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Design of Piezoresistive MEMS Force and Displacement Sensors Brigham Young University BYU ScholarsArchive Theses and Dissertations 2006-09-01 Design of Piezoresistive MEMS Force and Displacement Sensors Tyler Lane Waterfall Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Mechanical Engineering Commons BYU ScholarsArchive Citation Waterfall, Tyler Lane, "Design of Piezoresistive MEMS Force and Displacement Sensors" (2006). Theses and Dissertations. 806. https://scholarsarchive.byu.edu/etd/806 This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. DESIGN OF PIEZORESISTIVE MEMS FORCE AND DISPLACEMENT SENSORS by Tyler Lane Waterfall A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering Brigham Young University Thesis Completed December 2006 Copyright © 2006 Tyler Lane Waterfall All Rights Reserved BRIGHAM YOUNG UNIVERSITY GRADUATE COMMITTEE APPROVAL of a thesis submitted by Tyler Lane Waterfall This thesis has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. Date Brian D. Jensen, Chair Date Larry L. Howell Date Timothy W. McLain BRIGHAM YOUNG UNIVERSITY As chair of the candidate’s graduate committee, I have read the thesis of Tyler Lane Water- fall in its final form and have found that (1) its format, citations, and bibliographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library. Date Brian D. Jensen Chair, Graduate Committee Accepted for the Department Matthew R. Jones Graduate Coordinator Accepted for the College Alan R. Parkinson Dean, Ira A. Fulton College of Engineering and Technology ABSTRACT DESIGN OF PIEZORESISTIVE MEMS FORCE AND DISPLACEMENT SENSORS Tyler Lane Waterfall Department of Mechanical Engineering Master of Science MEMS (MicroElectroMechanical Systems) sensors are used in acceleration, flow, pressure and force sensing applications on the micro and macro levels. Much research has focused on improving sensor precision, range, reliability, and ease of manufacture and operation. One exciting possibility for improving the capability of micro sensors lies in exploiting the piezoresistive properties of silicon, the material of choice in many MEMS fabrication processes. Piezoresistivity—the change of electrical resistance due to an ap- plied strain—is a valuable material property of silicon due to its potential for high sig- nal output and on-chip and feedback-control possibilities. However, successful design of piezoresistive micro sensors requires a more accurate model of the piezoresistive behavior of polycrystalline silicon. This study sought to improve the existing piezoresistive model by investigating the piezoresistive behavior of compliant polysilicon structures subjected to tensile, bending and combined loads. Experimental characterization data showed that piezoresistive sensitivity is greatest and mostly linear for silicon members subject to tensile stresses and much lower and nonlinear for beams in bending and combined stress states. The data also illustrated the failure of existing piezoresistance models to accurately account for bending and combined loads. Two MEMS force and displacement sensors, the integral piezoresistive micro-Force And Displacement Sensor (FADS) and Closed-LOop sensor (CLOO-FADS), were de- signed and fabricated. Although limited in its piezoresistive sensitivity and out-of-plane stability, the FADS design showed promise of future application in microactuator charac- terization. Similarly, the CLOO-FADS exhibited possible feedback control capability, but was limited by control circuit complexity and implementation challenges. The piezoresistive behavior exhibited by the Thermomechanical In-plane Microac- tuator (TIM) led to a focused effort to characterize the TIM’s behavior in terms of force, displacement, actuation current and mechanism resistance. The gathered data facilitated the creation of an empirical, temperature-dependent model for the specific TIM. Based on the assumption of a nearly constant temperature for each current level, the model predicted the force and displacement for a given fractional change in resistance. Despite the success of the empirical model for the test TIM device, further investigation revealed the necessity of a calibration method to enable the model’s application to other TIM devices. ACKNOWLEDGMENTS Many people and organizations have been influential and supportive during my work on this thesis. I am grateful for the grant by the National Science Foundation which funded this research. I greatly appreciate the encouragement, enthusiasm and kindness of my advisor, Brian Jensen. From the beginning he has been a good friend to ‘study’ with. Dr. Howell and Dr. McLain of my committee also provided consistent support and