temporal and spatial resolu tion requirements for the shear stress sensor, we need to understand the relevant time and length scales asso ciated with a turbulent boundary layer. There are two regions in a turbulent bound ary layer: the inner laye r and outer layer [9] The semilog plot of the structure of a t ypical turbulent boundary layer is shown in Figure 14 The outer layer (wake region), is turbulent (eddy) sheardominated and the effect of the wall is communicated via shear stress. The inner 20% of the boundary layer is defined as the inner layer, where viscous shear dominates. The overlap layer smoothly connects the inner and outer layer. There are three regi ons within the inner layer: 05 y viscous sublayer (or linear) region uy 54 y 5 buffer region 450.2 y log region 1 ln uy k B where is the Karman constant and k B is the intercept. They are universal constants with and [7]. The nondimensional velocity u 0.41 k 5.0 B is defined as 19 PAGE 20 *uuu (19) where is given by *u wu (110) u is the mean velocity, and is the density of the fluid. The nondimensional distance y is defined as ** y ylyuv (111) where *lvu is the characteristic viscous length scal e. A turbulent flow possesses different length scales. The largest eddies are on the order of the boundary layer thickness, while the smallest eddies can approach the Kolmogorov length scales [8]. Kolmogorovs universal equilibrium theory states that the small scale mo tions are statistically i ndependent of the slower largescale turbulent structures, but depend on the rate at which the energy is supplied by largescale motions and on the kinematic viscosity [8]. In addition, the rate at which energy is supplied is assumed to be equal to the rate of dissipation. Thus, the small eddies must have a smaller time scale and are assumed to be locally isotropic. Therefore, the dissipation rate and kinetic viscosity are parameters governing sma ll scale motions. The scaling relationships between the small and large scale structur es in a boundary layer flow are [4, 8, 10] 34 34~eu Re (112) and 12 12~eu Tu Re (113) 20 PAGE 21 where and T are the Kolmogorov length a nd time scales respectively, is the eddy velocity (typically [4]. Substitution of Equation eu ~0.01e U uO (12) into Equation (112) and Equation (113) leads to estimates of the Kolm ogorov microscales in terms of Re x 1114~20xxRe (114) and 47400 ~xx TRe U (115) The relationship between the Kolmogorov micr oscales and Reynolds number is given in Figure 15 for a zero pressure gradient turbulent boundary layer with 50 ms U and at a distance downstream of the leading edge assuming a 1 m x 17th powerlaw velocity profile. In order to detect the wall sh ear stress generated by the sm allest eddies in a turbulent boundary layer, the sensor size must be of th e same order of magnitude as the Kolmogorov length scale [10], and have a flat frequency range greater than the reciprocal of the Kolmogorov time scale [4]. These microscales are rough estim ates, so some researchers used the viscous length scale and time scale, *l *tu *2 to estimate the required se nsor size and bandwidth [11, 12]. For example, Padmanabahn et al. [11] used in their sensor design, and Alfredsson et al.[12] used and in their experiments. GadelHak and Bandyopadhyay [13] reported these viscous scales are on the same order of the Kolmogorov scales. *4 l *10 l *8 l *2 l If the sensor size is larger than the Kolmogorov length scal e, the fluctuating component will be spatially averaged, which results in spectral attenuation and a corresponding underestimation of the turbulent parameters [14, 15]. It has been reported that the sensor smaller than wall units were free from spatial averaging effects [16] while the sensor lager than wall units suffered shear stress underestimation [17]. Equation 20 30 (112) and (113) indicate that as 21 PAGE 22 the Reynolds number increases, the sensor size shoul d decrease and the bandwidth of the sensor should increase. For example, at 710xRe the Kolmogorov length scale is and the characteristic frequency is From experiments and nu merical simulation results, and GadelHak stated that a sensor size of 35 times of Kolmogorov length is reliable for accurate turbulence measurem ent [10]. A summary of parameters and their analytical expressions for a zero pressure gradient turbulent boundary layer are listed in 65 m 3.7 kHz Lofdahl Table 12 [7, 8]. In addition, roughness is another factor that ma y disturb the turbulent boundary layer. The roughness height due to the flatne ss of the device die in the package, misalignment in tunnel installation, and gap size is denoted by s k and the characterized roughness is given by s sku k (116) In turbulent flow if the roughness protrudes above the thin viscous layer, causing wall friction to increase significantly [7]. If 5sk 4sk the wall surface is deemed hydraulically smooth and the roughness does not significantly dist urb the turbulent boundary layer [7]. Research Objectives The goal of this dissertation is to devel op a robust, high resolution, and high bandwidth silicon micromachined piezoresistive floating element shear stress sensor for turbulent boundary layer measurement. The shear stress sensor should possess high spatial and temporal resolution and a low minimum detectable signal (MDS). To date, the quantitative, timeresolved, continuous, direct measurement of fluctuating shear stress has not yet been realized [4]. Further effort is required to developed standard, reliable MEMS shears tress sensors with quantifiable uncertainties. The detailed description of the choice of the piezoresistive sensing scheme is discussed in Chapter 2. 22 PAGE 23 Depending on the application, there are severa l challenges in the de velopment of this device. An ideal shear stress sensor should have a large dynamic range ( 80 dB O ), large bandwidth and a spatial resolution of 10 kHz O 100 m O to capture the spectra of the fluctuating shear stress without sp atial averaging. The resolvable shear stress would to be on the order of resulting in force resolution of 0.1 mPa O 10 pN O for the desired spatial resolution of In addition, an ideal sensor should be packaged to allow for flushmounting on the measurement wall surface to avoid flow disturbances. 100 m O Traditional intrusive instruments suffer from insufficient spatial and temporal resolution. Microelectromechanical systems (MEMS) tech nology offers the potential to meet these requirements by extending siliconbased integr ated circuit manufacturing approaches to microfabrication of miniature structures [4 ]. From the perspective of measurement instrumentation, the small physical size and reduce d inertia of microsensors vastly improves both the temporal and spatial measurement resolution relative to conventional macroscale sensors. Thus, MEMS shear stress sensors offer the pos sibility of satisfying transduction challenges associated with measuring very small forces while maintaining a larg e dynamic range and high bandwidth. The previous research in MEMS shear stress sensors [1825] is di scussed in detail in Chapter 2. Three transduction schemes have been developed for direct measurement of shear stress: capacitive [18, 21, 24], optical [20, 22, 23] and piezoresistiv e [19, 25]. These previously developed sensors possess performance limitations and cannot be used for quantitative shear stress measurements. 23 PAGE 24 This research effort is the combination of multidisciplinary design and optimization, fabrication, packaging and calibration, which results in a truly fl ushmounted, MEMS direct wall shear stress sensor. The contribu tions to the above efforts are: Development of electromechanical m odeling and nonlinear constrained design optimization to achieve good sensor pe rformance for aerospace applications. Development and execution of a novel microfabrication process accounting for p/n junction isolation and highquality el ectrical and moisture passivation. Development of a sensor package that can be flushmounted on the wall surface. Realization and preliminary charact erization of a functioning device. Dissertation Overview This dissertation is organized into seven chap ters and five appendices. Chapter 1 provides the motivation for the topic of this dissertation. Background information regarding previous shear stress measurement technol ogy is discussed in Chapter 2. Sensor modeling is discussed in Chapter 3. This includes the electromechanical modeling, finite element analysis for model verification as well as specific de sign issues. Chapter 4 discusse s device optimization subjected to manufacturing constraints and specifications. Chapter 5 descri bes the detailed fabrication process and device packaging. Expe rimental characterization setups and results are presented in Chapter 6. The conclusion and future work are presented in Chapter 7. Information supporting this dissertation is given in appendices. Appendix A provides detailed derivations of the quasistatic beam models and dynamic models. The detailed modeling of the noise floor of the fully active Wheatstone bridge is discussed in Appendix B. A fabrication process flow is presented in A ppendix C. The process simulation using FLOOPS [26] is given in Appendix D. The recipes for pl asma etching are given in Appendix E. Finally, packaging details, vendors, and engineeri ng drawings are provided in Appendix F. 24 PAGE 25 Table 11. Summary of typica l skin friction contributions for various vehicles [5]. Vehicles Typical viscous loss Supersonic fighter 2530 % Large transport aircraft 40 % Executive aircraft 50 % Underwater bodies 70 % Ships at low/high speed 9030 % Table 12. Parameters in the turbulent boundary layer. Parameters Analytical expression Free stream velocity ms U U Typical eddy velocity mseu ~0.01euU Streamwise distance m x x Kinematic viscosity Reynolds number based on streamwise distance xUx Re Boundary layer thickness m 170.16xxRe Momentum thickness m 7 72 Reynolds number based on momentum thickness R e U Re Reynolds number based on boundary layer thickness eu Re Skin friction coefficient f C 170.027fxCRe Wall shear stress Paw 21 2wfCU Kolmogorov length scale m 34~ Re Kolmogorov time scale s T 0.5~eRe T u 25 PAGE 26 P y x uy w x Figure 11. Schematic of wall shear stress in a laminar boundary layer on an airfoil section. Figure 12. Schematic representation of the bounda ry layer transition process for a flatplate flow at a ZPG [7]. 26 PAGE 27 Turbulent Laminar Velocity y u Figure 13. Schematic of typical velocity profile for lowspee d laminar and turbulent boundary layers [9]. Figure 14. The structure of a typi cal turbulent boundary layer [8]. 27 PAGE 28 105 106 107 108 109 101 102 103 Kolmogorov Length Scale ( m )Reynolds Number Rex 102 103 104 Kolmogorov Time Scale 1/T (Hz) 1/T Figure 15. Estimates of Kolmogorov microscales of length and time as a function of Reynolds number based on a 1/7th powerlaw profile. 28 PAGE 29 CHAPTER 2 BACKGROUND This chapter provides an overview of the techniques for shear stress sensor measurement with a focus on floating element sensors. Previo us MEMS shear stress sensors are reviewed and their merits and limitations discussed. A sideimp lanted piezoresistive shear stress sensor is then proposed to achieve high spatial and tempor al resolution and quantifiable uncertainties. Techniques for Shear Stress Measurement The current techniques empl oyed in shear stress measur ement are grouped into two categories: direct and indirect [27]. Indirect techniques in fer the shear stress from other measured flow parameters, such as Joulean heati ng rate for thermal sensors, velocity profile for curvefitting techniques or Doppler shift for op tical sensors [27]. The uncertainty in these measurements is dominated by the validity of the model relating the flow parameter to wall shear stress [27]. The direct technique measures th e integrated shear force generated by wall shear stress on surface [4]. This technique includes th ree areas: floatingelement skin friction balance techniques, thinoilfilm techniques and liquid crystal techniques. The floatingelement skin friction balance techniques are a ddressed in this dissertation. A floating element sensor directly measures the integrated shear force produced by shear stress on a flushmounted movable floating element [27]. Direct measurem ent techniques are more attractive since no assumptions must be made about the relationshi p between the wall shear stress and the measured quantity and/or fluid prop erties. In addition, direct sensors can be used to calibrate indirect devices. Conventional shear stress sensors and MEMSb ased shear stress sensors are described in the following sections, with specific focu s on the MEMS floating element technique. 29 PAGE 30 Conventional Techniques Many conventional techniques have been develo ped to measure the wall shear stress [28], including indirect measurement techniques su ch as surface obstacle devices and heat transfer/mass transferbased devices, and dire ct measurement techniques such as a floatingelement skin friction balance. Several review papers [2729] catalog the merits and drawbacks of these devices in various flow situations and a wide range of applications. The indirect conventional techniques are summar ized in the following paragraph. Surface obstacle devices include the Preston tu be, Stanton tube/razor blade and sublayer fence. These devices are easy to fabricate a nd favorable in thick tu rbulent boundary layers. However, they are sensitive to the size and geom etry of the obstacle in the turbulent boundary layer. The device can only measure mean shear stress, and unable to measure the timeresolved fluctuating shear stress. In addition, they rely on an empirical co rrelation between a 2D turbulent boundary layer profile and property measured. Heat transfer/mass transferbas ed devices include hot films and hot wires. They have advantages of fast response, high sensitivity and simp le structure. However, they are sensitive to temperature drift, have tedious calibration pr ocedures, and suffer calibration repeatability problems due to heat loss to the substrate/air. In general, these device s are considered to be qualitative measurement tools [4]. The direct measurement techniques, known as skin friction balance or floating element balance, have been widely used in wind tunnel measurements since the early 1950s [28]. These techniques measure the integrated shear fo rce produced by the wall shear stress on a flushmounted laterallymovable floating element [29]. The typical device is shown in Figure 21 The floating element is attached to either a disp lacement transducer or to part of a feedback 30 PAGE 31 forcerebalance configuration. Winter [28] catal oged the limitations of this technique, which are summarized as follows: Compromise between sensor spatial resolution and de tectable shear force. Measurement errors associated with misalignment, necessary gap and pressure gradient. Crossaxis sensitivity to acceleration, pr essure, thermal expansion and vibration. Some of these limitations can be significantly mitigated if the dimension of the device is reduced, which is a motivation for the devel opment of MEMS floating element sensors. MEMSBased Techniques MEMS is a revolutionary new field that extends silicon integrated circuit (IC) micromachining technology for fabrication of mi niature systems. The MEMSbased sensors possess small physical size and large usable ba ndwidth. The utilization of these devices broadens the spectrum of applications, which range from fundamental scientific research to industrial flow control [6] and biomedical applications [30]. From the fluid dynamics perspective, MEMSb ased sensors provide a means of measuring fluctuating pressure and wall shear stress in turbulent boundary layers because the micromachined sensors can be fabricated on th e same order of magnitude of the Kolmogorov microscale [10]. and GadelHak reviewed MEMSbas ed pressure sensors for turbulent flow diagnosis [10] including background, design cr iteria, and calibration procedures. Recently, Naughton and Sheplak reviewed modern skinfric tion measurement techniques, such as MEMSbased sensors, thinoil film inte rferometry and liquid crystal coatings. They summarized the theory, development, limitations, uncertainties and misconceptions surrou nding these techniques [4]. Lofdahl Several microfabricated shear stress sensors of both direct and indirect types have been reported. The indirect MEMS wall shearstress sensors include thermal devices [3134], laser31 PAGE 32 based sensors [35], micropillar s [36, 37] and microfences [38] Thermal shear stress sensors operate on heat transfer princi ples. Laser Doppler sensors operate on the measurement of Doppler shift of light scattere d by particles passing through a di verging fringe pattern in the viscous sublayer of a turbulent boundary layer to yield the veloci ty gradient. Micropillars are based on a sensor film with micropillars arrays that are essentially ver tical cantilever arrays within the viscous sublayer. Th ese sensors employ optical techni ques to detect the wall shear stress in the viscous sublayer via pillar tip deflection. Microfe nces employ a cantilever structure to detect the shear stress vi a piezoresistive transduction. Direct shear stress sensors include floatingelement devices [1825]. Three transduction schemes have been used in floating element sensors: capacitive [18, 21, 24], piezoresistive [19, 25] and optical [20, 22, 23]. Floating Element Sensors Sensor Modeling and Scaling The typical MEMS floating element sh ear stress sensor is shown in Figure 22 The floating element, with a length of width of and thickness of is suspended over a recessed gap by four silicon tether s. These tethers act as restoring springs. The shear force induced displacement of the floating element is determin ed by EulerBernoulli beam theory to be [11] (the detailed derivation is given in Appendix A) eL eW tT 32 1 4weet tt ttee L WLLW ETWLW (21) where and are tether length, width a nd thickness respectively, and tL tW tT E is the elastic modulus of tether material. The mechanical sensitivity of the sensor with respect to the applied 32 PAGE 33 shear force, weeFWL is directly proportional to the m echanical compliance of the tethers 1 k [18] 32 11 1 4tt y ttee t L LW C kFETWLW (22) The tradeoff associated with spatial resoluti on versus decreasing shear stress sensitivity is illustrated in Equation (21) and Figure 23 For example, a sensor with floating element area of the integrated shear fore is 100 m100 m 10 pN O for a shear stress of 1 mPa O which requires the tethers to have a high compliance to get an apprec iable element detection. The compliance is limited by the maximum shear stress achievable before failure occurs or before nonlinearity in the forcedisplacement relations hip [4] becomes substantial. The minimum detectable shear stress is determined by the sensitivity and the total sensor noise [39]. Assuming a perfectly damped or underdamped system, the bandwidth is proportional to the first resonant frequency, kM where M is the effective mass, eet M LWT (23) where is the density of the floating elemen t material and it is assumed that Therefore, the shear stress sensitivit ybandwidth product is obtained as eettLWLW 3 211 4t eettL ELWTW kM (24) The sensitivitybandwidth product is a parameter useful in inve stigations of the scaling of mechanical sensors. MEMS technology enables the fabrication of sensors with small thickness and low mass, in addition to large compliance and a superior sensitivitybandwidth product comparable to conventional techniques [4]. A MEMS floating element has lengths of 33 PAGE 34 1000 meeLWO and whereas conventional floating element lengths are Therefore, with the scaling of ma ss alone, MEMSbased sensors have a sensitivitybandwidth product at least threeor ders of magnitude larg er than conventional sensors. MEMSbased sensors also possess spat ial resolution at least oneorder of magnitude higher than conventional sensors, which is vital for turbulence measurements to avoid spatial averaging [4]. 10 mtTO 1 cmeeLWO Error Analysis and Challenges Compared to conventional techniques, MEMS shear stress sensors have a negligible misalignment error. This error is limited by th e flatness of the device die [18] because the floating element, tethers and substrate are fabri cated monolithically in the same wafer. Other sources of misalignment include packaging and tu nnel installation, with pa ckaging the dominant source [4]. Packaginginduced compressive or tensile force may drastically alter the device sensitivity [18]. The necessary gap between the wall and floating element is also reduced, with a typical gap size smaller than [4]. 