advice relating to the design, testing and analysis of the mechanisms presented herein. I also feel fortunate to have been a part of the MEMS component of the Compliant Mechanisms Re- search group. For example, many test structures presented in Chapter 3 were designed by Gary Johns, and all of data for SUMMiT-fabricated devices was acquired by Robert Mes- senger. My daily interaction with intelligent and humorous peers in the basement of the Clyde Building contributed to my enjoyable graduate experience at BYU. I am indebted to my good family, for their generosity, encouragement, and belief in me. I am happy to say that I have done my best to merit some of Grandma Lane’s pride in her “little engineer”. Most importantly, I appreciate my kind, consistent and interested wife, Amy, who always believed in me, prayed for me, and listened to my whiteboard explanations of MEMS and piezoresistivity. Table of Contents Acknowledgements xiii List of Tables xix List of Figures xxi 1 Introduction 1 1.1 Importance of the Research . 1 1.2 Contributions of the Thesis . 2 1.3 Outline of the Thesis . 2 2 The Piezoresistive Effect of Silicon 5 2.1 Physical Phenomenon of Piezoresistance . 5 2.1.1 Crystalline Structure . 6 2.1.2 Energy Band Structure . 6 2.1.3 Carrier Transport . 7 2.1.4 Carrier Trapping at Grain Boundaries . 9 2.2 Modeling the Piezoresistance Effect . 10 2.3 Silicon as a Piezoresistive Material . 11 2.4 Gauge Factor . 13 2.5 Piezoresistance Coefficients . 14 2.5.1 Uniaxial Stress . 17 2.5.2 Plane Stress . 18 2.6 Gauge Factor Measurement Method . 18 2.7 Factors Influencing the Gauge Factor . 21 2.7.1 Fabrication Method . 21 2.7.2 Crystalline Structure . 21 2.7.3 Dopant Concentration Level . 24 2.7.4 p-type vs. n-type Silicon . 25 2.7.5 Annealing . 25 2.7.6 Operating Temperature . 28 2.7.7 Orientation of Applied Stress . 30 2.7.8 Additional Factors . 31 2.7.9 Summary of Piezoresistivity . 31 2.8 Example of Piezoresistance Analysis: Uniaxial Tension . 31 2.9 Conclusion . 35 xv 3 Investigation of Piezoresistive Property of Polysilicon in Bending 37 3.1 Introduction . 37 3.2 Background . 38 3.3 Test Devices and Experimental Setup . 39 3.4 Experimental Results . 43 3.4.1 Tensile Loads . 43 3.4.2 Bending Loads . 44 3.4.3 Combined Loads . 45 3.4.4 Summary of Results . 47 3.5 Conclusion . 50 4 MEMS Force and Displacement Sensors 51 4.1 Future Trends: Sensor Integration . 52 4.2 Design of an Integral Piezoresistive Force and Displacement Sensor . 54 4.2.1 Design Constraints . 55 4.2.2 Fabrication Process Limitations: MUMPs and SUMMiT . 55 4.2.3 Force and Displacement Measurement . 57 4.2.4 Mechanical, Electrical and Thermal Interactions . 58 4.2.5 Feedback Control . 58 4.3 Piezoresistive Force and Displacement Sensor, FADS . 58 4.3.1 Preliminary Force Sensitivity of FADS . 61 4.3.2 Out-of-Plane Stability Analysis of FADS . 63 4.4 Closed-loop Force and Displacement Sensor, CLOO-FADS . 64 4.5 An Alternative Approach . 66 4.6 Conclusion . 66 5 Characterization of the Piezoresistive Properties of the Thermomechanical In- plane Microactuator 69 5.1 Introduction . 69 5.2 Background . 70 5.3 Experiment . 72 5.3.1 Setup . 72 5.3.2 Method . 74 5.4 Results . 76 5.4.1 Repeatability and Drift . 77 5.4.2 Sensitivity . 78 5.4.3 Empirical Model . 79 5.5 Application . 83 5.6 Need for Calibration . 85 5.7 Conclusions . 87 6 Conclusions and Recommendations 89 6.1 Conclusions . 89 6.2 Recommendations . 90 6.2.1 Piezoresistance of Monocrystalline Silicon . 90 xvi 6.2.2 Optimization of Piezoresistive Sensors . 91 6.2.3 Calibration Method for TIM . 91 6.2.4 Multi-Physics Model of TIM . 92 A TIM Characterization Data 93 Bibliography 106 xvii xviii List of Tables 2.1 Piezoresistive coefficients of silicon. 19 2.2 Comparison of longitudinal gauge factor for three types of silicon. 22 2.3 Properties of beam in uniaxial tension. 33 2.4 Results of analysis for uniaxial tension example. 34 3.1 Piezoresistance test structures. 40 3.2 Nominal dimensions of piezoresistive tensile and bending structures. 40 3.3 Dimensions of piezoresistance combined-load structures. 40 3.4 Published and measured piezoresistance gauge factors. 48 4.1 Comparison of MUMPs and SUMMiT Fabrication Processes. 56 4.2 Dimensions of FADS hat. 60 4.3 Preliminary force resolution per unit resistance for FADS sensor. 63 5.1 Dimensions of TIM. 72 5.2 Summary of user repeatability. 78 xix xx List of Figures 2.1 Diamond cubic crystal structure of silicon [1]. 6 2.2 Electron energy band structure for semiconductors. 8 2.3 Hole transport of boron-doped (p-type) silicon due to external electric field. 8 2.4 Effect of tensile stress on constant energy surfaces in multiple crystal di- rections.
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