5 m Effect of misalignment Misalignment of the floating element results in the element not being perfectly flushmounted with the wall surface, which disturbs th e flow field around the sensor. The effective shear stress is estimated by integrating the stagnation pressure 2 yu over the floating element surface and dividing by th e element area [39] to get 2 0 k s y MA eudz L (25) 34 PAGE 35 where s k is the height of protrusion or recession above or below the wall. Streamwise velocity is obtained via relationship be tween shear stress and velocity gradient in the sublayer, yu y wu z (26) where and are the density and dynamic viscosity of the fluid, respectively, and z is the distance from the wall. Substituting Equation (26) into Equation (25) to obtain the effective shear stress yields 3 21 3 s w MA ek L (27) For a sensor with 1000 meL 10 msk under the surface, and 5 Paw in air, the misalignment error is about 0.12%. Therefore it may be neglected. Effect of pressure gradient Error due to a pressure gradient is also greatly decreased for MEMS sensors. As illustrated in Figure 24 there are two sources which introduce pre ssure gradient errors; one is the recessed gap beneath the floating element and the other is the net pressure force acting on the lip of the floating element [26]. The net force acting on the lip of the floating element is given as p teteedP FTWPTWL dy (28) The associated effective shear stress is obtained by dividing by the sensor area, eeWL p tdP T dy (29) The pressure gradient also introduces a shear stress underneath the floating element that can be estimated to firstorder by assuming fullydeveloped Poiseuille flow, 35 PAGE 36 2ggdP dy (210) where is the height of the recesse d gap beneath the floating element. The total effective shear stress acting on the floating element is g **1 22t effw t wT dPg g T dy (211) where wdP dy is called Clausers equilibrium parame ter, which is employed to compare the external pressure gradient to wall friction in a turbulent boundary layer [7]. The displacement thickness is a parameter quantifying the mass flux defic it due to viscous effects. As indicated in Equation (211) the error is dependent on the gap si ze and thickness of the floating element and independent of the size of the floating elem ent. The smaller ga p and thickness of the MEMS sensors result in smaller e rrors compared to conventional floating element sensors; the MEMS sensors provide approximately a twoor der of magnitude improvement in lip force induced error. To get a more accurate estimate of these errors, direct numerical simulation of the flow around the sensor is required. Effect of crossaxis vibration and pressure fluctuations Errors due to streamwise acceleration scale favorably for low mass MEMS sensors [28]. The equivalent shear stress due to acceleration is approximated as eet a ffeeWLTa FMa Ta AAWL t (212) where is the acceleration and a f A is the surface area of the fl oating element, respectively. Equation (212) indicates that the effective shear st ress due to streamwise acceleration is proportional to the tether thickness. Assuming the streamwise acceleration is 1 g, for a 36 PAGE 37 proposed optimum sensor design with element dimensions of 1 000 m1000 m50 m and the tethers dimension of 1, the effective stress is found to be 1.14 in the 000 m30 m50 m Pa y direction. Depending on the aerodynamic body acceleration levels, local acceleration measurements in conjunction with coherent pow er data analysis may be used to mitigate acceleration effects [40]. The streamwise deflection is obtained from c cMa y M aC k (213) where and are the streamwise stiffness and compliance of the tether s, respectively. Therefore, the streamwise acceleration sensitivity is proportional to Assuming flow over the floating element in the direction ( ck yC yC y Figure 24 ), the crossaxis compliances according to smalldeflection beam theory are 4t x ttL C E WT (214) and 31 4t z tt L C E WT (215) The ratios of transverse compliances to compliance in the flow direction are 2 y t xtC L CW (216) and 2 y t ztC T CW (217) If and the compliance in the ~50 mttTWO ~1 mmtLO x direction is four orders of magnitude less than the complia nce in the flow direction ( y direction). Since the deflection is proportional to the compliance in the associat ed direction, the transverse deflection ( x direction) 37 PAGE 38 is fourorders of magnitude smalle r than in the flow direction ( direction). Therefore, the transverse acceleration effect in y x direction is negligible. However, the compliances in the and z y directions are of the same order, and thus tr ansverse acceleration eff ects in the z direction must be taken into account. This can be mitigated by using piezoresistive transduction scheme via a fullyactive Wheatstone bridge configuration. The transverse acceleration and pressure in the direction supplies a common mode signal to the Wheatstone bri dge, which can be rejected by the differential voltage output. It is critical to minimize the pressure sensitivity as pressure fluctuations in wallbounded turb ulent flows are much larger in magnitude than wall shear stress fluctuations [41]. Hu et al. [41] found that the wall pressure fluctuations is (depending on frequency) higher than the fluctua tions for the streamwise wall shear stress, and higher than that for spanwise component. The detailed discussion is given in Chapter 3. z 720 dB 1520 dB Previous MEMS Floating Element Shear Stress Sensors Previous research in the floating element shear stress sensor is review ed in this section. This review is divided into capacitive, optical and piezoresistive sensing in terms of transduction schemes. Their respective performance merits and drawbacks are discussed. Capacitive Shear Stress Sensors Realizing the merits of scali ng shear stress sensors to the microscale, Schmidt et al. [18, 39] first reported the development of a micromac hined floating element shear stress sensor with an integrated readout for applications in lo w speed turbulent boundary layers, As shown in Figure 25 the sensor was comprised a square floating element (50 0 m500 m32 m ) suspended by four tethers (1000 m5 m32 m ) and fabricated usi ng polyimide/aluminum surface micromachining techniques. A differentia l capacitive scheme was employed to sense the 38 PAGE 39 deflection of the floating element. This differe ntial capacitive scheme is insensitive to the transverse movement to first order. The sens or was calibrated in a laminar flow using dry compressed air up to a shear stress of 1 P. The achieved minimum detectable shear stress was with a bandwidth of 10. The measurement data was in agreement with the design model. However, the sensor was sensitive to electromagnetic interference (EMI) due to the high input impedance, and suffered from the sensi tivity drift due to mois tureinduced polyimide property variation. In addition, the capacitive sensing scheme was limited to nonconductive fluids. a 0.1 Pa kHz Pan et al. [21, 42] presented a forcefeedback capacitive design that monolithically integrated sensing, actuation a nd electronics control on a single chip using polysiliconsurfacemicromachining technology. The sensor has a comb finger structure with folded beam suspension. The folded beam provided higher sens itivity and internal stress relief. The floating element motion was measured by a differential cap acitive sensing scheme while the folded beam served as mechanical springs ( Figure 26 ). A linear measurement sensitivity of 1.02 VPa over a pressure range of to 3.7 was achieved in a 2D continuum laminar flow channel. No dynamic response, linearity and noise floor result s were reported. In addition, the front wire bonds may disturb the flow in turbulent flow measurements. 0.5 Pa Zhe et al. [24] developed a floating elemen t shear stress sensor using a differential capacitive sensing technique, with an optical technique as a selftest. The sensor was fabricated on an ultrathin ( ) silicon wafer using wafer bonding and DRIE techniques. As shown in 50 m Figure 27 the sensor consisted of two sensor elec trodes, two actuation el ectrodes, a floating element (20in width and 500 in length) and a cantilever beam ( in length). The shear stress was detected by a cantilever beam deflection, with a mechanical sensitivity of 0 m m 3 mm 39 PAGE 40 1 mPa This sensor was capable of measuring a shear force as small as 5 n that corresponded to a shear stress of 50. The static calibration in a rectangular channel shows a minimum detectable shear stress of with 8% uncertainty up to which is the limit of the calibration technique. No fr equency response results were reported. N mPa 0.04 Pa 0.2 Pa Optical Shear Stress Sensors Padmanabhan et al. [20] developed two genera tions of differential optical shutterbased floating element sensors for turbulent flow measurement. As shown in Figure 28 the floating element (120 and 500 m120 m7 m m500 m7 m ) is suspended 1. above the silicon substrate by four tethers. Two photodiodes were integrated into the substrate under the leading and trailing edges of th e opaque floating element. The floating element motion induced by shear force causes the photodiodes shuttering. Under uniform illumination from above, the normalized differential photocurrent is proportional to the lateral displacement of the element and the wall shear stress. The sensor could measure a wall shear stress from up to 10, with a sensitivity of 0 m 3 mPa Pa 0.4 VmPa (without integration of detection electronics ). The dynamic response of the sensor was quantified up to the characterization limit of [43]. The measured shear stress was consiste nt with predicted theoretical va lues. The sensor showed very good repeatability, longterm stability, minimal drif t, and EMI immunity. The main drawback to this sensor was that vibrations of the light source relative to the sens or resulted in erroneous signals. 4 kHz Tseng et al. [22] developed a novel FebryPero t shear stress sensor that employed optical fibers and a polymer MEMSbased structur e. The sensor was micromachined using micromolding, UV lithography and RIE processes. As shown in Figure 29 a membrane was used to protect the inner sensing parts and support the floating element displacement 40 PAGE 41 measurement. The displacement of the floating element (40 high, wide) induced by the wall shear stress on the membrane (1 0 m 200 m .5 mm1.5 mm20 m ) was detected via an optical fiber using FabryPerot interferometer. The sens or was tested in a steady laminar flow between parallel plates and the results demonstrated a shear stress resolution of 0.65 Panm The minimum detectable shear stress was The fragile sensing parts were not exposed to the testing environment, making the sensor suitable for applications in harsh environments. This sensor was not tested in flows. The dynamic response and linearity of this sensor are questionable due to the potential buckling of diaphr agm. Furthermore, crossaxis sensitivity due to vibration and pressure may be significant given the geometry of the sensing element. 0.065 Pa Horowitz et al. [23] develope d a floatingelement shear stre ss sensor based on geometric Moir interferometer ( Figure 210 ). The device structure consisted of a silicon floating element (1280) suspended above a Pyrex wafer by four tethers ( ). The sensor was fabricated via DRIE and a wafer bonding/thin back process. When the device was illuminated throu gh the Pyrex, light was reflected by the top and bottom gratings, creating a translationdependent Moir fringe pattern. The shift of the Moir fringe was amplified with respect to the elem ent displacement by the ratio of fringe pitch G to the movable grating pitch The sensor die was flushmounted on a Lucite plug front side, and the imaging optics and a CCD camera was inst alled on the backside for the displacement measurement. Experimental characteriza tion indicated a stat ic sensitivity of m400 m10 m 2.0 m 545 m6 m10 m 2g 0.26 mP a a resonant frequency of 1.7, and a noise floor of kHz 6.2 mPaHz Drawbacks to this sensor included an optical packaging scheme not f easible for wind tunnel measurement and limited bandwidth. 41 PAGE 42 Piezoresistive Shear Stress Sensors Shajii et al. [19] and Goldberg et al. [ 44] extended Schmidts work to develop a piezoresistive based floating element sensor for polymer extrusion feedback control ( Figure 211 ). The polyimide/aluminum composite floating el ement was replaced by single crystal silicon. These sensors were designed for operation in high shear stress 1 kPa100 kPa high static pressure (up to ) and high temperature (up to 300) flow conditions. The floating element size was 120 in Ngs design, and 500 40 MPa C m140 m m500 m in Goldbergs design. The element motion was sensed by axial surface pi ezoresistors in the tethers via configuration these piezoresistors to a half White stone bridge. This sensor was not suitable for turbulent flow measurement due to low sensitivity as it was de signed for maximum shearstress levels 5 ordersofmagnitude larger than those in a typical turbulent flow. However, Goldberg et al. [44] developed a backside contact st ructure to protect the wirebon ds from the harsh external environment, which reduced the flow disturban ce and associated measurement uncertainty for turbulence measurement. Barlian et al [25] developed a piezoresistive shear stress sens or for direct measurement of shear stress underwater. The si dewallimplanted piezoresistors measured the integrated shear force, and the topimplanted piezor esistors detected the pressure ( Figure 212 ). The displacement of the floating element was detected using a Wheatstone bridge. The experimental measurements indicated the inpla ne force sensitivity ranged from 0.0410.063 mVPa while the predicted sensitivity was 0.068 mVPa The transverse sensitivity was 0.04 mVPa with a corresponding transverse resonant frequency of 18. This was done by using a mechanical cantilever as an input. The dynamic analysis wa s performed using a lase r Doppler vibrometer with a piezoelectric shaker to drive the inplane or outofplan e motion. The inplane resonant .4 kHz 42 PAGE 43 frequency was experimentally found to be 19 compared to a predicted value of 13.4. The integrated noise floor was 0.16 over bandwidth of 1 kHz kHz V Hz100 kHz The sensitivity of the piezoresistors to changes in temperature was investigated in a deion ized (DI) water bath, and the temperature coefficient of sensitivity was found to be o0.0081 k C No electrical characteristics of p/n junction isolation and flow characteri zation are reported and no fluid mechanics characterization was performed. A FullBridge SideImplanted Pi ezoresistive Shear Stress Sensor According the above discussion, the most su ccessful MEMS floating element sensor to date used integrated photodiodes to detect the lateral displacement via a differential optical shutter [20]. This sensor can de tect the shear stress as low as 1.4. However, it is not suitable for wind tunnel testing because the sens ing system is sensitive to tunnel shock and vibration. The capacitive transduction techniqu e integrated the mechanical sensor and electronics on one chip to eliminate the parasi tic capacitance [45], and has the capability to measure small signals. Unfortunately, the sensitivity drifted due to the charge accumulation in the electrodes [18], which can be mitigated by hermetic sealing [46] or by employing metal electrodes. However, the shear stress sensor must be exposed to the flow for shear stress measurement and wind tunnels are typically not humidity controlled environments. mPa The piezoresistive transduction scheme is wide ly used in commercial pressure sensors and microphones due to its low cost, simple fabricat ion, and higher reliabi lity than capacitive transduction. In addition, piezoresistive techno logy can resolve sufficiently small forces up to [47]. Shajii et al. [19] proposed a backsi decontact, piezoresistive sensor to measure very high shear stress in a polymer extruder. Ax ial mode piezoresistive transducers [19, 25] for highshear industrial applicati ons have been fabricated us ing standard ionimplantation 1510N O 43 PAGE 44 techniques, but more sensitive bendingmode transducers require that the piezoresistors be located on the tether sidewall. This concept ha s been proposed by Sheplak et al.[48] and applied by Barlian et al. who presented an integrated pressure/shear stress sensors for underwater applications [25]. The authors did not present a comprehensive fluidinduced shear stress characterization of their sensor Rather, the sensor was sta tically characterized using a mechanical cantilever and dynamically charac terized using an acceleration input. In a conference paper, the authors presented some wa ter flow results possessing a large uncertainty and an unexplained sensitivity that was larger than the value predicted by beam mechanics [49]. None of these devices have successfully tr ansitioned to wind tunnel measurement tools because of performance limitations and/or packag ing impracticalities [2]. For use in a wind tunnel, the sensor package must be flush m ounted in an aerodynamic model, robust enough to tolerate humidity variations and immune to el ectromagnetic interferen ce (EMI). We have attempted to address these limitations via the de velopment of a fullyactive Wheatstone bridge sideimplanted piezoresistive sensor. This approach was motivated by the following two sideimplanted piezoresistive transduc er concepts. Chui et al. [ 50] first presented a dualaxis piezoresistive cantile ver using a novel oblique ion implantation technique. Later, Partridge et al. [51] leveraged the sideimplant process to fabr icate a high performance lateral accelerometer. The device structure developed in th is dissertation is illustrated in Figure 213 which shows an isometric view of the floating element, sidewall implanted ptype silicon piezoresistors, heavily doped endcap region, and bond pads. In this transduction scheme, the integrated force produced by the wall shear stress on the floating el ement causes the tethers to deform and thus induces a mechanical stress field. The piezoresistor s respond to the stress field with a change in resistance from its nominal, unstressed value due to a change in the mobility (or number of 44 PAGE 45 charge carriers) within the pi ezoresistor [52]. The conversio n of the shear stress induced resistance change into an electrical volta ge is accomplished via configuration of the piezoresistors into a fullyactive Wheatstone bridge to increase the sensitivity of the circuit compared to half bridge configuration. This bridge requires the presence of a bias current through the piezoresistors, typicall y, it is driven by constant volta ge excitation. This sensor is designed to measure shear stress only and to m itigate pressure sensitivity. An onchip dummy bridge located next to the sensor is used for temperature corrections. Ideally, common mode disturbances do not have any effect while differential disturbances are linearly converted into the br idge output. To achieve a differe ntial signal, the piezoresistors are oriented such that the resi stance modulation in each resistor of a given leg is equal in magnitude but opposite in sign. These conditions are achieved by placing the side implanted resistors facing one another such that when one resi stor is in tension, the other is in compression. This results in equal mean resi stance but opposit e perturbation. Once the transduction scheme is selected, the mechanical models and transduction sensing models need to be developed to get sensor performance, such as sensitivity, linea rity, bandwidth, noise floor, dynamic range, MDS. The detailed di scussion of the electrom echanical modeling is given in Chapter 3. 45 PAGE 46 Figure 21. Schematic crosssectional view of the floating element based sensor. Figure 22. Schematic plan view and crosssection of a typical floating element sensor [4]. 46 PAGE 47 102 100 102 1012 1010 108 106 104 102 Shear Stress w (Pa)Shear Force (N) 100X100 m2 250X250 m2 500X500 m2 1X1 mm2 2X2 mm2 103103 Figure 23. Integrated shear fo rce variation as a function of sensor resolution for different element areas. Figure 24. Schematic illustrating pressure gradient effects on the force balance of a floating element. 47 PAGE 48 Embeded Conductor Floating Element Cps1Cps2CdpVDS Passivated Electrodes Csb1Csb2Silicon on chip off chip Sense Capacitor Sense Capacitor Drive Capacitor Figure 25. Schematic crosssectional view of the capacitive floating element sensor developed by Schmidt et al. [18]. Release Holes Floating Element Tether Expanded View of Comb Finger Structures C1 C2 VV+ Figure 26. Planview of a hor izontalelectrode capacitive fl oating element sensor [21]. 48 PAGE 49 Figure 27. Schematic topvi ew of a differential capacitiv e shear stress sensor [24]. Figure 28. A schematic crosssectional view of an optical differentia l shutterbased floating element shear stress sensor [11]. 49 PAGE 50 Figure 29. Schematic top and crosssectional vi ew of a FebryPerot sh ear stress sensor [22]. Tethers Aluminum Gratings (Floating Element & Base Gratings) Reflected Moir Fringe Floating Element Silicon Pyrex Laminar Flow Cell Incident Incoherent Light Figure 210. Top and crosssectional view of Moir optical shear stress sensor [23]. 50 PAGE 51 Flow 180 m 120 120 m 10m m Figure 211. A schematic top view of an axial piezoresistive floating element sensor [19]. Figure 212. A schematic top view of a laterallyimplanted piezoresistiv e shear stress sensor [25]. 51 PAGE 52 R R R R R R R RoVBV1V2V Figure 213. A schematic 3D view of the sidei mplanted piezoresistive floating element sensor. 52 PAGE 53 CHAPTER 3 SHEAR STRESS SENSOR MODELING This chapter presents the electromechani cal modeling of the ME MS sideimplanted piezoresistive shear stress sensor. These mode ls are leveraged for use in finding an optimal sensor design (detailed discussion in Chapter 4). Formulation of th e objective function for performance optimization begins with structural and electronic device models of the shear stress sensors. The structural response directly dete rmines the mechanical sensitivity, bandwidth, and linearity of the dynamic response. The piezore sistor design determines the overall sensitivity and contributes to the electronic noise floor of the device. The organization of this chapter is as follows. First, the mechanical modeling is discussed, including quasistatic modeling and dynamic response analysis. Linear and nonlinear quasistatic behaviors are presented. Lumped element modeling is employed to find the dynamic behavior of the sensor. These analytical models were verified using finite element analysis (FEA) in CoventorWare. Second, the piezoresistive sensing electrom echanical model is developed, where the resistance and piezoresistive sensitivity for nonuniform doping are derive d via stress averaging and a conductanceweighted piezores istance coefficient. Two domi nant electrical noise sources in the piezoresistive shear stress sensor, 1 f noise and thermal noise, as well as amplifier noise are considered to determine the noise floor. Finally, some device specific issues are addressed, including transverse sensitivity, acceleration sensitivity, pressure sensitivity, junction isolation issues and temperature compensation via a dummy bridge. 53 PAGE 54 QuasiStatic Modeling In this section, the sensor structure is disc ussed and modeled. Quas istatic models for small and large floating element deflections that make use of EulerBernoulli beam theory and the von Krmn stain assumption, respectively, are presented. Two methods are used in large deflection analysis, an energy method and an exact analytical method. Structural Modeling Floating element sensors are composed of four tethers and a square floating element. A schematic of the piezoresistive sh ear stress sensor is shown in Figure 31 The floating element is suspended above the surface of the silicon wafer by tethers, each of which is attached at its end to the substrate. Sideimpla nted boron in the sidewalls of the tethers forms the four piezoresistors. These resistors are aligned in th e <110> direction and loca ted near the edge zone of the tethers to achieve the maximum sensitiv ity. Two resistors are oriented along opposite sides of each tether. When the fluid flows over the floating element, the integrated shear force causes the tethers to deform a nd induces a bending stress. For the mechanical analysis, the floating elements and tethers are assumed to be homogeneous, linearly elastic, and symme tric. In practice, this is not strictly valid as the beam is partially covered by thin silicon dioxide and si licon nitride layers. The floating element is assumed to move rigidly under the applied shea r stress, and the motion is permitted inplane only. The tethers are assumed to be perfectly clamped on the edge. The effects of pressure gradient and gap errors are i gnored. Furthermore, the Youngs modulus and Poisson ratio are assumed to be constant and do not change with processing. 54 PAGE 55 Small Deflection Theory Assuming that the tethers can be modeled as a pair of clampedclamped beams with a length of subjected to a uniform distributed load (per unit length) and a central point load [39], as shown in ttLW tT 2tL Q P Figure 32 The distributed load is due to the shear stress acting on the tethers and is given as wtQW (31) The point load, is the effect of the resultant shear force on the floating element and is given by P 2weePWL (32) where the factor of 1/2 comes from the symmet ry of the problem. The maximum deflection and bending stress distribution is obt ained using Euler Bernoulli beam theory. The detailed derivation is given in Appendix A. The la teral displacement of the beam is given by 22 34 3()38282 (0) 4w eettt eett t t ttwx WLLWLxWLWLxWxxL EWT Pa (33) where is the Youngs modulus of silicon in the 168 EG 110 direction [53]. The maximum deflection occurs at the center of the beam and is obtained by substituting t x L into Equation (33) to get 312 4weet tt tteeWLLWL E TWWL (34) This corresponds to the floating element displ acement. The second term in the brackets of Equation (34) is a correction for the distributed wa ll shear stress on the tethers. Equation (34) indicates that the important parameters affecti ng the scaling of the device are the area of the floating element, ratio of the tether lengt h to the tether width, eeWL tLW t and ratio of the area 55 PAGE 56 of a tether to that of the floating element, tteeWLWL If the tether surface area the stiffness is approximated as tteeWLWL 311 4t weett L kWLETW (35) This indicates that the stiffness is proportional to the tether thickness and ra tio of the tether width and length. The bending stress di stribution through the width and le ngth of the tether is given by 2 20 263 233 ,1 0 42t weet tt tt tt l t ttt ee eeteet x L WLL WLWLWL yx x xy yW WTWWLWLLWLL ,(36) where is at the end of the beam, and 0 x 0y is on the side wall surface. Equation (36) indicates that the maximum shear stress is locate d at the end of the beam and on the side wall surface ( in ,xy 0 Figure 32 ). Linear EulerBernoulli beam theory [54] fails for sufficiently large wall shear stresses because the midplane of the beam is strained [46]. The beam grows stiffer as the deflection becomes large. Furthermore, the nonlinear motion generates undesired harmonic distortion in the frequency domain. The sensor is required to maintain a li near relationship between shear stress and displacement in order to preserve spectral fidelity for time resolved measurement. This requirement places a nonlinear constraint in the sensor design optimization (discussed in Chapter 4). A large deflection mechanical model was therefore developed for use in determining this constraint. Large Deflection Theory Large deflection theory provides a measure of the maximum shear stress that may be measured while maintaining mechanical linearit y. Two analysis techniques are pursued to 56 PAGE 57 determine the nonlinear mechanical behavior of th e sensor: the strain en ergy method [46] and an exact analytical method. The detailed derivations are given in Appendix A. Energy method The deflection predicted by the strain energy method [46] is obtained by assuming a trial function which meets both the clamped boundary condition and symmetry condition of the beam, 1cos 2t NL tLx wx L (37) where N L is the floating element deflection. The tria l function is substituted into the expression for strain energy in the beam and the principle of minimum potential en ergy is applied. The result is 23 term3 1 44NL weet tt NL tt t NLWLLWL WETWW 1 2e eL (38) Comparing this result to Equation (34) one can see that cubic nonlinearity term has been added. The mechanical response of the floating element sensor will be linear provided that the nonlinear term is small with respect to unity; that is if the displacement of the sensor is small in comparison to the tether width, 21NLtW The nonlinear term is cubic and therefore represents a Duffing spring behavior or stiffening of the beam as deflections become large. This means that the nonlinear deflection is smaller th an the ideal linear deflection for large shear stresses. Exact analytical model In the large deflection model, the neutral axis tension force is taken into account. The average axial tension force is ob tained by integrating the neutral axis strain along the length of aF 57 PAGE 58 the beam. It then serves as a constitutive equa tion between axial force and strain. The detailed model development procedure is given in Appe ndix A. The maximum deflection predicted by the exact analytical method is obtaine d using von Krmn strain assumption, 2cosh()1 sinh() cosh()+ 2 sinh()22 22tt AL t t t aat aLQ PP P LQ LL FFL F t aL P L F (39) where the axial force is given by aF 2 02Lt tt a tdwx ETW F dx Ldx (310) and is given by 3=12attFETW (311) There are five variables, four boundary condi tions and one constitutive equation. But the equation is indeterminate, so the final solution is obtained using an ite rative technique to find and therefore obtain the maximum deflection. Lumped Element Modeling Lumped element modeling is used to represen t the fluidic to mechanical transduction of the shear stress sensor and fac ilitates the prediction of the dynamic response. The main assumption of LEM is that the length scale of th e physical phenomena of interest is be much larger than the characteristic length scale of the device [55]. For the shear stress sensor, this means that the bending wavelength of the beam mu st be much larger than the length of the tethers. The LEM provides a simple way to estimate the dynamic response of a system for low frequencies, up to just beyond the first resona nt frequency, which is appropriate for design purposes [56]. 58 PAGE 59 There are several types of elements in the lumped element model. For example, in a lumped mechanical system, mass represents the st orage of kinetic energy compliance of a spring (inverse of stiffness) represents the storage of potential energy, and a damper represents the loss of energy through dissipation. Si milarly, in lumped electrical systems, generalized potential energy is stored in a capacitor, generalized kinetic energy is stored in an inductor, and energy is dissipated via a resistor. From a LEM perspective, the two sets of te thers are modeled as a spring possessing an effective compliance In an impedance analogy, this compliance shares a common displacement with the effective mass meC me M of the tethers and floating element as well as the damper, d R of the system. The main source of damp ing is the viscous damping underneath the element, and thermoelastic damping, compliant boundaries and vibrati on radiation to the structure boundaries are neglected in this research. Therefore, the sensor is modeled as a springmassdashpot system, as schematically shown in Figure 33 In the equivalent circuit, the voltage and current are analogous to force and velocity, respectively. The motion of the massspringdashpot system is described by the cl assic secondorder differential equation, 2 2() 1me d medd FtMRC dtdt (312) Therefore, the frequency response func tion of the device is found to be 21 () () 1medmej Hj Fj j MjRC (313) where the angular frequency 2 f f is the cyclic frequency, and 1j Assuming a lightly damped system, the first resonant frequency r f is 59 PAGE 60 1 2r memef CM (314) The detailed derivation of the lumped elemen ts is given in Appendix A. The effective mechanical compliance is determined by equating th e potential energy stored in the beam to that of an equivalent lumped system and is 321 1214 21tt tt tt t me tt ee ee eeLWLWLWL C ETWWLWLWL 26 4 5 (315) The effective mass is obtained by eq uating the kinetic energy of the sensor to that of a lumped system and is 23149422381024 11 315315 315tt tt tt tt mesieet ee ee ee eeWLWLWL WL MWLT WLWLWLWL 22 (316) where 32331 kgmsi is the density of silicon [53]. Finite Element Analysis To verify the analytical models, a finite element analysis with a clamped boundary condition on the edge of the tethers is perfor med. The material properties of silicon and the geometry of a representati ve structure are given in Table 31 Finite element analysis is performed in CoventorWare using the multimesh model by partitioning the continuum solid model into plate and tether volumes. A fine mesh is used in the tethers because of the large stress gradients with respect to those found in the plate. These volumes are joined to form one volume via RigidLink after meshing. The mesh is composed of parabolic Manhattan brick elements. A mesh refinement study revealed sufficient elements dimensions are 3 in length, width and thickness within the tethers, m,0.5 m and 1 m 60 PAGE 61 respectively, and 10 within the plate. Since the device is symmetric, only half of the structure is analyzed in the model, with 6600 elements in the analysis. m,10 m,1 m A representative displacement field of the tethers at 5 Paw is shown in Figure 34 The comparison in Figure 34 indicates that the nonlinear analyti cal model is in agreement with FEA simulation results. Figure 35 shows the maximum displacement of the floating element as a function of applied shear stress for analytical linear and nonlinear models, nonlinear energy method model and FEA model. This comparison in Figure 35 indicates that al l results are in agreement in the linear range ( approximately), while the nonlinear analytical model, nonlinear energy method model and FEA models agree in this nonlinear deflection region. 50 Pa Figure 36 shows the stress distribution usi ng analytical linear model (Equation (36) ) and FEA results along the tether le ngth on the sidewall surface ( 0y ) for the representative structure. Figure 36 demonstrates that the analytical model is in agreement with the FEA model. The bending stress varies from tensile to compressive in a parabolic distribution along the tether length. Figure 36 shows that the maximum stress occurs on the edge zone ( ) of the tether. ,xy 0 The resonant frequenc y obtained from LEM (12.44) and FEA (12.47) agree well, as shown in kHz kHz Table 32 The next 5 modes were also found using FEA and are given in Table 33 The first six mode shapes are shown in Figure 37 The inplane resonant frequency (second mode) is 17.08, greater than the outofplane resonant frequency (first mode) because the tether width is greater than the tether thickness for the verification studies ( kHz Table 31 ). Clearly, the representative dimensions used for model verification are not a preferred design, let alone an optimized design. 61 PAGE 62 Piezoresistive Transduction In 1954, Smith [52] discovered the piezoresistan ce effect in silicon and germanium. The piezoresistance effect is defined as the change of semiconductor resistivity due to a change in carrier mobility that results from an applied mechanical stress. In piezoresistive transduction, the resistance modulation is a function of the a pplied stress and piezoresistive coefficients ij [57]. For the cubic crystal structure of silicon under small strain, the corr elation of normalized piezoresistivity and stress for reduced tensor notation reduces to 1111212 2121112 3121211 23 44 23 13 44 13 12 4412000 000 000 1 00000 00000 00000 1 2 3 (317) where is the change in resistivity, i are normal stresses along the cubic crystal axes, and 100 ij are shear stresses. For a given resistor geometry, there are two piezoresistive coefficients used for piezoresistive sensing analysis in terms of stre ss orientation with respect to the current. The longitudinal piezoresistive coefficient captures th e effect of an applied stress in the same direction as the current, and the transverse piezo resistance coefficient captures the effect of an applied stress in the direction perpendicular to the current. The longitudinal and transverse piezoresistive coefficients in terms of the funda mental piezoresistive coe fficients and direction cosines are given by, respectively [58], 222222 114412111111112lmlnmnl (318) and 222222 12441211121212llmmnnt (319) 62 PAGE 63 where 111,, lmn is the set of direction co sines between the longitudina l direction an d the crystal axis, and is the set of direction cosines betw een the transverse direction and the crystal axis. The direction cosines are given in terms of Eulers angles [59] 222,, lmn 111 222 333lmncccssscccssc lmnccsscscsccss lmncsssc (320) where cos c sin s and etc. The geometry of the Eulers angle is shown in Figure 38 In this research, a wafer is used, thus 100 0 0 and sweeps from 0 to 180 degree in Figure 38 Therefore, the matrix (320) reduces to, (321) 111 222 3330 0 001 lmncs lmnsc lmn The piezoresistive coefficients, 111244, and are given in Table 34 for both ptype and ntype piezoresistors at room temperatur e for low doping concentrations. For this piezoresistive device, the floating element sensor features integrated sideimplanted diffused resistors [25, 50, 51] in the el ement tethers for piezoresistive detection. In this transduction scheme, the integrated force produced by the wall shea r stress on the floating element causes the tethers to deform and thus create s a mechanical stress field in the tethers. The piezoresistors respond to the mechan ical stress field with a change in resistance from its nominal unstressed value [46] as indicated by llttR R (322) 63 PAGE 64 where and R are the resistivity and resistance of the piezoresistor, respectively, signifies the perturbation in the resist ance and resistivity due to the piezoresistive effect, l is the bending stress along the beam, and t is the transverse stress. For a beam subjected to pure bending, Equation (322) simplifies to llR R (323) Piezoresistive Coefficients The piezoresistive coefficients depend on crys tal orientation, doping type and level, and temperature. This dependence is typically expr essed as a product of th e coefficients lowdoped room temperature value 0 and a piezoresistive factor [59] (,)PNT 0,( NTPNT ,) (324) where is the doping co ncentration and T is the temperature. For a N 100 wafer, the dependence of the piezoresistive coefficien t on the crystal direction is given in Figure 39 and Figure 310 for ptype and ntype piezore sistors, respectively. This indicates that the maximum piezoresistive coefficient for ptype silicon is in the 110 direction, while for ntype silicon the maximum is in the 100 direction. Also note that nty pe silicon has a larger achievable piezoresistive coefficient than ptype silicon. The longitudinal and tr ansverse piezoresistive coefficients l and t in the 110 direction for ntype and ptype silicon are given in Table 35 [52]. As shown in Table 35 piezoresistors in ptype silicon are more sensitive than for ntype in the 110 direction, which is parallel or perpendicular to the flat of a 100 wafer. In this design, the ptype piezoresistors are c hosen due to its high sensitivity in the 110 direction and 64 PAGE 65 because of the lower temperature sensitivity at higher doping concentrations compared to ntype piezoresistors [60]. Many theoretical [59] and experimental [6163] studies have repor ted the dependence of the piezoresistive factor on doping concentration at room temperature. Kandas model [59] is most popular and is accurate for low c oncentrations. However, when compared to experimental data [6163], Kandas model under predicts the rolloff of for concentrations above For doping concentration above the fundamental piezoresistive coefficient is expressed as a pr oduct of its lightlydoped room temperature value (,)PNT (,)PNT 17310 cm 17310 cm 0 and the experimentally fitted piezoresistive factor [47], (,)PNT 0.2014 223 001.5310 cm ,(,)logNTPNT N (325) The piezoresistive factor is plotted in Figure 311 versus concentration at room temperature. The piezoresistive coefficient is also temperature dependent. At higher doping concentrations, there will be a reduction in both thermal noise and 1 f noise compared to lower doping concentrations [47]. In addition, the temper ature dependence of the piezoresi stance coefficient is reduced significantly as the concentr ation increases at low doping concentration. For doping concentrations above the piezoresistance coefficient is almost independent of temperature variation [61]. Howe ver, the sensitivity degrades due to the reduced piezoresistive coefficient at a high doping level [62]. Thus, th ere is a tradeoff between sensitivity and noise floor. This tradeoff suggests optimization is necessa ry to obtain the best performance, as will be discussed in chapter 4. 20310 cm 65 PAGE 66 Piezoresistive Sensitivity For the structure shown in Figure 312 the sideimplanted piezoresistors are fabricated by first implanting ptype impurities (boron) into th e sidewall, followed by a diffusion step to drivein and to electronically activate the impurities. The impurities diffuse laterally, and the resulting impurity concentration profile decreases from the su rface of the side wall to the junction depth. If the unstrained impurity prof ile as a function of depth, Ny is known, the piezoresistive coefficient profile ()y can be determined. As shown in Equation (36) the stress varies along the beam, and varies across the junction depth, j y as well. Therefore, the product of the stress and the piezoresistive coefficient distributions need to be integr ated in the electromechanical model. Several models have been developed for piezo resistive sensitivity. Tortonese [64] and Harley [65] built a twostep model for nonuni form doping concentration and formulated an efficiency factor to be inserted into the numerator of the surface sensitivity equation. In integrating across the beam, their model does no t account for the junction isolation of diffused resistors. Senturia [46] presents the piezo resistive coefficient de pendence of the doping concentration, but does not account for stress variation as a function of depth. S zes model [57] addresses stress variations across the resistors ( direction) and incor porates a conductanceweighted piezoresistance coefficient. Sze, how ever, did not account for th e stress variation along the piezoresistor ( y x direction). Based on Harleys wo rk, a new model was developed by involving stress averaging along the tether length and across the dept h of piezoresistor, and using a conductanceweighted piezoresistive coefficient. Two issues need to be consid ered in calculating the piezores istive response. One is that the piezoresistors are typically formed by diffu sion, thus have a nonuni form doping profile with 66 PAGE 67 respect to junction depth. The second issue is that piezoresistors also span a finite area on the device, and hence have nonuniform stress with respect to length and depth. The derivation of the resistance of the piezoresis tor begins with the nonuniform doping concentr ation that varies from the sidewall surface to the junction depth ( direction). The stress varies in this direction as well. As shown in y Figure 312 the resistor can be considered as a stack of slices, where each slice has a slightly different doping concentra tion and stress. The current flow is in x direction, so the slices ( ) are connected electrically in parallel because they share the same potential. The stress also varies along the length of the resistor ( dy x direction). Thus, the resistor is also segmented along its length. These segments ( ) are connected in series due to the same current flow. The mechanical model assumes that thus the differential resistance of a unit cell for a small segment and a small slice with width of is given by dx and ttLW tT dx dy rW 1 ,e unit unit r x ydx dRxy dGxyWdy (326) where it is assumed that at the surface and 0y 2tyW at the neutral axis. In Equation (326) ,e x y is the stressed resistiv ity determined by [46] (,)()1()(,)ee oll x yyyx y (327) where ()eo y is the unstressed resistivity and (,)l x y is given in Equation (36) For nonuniform doping, ()eo y is given by [66] 1 () ()()eo pAy yqNy (328) where is the electronic charge of an electron and 191.60210 q C ()py is the boron mobility. In this research, the mobility is obtained from [67]. To simply the calculation process, 67 PAGE 68 we use conductance 1 G R rather than resistance in the deri vation. The total conductance for segment is obtained by summing the conductance of each unit dx 0 01 ()1()(,)j jy y r slice unit eo llWdy dGdG dxyyxy (329) The total resistance is determined by summing the resistance of the small segments, dx 01 1/ ()1()(,)Rr Rr j RRLL LL slice y LL r eo ll R RdG Wdy yyxy dx (330) where is the overlap end cap and it does not change the resistance value. The total unstressed resistance is similarl y found by integrating along the leng th of the resistor using the unstressed resistivity, 10 mRL 01 1 ()Rr Rr j R RLL LL slice y L L r eo R dG dx Wdy y (331) Then the resistance modulation is obtained by arranging Equation (330) and (331) 0 0() 1 1 ()1()(,)y j LL Rr eo y j L r R eo lldy y RRRR dx RRL dy yyxy (332) Electromechanical Sensitivity The four sidewall implanted piezoresistors form a full Wheatstone bridge circuit that provides sensitivity enhancement for a small change in resistance. As illustrated in Figure 313 when the tether deflects in the y direction, piezoresistors 1 a nd 3 experience a compressive stress while 2 and 4 experience a tensile stress. These resistors experience a change in resistance 68 PAGE 69 of R and R respectively. For an ideal bridge, 13 R RRR and 24 R RRR so that the output voltage, for a given bias voltage is oV BV 41 3412 oRR B B R VV RRRRR V (333) The sensitivity of the piezoresistive sensor is de fined as the change of ou tput voltage per unit of applied shear stress and for a linear sensor is expressed as o EM wwVV S o (334) Substituting in Equation (333) the electromechanical sensitivity is rewritten as B EM wVR S R (335) Noise Model The key sources of the electrical noise in piezoresistive sensors are thermal noise, low frequency 1 f noise, and amplifier noise [ 65]. Physical fluctuations of the floating element at an equilibrium temperature, T, can result in random motion of the device; however, the contribution of thermomechanical displacement noi se has been found to be much smaller than the electronic noise sources excep t at mechanical resonance [47] For an ideally balanced Wheatstone bridge, the bi as source noise will be common mode rejected. Thermal Noise Thermal noise, also known as Nyquist or J ohnson noise, is produ ced when electrons are scattered by thermal vibration of the lattice stru cture [68]. Since higher temperatures lead to increased vibrational motion, thermal noise power spectral density (PSD) is directly proportional to temperature. Moreover, thermal noise is present in thermodynamic equilibrium, and its PSD is independent of frequency si nce random thermal vibrations ar e not characterized by discrete 69 PAGE 70 time constants. The thermal noise PSD ( ) is modeled by Nyquist [68], which was experimentally verified by Johnson [69], as vTS 4 vTBSkT R (336) where 1.38e23 Bk JK is the Boltzmann constant, R is the total resistance in the resistor, and is the temperature in Kelvin. In a piezoresistor, the rms noise voltage, due to thermal noise is obtained by taking the square root of the thermal noise PSD integrated over the bin width of interest T tRV 2 1 f ff [68], 2 14f tR vT B fVSdfkTR f (337) 1 f Noise The dominant noise source for most ionimplanted piezoresistors is 1 f noise. Hooge [70] first reported that the 1 f noise PSD of a piezoresistor is inversely proportional to the total number of carriers in the resistor when an external dc bias voltage is applied, and is given by 2 1 H R vf cV S Nf (338) where is the voltage across the resistor, is the total number of ionized carriers in the resistor, RV cN f is frequency, and H is Hooge parameter, with the ex perimental values ranging from to [71]. Hooges parameter is sensitive to bulk crystalline silicon imperfections and the interface quality. Low frequency noise occurs under nonequilibrium conditions and its spectra is proportional to the square of the app lied voltage. Two physical mechanisms have been proposed to account for the low frequency noise: random trapping/detrapping of carriers at the 6510 3210 70 PAGE 71 surface and bulk electronic traps, and random mobility fluctuations [72]. The noise power of 1 f noise is obtained by integrating Equation (338) over a frequency range of operation 2 2 1 1lnHR fR cVf V Nf (339) The total number of ionized car riers in the resistors for th e piezoresistor geometry in Figure 312 is given as (340) 0()jy crrANLWNyd y where is the type doping concentration. As indicated in Equation ()ANy p (339) 1 f noise increases for small volumes and hi ghly resistive piezoresistors. In this dissertation, th e typical input noise of a low noise amplifier at 1k, Hz 4 nVHz [73], is used in the noise floor model. For an ideally balanced Wheatstone bridge assuming a unity gain amplifier, the total rms output noise voltage is NV 2 2 2 11 ln449 4HB NB cVf Vk T R f Nf e f (341) where the first, second and third terms in Equation (341) are the contribution of 1 f noise, thermal noise, and the amplifier noise, respec tively. The detailed derivation of Equation (341) is given in Appendix B. Since narrow bin turbulence spectra are desired, a figure of merit bin width of centered at 1 k is used in this dissertation; therefore, and 1 Hzf Hz 1999.5 Hz f 21000.5 Hz f The minimum detectable shear stress (MDS) or input noise, min is the minimum shear stress that the shear stress sensor can resolv e in the presence of noise and is defined as 71 PAGE 72 minN EMV S (342) The dynamic range (DR) is then given by max min20log DR (343) Device Specific Issues In this section, a few specific design issues are addressed, including transverse sensitivity, acceleration sensitivity, pressure sensitivity, temperature compensation and device junction isolation issues. Transverse Sensitivity Transverse sensitivity was di scussed in Chapter 2 (Equation (216) ), and restated here briefly. Recall that the transver se mechanical sensitivity in the x direction can be neglected due to the large differences in bending versus axial s tiffness, while transverse mechanical sensitivity in the direction is of the same order as in the flow direction. The z x direction also possesses electromechanical rejection for an ideally balanced bridge. Assuming the flow is in the direction, when the sensor is subjected to an xaxis acceleration, piezoresistors 1 and 2 experience a tensile stress while 3 and 4 experience a compressive stress. These resistors experience a change in resistance of y R (piezoresistors 1 and 2 and R (piezoresistors 3 and 4), respectively ( Figure 314 (a)). The resistances in the bridge become 12 R RRR 34 R RRR The output voltage, for a given bias voltage is given by oV BV 3 1 12340 2222oR RR RR V RRRRRRRR R (344) 72 PAGE 73 When the fluctuating pre ssure load acts in the direction, the stress distribution in all four tethers is the same, leading to equal resistance perturbations ( z R ) in all four piezoresistors. The reaction of the Wheatstone bridge due to pressure is shown in Figure 314 (b). The total pressure effect is to supply a common mode signal into this differential sensing scheme, which does not affect the voltage output. Therefore, the ideal elect romechanical sensitivity due to the xaxis load and pressure disturbance is ideally equal to zero. In reality, there will still be transverse sensitivity due to bridge mismatch. Temperature Compensation The output voltage of a piezore sistive sensor is dependen t on temperature due to the thermal sensitivity of the resistance, strain a nd piezoresistive coefficient [46]. In this dissertation, it is assumed that the thermal coe fficient of resistance will dominate over thermal strain effects and changes in the piezoresistive co efficient. The typical temperature coefficient of resistance for a laterally implan ted sensor is reported to be o0.0081 k C which is much larger than the shear stress sensitivity [25]. Since it is impossible in practice to have absolute temperature control in a wind t unnel, temperature compensation of the output signal must be employed. In it important that the temperature is measure as close as possible to the sensing element to avoid compensation errors due to temperat ure gradients in the flow. In this thesis, the temperature compensation of the resistors are ach ieved using a double bridge configuration [74]. As shown in Figure 315 two Wheatstone bridges are used on one chip; one is the active Wheatstone bridge with output that is a function of shear stress a nd temperature, while the other is a dummy compensation Wheatstone bridge with output that acts as a thermometer and only depends on temperature. The dimension of the co mpensation bridge resistors is identical to the active bridge and is kept as close as possi ble to the active bridge (safe distance of 10 0 m 73 PAGE 74 suggested for the peripheral circuits [75] ). The detailed temperature compensation procedure for the nonideal case of a sta tically unbalanced bridge is discussed in Chapter 6. For ideally balanced Wheatstone bridge, the power supply noise is just a common mode signal to the bridge and would not affect the bridge voltage ou tput. In most physically realized devices, the bridge is not exactly balanced. Therefore, the powe r supply noise contribution to the noise scales with the bridge offset volta ge output normalized by the bias voltage. Device Junction Isolation One design issue is the difficulty of realizing a junctionisolat ed, laterally diffused resistor in the sidewall of a tether. As shown in Figure 316 the ptype piezoresi stor (with resistance S R ), the p++ interconnects (with resistance L R ) and the ntype substrate form a p/n diode. For an ideal p/n diode, the leakage cu rrent is negligible in the reve rse bias region [76]. When the reverse voltage exceeds a certain value, the reve rse current will increase rapidly and the diode will breakdown. To ensure the current flows exclusively through the ptype regions, the p/n junction must be reversebiased for all possi ble bias voltages along the entire length of the piezoresistor and interconnect. Th is section addressed design issues associated with this design constraint. Two issues must be taken into account in th e design: (1) maintaini ng junction isolation and (2) avoiding p/n junction breakdow n while achieving the desired piezo resistor sensitivity. When a voltage is applied between the two p++ interc onnects, the p/n junction voltage varies linearly with position due to a linear volta ge drop across a distribu ted resistance. For junction isolation, the p/n junction must be reversebi ased at all spatial locations. Under reverse bias, a p/n junction develops a space charge layer due to the depletion of carriers [76]. In order to maintain electrical is olation, it is necessary to ensure that the space 74 PAGE 75 charge layers for adjacent ptype regions extending into the nty pe substrate do not overlap or punchthrough. The space charge layers punchthrough will cause the corresponding p regions to become shorted, resulting in a nonfuncti onal device. Assuming uniform doping, the acceptor concentration in the p re gion is assumed to be and the donor concentra tion in the n region is assumed to be AN D N The space charge layer widths on the pside p x and nside n x are given as a function of the junction voltage [76], jV 2Si D p j AADN b i j x V qNNN V V (345) and 2Si A nj bij DADN x V qNNN V V (346) where 12 Si1.04510 Fcm is the silicon permittivity, and th e intrinsic number of electrons is 10310 cmin in silicon at room temperature. The builtin voltage is given as 2lnAD bi iNN kT V qn (347) In order to electrically isolate the p++ regions, the en tire length of the p/n junction must be reversebiased The space charge layer width in the p and n region, 0jV p x and n x respectively, increases with reverse bias. The to tal space charge width on the n side is given by jnjnBjWVxVxVV (348) If the total space charge layer width on the n side, jWV increases to the width between the piezoresistor and the p++ interconnect, or to the width between the p++ interconnects, the space charge layers will punchthrough, causing the corresponding p regions to be shorted. 1L 2L 75 PAGE 76 To avoid punchthrough, 1 jWVL must be satisfied fo r all junction voltages, Additionally, lateral diffusion that occurs during high temperature process steps, leading to an increase in the actual width of the ptype region compared to the designed width, must be taken into account. Therefore, the total isolation wi dth is approximated by jV 2isoj dnjnBjWVLxVxVV (349) where is the lateral diffusion width estimated from the net effect of high temperature process time on the diffusion length (thermal budget) [77]. The total thermal budget dL tot D t is equal to the sum of the diffusion time, D t products for all high temperature cycles affecting the lateral diffusion, i tot i D t Dt where and are the diffusion coefficient and time associated with each processing step. iD it In this design, the doping profile is nonunifo rm, and the acceptor c oncentration in the p region and the donor concentration in the n region ANy DNy vary with depth, as shown in Figure 317 The nonuniform doping prof iles are obtained by FLOOPS simulation [78], where sidewall boron implantation in amorphosized si licon is simulated by SRIM [79] and then imported to FLOOPS The crosssectional vi ew of the isolation widt h for a doping profile at a bias voltage of 10 V is shown in Figure 318 and Figure 319 which are associated with the AA and BB cuts shown in Figure 320 The dimensions of the tether width the sidewall implanted piezoresistor depth the p++ interconnect width and the space parameters, and are listed in tW 4L 3L 1L 2L 5L Table 36 for the actual device. There is a tradeoff between the p++ interconnect widths, and and the punchthrough width A large value of and is desired to reduce the lead resistance. The 3L 4L 1L 3L 4L 76 PAGE 77 resulting narrow gap, may cause p/n junction punchthrough. On the edge of the tethers, the p++ interconnects are tilted degrees from the tether centerline to increase the isolation gap spacing. For the worst case, at left and 0 V on the right, as shown in 1L 24 10 VjV Figure 320 there is about between adjacent p++ interconnect s assuming a lateral diffusion of Meanwhile, a crossover between the piezoresistor and p++ interconnects must be avoided. As shown in 9 m ~1.1 m Figure 319 the space charge layer of the piezoresistor in the nwell increases as the depth increases. If the space be tween the piezoresistor and the p++ interconnect is too close, there will be crossover and the pregion will punch through. A top view of the isolation width is shown in Figure 320 The blue region is the tether, the cyan region is the p++ interconnects, the green region is the piezoresistor, and the pink lin e is the final isolation width considering lateral diffusion and spac e charge diffusion to the nwell at (worst case). 10 VjV In order to minimize the space charge width in the nwell, one can increase the doping concentration of the nwell, D N There is, however, a tradeoff between increased nwell doping concentration and reduced reverse breakdown volta ge. With increasing doping, the internal electric field increases and th e reverse junction breakdown volta ge decreases [80, 81]. The breakdown voltage decreases from to ~1 when the impurity concentration increases from to ~50 V 0 V 1631.010 cm 1731.010 cm The curvature of the tether corner and the cu rvature of the junction regions must also be considered. A sharp corner dramatically increa ses the mechanical stress, which could lead to possible failure of the material s [82]. Additionally, a sharp corner in the p/n junction may increase the local electric fiel d and decrease the breakdown voltage [83]. Thus, the corner is rounded. The stress concentration factor, K, de pends on the fillet radius for a given thickness [82] and is relatively high when the ratio of the fillet radius and tether width is less than 0.5. In 77 PAGE 78 this design, K is chosen as 0.9. In addition, 4 slots in the substrate near the edge of each tether are designed to relieve stress concentrati ons that arise duri ng fabrication [51]. In order to avoid thes e issues, a metal contact design is employed, where the metal lines run on the top of the tethers to connect either side of the laterally implanted piezoresistors, as shown in Figure 321 Because there are two deep trenches on both sides of the tether for tether release, the fabrication process of this design is very challenging and is discussed in detail in Chapter 5. 50 m Summary Electromechanical modeling of a sideimpla nted piezoresistive floating element shear stress sensor has been developed for aerospa ce applications. Two Wheatstone bridges are employed, an active bridge for shear stress sensing and a dummy bridge for temperature compensation. The predicted sensitivity, noise floor, dynamic range and MDS have been modeled and verified by FEA. To accurately resolve the fluctuating shear st ress in a turbulent boundary layer, the shear stress sensor is desired to possess a small size, large usable bandwidth and a low MDS. MDS depends on the geometry of sensors and piezoresistors, dopant profile, process parameters, and sensor excitation. To achieve a low MDS, it is favorable to maximize sensitivity and minimize noise. However, there are tradeoffs between se nsitivity and noise floor. It is necessary to perform design optimization to balance these conf licting requirements. Additionally, the sensor design is constrained by temporal and spatial resolution requirements as well as structural limits. The detailed optimization is discussed in Chapter 4. 78 PAGE 79 Table 31. Material properties [53] and geometry para meters used for model validation. Density of silicon 3kg/mSi 2330 Youngs modulus in [110] orientation GPa E 168 Poisson ratio p 0.27 Length of tethers mtL 400 Thickness of the tethers mtT 3 Width of the tethers mtW 4 Length of the square floating element meL 150 Table 32. Resonant fre quency and effective mass predicted by LEM and FEA for the representative structure given in Table 31 Frequency kHz Effective Mass kg LEM 12.44 1.66e10 FEA 12.47 1.72e10 Table 33. First 6 modes and effective mass pr edicted by FEA for the representative structure given in Table 31 Mode Domain Frequency kHz Effective Mass kg 1 12.47 (translational in direction) z 1.72e10 2 17.08 (translational in direction) y 1.74e10 3 34.95 (rocking mode about x axis) 6.82e10 4 162.33 (rocking mode about axis) y 1.81e11 5 170.11 (rocking mode about axis) z 1.84e11 6 219.50 (translational in x direction) 1.70e11 Table 34. Piezoresistive coefficients for ntype and ptype silicon [53]. 11 (1011Pa1) 12 (1011Pa1) 44 (1011Pa1) ntype 102.2 53.4 13.6 ptype 6.6 1.1 138.1 79 PAGE 80 Table 35. Piezoresistive coeffici ents for ntype and ptype sili con in the <110> direction [53]. l (*1011Pa1) t (*1011Pa1) ntype 31.2 17.6 ptype 71.8 66.3 Table 36. Space parameter dime nsions for junction isolation. tW tL 2L 3L 4L 5L 30 m 9 m 13.6 m 15 m 1 m 33 m 80 PAGE 81 Figure 31. Schematic top view of the structure of a piezoresistive floating element sensor. P Q 0 x Floating Element Tether Wt Lt y LtLeWe/2 WtTt 2Lt Figure 32. The simplified clampedclamped b eam model of the floating element structure. Figure 33. Lumped element mode l of a floating element sensor: (a) springmassdashpot system (mechanical) and (b) equivalent electrical LCR circuit. 81 PAGE 82 0 0.2 0.4 0.6 0.8 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Normalized Tether Length x/LtDisplacement ( m ) FEA Nonlinear Analytical Figure 34. Representative resu lts of displacement of tethers for the representative structure given in Table 31 at 5 Paw 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Wall Shear Stress w (Pa) Maximum Displacement ( m) Nonlinear Linear Energy FEA Figure 35. Representative load deflection characteristics of an alytical models and FEA for the representative structure given in Table 31 and 5 Paw 82 PAGE 83 0 0.2 0.4 0.6 0.8 1 1 0.5 0 0.5 1 Normalized Tether Length x/LtBending Stress ( MPa ) FEA Linear Analytical Figure 36. Verifi cation of the analytically predicted stress profile (Equation (36) ) with FEA results for the representative structure of Table 31 and 5 Paw Translational in direction Translational in direction Rocking mode about z y x axis Rocking mode about axis Rocking mode about axis Translational in y z x direction Figure 37. The mode shape for the representative structure of Table 31 and 5 Paw 83 PAGE 84 z x y*y* z x Figure 38. Geometry used in co mputation of Eulers angles [59]. 2e010 4e010 6e010 8e010 30 210 60 240 90 270 120 300 150 330 180 0 t l <110> <110> Figure 39. Polar dependence of pi ezoresistive coefficients for pt ype silicon in the (100) plane. 84 PAGE 85 5e010 1e009 1.5e009 30 210 60 240 90 270 120 300 150 330 180 0 l t <100> <100> Figure 310. Polar dependence of piezoresistive coefficients for ntype silicon in the (100) plane. 1016 1017 1018 1019 1020 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Boron Concentration (cm3)Piezoresistance Factor Kanda Harley Figure 311. Piezoresistive factor as a function of impurity concen tration for ptype silicon at [47]. 300K 85 PAGE 86 Figure 312. Schematic illustrating the releva nt geometric parameters for piezoresistor sensitivity calculations. Figure 313. Schematic representative of a defl ected sideimplanted piezoresistive shear stress sensor and corresponding resistance changes in Wheatstone bridge. 86 PAGE 87 VBR1R2R3R4 Vo VBR1R2R3R4 Vo(a) (b) Figure 314. Wheatstone bridge subjected to crossaxis acceler ation (a) and pressure (b). Figure 315. Schematic of the doublebridge temperature compensation configuration. 87 PAGE 88 + + n++ p++ p++ RSRLRL (a) (b) Figure 316. Top view schematic of the sideimpla nted piezoresistor and p++ interconnect in an nwell (a) and equivalent elec tric circuit indicating that the sensor and leads are junction isolated (b). 0 0.5 1 1.5 2 105 1010 1015 1020 1025 Depth(um)Doping Concentration(cm3) nwell p++ interconnect piezoresistor Figure 317. Doping profile of nwell, p++ interconnect, and piezore sistor using FLOOPS simulation. 88 PAGE 89 0 5 10 15 20 0 0.4 0.8 1.2 1.6 2 Depth (m)Isolation Width (m) p++ p++ Piezoresistor nwell Figure 318. Cross view of isolation width between p++ interconnects (AA cut in Figure 320 ). 0 2 4 6 8 10 12 14 0 0.4 0.8 1.2 1.6 2 Depth (m)Isolation Width (m) p++ Piezoresistor 4.8 m nwell Figure 319. Cross view of isolation width between p++ interconn ect and piezoresistor (BB cut in Figure 320 ). 89 PAGE 90 Figure 320. Top view of the isolation widths on a sensor tether. Figure 321. Top view schematic of the sideimp lanted piezoresistor with a metal line contact. 90 PAGE 91 CHAPTER 4 DEVICE OPTIMIZATION This chapter presents the nonlinearly constr ained design optimization of a micromachined floating element piezoresistive shear stress sensor. First, the problem form ulation is discussed, including the objective functi on and constraints based on fl ow conditions. Next, the optimization methodology is outlined. The op timization results are then presented and discussed. Finally, a postopt imization sensitivity analysis of the objective function is performed. Problem Formulation The objective function is selected based on tradeoffs identified between the sensitivity and noise floor of the shear stress sensor. The c onstraints are formed due to physical bounds, manufacturing limits and opera tional requirements [84], a nd are dependent on the flow conditions of the desired applications. The objective function and constr aints are functions of the de sign variables, including the geometry of the floating element structure and the piezoresistors, the surface doping concentration, and sensor excitati on. The detailed discussion of the design variables chosen is presented in next subsection. Design Variables The objective function and constraints depend on geometry of sens ors structures and piezoresistors, process related parameters, and sensor operational parameters. The geometry parameters include tether length tether width tether thickness, floating element length and piezoresistor length piezoresistor width The process related parameters include piezoresistor surface concentration and junction depth (assuming a uniform doping profile). The sensor operational para meter is the supplied bias voltage. tL tW tT eL rL rW SN jy 91 PAGE 92 The geometry parameters of the sensor stru cture determine the mechanical characteristics of the sensor, such as sensitivity, linearity and bandwidth. Design issues related to the tether width and tether thickness are addressed here. As discu ssed in Chapter 3, the minimum tether width is set to to avoid p/n junction punch thr ough. The tether thickness must be larger than the tether width to ensure that th e crossaxis resonant freq uency is larger than the inplane resonant frequency. As shown in the representative structure in tW tT tW 30 m Table 31 the first mode is out of plane due to the tether thickness larger than the tether width. The increases in tether thickness results in bending stress decreases (Equation (36) ), and thus sensitivity decreases (Equation (323) ). On the other hand, the piezoresi stor related parameters, such as piezoresistor length piezoresistor width and p/n junction depth rL rW j y and surface concentration are related to noise floor and sensitivity. SN For each design optimization, different tether thickness, junction depth and tether width may be achieved, but all designs are fabricated in one wafer due to economic constraints. Thus these parameters for each design mu st be set to the same value. In this research, the tether thickness is set to 50 considering the sensitivity of the shear stress sensor and SOI wafer availability. Due to the rough si dewall surface near the buried oxide layer after DRIE process and no passivation on the bottom of the te thers after final release, the high m 1 f noise and current leakage became issues in the piezoresistor design [85]. Partridge et al .[51] investigated the accelerators with piezoresist ors implanted in the top 15 (total thickness), 5 of the flexures, and found that 3 case has large sensitivity and low m m 3 m m 1 f noise. In this research, piezoresistor width 5 mrW is chosen to avoid current leakage while maintaining high 92 PAGE 93 performance. A junction depth of 1 m jy is chosen taking account the piezoresistor and p++ interconnection and the manu facturing constraint. In summary, six design variables are include d in the optimization design, and they are tether length tether width floating element length and piezoresistor length piezoresistor surface doping concentration and bias voltage tL tW eL rL SN B V Objective Function As stated in Chapter 1, to accurately rec ognize the fluctuating wall shear stress in the turbulent boundary layer, the measurement de vice must possess sufficiently high spatial and temporal resolution as well as a low MDS, which is defined as the ratio of noise floor to the sensitivity. Therefore, lowering the noise floor and increasing se nsitivity are favorable in shear stress sensor design to achiev e a low MDS [84]. Some parame ters, such as junction depth, surface doping concentration and bias voltage, a ffect both sensitivity and noise floor creating tradeoffs between these performance parameters The following discusses the tradeoffs in sensitivity and noise floor a nd the arrival at th e MDS as the objective function of the optimization. Junction depth, j y and surface doping concentration, are two major factors involved in processing that affect sensit ivity and noise floor. As disc ussed in chapter 3, changes in while keeping SN SN j y constant invoke tradeoffs between noise and sensitivity. If increases, the resistivity of the piezoresistor decreases and the total carrier number increases. This leads to the reduction of thermal noise and SN 1 f noise. Conversely, sensitivity decreases due to the reduction of the piezoresistive coefficient l from high doping concentration (Equation (323) ). 93 PAGE 94 The bias voltage B V also affects both sensitivity and noise floor. As B V increases, the sensitivity increases (Equation (335) ) because the output voltage is directly proportional to the bias voltage. The voltage noise contribution from 1 f noise also increases squarely as indicated by Equation (338) By establishing the MDS as the objective f unction, a balance between noise floor and sensitivity is achieved. Previous researchers have investigated the potential and methods in piezoresistive sensor optimizati on. Harley and Kenny [47] pres ented an informal graphical design optimization guidelines in the form of de sign charts by varying the dimensions of the cantilever, the geometry of the piezoresistor, doping level, and proce ss issues related to sensitivity and noise floor. Papila et al. [84] performed a piezore sistive microphone Pareto design optimization, in which the tradeoff between pressure sensitivity and electronic noise is investigated. The Pareto curve indicated that th e MDS in units of pressu re is the appropriate parameter for performance optimization. Constraints The constraints are determined by physical bounds, fabrication lim its and performance requirements [84]. The constraints used in th is optimization and their associated physical explanations are listed below: Piezoresistor geometry: 0.4rtLL as discussed in Chapter 3, stress changes sign at the longitudinal center of the tether (shown in Figure 36 ). Thus, the sensitivity will be reduced if the length of the pi ezoresistor is larger than 2tL As a result, the maximum piezoresistor length is limited to of the tether length 40% Resistance: 3SLRR represents a balance betw een the sensor resistance S R being 3 times larger than the interconnect resistance L R but small enough to minimize electromagnetic in terference (EMI). Frequency: minr f f puts a bandwidth constraint in the design. The constraint changes with flow conditions. 94 PAGE 95 Power consumption: where 0.1owP 2owBSLPVRR When increases to a large value, the temperature of the piezoresistor will increase due to Joul e heating resulting in voltage drift and eventually electromigration. owP Nonlinearity: 3%NLLNL device linearity is required to keep spectral fidelity for timeresolved measurements. Inplane resonant frequency: To avoid disturbing the flow at the sensor resonance, the tether thickness is required to be larger than tether width to ensure the onset of the inplane resonant frequency o ccurs before the out of plane. In this dissertation, the minimum tether width is 30 and its upper bound is set to 40, thus the tether thickness is set to 50. tTW t tT tW m m m Lower bounds (LB) and upper bounds (UB): ,,,,,tterSBLBLWWLNVUB present the limitation of the design variables. LB and UB are given in Table 42 based on the candidate shear stress design specifications and design issues related to fabrication. In summary, both the objective function and c onstraints are nonlinear. Therefore, the optimal performance design deals with solving the constrained nonlinear optimization problem. Candidate Flows Several sensor specifications associated w ith various flow phenomena, ranging from low speed flow to supersonic and hypersonic flow, are listed in Table 41 Here max is the maximum shear stress to be measured and constrained by nonlinearity, min f is the minimum resonant frequency to provide adequa te temporal resolution and is the maximum floating element size that determines the lowest tolerable spatial resolution, is the minimum tether width that is limited by the junction isolation, and is the minimum thickness that is constrained by the inplane resonant frequency. The temporal and spatial resolution maxeL mintW tT min f and are chosen to approach the Kolmogorov time and length scales, but are sufficiently c onservative to yield a proof of concept device. maxeL 95 PAGE 96 Methodology The design problem is formulated to find the optimum dimensions of the floating element and tethers, geometry and surface doping concentr ation of piezoresistors, and bias voltage for each candidate flow. Mathematically, the optim ization seeks to minimize the MDS subject to constraints. The key points rega rding the optimization of the minimum detectable shear stress, min are summarized below: Design variables: , tL tW eW rL B V and SN Objective function: minimize minFX where X is the design variable vector. Constraints: 10.410rtgLL ; 2min10rgff ; 313SLgRR 0 ; 2 410 10BSLgVRR ; 50.0310NLL NLg ; 10, 6,8,...,11iiigLBxi ; 10, 12, 13...17ji igxUBj where ,,,, and itterSB x LWWLNV Since the magnitudes of de sign variables differ by several order of magnitude ( Table 42 ), all variables are nondimensiona lized to avoid singularities in the program. This nonlinear constrained optim ization is implemented using the function fmincon in MATLAB (2006b) [86] optimization Toolbox, which employs sequential quadratic programming (SQP) for nonlinear constrained problems and calcula tes the gradients by finite difference method. The optimum value of for different designs might be different. All designs, however, are fabricated on one wafer. Therefore, surface concentration, for all designs must be set to the same value. In this dissertation, the optimal for first three cases were the same and is This value was chosen as the surface concentration for SN SN SN 193=7.710 cmSN 96 PAGE 97 all designs. The optimization was reimplemented using this fixed conc entration following the same steps described above. The SQP method is a local optimizer and is hi ghly dependent on the initial value. The initial designs are selected randomly, and a numbe r of local optimum solutions from different initial designs were obtained. The solution iden tifies one best design points as the optimal solution. A global optimization algorithm using partic le swarms [87] is also employed to investigate the possibility of improving the optimum solutions. It is found that global optimization solution is very similar to the optimization results obtained by fmincon function. The global optimization results have a large computational cost. Optimization Results and Discussion In the optimization, the doping pr ofile is assumed to be uniform to simplify the modeling. The Gaussian profile is more accurate than a uniform profile, but it is not employed in this research to avoid computationa l cost. The doping concentration for p++ interconnect is achieved as with a junction depth of 1 for all designs. In this research, the material properties of silicon is fixed. 2032.0 cm m The resulting optimizati on design is shown in Table 43 The highlights are active constraints. Since the low resistance result s in low thermal noise, but the power dissipation increases. Therefore, the power constraint is always active (close for case 9). For each device, the dynamic range from the optimum design is in excess of KuhnTucker conditions [88] are conducted to check the optimality and ac tive constraints, which are stated as follows: 75 dB Lagrange multipliers j are nonnegative, and satisfy equation (41) 10 i=1,2...mgn j j j iig F xx (41) 97 PAGE 98 where g n is the total number of constraints, and is the total number of design variables. Lagrange multipliers m j are obtained by the fmincon MATLAB function. The corresponding j is zero if a constraint is not ac tive. The active constraints for each case are indicated in bold font in Table 43 Once the optimum design for uniform doping is obtained, nonuniform doping profiles are applied to achieve the final perf ormance of the sensor. The optim ization flow chart is shown in Figure 41 The nonuniform doping profiles are obt ained by FLOOPS simu lation [26], where sidewall boron implantation to amorphous silic on is simulated by SRIM simulation [79] and imported to FLOOPS. The surface concentratio n of the piezoresistor, the piezoresistive interconnection, and nwell are achieved to and respectively, as shown in 1937.7 cm 2032.0 cm 1637 cm Figure 317 The results indicate th at nonuniform doping profiles yield approximately a decrease in dynamic range. Therefore, implementing a Gaussian profile as part of the optimization would resu lt in a more accurate model and thus optimal design. 5 dB Sensitivity Analysis Due to parameter uncertainty caused by process, min may achieve different values than theoretical optimization. The sensitivity analysis is implemen ted to understand sensitivity of MDS to the variations of the de sign variables, constrai nts, and fixed parameters at the optimum design. Therefore, sensitivity analysis is a postoptimization step, which involves two parts: Sensitivity of the objective function to de sign variables at the optimum design. Sensitivity of the objective functions to the fixed parameters at the optimum design, where the effect of a change in the active constr aints on the objective f unction is taken into account. 98 PAGE 99 For the sensitivity analysis with respect to the design variables, logarithmic derivative [88] is employed to measure the sensitivity of MDS to uncertainty of design parameters at the optimum design, min min minlog logi ii x xx (42) where ,,,, and itterB S x LWWLVN For the sensitivity analysis with respect to the fixed parameters, equation (42) is invalid if the nonlinear inequality constraints are active. Lagrange multipliers based on the KuhnTucker conditions [88] is employed to calculate the sensitiv ity of the optimal so lution to the fixed parameters. Assuming that the objective f unction and the constraints depend on a fixed parameter p so that the optimization problem is defines as, jminimize such that g,0 j=1,2...17.FXp Xp (43) The gradient of with respect to is given as [88], F p T ag dFF dppp (44) where denotes the active cons traint functions and ag 0ag from KuhnTucker conditions. The equation (44) indicates that the Lagrange multipliers are a measure of the effect of a change of the constraints to the objective function. Lagrange multipliers 0 for active constraints, otherwise it is obtained by 1TTNNNF (45) where and are defined as N F j=1,2...17, i=1,2...6j ig N x (46) 99 PAGE 100 and F F= i=1,2...6ix (47) The sensitivity of min to uncertainty of the fixed parameters is given as minmin min min T ag p pppp (48) can be obtained from the output of fmincon function directly. The fixed parameters are ,,,jrtpyWTN S For case 1, power is the active inequality constraint, and the associated Lagrange multiplier, 0.0026179 is obtained from MATLAB calcu lation. Therefore, Equation (42) is employed to calculate the sensitivity of MDS to uncertainty of design parameters ( and tL tW eW rL B V ) at the optimum design. Equation (48) is employed for the fixed parameters ( and ). jy rW tT SN Figure 41 shows the sensitivity of min to uncertainty of the design variables and fixed parameters for case 1, i.e., 10% change of the tether width causes 19% change of the minimum detectable shear stress. It is illustrated that min is sensitive to variation of tether width, tether length, floating element width, and junction depth, The MDS is less sensitive to variation of piezoresistor length In summary, tW tL eW jy rL min is very sensitive to uncertainties of tether and element dimensions, junction depth and width of the piezoresistors, and less sensitive to uncertainties of piezoresistor length. Summary This section described the c hoice of objective function and a ssociated constraints. The optimization has been implemented for nine designs, from low Reynolds number flow to supersonic and hypersonic flow. The optimization results indicate that the dynamic range exceeds 75 for all designs based on a uniform doping profile. Accounting for nonuniform dB 100 PAGE 101 doping profile results in a 5 d decrease in dynamic range. The sensitivity analysis indicates that the MDS is very sensitive to uncertainties of tether and element dimensions, junction depth and width of the piezoresistors, and less sensitivity to uncertainties of piezoresistor length. B 101 PAGE 102 Table 41. The candidate shea r stress sensor specifications. Low Speed Supersonic, High Re Hypersonic, Underwater Device 1 2 3 4 5 6 7 8 9 maxPa 5 5 5 50 50 100 100 500 500 minkHz f 5 5 10 10 50 50 100 100 200 max meL 1000 1500 1000 1000 1000 1000 500 500 500 min mtW 30 30 30 30 30 30 30 30 30 mtT 50 50 50 50 50 50 50 50 50 Table 42. Upper and lower bounds asso ciated with the sp ecifications in Table 41 Design Variables and UB LB Flow Description mtL mtW meL mrL VBV 3cmSN minPa minkHz f 1 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 5 5 2 100 1000 30 40 100 1500 50 400 5 10 5e+18 2e+20 5 5 3 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 5 10 4 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 50 10 5 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 50 50 6 100 1000 30 40 100 1000 50 400 5 10 5e+18 2e+20 100 50 7 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 100 100 8 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 500 100 9 100 1000 30 40 100 500 50 400 5 10 5e+18 2e+20 500 200 102 PAGE 103 Table 43. Optimization results for the cases specified in Table 41 (bold for active constraints). Parameter Case1 Case2 Case3 Case 4 Case5 Case6 Case7 Case8 Case9 maxPa 5 5 5 50 50 100 100 500 500 mtL 1000 1000 1000 991.2 343.6 348.7 308.8 500.4 500 mtW 30 30 30 30 30 30.7 30 30 30 meW 1000 1500 983.5 996.1 1000 993.3 499.1 250.2 100 mrL 228.5 228.5 228.5 228.5 98.8 99.9 88.6 126.8 117.7 VBV 10 10 10 10 6.8 6.8 6.5 7.6 6.0 WowP 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.07 kHzrf 9.8 6.60 10 10 50.53 50.01 130.15 104.07 231.11 SR 851 851 851 851 368 372 330 470 438 LR 149 149 149 149 94 94 89 105 102 VPaMS 3.65e5 7.92e5 3.54e5 3.58e5 6.64e 6 6.40e6 1.47e6 1.13e6 4.20e7 nVNV 21.1 21.1 21.1 21.1 11.0 10.97 10.95 11.19 9.54 minmPa 0.58 0.27 0.60 0.33 1.66 1.72 7.44 9.88 2.28e2 dB DR 78.7 85.4 78.5 103.7 89.6 95.3 82.6 94.1 86.8 103 PAGE 104 Figure 41. Flow chart of design optimization of the piezo resistive shear stress sensor. Lt Wt We Tt VB Ns yj Wr Lr 1.5 1 0.5 0 0.5 1 1.5 2 dmin/dxi*xi/min Figure 42. Logarithmic de rivative of objective function min with respect to parameters (Case1). 104 PAGE 105 CHAPTER 5 FABRICATION AND PACKAGING The fabrication process and packaging of the sideimplanted piezoresistive shear stress sensor are presented in this chapter, with the ai d of masks and schematic cross section drawings. A detailed process flow is given in Appendi x C, which lists all the process parameters, equipments and labs for each step. The detaile d packaging approach for wind tunnel testing is also presented. Fabrication Overview and Challenges The first generation of the shear stress sensor is fabricated in an 8mask, silicon bulkmicromachining process. All the masks are generated using AutoCAD 2002 and manufactured in Photo Sciences, Inc (PSI). It is described in detail in the following sections. Some challenges in this process are addressed before starting the process flow: Sideimplanted piezoresistors: boron is side implanted into the silicon tethers to form the piezoresistors with an oblique angle of normal to the top surface. The traditional piezoresistor is formed by top implantation. The doping profile for sideimplantation is simulated via FLOOPS, and the accuracy of the profile n eeds to be judged only after device testing. o54 Trench filling: 50mdeep trenches were etched on the top surface to define the tethers. Trench filling is requ ired to obtain good photoresist coverage before subsequent deposition and patterning of the metallization layer. Junction isolation: the space between piezoresi stors and p++ interconnects should be larger than the isolation width to avoid p/n punch through, as discussed in chapter 3. Fabrication Process The fabrication process starts with a 100mm (100) si licononinsulator (SOI) wafer with a 50mthick 1~5 cm ntype silicon de vice layer above a 1.5mthick buried silicon dioxide (BOX) layer. The corresponding bac kground doping concentration is from to The total wafer thickness is 45. A brief overview of the process is as follows. The four sideimplanted piezoresistors are first formed by boron oblique implantation. 1532.510 cm 143510 cm 0 m 105 PAGE 106 The structure of the sensor is then defined by DR IE Si etch. Thermal dry oxide is grown for high quality passivation. AlSi (1%) is deposited and patterned to form the bond pads. PECVD nitride is deposited as a moisture barrier layer. Finally, the structure is released from the backside via DRIE Si and RIE of the oxide and nitride. The process flow is broken down into 8 major steps as follows: a. The nwell formation: the fabrication begins with the formation of the nwell by a phosphorus blanket implantation ( Figure 51 (2)). An energy of 150 and a dose of are used to achieve a surface concentration of keV 1224.010 cm 1636.510 cm to control the spacecharge layer thickness of the reversebiased p/n junctionisolated piezoresistors. b. Reverse bias contact: a 100 thin oxide layer is then deposited via plasmaenhanced chemical vapor deposition (PECVD) and patterned, then etched vi a buffered oxide etch (BOE) in preparation of the reversebias contact implant. This step al so creates alignment marks on the top surface. Phosphorus is th en implanted with energy of 80 and dose of to achieve a n++ region with a surface concentration of nm keV 1329.010 cm 1831.810 cm ( Figure 51 (4)). The device is then annealed at 1000 for minutes to drivein the inpurities. C 450 c. Piezoresistor interconnects: the oxide is selectively remove d by BOE. Then, a twostep Ge preamorphization implant is performed to mi nimize the effect of random channeling tail caused by the subsequent highdose boron implan tation [66], which provides a heavily doped Ohmic body contact. The preamorphization implant energies are 16 and respectively, and a dose of This preamorphization is to ensure no more than 2% of the implanted boron dose penetrates into the substrate [89]. Then boron is impl anted into the silicon with a dose of and an energy of 50 to provide Ohmic contacts ( 0keV 50 keV 15210 cm 1621.210 cm keV Figure 51 (5)). The resulting surface con centration and junction depth, jp x while taking into account the 106 PAGE 107 thermal budget of the entire process, are simulated by FLOOPS to be and 1 respectively. The interconnect region begins from the edge of the tether and distributes symmetrically along the cente rline of the tethers to minimize the sensitivity error, with a larger width on the end cap to decrease the resistan ce. The FLOOPS simulation file is given in Appendix D. 2031.9610 cm m d. Nested mask release: a 1 oxide layer is deposited via PECVD and patterned via reactive ion etch (RIE) [90] to serve as a nested mask for the deep reactive ion etch (DRIE) [91] that defines the tether s and floating element ( m Figure 51 (7)). New alignment marks are also created in this step. e. Side wall etch and side wall implantation: the wafers are then patterned using the mask SIM ( Figure 51 (8)). To ensure good contact be tween the piezoresistor and the p++ interconnect, the SIM mask has a 4 overlap with the p++ inte rconnect on the edge of the tether, 10 overlap with the p++ inte rconnect on the end cap, and 4 overlap with sidewall. Prior to DRIE, the native oxide or oxide residues are et ched via BOE about one 1minute. The Si is then etch ed vertically to approximately deep by DRIE to form the trenches for the sidewall oblique implant, as shown in m m m 8 m Figure 52 (scanning electron microscope (SEM) top view). The trench width is set to 51.1 mtan548.5 m to achieve a 5 implant, where 54 is the implant tilt angle from the normal axis, and 1.1is the thickness of the oxide layer. The sidewall impl antation is restricted on the top 5 to ensure the silicon surface on which the boron implanted is smooth a nd avoid forming the current leakage path on the bottom [85]. This can reduce the m m m 1 f noise at low frequency [85] The basic recipes on STS DRIE system and Unaxis RIE sy stems are shown in Appendix E. 107 PAGE 108 The extruded oxide resulting from the DRIE is etched via BOE (6:1) for one minute, as shown via the scanning electron microscope image in Figure 53 This avoids the protruded oxide blocking the implant dosage to the side wall. Hydrogen annealing (1000 10 mTorr for 5 minutes) [92] is performed to smooth the scallops on the sidewa lls that arise from the DRIE process, which will improve the noise floor [25]. A oxide layer is thermally grown as a thin implant oxide layer on the sidewall, which must be accounted for in the thermal budget. C 0.1 m After a twostep Germanium pr eamorphization implant, boron is then implanted with an energy of a dose of (two times of the simulation dose to compensate the solubility loss at high dosage ) and an oblique angle of 54 to achieve a 5 shadow side wall implantation (shown in 50 keV 162210 cm m Figure 51 (9)). f. Tether definition: the oxide on the trench bottom is then etched via DRIE while the oxide on the sidewall is left to pr otect the doped sidewall, as shown in Figure 54 This is a timecontrolled process: an overetch will expose silic on on the edge of the sidewall of the tether ( Figure 55 ), while an underetch will create a silicon grass effect [93] after the subsequent DRIE silicon etch due to the oxide residues that acts as a micromask ( Figure 56 ). The channels/trenches are then etched via DRIE w ith the BOX as an etch stop, as shown in Figure 57 (note the rough surface is caused by the dicing saw) The tether sidewall oxide is then etched for two minutes by BOE (6:1). Subsequen tly, the wafers are annealed at 1000 for 60 min to drive in the boron to form the piezoresistors. A thin dry oxide layer was thermally grown at 975 as an electrical passivation layer. The temperature 975 is selected to avoid excessive diffusion and excessive compressive stress when the temperature is below 9 [94]. Meanwhile, the boron is segregated into the oxide from the silicon. C 0.1 m C C 50 C 108 PAGE 109 g. Metallization and nitride passivation: since there are 50mdeep trenches on the wafer for tether release, it is necessary to fill the trench to achieve good phot oresist coverage before subsequent wafer patterning. A twostep trench filling process is performed as follows: first, a thin layer of photoresist AZ1512 is coated and so ft baked, then a thick photoresist AZ9260 is coated and soft baked; second, the wafer is flood exposed for 300 seconds and developed using developer AZ400 until the surface is clear. Thus, the trench can be reduced from to only deep if following the above process once or twice. 50 m 5~6 m After filling the trenches with photoresist, the oxide is patterned and then etched via BOE (6:1) to open contact vias for Al sputtering. This step is very critical for the quality of the metal contact. Since the boron laden silicon dioxide etches much sl ower than the standard oxide etching ( 1000 Amin ), an over etch is required to remove a ll oxide to ensure an Ohmic contact. Any residual oxide left ov er will result in Schottky diode effect. A 1mthick layer of AlSi (1%) is sputtered and patterned via RIE to form the metal interconnects ( Figure 51 (12)). A 200nmthick, lowstress silicon nitride layer is deposited via PECVD to from a protective moisture barrier. The bond pads are exposed by patterning and plasma etching the silicon nitride via RIE. h. Backside release: to protect the device, the front side of the wafer is coated with a 10mthick photoresist layer. The wafers are then patterned from the backsi de using fronttoback alignment. The structure is released from the backside using DRIE up to the BOX layer ( Figure 51 (14)), along with an oxide and nitride etch using RIE ( Figure 51 (15)). Finally, a postmetallization anneal is performed in forming gas (4% 96% ) at for 1 hour [95]. This annealing allows the aluminum to react with the native oxide to remove the tunneling oxide, and allow the hydrogen to passivate the interface tr aps. This improves the contact resistance and 2H 2N 450 C 109 PAGE 110 reduces the electrical nois e floor [25]. The fabricated device is shown in Figure 58 and the close view of the piezoresistors is shown in Figure 59 The trenches between each device were patterned and created during back side release, thus the die can be easily separated by tweezers. Sensor Packaging for Wind Tunnel Testing After fabrication, the individual die (6.) were then packaged in a custom printed circuit board (PCB) ( ) designed for modularity. The PCB layout was performed using Protel and was manufactured by a commercial ve ndor, Sierra Proto Express. The MEMS device die and PCB were then packag ed by Engent Inc. The MEMS die are flushmounted into a machined cavity in the PCB a nd sealed with epoxy at the perimeter. The aluminum bond pads are then bonded to gold pa ds on the PCB. Subsequent to the bonding process, the wire bonds are cove red by nonconductive epoxy to protect the wire bonds from the gas flow in the calibration wind tunnel or flow cell. The roug hness of the epoxy is less than and is located (3.2) downstream of the sensing element to mitigate flow disturbances. The PCB package is then flushmounted into a Luc ite package, which in turn is flush mounted in an aluminum plat e to minimize flow disturbance. 2 mm.2 mm 20 mm mm 300 m mm Figure 510 shows the PCB embedded in the Lucite package. Copper wires (gauge 26) pass from underneath up through the vias in the PCB and are soldered to PCB via rings. The wire is reinforced by the glue on the backside of the Lucite package. An interface circuit board was designed for offset compensation and signal amplification, as shown in Figure 511 This board includes two sets of compensation circuitry: one for active bridge, another for dummy bridge. Each circuit has two amplifying stages: the first stage is used to null the amplified offset, a nd the second stage is to amplif y the compensated signal. The detailed description of the interf ace circuit for offset compensation is given in Chapter 6. This 110 PAGE 111 board is attached on the backside of the device package and supported by two screws that connect it to the Lucite packaging. The copper wires for the signal output and voltage supply from the Lucite plug are soldered to this board. There are eight BNC connectors for the amplified signal outputs and power supplies. 111 PAGE 112 Figure 51. Process flow of the sideimplanted piezoresistive shear stress sensor. 112 PAGE 113 Figure 52. SEM side view of side wall trench after DRIE Si. Figure 53. SEM side view of the notch at the interface of oxide and Si after DRIE. 113 PAGE 114 Figure 54. SEM top view of the trench after DRIE oxide and Si. Figure 55. SEM top views of the trench af ter DRIE oxide and Si with oxide overetch. 114 PAGE 115 Figure 56. SEM top views of the trench with si licon grass through a micromasking effect due to oxide underetch. Figure 57. SEM side view of th e trench after DRIE oxide and Si. 115 PAGE 116 Figure 58. Photograph of the fabricated device. Figure 59. A photograph of the de vice with a close up view of the sideimplanted piezoresistor. 116 PAGE 117 Figure 510. Photograph of the P CB embedded in Lucite package. Figure 511. Interface circuit board for offset compensation. 117 PAGE 118 CHAPTER 6 EXPERIMENTAL CHARACTERIZATION Preliminary electrical and fl uidic characterization were performed to determine the performance of the shear stress sensor and to partially compare to the analytical models discussed in Chapter 3. The expe rimental setup for sensor charac terization is described and then the results are presented. The experiments incl ude measurement of characteristics of p/n diode, system noise, sensor sensitivity and linearity, and frequency response. Experimental Characterization Issues There are two complicating issues in characterizing the sensors: the initial offset voltage output without shear stress applied and the temperat ure sensitivity of the bridge output. These two issues directly affect the measurement resolution and static sensitivity. Therefore, offset compensation and temperature compensation mu st be employed for the static calibration experiments. The motivation and methodology for offset compensation is discussed in the following paragraphs. The temperature compensation was not performed and will be discussed in Chapter 7. For a balanced Wheatstone bridge, the differentia l voltage output of the sensor is directly proportional to the applied shear stress. In re ality, the Wheatstone bridge is not perfectly balanced due to uncertainty in the fabrication process. As shown in Figure 61 the dc offset exists without applied shear stress, and is directly propor tional to the bias vo ltage. The offset is typically 10 mVV O or even larger in some device die. The optimization results in Chapter 4 indicate that the normalized sensi tivity of the sensor designs is 1 VVPa O Such a small sensitivity requires high gain amplification pr ior to being sampled by data acquisition board. However, a dc offset will cause amplifier saturation even at a relatively low gain. Therefore, it is imperative to minimize or eliminate the o ffset to maximize the dynamic range of the 118 PAGE 119 measurement system. An approach for the interface circui t readout is discussed as follows for dc offset compensation. The interface circuit consists of a precision programmable instrumentation amplifier AD625 and a high speed precision Op Amp AD 711 from Analog Devices [73], as shown in Figure 62 The gain of the AD625 is set by adjusting exte rnal resistors F R and G R and is given by 4FGRR 1 The AD711 acts as a unity buffer. Th e initial offset voltage goes through the amplifier AD625 with a set gain of 21. Then the amplified offset voltage is precisely controlled by adjusting the input of the AD711, which is pr ovided by a Stanford Research Systems SIM928 isolated voltage source [96]. SIM928 is an ultra low noise voltage source (10 at 1 k bandwidth) that provides a stable lownoise voltage reference with mV resolution. Unfortunately, there was an error in the second amplifier stage of the PCB and a decision was made to just proceed with AC shear stress cal ibrations to demonstrate proof of concept functionality. Vrms Hz Experimental Setup In this section, the experimental setup fo r the shear stress sensor characterization is discussed. A probe station is used to measure the currentvolta ge (IV) characteristics of the sensor. A plane wave tube (PWT) is then used to determine the sensor linearity, sensitivity and frequency response. Then sensor system noise is measured with dynamic calibration setup in the plane wave tube with speaker amplifier off. Electrical Characterization Electrical characterization in cludes measurement of the bridge impedance and leakage current of the junctionisolated devices, as well as the breakd own voltage. All measurements 119 PAGE 120 were made using an Agilent 4155C semiconductor parameter analyzer and a wafer level probe station. As discussed in Chapter 5, the p/n junctions are formed by the ptype piezoresistor and the p++ interconnects with the nwell. To ensure that the current flows en tirely through the ptype regions, the p/n junction must be reverse biased and the leakage current should be ne gligible. In this experiment, the reverse bias characteristics of the p/n junction were measured to determine the leakage current from the piezoresistors to th e ntype substrate. Th e resistance is extracted from the IV characteristics of the piezoresistors in the p/n forward bias region. Dynamic Calibration The frequency response and linearity were deduc ed using Stokes layer excitation of shearstress in a planewave tube (PWT). This technique utilizes acoustic plane waves in a duct to generate known oscillating wall sh ear stresses [97]. This technique relies on the fact that the particle velocity of the acousti c waves is zero at the wall due to the noslip boundary condition. This leads to the generati on of a frequencydependent boundary layer thickness and a corresponding wall shear stress. Therefore, at a given location, the relationship between the fluctuating shear stress and acoustic pressure is theoretically know n. The acousticallygenerated wall shear stress for the frequenc y range of excitation in this paper is approximated by [97] 2' 'jtkx wallpjv e c t a n h j (61) where is the amplitude of the acoustic perturbation, 'p 1j v is the kinematic viscosity, is the angular frequency, k c is the acoustic wave number, 2b is the nondimensional Stokes number and is the half height of the duct. b 120 PAGE 121 A conceptual schematic of the dynami cal calibration setup is shown in Figure 63 The plane wave is generated by a BMS 4590P compressi on driver (speaker) that is mounted at one end of the PWT. The PWT consists of a rigidwall 1x1 duct with an anechoic termination (a 30.7 long fiberglass wedge), which is respon sible for supporting acous tic plane progressive waves propagation along the duct [97]. The se nsor and a reference microphone (B&K 4138) are flushmounted at the same axial position from the driver. The usable bandwidth for plane waves in the PWT is defined by the cuton frequency of the first higher order mode which is 6.7 in air and in helium. The compensated output voltage from the AD625 interface circuit is accoupled and amplified 46 dB by the SR560 low noise preamplifier. A B&K PULSE MultiAnalyzer System (Type 3109) is used as the microphone power supply, data acquisition unit, a nd signal generator for the source signal in the plane wave tube. kHz 20 kHz Noise Measurement A noise measurement is necessary to determ ine the minimum detectable signal (MDS). The sensor is mounted on the sidewall of the plan e wave tube and the speaker amplifier is turned off. This provides a reasonable estimate of the en tire sensor system noise floor as installed in a calibration chamber. The compensated voltage output is amplified by the AD625 and the SR560 low noise preamplifier (ac coupled ), and then fed into the SRS 785 spectrum analyzer [98]. The spectrum analyzer measures the noise power spec tral density (PSD), us ing a Hanning window to minimize PSD leakage. The measured noise PSD includes the sensor noise and the setup noise, including noise from sources such as EMI, the amplifier, the spectrum analyzer, and the power supply. LabVIEW is used for data acquisition an d manipulation. The noise PSD is measured in three overlapping frequency spans from 10 to 1024. The settings for three frequency ranges are listed in Hz Hz Table 61 121 PAGE 122 Experimental Results Electrical Characterization As shown in Figure 64 IV characterization results indica te a negligible leakage current (< ) up to a reverse bias voltage of 10 V. The reverse bias breakdown voltage for the P/N junction is around 20 V or greater ( 0.12 A Figure 65 ). IV measurements of the diffused resistors across the Wheatstone br idge are shown in Figure 66 for a representative design in Table 62 One curve is for the resistors across the bias voltage port and ground, a nother is for the resistor s across the output ports and The nonlinearity of the IV curve is obtained subtract ing the actual voltage in the VBGND curve (or V1V2) from a linear cu rve fit (fit between 1V 2V 0.5 V to 0.5 and extended to ), then normalizing by the linear curve and multiplyi ng by 100. The nonlinearity is shown in V 10 V Figure 67 The linear variation of current with voltage below 5 V (3% nonlinearity in Figure 67 ) indicates Ohmic behavior of the piezoresistors and p ++ interconnects. The average resistances across the bridge are 397 and 41 1 respectively, while the predicted value for the individual resistor is 1 k. The smaller than predicted resistances may due to the high implant dosage (double of the simulation value to a void solubility loss). The asymmetry of curve may be due to the Schottky effect. The as ymmetry may also be due to residual heating as the voltage was swept from 10 V to 10 V instead of performing two test s sweeping the voltage from 0 to 10V and 0 to 10 V. The root cause of this asymmetry re quires further study. V1V2 Dynamic Calibration Results and Discussion The dynamic sensitivity and lineari ty of the sensor were test ed with a single tone of as a function of increasing sound pressure levels (SPL). The chosen frequency of is far enough below the expected resonan ce so that it is a reasonable approximation 2.088 kHz 2.088 kHz 122 PAGE 123 of the static sensitivity. In this measurement, the frequency span was with a frequency resolution of 32 H. 3000 linear averages with 0% overlap were taken to minimize the random error. The sensor wa s operated at bias voltages of 1.0, 1.25 Vand 1.5. This is substantially lower than the optimized bias volta ge of 10 V because elect ronic testing indicated nonlinearities in the currentvoltage relationship at excitation voltages abov e 4.5 V from resistor selfheating. Any resistor selfheating will lead to temperatureresistive voltage fluctuations due to unsteady convective coo ling [38]. In other words, the direct sensor will behave somewhat like an indirect sensor. To avoi d this phenomenon, testing was limited to bias voltages of 1.5 and below. 0.26.4 kHz z V V V The dynamic sensitivity is the ratio of the differential sensor output voltage to the input wall shear stress. Ideally, the lateral displacem ent of the floating element will be solely a function of the acoustically genera ted wall shear stress. In practi ce, however, it is known that there will be an additional displacement due to the local pressure gradient forces generated by traveling acoustic waves across th e floating element [43]. The ma gnitude of the effective shear stress including pressuregradien t effects for a purelytraveling acoustic wave in a duct is [43] 22 1 2wall effgff ft (62) The second and third terms of Equation (62) represent the error due to the fluctuating flow beneath the element and the net fluctuating pres sure force acting on the lip (assuming a square element). Accounting for the fact that the actual shear stress is proportional to f the magnitude of the error terms is proportional to f The second term of Equation (62) assumes that so that the flow underneath the elem ent can be approximated by fullydeveloped pressuredriven flow in a slot. For the current sensor, eL g 400 mg and Clearly, 1000 meL 123 PAGE 124 this approximation is invalid and the flow beneath the element is sufficiently complex and must be evaluated using computationa l techniques. Therefore, only an estimate for the pressure gradient force acting on the thickness can be provided. The maximum error for this term is ( 7.5 dB 2.4wall ) at the highest frequency tested, The error terms are also 6.7 kHz /2 out of phase with the actual shear stress. By adjusting the SPL from 123 dB to 157, the induced shear stress varies from to dB 0.04 Pa 2.0 Pa Figure 68 shows output voltages response to the shear stress variation at different bias voltages. The slopes of the plots shown in Figure 68 indicate the dynamic sensitivity of the sensor at different bias volta ges. For all bias cond itions, the sensors respond linearly up to and the sensitivities are 2.0 Pa 2.905 VPa 3.602 VPa and 4.242 VPa at bias voltages of 1.0 V, 1.25 V and 1.5 V, respectively. The normalized sensitivity is defined as the ratio of sensitivity to applied bias voltage. For a Wheatstone bridge without resist or selfheating, the normalized se nsitivity is a constant. If resistor selfheating is occurring, a powerlaw dependence on the pow er dissipation is expected. The slopes of Figure 69 are the normalized sensitivities at bias voltages of 1.0 V, 1.25 V and respectively, which are 1.5 V 2.905 VVPa 2.882 VVPa and 2.828. The predicted normalized sensitivity is VVPa 3.65 VVPa Note that for Figure 69 the initial offset voltages were subtracted for normalized slope comparison purposes. The close match in normalized sensitivities (<3% vari ation) indicates that the sensor is responding solely to the piezoresistive effects and not unsteady convective cooling. This piezoresistive effect is a combination of shear stress sensitivity, pressure gradient sensitivity and normal pressure sensitivity. 124 PAGE 125 The frequency response at a bias voltage of 1.5 was also investigated in this experiment. For this test, the generator is set to a random signal with a span of and a center frequency of to ensure that all harmonics up to 6 kH are captured. A 200 line FFT is used corresponding to frequency resolution of At each measurement frequency, 2000 linear averages are taken with 0% overlap. The input shear stress is desired to be The theoretical SPL for each measuremen t frequency obtained via Equation V 6.4 kHz 3.4 kHz z 32 Hz 0.3 Pa (61) By adjusting the SPL at specific frequency, the targ et shear stress is then achieved. The normalized frequency res ponse function of the shear stre ss sensor is given as [43] out wallVf Hf f V (63) where is the sensor output with a known input, outVf wall f is obtained via Equation (61) and V is the flat band sensitivity. For this experiment, the sensitivity at from the linearity test was used for normalization. 2.088 kHz Figure 610 demonstrates the magnitude and phase of the actual frequency response function of the shear stress sensor for a nominal input shearstress magnitude of 0.. The gain factor is flat and is between 3 Pa 3.01 dB to for this test. The phase is flat up to It is noted that the ga in factor at frequency of is not 0 d, which may be due to the setup and temperature variation in these two measurements. These results ar e not corrected for nonidealities in the anechoic termination which results in a finite reflected wave [97]. In addition, there is some su spicion that the results above are corrupted by the scattered evanes cent field near the termination. Regardless, there is no apparent resonance in this sensor up to 0.09 dB 4.552 kHz 2.088 kHz B 4.552 kHz 6.7 kHz To check the wave reflection effect on the measurement, the twomicrophone method [99] is used to measure the reflection coefficient, as shown in Figure 611 The frequency spans from 125 PAGE 126 0.2 Hz to 6.4 kH. The FFT line is set to 400 gi ving a frequency resolution of 16 H. 1000 linear averages with 0% overlap are taken. Th e results indicated that the magnitude of the reflection coefficient is comparativel y large when the frequency is below 1 k. Therefore, the frequency in the measurement for both lin earity and frequency response are above 1 k to minimize the uncertainty. z z Hz Hz The lower end of the dynamic range of the se nsor is ultimately limited by the device noise floor. The outputreferred noise floor of the sensor and measurement system is shown in Figure 612 for a bias voltage of 1.5. As expected, the noise spectrum is dominated by V 1 f noise indicating that the signaltonoise ratio for this sensor is a strong functi on of frequency. At (with 1 Hz bin) the outputreferred noise floor of the sensor a nd measurement system is 1 kHz 48.2 nV Hz which corresponds to the minimum detectable shear stress of 11.4 m. Pa Summary Preliminary electrical and dynamic characterization and the noise determination are presented to demonstrate device functionality. At a bias voltage of 1.5, the dynamic characterization of the device reveal ed a linear response up to at least and a flat response up to the frequency testing limit of The theoretically predic ted resonant frequency is Noise floor measurements indicate that V 2.0 Pa 6.7kHz 9.8 kHz 1 f noise dominates and the minimum detectable shear stress at 1 kHz is 11. Therefore, the experimentally verified dynamic range is 11 m. The theoretically predicted upper e nd of the dynamic range at 3% static nonlinearity is 5 Pa. The upper ends of the dynamic range and bandwidth, however, could not be verified due to constraints in the calibration apparatus. A summary of the experimental results compared to the predicted results for a bias voltage of 1.5 V are listed in .4 mPa Pa2 Pa Table 64 The normalized sensitivity is close to the predicted de sign value, but resistor heating precluded using 126 PAGE 127 higher bias voltages, thus lowering th e maximum allowable sensitivity by 16.5 dB. Furthermore, the noise floor is roughly a factor of 7 higher than predicted. This may be due to the noise floor measured is the total system noise, which includes setup noise and sensor noise, whereas the predicted valu e is just due to the se nsor and the AD 625 circuit. There are also substantial differences in the pr edicted versus realized bridge impedance which means that the voltage noise of the resistors may al so be higher than predicted. 127 PAGE 128 Table 61. LabVIEW settings for noise PSD measurement Frequency Range (Hz) Bin Width ( ) Hz Number of Averages 10200 0.25 2300 2001600 2 4000 1600102400 128 30000 Table 62. The optimal geometry of the shear stress sensor that was characterized. Parameters Design Values Target Shear Stress maxPa 5 Tether Length mtL 1000 Tether Width mtW 30 Tether Thickness mtT 50 Floating Element Width meW 1000 Piezoresistor Length mrL 228.5 Piezoresistor Width mrW 5 Piezoresistor Depth mjy 1 Table 63. Sensitivity at different bias voltage for the tested sensor. Bias Voltage (V) Sensitivity mVPa 1.5 0.27 2.95 0.71 3.1 0.93 4.8 3.0 128 PAGE 129 Table 64. A comparison of the predicted versus realized perfor mance of the sensor under test for a bias voltage of 1.5V. Parameters Theoretical Value Experimental Result Normalized Sensitivity VVPa 3.65 2.83 Noise Floor nV 6.5 48.2 MDS mPa 1.2 11.4 Bandwidth kHz 9.8 >6.7 Resistance 1000 397 maxPa 5 >2 129 PAGE 130 0 1 2 3 4 5 0.06 0.05 0.04 0.03 0.02 0.01 0 Bias Voltage( V )Offset Voltage ( V ) Figure 61. The bridge dc offs et voltage as a function of bias voltages for the tested sensor. Figure 62. An electrical schematic of th e interface circuit for offset compensation. 130 PAGE 131 Figure 63. A schematic of the experimental setup for the dynamic calibration experiements. 10 8 6 4 2 0 2 2 0 2 4 6 8 10 Bias Voltage ( V )Current ( A ) Reverse Bias Forward Bias Figure 64. Forward and reverse bias characterist ics of the p/n junction. 131 PAGE 132 20 15 10 5 0 10 8 6 4 2 0 2 Bias Voltage ( V )Current ( A ) Figure 65. Reverse bias breakdow n voltage of the P/N junction. 10 5 0 5 10 30 20 10 0 10 20 30 Bias Voltage( V )Current( mA ) y = 2.52*x 0.01 R2 = 0.9992 y = 2.43*x + 0.273 R2 = 0.9990 VBGND V1V2 Linear Fitting VB GND Linear Fitting V1 V2 Linear Fitting Figure 66. IV characteristic s of the input and output term inals of the Wheatstone bridge. 132 PAGE 133 10 5 0 5 10 2 0 2 4 6 8 10 12 Voltage (Volts)Nonlinearity (%) V1V2 VBGND Figure 67. The nonlinearity of the IV curve in Figure 66 at different sweeping voltages. 0 0.5 1 1.5 2 0 1 2 3 4 5 6 7 8 9 Shear Stress (Pa)Output Voltage ( V) y = 3.602*x + 0.01884 y = 4.242*x + 0.0231 y = 2.905*x + 0.004146 VB=1 V VB=1.25 V VB=1.5 V Figure 68. The output vo ltage as a function of shear stress ma gnitude of the sensor at a forcing frequency of 2.088 kHz as a function bias voltage. 133 PAGE 134 0 0.5 1 1.5 2 0 1 2 3 4 5 6 Shear Stress (Pa)Normalized Output Voltage ( V/V) y = 2.905*x 0.3113 for VB=1.0V y = 2.882*x 0.2964 for VB=1.25V y = 2.828*x 0.2914 for VB=1.5V VB=1.0 V VB=1.25 V VB=1.5 V Linear Fitting Figure 69. The normalized output voltage as a function of shear stress magnitude of the sensor at a forcing frequency of 2.088 kHz for several bias voltages. 1 2 3 4 5 6 10 0 10 Frequency (kHz)H(f) (dB) 1 2 3 4 5 6 50 0 50 Frequency (kHz)Phase (Deg) Figure 610. Gain and phase factors of the frequency response function. 134 PAGE 135 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 RFreq [kHz] 1 2 3 4 5 6 200 100 0 100 200 Phase [deg]Freq [kHz] Figure 611. The magnitude and phase angle of th e reflection coefficient of the plane wave tube. 135 PAGE 136 101 102 103 104 105 100 101 102 103 Noise Floor (nV/Hz)Frequency (Hz) System "Thermal Noise" System Noise Figure 612. Outputreferred noise floor of the measurement system at a bias voltage of 1.5V. 136 PAGE 137 CHAPTER 7 CONCLUSION AND FUTURE WORK Summary and Conclusions A proofofconcept micromachined, floating el ement shearstress sensor was developed that employs laterallyimplanted piezoresistors for the direct measurement of fluctuating wall shear stress. The shear force on the element induces a mechanical stress field in the tethers and thus a resistance change. The piezoresistors are arranged in a fullyactive Wheatstone bridge to provide rejection to common mode disturbances, su ch as pressure fluctuat ions. A dummy bridge located next to the sensor is used for temperature corrections. The device modeling, optimal design, fabrication process, packaging and comprehensive calibration were presented. Mechanical models for small and large defl ection of the floating element have been developed. These models are combined with a pi ezoresistive model to determine the sensitivity. The dynamic response of the shear stress sens or was explored by combining the above fundamental mechanical analysis with a lumpedelement model. Finite element analysis is employed to verify the mechanical models and lumpedelement model results. Dominant electrical noise sources in the piezoresistive shear stress sensor, 1 f noise and thermal noise, together with amplifier noise, are considered to determine the noise floor. These models are then leveraged to obtain optimal sensor designs for m easuring shear stress in se veral flow regimes. The cost function, minimum detectable signal (MDS) formulated in terms of sensitivity and noise floor, is minimized subject to nonlinea r constraints on geometric dimensions, linearity, bandwidth, power, resistance, and manufacturing constraints. The optimization results indicate that the predicted optimal device performance is improved with respect to existing shear stress sensors, with a MDS of O(0.1 mPa) and dyna mic range greater than 75 dB. A sensitivity 137 PAGE 138 analysis indicates that the devi ce performance is most respons ive to variations in tether geometry. The process flow used an 8mask bulk micromachining process, involving PECVD, thermal oxidation, wet etch, sputtering, DRIE and RIE fabrication techniques. After fabrication, the die was packaged for wind tunn el testing in a custom printe d circuit board for modularity. An interface circuit board was designed for amplification and offset compensation. Then the sensor was calibrated electrically and dynamically. Electrical characterization indicates linear junctionisolated resistors, and a negligible leakage current (<0.12) for the junctionisolated diffused piezoresistors up to a reverse bias voltage of 10 V. Using a known acousticallyexcited wall shear stress for calibration at a bias voltage of 1.5, the sensor exhibited a sensitivity of a noise floor of A V 4.24 V/Pa 11.4 mPa/Hz at 1 kHz, a linear response up to the maximum testing range of and a flat dynamic re sponse up to the testing limit of6.7 kH. These results coupled with a windtu nnel suitable package are a significant first step towards the development of an instru ment for turbulence meas urements in lowspeed flows. The system noise is 2 Pa z 48.2 nVHz at 1 k (with 1 Hz bin), and is roughly 7 times higher than predicted. Static heating lim itations limited the maximum bias voltage to 1.5 instead of 10. Hz V V Suggestions for Future Work Future work should focus on the comprehensive characterization of the sensor to determine absolute performance and to compare against all of the theoretical predictions. An uncertainty analysis of all experime nts and accurate measurement of the sensor geometry are required to enable this comparison. Specifically, a temperatur e compensation approach must be realized that will enable the static calibration of the sensor as well as any dc measurement application. The 138 PAGE 139 resonant frequency of the sensor s must be determined. Sensitiv ity to vibration and pressure fluctuations must also be determined. Detailed noise measurements that isolate the contribution from the piezoresistor should be carried out. Finally, the flow around the floating element will be investigated via numerical si mulations to provide an improved estimate of pressure gradient induced errors. In the following subsection, several suggestions for carrying out these measurements are discussed below. Temperature Compensation The sensitivity of the shear stress sensor chan ges with temperature due to the variation of the piezoresistive coefficient with te mperature, as indicated in Equation (323) and (324) In sensor static calibration in a 2D laminar cell, the sensitivity is de fined as the slope of the curve of voltage output versus shear stress. However, due to the temperature effect, the output voltage is a function of shear stress and temperature. Thus the temperature induced voltage output should be subtracted from the ac tive bridge voltage output. For the identical active and dummy Wheatstone bridge, the temperature effect on them should be same Therefore, the temperature effect on the active bridge in the static calib ration can be removed by subtracting the voltage output of the dummy bridge. Unfortunately, the active bridge and dummy br idge are not identical due to Wheatstone mismatch. So the voltage output dependence of the temperature need to be measured for both active bridge and dummy bridge. The output voltage of the active bridge is a function of shear stress and temperature variations, while the du mmy bridge depends on temperature variation only. The measured output volta ges in the laminar flow are ,awVT for the active bridge and for the dummy bridge, respectively. The sl ope of the voltage vs. temperature curve is dVT TaS 139 PAGE 140 for active bridge and for dummy bridge. In the static calibration, th e output voltage dependence of shear stress is given as TdS ,awawaVVTV T (71) Assuming that the slope of the curve remains constant and they are given as, vs. ToV 0 0 aa Ta ddVTVT S VTVTS T d (72) Substituting from Equation aVT (71) into (72) and rearranging it, the shear stress dependent output voltage is obtained as 0,Ta awawa dd TdS VVTVTVTVT S 0 (73) where 0 aVT is the initial voltage value at room temperature. The Equation (73) indicates that and must be obtained in order to get TaS TdS awV Preliminary experiments prior to employing dc offset nulling were performed to determine the temperature sensitivity. Unfortunately, the large dc offset limited the quality of the results. The ex perimental set up is as follows. The voltage output dependence of temperature variation is conducted in two bath settings. Both bathes are filled with DI water. The out er bath is the chamber of Isotemp refrigerated circulator, and the inner bath is glass beaker. The packaged sensor is sitting on the top of the beaker. The beaker is used to protect the se nsor from flow circulat ion disturbance. The compensated voltage output is connected to a HP34970A data acquisition unit and DAQ card. A HP34970A digital voltage meter is used to minimize the 60 noise. LabVIEW is used for data acquisition. Hz 140 PAGE 141 Static Characterization Initially, we attempted to statically characte rize the sensor, but the temperature sensitivity and dc offset issues prevented any meaningful resu lts. The goal of the static characterization is to verify the sensor design and characterize th e sensitivity and linearity. After temperature compensation and dc nulling have been achieved, a static calibration can be performed. The flow cell design is such that an ideal onedim ensional fully developed incompressible laminar flow exists between two semiinfinite parallel plates (Poiseuille flow between two parallel plates). For this case, the pressure drop is constant and the wall shear stress is given by the theoretical relation [7] 2whdP dx (74) where is the height of the channel in meters and P is pressure in Pascals. Detailed setup information can be found in [34]. h The incompressible flow is first verified be fore the sensor static calibration. The incompressible flow exhibits a linear pressure drop versus length for wall shear stress up to which is a necessary assumption for Equation 2 Pa (74) The pressure measurements are carried out using the Scannivalve pressure measurement system. This multiplexing valve system allows the pressure taps to be reached sequent ially to measure pressure drop between the first pressure tap and other taps downstream. The in let flow rate is regul ated using a mass flow controller (GFC4715). A linear pressure drop versus length is displayed in Figure 71 Figure 72 shows the experimental setup for the st atic calibration of the wall shear stress sensor. The sensor is flushmounted on one wa ll of the laminar flow cell and oriented for measuring wall shear stress in th e flow direction. The corresponding pressure drops across two pressure taps and is measured using a differential pre ssure gauge, Heise pr essure meter. 1P 2P 141 PAGE 142 The voltage output is first fed into the compensa tion circuit. The compensated signal is then supplied to a HP34970A preci sion digital voltage meter to elim inate 60Hz noise from the power supply by averaging. The mass flow rates are controlled automatically by LabVIEW to obtain different pressure drops and co rrespondingly wall shear stress. LabVIEW is also used for data acquisition and manipulation. Noise Measurement In order to determine the isolat ed resistor noise characteristic s, the sensor is placed in a doublenested Faraday Cages to improve the elec tromagnetic interference (EMI) reduction [98]. The compensated voltage output is amplified by a SR560 preamplifier, a nd then fed into the spectrum analyzer (SRS785). The spectrum anal yzer (ac coupled) measures the noise power spectral density (PSD), using a Hanning window to avoid PSD leak age. The noise PSD of the sensor is obtained by subtracting the setup noise PSD from the total measurement noise PSD. The setup noise sources include EMI and noise from the amplifier, spec tra analyzer, and power source. Recommendations for Future Sensor Designs Based on lessons learned during the first gene ration shear stress sensor fabrication and characterization, there are several issues that need to be addressed in future designs. Specifically, issues regarding resistor selfheating and pressure sens itivity need to be addressed. In the sensor calibration, piezoresistor selfheating was clearly present when the dissipated power was greater than 10. A study of the normalized sens itivities indicated that selfheating could be avoided all together for a power dissipation limit of Therefore, the power dissipation limit in the design op timization should be decreased from 100 down to to avoid resistor self heating. The power limit will be a function of the tether geometry, but the order of magnitude in power reduction will provide a better estimate of appropriate mW 5.7 mW mW 10 mW 142 PAGE 143 biasing conditions for design purposes. A detailed nume rical study of the re sistor heating may also provide insight into this phenomenon, but this may be challe nging due to the complexity of the convective boundary conditions at the tether surface. For a balanced Wheatstone bridge, pressure fl uctuations should not affect the voltage output. Preliminary pressure calibrations, however, indicate that the pressure sensitivity is only lower than the shear stress sensitivity. In addition to achieving better control of the resistor implant process to balance the bridge, this can be mitigated by extending the sideimplanted resistor all the way down tether thic kness. The fabrication process should change correspondingly to protect the botto m of the piezoresistor with a high quality passivation. In current sensor design, the piezoresistor is implanted on the top of the tether thickness to avoid resistor current leakage. So in the fina l backside release step, the BOX layer was removed to release the structure a nd the tether bottom is exposed to the flow without any protection. This will cause sensitivity drifting if the piezoresistor is implanted on the whole tether thickness. A process flow must be designed to realize an electrically passivate d resistor that extends to the bottom of the resistor thickness. 10 dB O 5 m In general, improved test structures are need ed to provide additional information about the sideplanted resistors. Specifically, a test struct ure must be added into the mask design to enable the measurement resistor doping profile via s econdary ion mass spectroscopy (SIMS). In addition, providing additional bond pads for each resistor will permit a resistor trim based approach to bridge balancing a nd temperature compensation [60]. 143 PAGE 144 1 2 3 4 5 6 7 20 40 60 80 100 120 140 Length (Inch)Pressure Drop (Pa) Testing Data linear Fitting Figure 71. Pressure dr ops versus length between taps in the flow cell. Piezoresistive Shear Stres Sensor P1P2 L Amplifier Mass Flow Controller SourceMeter u(y)Flow Cell Gas Pressure Meter Voltage MeterdPVolts DAQ PC (LabView) Compensation Circuit Figure 72. Experimental se tup of static calibration. 144 PAGE 145 APPENDIX A MECHANICAL ANALYSIS A clampedclamped beam with a central point force and a distributed pressure load is shown in Figure A1 (a). This is a second order stat ically indeterminate problem. Euler Bernoulli beam theory is used to predict the linear, small deflection behavior and Von Krmn strain is included in the nonlin ear, large deflection models. Two methods, an energy method and an exact analytical method, ar e used to solve the large de flection problem. Using EulerBernoulli beam theory, the stress distribution is also derived. Small Deflection Equilibrium equations may be written base d on the free body diagram of the symmetric structure, Figure A1(b). The relatio nships between the resultant forces, A R and B R point load and distributed load Q are thus P 2AB t R RPQL (A1) where 2weePWL wtQW and w is the wall shear stress. The nonlinear differential equation governing the beam deflecti on caused by bending is given as [82] 22 32 2() 1 x dwxdx E I dwdx M (A2) where is the deflection in the direction, wx z E is the Youngs Modulus, I is the area moment of inertia given as 312ttITW and x M is the resisting moment in cross of x Writing the equation for moment equilibrium, 0DM yields 22xAA M MRxQx (A3) 145 PAGE 146 where A M is the resisting moment, and A B M M due to the symmetry of the structure. Assuming the rotation dwdx is very small, Equation (A2) is simplified to 2 2() x M dwx dxEI (A4) Integrating Equation (A4) yields the rotation and deflection of the beam along its length, 23 1111 26AAdwx M xRxQxc dxEI (A5) and 2 34 1111 () 2624A AMx wx RxQxcxc EI 2 (A6) where and are constants. There are three unknown quantities in Equations 1c 2c (A5) and (A6) A M and Therefore, three boundary conditions should be employed, 1c 2c 00 (clamped) w (A7) 0 0 (clamped) dw dx (A8) and 0 (symmety)tdwL dx (A9) Substituting the above boundary conditions and A R from (A1) into (A6) one obtains 120 cc (A10) and 211 43At t M PLQL (A11) The displacement is then obtained by substituting Equation wx (A10) (A11) and momentum of inertia 312ttITW into (A6) 22 34 t 338282, 0x 4w eettt eett t ttwx WLLWLxWLWLxWx EWT L (A12) 146 PAGE 147 The maximum deflection at the center of the beam is given as 32 1 4weet tt Lt tteeWLLWL wL E TWWL (A13) Large DeflectionEnergy Method In a large lateral deflection, the beam experi ences bending and stretchi ng. The total strain is composed of bending and stretching strain [42] tbendingstrenching (A14) where bending 2 2dw y dx y is the position upward. The axial strain at 2tyW is given as [100] 21 2adudw dxdx (A15) The total change in beam length is given by 2 22 001 2LL tt adudw L dx dx dxdx (A16) The integration of the first term is zero due to the clampedclamped boundary condition. The axial stain is the total change in beam le ngth divided by the total length of the beam 2 2 01 24L t strentching ttLdw dx LLdx (A17) The total strain is obtained as 2 2 2 2 01 4L t t tdwdw y dxLdx d x (A18) For large deflection, a trial function in the form of a cosine is assumed, as it automatically satisfies the doubly clamped boundary condition and is a maximum at the center of the beam. The trial function is thus 147 PAGE 148 1cos 2t NL tLx wx L (A19) where N L is the maximum deflection at the center of the beam. Substituting this model into (A18) yields sin 2t NL ttLx dw dxLL (A20) and 2 2 22cos 2t NL ttLx dw dxLL (A21) Substituting Equation (A20) into Equation (A18) yields 22 2cos 21t NL NL t ttLx y LL 2 26tL (A22) The strain energy density is given as 2 22 2 0 2 011 cos 222 16t t NL NL t ttLx UdEEy LLL 2 2 t (A23) The strain energy is then obtained 2 2 0 002WL tt t tET UUdV dxdy (A24) The total strain energy is obt ained by integrating Equation (A24) to yield 24344 396256NLtNLt t ttW UET LL 3W (A25) Based on the principle of virtual work, the total potential energy W is equal to the stored strain energy minus the work done by the external force K WUK (A26) where K is given by 148 PAGE 149 2 01cos 2L t t NL NL t tLx KPQ dxPQL L (A27) The equilibrium configuration is that in which the potential energy is minimized. The minimum is obtained when 4334 331 0 48642NLtNLt tw e ttWW dW ET WLWL dLL e w t t (A28) Rearranging Equation (A28) yields 23 442 1 96128 4NL wee ttt NL tte eWLWLL WETWL tW (A29) Simplifying the above equation, 41 96 and 43 1284 yields an approxima te large deflection solution, 232 3 11 44NL wee ttt NL tte eWLWLL WETWL tW (A30) Large DeflectionAnalytical Method For large deflection, axial force in the beam is not zero as in the small deflection model, and serves as a constitutive equation in the m odeling analysis. Since the beam is symmetric, only half of the beam is analyzed, as shown in Figure A3 For large deflections, taking axial force into account, the differen tial equation governing the b eam deflection caused by bending is given as aF 2 2() ()dwx E IM dx x (A31) where the slope of beam caused by large deflection is assumed 1 dwdx and therefore 2dwdx is negligible. The moment M x is given by 149 PAGE 150 2 01 () ((0)()) 22aP M xQxxMFwwx (A32) where 0 w is an unknown constant. Substituting Equation (A32) into Equation (A31) yields 2 2 0 2()1 () (0) 22adwx P EIFwxQxxMFw dx a (A33) The above equation can be solved as a superposition of one general solution and a particular solution nw s w ()()()nswxwxwx (A34) 12where ()Csinh()cosh()nwxxCx and 2 ()swxaxbxc assuming =aFEI Substituting s w into Equation (A33) a, b, and c are obtained as 0 2 aQ a = and c = (0) 2F2aaM PQ bw FF aF Equation (A34) can be rewritten as 2 0 12 2()sinh()cosh() (0) 22aaaaM QPQ wxCxCxxxw FFFF (A35) for which the boundary conditions are: 0 =0 dw dx (A36) () =0tdwL dx (A37) and 0twL (A38) For large deflection, the axial strain at 2tyW is nonlinear and is given as 2 01 2 x a xdu F dw dxdxEEA (A39) 150 PAGE 151 where Integrating the above equation yields ttATW 2 0 01 2L t a tdu EA dw F dx Ldxdx (A40) The first term in the integration is zero due to the doubly clamped boundary condition. Axial force in the neutral axis aF 2tyW is then obtained as 2 02L t a tEAdw F dx Ldx (A41) There are five unknown variables: and thus five boundary conditions are needed to solve for these unknown variables. However, only three boundary conditions 120,,,,aCCFM (0)w (A36) (A38) and one constitutive equation (A41) are available. Another condition is 00 ww The problem is indeterminate and an iterative tec hnique must be used to find the final result. First, we applied boundary conditions (A36) (A38) and the constitutive equation (A41) into Equation (A35) and solve it to get the maximum defl ection as a function of the axial force in the neutral axis, The detailed procedure for solving th is problem is given in the following. aF Substituting (A35) into boundary conditions (A36) and (A37) yields 121 and cosh() 2 sinh()22t aatPP CCQ L FFL tP L (A42) Substituting and into 1C 2C (A35) and setting 0 x yields 0 21 cosh() sinh()22t tQP P t M QL L L (A43) Substituting 0 M from (A43) and and from 1C 2C (A42) into (A35) yields 2cosh()1 sinh() cosh() (0) 2 sinh()22 22tt aat aaPxP PQ P wx x QL Lxxw FFL FF (A44) 151 PAGE 152 Substituting (A38) into (A44) yields deflecti on at the center, 2cosh()1 (0)sinh() cosh()+ 2 sinh()22 22tt ttt aat aLQ PP P wLQ LL FFL F t aL P L F (A45) Derivative Equation (A44) to obtain 1 sinh() cosh() cosh() 2sinh()22 2 tt atdwx PxP P xQ LLQ x dxF L P (A46) Secondly, we solve the ma ximum deflection equation (A45) by iterating An initial value is selected randomly and the fo llowing steps are performed to obtain the maximum deflection, aF 4 aF=10 Pa 0 w 1) Substitute into aF (A46) to get dw dx where Fa EI 2) Substitute dw dx into (A41) to obtain new aF 3) Repeat 1), 2) until the relative error 11FaFaFa16nnne 4) Substitute into aF (A45) to find the maximum deflection 0 w Stress Analysis The bending stress along a beam (shown in (A3) ) is given as [82] z x z M yF A I (A47) where z I is the moments of inertia for the axis, and z 312zttITW In small deflection, the axial force A free body diagram of the clamped b eam is shown based on the discussion 0aF 152 PAGE 153 in the small deflections section, where A R and A M are obtained from Equation (A1) and (A11) respectively. The moment for a certain length from the edge of the beam is obtained as, 21111 4322zttt 2 M PLQLPQLxQx (A48) Substituting Equation (A48) into (A47) and simplifying the equa tion to obtain the bending stress along the beam 0t x L0y at 2 2263 33 42weet tt tt tt x tt ee eeteetWLLWLWLWL x WTWLWLLWLL x (A49) Effective Mechanical Mass and Compliance In this section, the mechanical lumped para meters for a clampedclamped beam are found. These parameters include lumped compliance obt ained via the storage of potential energy and lumped mass obtained via the storage of kinetic en ergy. These results are used in Chapter 3 to develop the lumped element model of a laterally diffused piezoresistive shear stress sensor. Recall that the lateral disp lacement and maximum displacement of the clampedclamped beam in small deflection given in Chapter 2, 22 34 3()38282 (0) 4w eett eett t t ttwx WLLWLtxWLWLxWxxL EWT (A50) and 312 4weet tt t tteeWLLWL wL E TWWL (A51) The kinetic coenergy K EW of a rectilinear system with a total effective mass m moving with velocity uis given as, *1 2KEWm 2u (A52) For a simple harmonic motion, the velocity a nd displacement of the beam are related by 153 PAGE 154 uxjwx (A53) where is the frequency and t t uL. ux is then expressed as jwL t twx uxuL wL (A54) For an infinitesimal element on the beam with a mass of sittWTdx the kinetic coenergy K EdW is calculated using Equations (A52) and (A54) to be 2 *2 2 21 22sittt KE sitt tWTuL dWWTux wxdx wL (A55) where s i is the density of silicon. Integrating Equation (A55) over the beam gives the total kinetic coenergy of the system, 2 ** 2 2 002LL tt sittt KE KE tWTuL WdWwx wL ( ) dx (A56) The reference point is t x L which corresponds to the maximum deflection of the beam twL The distributed deflectio n of the beam can be lumped into a rectilinear pi ston by equating the kinetic energy obtained in Equation (A56) to the kinetic energy of th e rectilinear piston of mass tme M 22tmet KE M uL W (A57) Equating Equation (A57) and (A56) yields effective mechanical mass as 2 2 02L t sitt tme tWT M wxdx wL (A58) Since the velocity of the plate is tujwL the effective mechanical mass of the device is the sum of the mass of th e plate and the effective m echanical mass of the beam, 154 PAGE 155 meptmesieettme M MMLWTM (A59) The strain energy stored in the beam due to its deflection can be expressed as 2 2 2 0()L t SEdwx WEId dx x (A60) The strain energy of an equivalent spring is given by 211 2SE t meWw C L (A61) where is the mechanical compliance of the beam. Equating Equation meC (A61) and (A60) yields 2 2 2 2 0() 2t me L twL C dwx E Id dx x (A62) Substituting and in Equation wx twL (A50) and (A51) into (A59) and (A62) yields 23 2149422381024 1 315315315 12tt tt tt ee ee ee mesieet tt eeWLWLWL WLWLWL MWLT WL WL (A63) and 2 3 212 1 2 64 14 15tt ee t me tt tt tt ee eeWL WL L C ETW WLWL WLWL (A64) 155 PAGE 156 x y z Figure A1. The clamped beam and free body di agram. a) Clampedclamped beam. b) Free body diagram of the beam. c) Free body diagram of part of the beam. FaP/2 Q Lt M0 Figure A2. Clampedclamped beam in large deflection. My MAV x D A RAQ x=0 (a) (b) Figure A3. Clampedclamped beam in sma ll deflection (a) and free body diagram of the clamped beam (b). 156 PAGE 157 APPENDIX B NOISE FLOOR OF THE WHEATSTONE BRIDGE For a Wheatstone bridge shown in Figure B1 assuming 1234 R RRRR we get 12BVV therefore the voltage across each resistor is 2RBBBVVVV 2 (B1) The current through th e resistor is 2B RV I R (B2) Assuming the noise sources are uncorrelated, the mean square noise can be solved as a superposition of the mean square thermal noise, the 1 f noise, and the amplifier noise. For thermal noise, the equivalent noise model is given in Figure B2 The rms thermal voltage is given as 22 ,121 23 4444nthermal B B BVEEkTRRfkTRRfkT Rf (B3) For 1 f noise, the equivalent noise model is given in Figure B3 The mean square current noise is 2 2 2 1 11lnHR c I f I Nf (B4) The mean square voltage noise 2 1 E is obtained as 2 222 11212EIIRR (B5) Substituting Equation (B4) and (B2) into (B5) to obtain 22 2 2 22 11 1121 22 2 22 12 22 11ln ln =ln ln 44HR HR cc HB HB ccIfIf ER NfNf VfVf 2R R R NRfNRf (B6) 157 PAGE 158 Rearrange the above equation to get 2 2 2 1 1 =ln 8HB cVf E Nf (B7) The rms 1 f voltage is obtained as 22 22 2 ,1 12 112lnln 84HB HB nf ccVfVf VEE NfNf 2 (B8) The total noise floor is obtained via the superposition of the mean square noises 2 2 2 1ln449 4HB nB cVf Vk T R f Nf e (B9) where the last term in the above equation is the low amplifier noise. 158 PAGE 159 Figure B1. The Wh eatstone bridge. R1R2R4R3 V1V2 R1 R2 R4 R3 V1V2 E1E2 Figure B2. The thermal noise m odel of the Wheatstone bridge. Figure B3. The 1 f noise model of the Wheatstone bridge. 159 PAGE 160 APPENDIX C PROCESS TRAVELER Wafer: ntype <100> 15 ohmcm, SOI wafer Start with SOI wafer (nSi (100) 15 cm) with 50 m silicon on 1.5um buried oxide (BOX). DI rinse Masks Reversed biased maskRBM Piezo contact maskPCM Nested maskNM Side implant maskSIM Bond pad cuts maskBPCM Metal maskMM Bond pad maskBPM Process Steps 1. nwell Implant Ion implantdopant = phosphorus, energy = 150 keV, dose = 4e12 cm2. 7 degree tilt, blanket implantation. This forms the nwell. This needs to be simulated first. Piranha clean 2. PECVD oxide: deposit oxide 0.1m via PECVD 3. Reverse Bias Contact Coat and pattern photoresi st/oxide on front side o HMDS evaporation for 5min o Spin AZ1529 at 4000rpm for 50sec & softbake at 90 oven for 30min C o Pattern by mask RBM Exposure 60sec at 8.8mJ/cm2 Develop at AZ300MIF for 50sec Hard bake at 90 oven for 60min C 160 PAGE 161 BOE(7:1) : ~80sec to etch 0.1um oxide. This step puts alignment marks on the wafer Ion implantdopant =phosphorus, energy = 80 keV, dose = 9e13 cm2. 7 degree tilt Ash strip photoresist RCA clean Thermal annealing at time=420sec in nitrogen 1000 CoT 4. Inplant Interconnection Contact Coat and pattern photoresi st/oxide on front side o HMDS evaporation for 5min o Spin AZ1529 at 4000rpm for 50sec & softbake at 90 oven for 30min C o Pattern by mask PCM, align to the alignment marks created via RBM Exposure 60sec at 8.8mJ/cm2 Develop at AZ300MIF for 50sec Hard bake at 90 oven for 60min C BOE(7:1) : 90sec to etch 0.1um oxide. This step puts alignment marks on the wafer Preamorphization Implant Ion implantdopant = Ge, energy = 160 keV, dose = 1e15 7 degree tilt 2cm Ion implantdopant = Ge, energy = 50 keV, dose = 1e15 7 degree tilt 2cm Ion implantdopant = boron, energy = 50 keV, dose = 1.2e16 7 degree tilt 2cm Ash strip photoresist Piranha clean 5. Nested Mask Release Deposit PECVD oxide 1 m Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1529 at 2000rpm for 50sec & softbake at 95 convection oven for 25min C o Pattern by mask NM, align to the alignment marks created via PCM Exposure 85sec at 7.9 mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90 oven for 60min C Plasma dry oxide etch. This step puts new alignment marks on the wafer 161 PAGE 162 BOE(6:1) oxide etch to re move the oxide residues 6. Etch Sidewalls Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1512 at 2000rpm for 40sec & softbake at 95 hotplate for 50sec C o Pattern by side implantion ma sk(SIM), align to the alignment marks created via NM Exposure 19sec at 4.5mJ/cm2 Develop at AZ300MIF for 70sec Hard bake at 90 oven for 60min C BOE(6:1) oxide for 2min DRIE silicon to deep ~8 m BOE(6:1) oxide for 60sec to av oid Piezoresistor and Piezo contact disconnection due to DRIE undercut Ash strip photoresist Piranha clean 7. Hydrogen Annealing P=for 5min in pure hydrogen for surface roughness reduction 1000 TC 5mTorr 8. Oxidation: thermal grown wet oxide 1000A at oT=1000C 9. Side Wall Implantation Preamorphization implant Ion implantdopant = Ge, energy = 160 keV, dose = 1e15 54 degree tilt 2cm Ion implantdopant = Ge, energy = 50 keV, dose = 1e15 54 degree tilt 2cm Ion implantdopant = boron, energy = 50 keV, dose = 1e16 54 degree tilt 2cm Piranha clean 10. Beam Definition Etch oxide by reactive ion etch via dielectric setting in STS DRIE silicon to BOX BOE(6:1) 2min to remove oxide (ensur e to remove 0.1um oxide on sidewall) 162 PAGE 163 11. Oxidation Piranha clean Annealing at for 60min in nitrogen oT=1000C Thermal dry oxide grown at for 235min oT=975C 0.1 m 12. Bond Pad Cuts Trench filling o Spin AZ1512 at 800rpm for 40sec & softbake at 95hotplate for 50sec C o Spin AZ9260 at 800rpm for 50sec & softbake at 90 oven for 30min C o Flood exposure Exposure 300sec at 7.9mJ/cm2 Develop at AZ400MIF till clear Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1512 at 0.5k/2k for 5/40sec & softbake at 95hotplate for 50sec C o Pattern by bond pad cuts mask(BPCM), align to the alignment marks created via PCM Exposure 45sec at 4.5mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90 oven for 60min C BOE(6:1) oxide for 15min Remove photoresist 13. Metalization Trench filling Desccum in oxygen plasma Deposit 1um AlSi(1%) to av oid spiking via sputtering Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1529 at 0.2k rpm and stay for 2min. Then spin at 0.2k/2k rpm for 10/50sec with ramp rate of 100/500 rmp/s o Softbake at 90 oven for 30min C o Pattern by metal mask (MM), align to the alignment marks created via BPCM Exposure 100sec at 7.9mJ/cm2 Develop at AZ300MIF for 1min 30sec 163 PAGE 164 Hard bake at 90 oven for 60min C Etch Al by RIE Remove photoresist 14. Nitride Passivation Deposit 2000A PECVD silicon nitride Trench filling Coat and pattern photo resist on front side o HMDS evaporation for 5min o Spin AZ1512 at 4000rpm for 40sec & softbake at 95hotplate for 50sec C o Pattern by bond pad mask(BPM), align to the alignment marks created via MM Exposure 18sec at 4.5mJ/cm2 Develop at AZ300MIF for 60sec Hard bake at 90oven for 60min C Etch nitride by RIE Remove photoresist 15. Final Release (a) Device wafer Spin AZ9260 on front side of the device wafer o Spin speed 200rpm, ramp rate 100rpm/s for 10s, wait for 1min. Run this recipe twice o Spin speed 4000rpm, ramp rate 1000rpm/s for 50s o Soft bake at 90 oven for 30min C HMDS on the backside Spin AZ9260 on backside of the device wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s o Soft bake in 90 oven for 30min C Pattern by back release mask(BRM), align to the alignment marks created via NM o Exposure 25sec in E VG520 mask aligner o Develop at AZ300MIF for 3min 40sec 164 PAGE 165 o Hard bake at 90oven for 60min C (b) Carrier wafer Spin PR AZ9260 on a carrier wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s Soft bake at 90 oven for 2030min C Put some cool grease on the edge of the carrier wafer Bake on hotplate, 60 for 5min C Put the device wafer face down on the carrier wafer. Put on the hotplate, apply pressure using swab (c) DRIE Run DRIE, stopped until 50um silicon left Put the wafer on the hotplate 6 for 5min, separate from the carrier wafer 0 C Separate the wafer into individual dies (d) Process on individual dies Spin AZ9260 on a carrier wafer o Spin speed 2000rpm, ramp rate 1000rpm/s for 50s o Put the device die on the top of the carri er wafer, apply pressure using swab o Soft bake in 90 oven for 30min C DRIE to BOX layer RIE BOX layer for 15min, run BOE 510min to remove the residues RIE nitride for 6min Remove the device die using tweezers Put the device die in AZ400 PR stripper Plasma clean in Asher for 10min 165 PAGE 166 APPENDIX D PROCESS SIMULATION This chapter includes the FLOOPS proce ss simulation of the piezoresistor, p++ interconnects and nwell, as well as the reverser bias connections. (a). Piezoresistor This program simulates the doping profile of piezoresistor in the silicon layer after ion implantation, anneal and thermal oxidation. Th e boron is implanted into preamorphization Si layer with oxide as a screen layer. Its init ial doping profile is simulated by SRIM, and then imported to FLOOPS file for subs equent process simulation. line x loc=0.1 spa=0.005 tag=SiO2top line x loc=0 spa=0.005 tag=top line x loc=1.5 spa=0.01 tag=bot region oxide xlo=SiO2top xhi=top region silicon xlo=top xhi=bot init #profile name=B_SRIM inf=/home/yawei/Floops_new/SRIM _B_50keV_0.1umSiO2_Si_only.txt sel z=B_SRIM*5 name=Boron sel z=log(Boron) layer etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=235 puts "### Oxide thickness after thermal oxide is [e xpr [interface oxide /si licon] [interface gas /oxide]] um." sel z=log10(Boron) plot.1d bound !cle label=PZR set cout [open /home/yawei/Floops_new/pzrda ta w] puts $cout [print.1d] close $cout sel z=log10(5.0e14) plot.1d !cle label=background sel z = Boron5e14 puts "The Junction Depth is [interpolate silicon z=0.0]" set z=Boron layer (b). P++ interconnection and nwell #p++ surface concentration is ~1e+21 and nwell Ns~1e+16 # generate grid 166 PAGE 167 line x loc=0 spa=0.001 tag=top line x loc=1.0 spa=0.01 line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot init sel z=5e14 name=Phosphorus implant phosph dose=4.0e12 energy=150 tilt=7 #deposit 0.1um PECVD oxide deposit time=4 rate =0.030 oxide grid=10 puts "O xide thickness after PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." diffuse temp=1000 time=450 strip oxide implant boron dose=1.2e16 energy=50 tilt=7 #strip oxide #deposit 1um PECVD oxide deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD oxide is [expr [interface oxide /sil icon] [interface gas /oxide]] um." diffuse temp=1000 wet time=9.2 # oxide thickness is 1000A etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=235 sel z=log10(Phosphorus+1) plot.1d bound !cle color=blue label=nwell set cout [open /home/yawei/Floops_new/nwelld ata w] puts $cout [print.1d] close $cout sel z=log10(5e14) plot.1d !cle color=pink label=background sel z=log10(Boron+1) plot.1d bound !cle color=red label=p++ set cout [open /home/yawei/Floops_new/ohmicda ta w] puts $cout [print.1d] close $cout sel z = BoronPhosphorus layer puts "The Junction Depth is [interpolate silicon z=0.0]" (c). Reverse biased contact line x loc=0 spa=0.005 tag=top line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot init sel z=5.0e14 name=Phosphorus implant phosph dose=4.0e12 energy=150 #deposit 0.1um PECVD oxide deposit time=4.19 rate =0.0239 oxide grid=10 puts "Oxide thickness after PECVD oxide is [expr [interface oxide /silicon] [interface gas /oxide]] um." strip oxide smooth set t [open temp.P w+] 167 PAGE 168 sel z=Phosphorus puts $t [print.1d] close $t # start with a new grid ... si nce strip oxide removes the nodes near the surface where the new phosphorus profile is about to go set fo rmer_interface [interface gas /silicon] line x loc=$former_interface spa=0.0001 tag=top line x loc=0.1 spa=0.001 line x loc=1.0 spa=0.01 line x loc=2.5 spa=0.01 tag=bot region silicon xlo=top xhi=bot init profile name=Phosphorus inf=temp.P # inplant phosphorus for reverse bias contact implant phosph dose=9.0e13 energy=80 tilt=7 sel z=log10(Phosphorus) plot.1d bound !cle color= red label=Profile_ini #Thermal Annealing 450min at T=1000 deg diffuse temp=1000 time=450 #deposit 1um PECVD oxide deposit time=41.9 rate =0.0239 oxide grid=10 puts "### Oxide thickness after 2nd PECVD oxide is [expr [interface oxide /sil icon] [interface gas /oxide]] um." # thermal grown oxide 1000A at T=975 deg diffuse temp=1000 dry time=9.2 etch oxide time=1 rate=0.1 iso diffuse temp=1000 time=60 diffuse temp=975 dry time=235 puts "### Oxide thickness after thermal oxide is [e xpr [interface oxide /si licon] [interface gas /oxide]] um." sel z=log10(5.0e+14) plot.1d bound !cle color= black label=background sel z=log10(Phosphorus+1) plot.1d bound !cle color=bl ue label=reverse_bias set cout [open /home/yawei/Floops_new/reversedata w] puts $cout [print.1d] close $cout layers 168 PAGE 169 APPENDIX E MICROFABRICATION RECIPE FO R RIE AND DRIE PROCESS Table E1. Input parameters in the ASE on STS DRIE systems. Parameters 50 m Si etch 8 m Si etch 2SiO etch Coil power 600 W 600 W 800 W Platen power 12 W 12 W 130 APC (mTorr) 28 (fixed) 28 (fixed) 50 (auto) Etching process 11 6 Passivation process 6.5 4 6SF flow (sccm) 130 130 2O flow (sccm) 13 13 48CF flow (sccm) 85 85 Etching cycle Varies Varies Varies Passivation cycle Varies Varies Varies Table E2. Anisotropic oxide /nitride etch recipe on the Unaxis ICP Etcher system. Parameters Oxide Nitride 3CHF flow (sccm) 45 6SF flow (sccm) 15 2O flow (sccm) 3 5 RF2 power (W) 600 300 RF1 power (W) 100 100 Chamber pressure (mTorr) 15 20 Helium flow (sccm) 20 10 Table E3. Anisotropic aluminum etch re cipe on the Unaxis ICP Etcher system. Parameters Settings Ar flow (sccm) 5 2Cl flow (sccm) 30 3BCl flow (sccm) 15 RF2 power (W) 500 RF1 power (W) 100 Chamber pressure (mTorr) 5 Helium flow (sccm) 20 169 PAGE 170 APPENDIX F PACKAGING DRAWINGS 25 12.70 20Measurements Units: mm SIDE VIEW TOP VIEW Insert Oring 19.05 ?? 20 Note: Sharp Corner Is Required 6.35 R 15 R 25 Screw AMaterial: LuciteUsing device chip to ensure it flushmounted Hole Through the Lucite to Take Out the PCB Package Holes Through the Lucite R3 Figure E1. The drawing illustrating the Lucite packaging. 170 PAGE 171 Figure E2. The aluminum plate for the plane wave tube interface connection. 171 PAGE 172 Figure E3. Aluminum packaging for pressure sensitivity testing. 172 PAGE 173 LIST OF REFERENCES [1] P. J. Johnston, J. Allen H. Whitehead, and G. T. Chapman, "Fitting Aerodynamics and Propulsion into the Puzzle," Aerospace America, pp. 3242, 1987. [2] W. Shyy, M. Berg, and D. 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Reddy, Theory and Analysis of Elastic Plates : Taylor and Francis, 1999, pp. 25. 179 PAGE 180 BIOGRAPHICAL SKETCH Yawei Li received her BS and MS degree in Aerospace Engineering at Beijing University of Aeronautics and Astronautics, China. She wo rked with China Aerospace Corporation before she joined University of Florida. She also received MS (2003) in Aerospace Engineering and ME (2006) in Electrical Engineering from University of Florida, respectively. She is currently a Ph.D student in the Department of Mechanical and Aerospace Engineering at the University of Florida. Her current research focuses on the sensor modeling, design optimization, fabrication, and characteriza tion of MEMSbased piezo resistive sensors that enable the measurement and control of wall shear stress in turbulent flow. 