Package Consideration in Capacitive Sensor Design

MECHANICALLY AMPLIFIED CAPACITIVE STRAIN SENSOR by JUN GUO Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Adviser: Dr. Wen H. Ko Department of Electrical Engineering and Computer Science CASE WESTERN RESERVE UNIVERSITY May, 2007 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of Jun Guo ______________________________________________________ candidate for the Ph.D. degree *. Wen H. Ko (signed)_______________________________________________ (chair of the committee) Alexis R. Abramson ________________________________________________ Thomas P. Kicher ________________________________________________ Steven Garverick ________________________________________________ Darrin J. Young ________________________________________________ Christian A. Zorman ________________________________________________ 03/23/2007 (date) _______________________ *We also certify that written approval has been obtained for any proprietary material contained therein. Dedication To my parents. TABLE OF CONTENTS Mechanical Amplified Capacitive Strain Sensor Table of Contents ......................................................................................................................... <a href="#4_0">1 </a>List of Tables ................................................................................................................................ <a href="#10_0">7 </a>List of Figures .............................................................................................................................. <a href="#12_0">9 </a>Acknowledgements .................................................................................................................. <a href="#18_0">15 </a><ul style="display: flex;"><li style="flex:1">Abstract </li><li style="flex:1">................................................................................................................................. <a href="#19_0">16 </a></li></ul><ul style="display: flex;"><li style="flex:1">Chapter 1 </li><li style="flex:1">Introduction to Strain Measurement ................................................. <a href="#0_0">18 </a></li></ul>1.1. 1.2. Introduction and motivation............................................................................................ <a href="#0_0">18 </a>Thesis organization ......................................................................................................... <a href="#0_0">23 </a><ul style="display: flex;"><li style="flex:1">Chapter 2 </li><li style="flex:1">A Review of Micromachined Strain Gages ........................................ <a href="#0_0">25 </a></li></ul>2.1. 2.2. Introduction..................................................................................................................... <a href="#0_0">25 </a>Metallic-foil strain gage.................................................................................................. <a href="#0_0">25 </a>2.2.1 Principle........................................................................................................ <a href="#0_0">26 </a>2.2.2 Gage factor and sensitivity............................................................................ <a href="#0_0">28 </a>2.2.3 Instrumentation ............................................................................................. <a href="#0_0">29 </a>2.2.4 Resolution of a typical metallic-foil strain gage........................................... <a href="#0_0">30 </a>Piezoresistive strain gage................................................................................................ <a href="#0_0">32 </a>2.3.1 Piezoresistive effect ...................................................................................... <a href="#0_0">32 </a>2.3. 1 2.3.2 Longitudinal and transverse piezoresistive coefficients ............................... <a href="#0_0">33 </a>2.3.3 Impurity concentration (doping level) and temperature effect on piezoresistance coefficients....................................................................................... <a href="#0_0">35 </a>2.3.4 Resolution and issues.................................................................................... <a href="#0_0">36 </a>Resonant silicon micromachined strain gage.................................................................. <a href="#0_0">37 </a>2.4.1 Principle........................................................................................................ <a href="#0_0">38 </a>2.4.2 Excitation and detection scheme................................................................... <a href="#0_0">39 </a>2.4.3 Resolution: minimum detectable frequency ................................................. <a href="#0_0">40 </a>Capacitive strain gage..................................................................................................... <a href="#0_0">42 </a>2.5.1 Principle and configurations ......................................................................... <a href="#0_0">42 </a>2.5.2 Performance of capacitive strain gage.......................................................... <a href="#0_0">44 </a>Summary......................................................................................................................... <a href="#0_0">46 </a> 2.4. 2.5. 2.6. <ul style="display: flex;"><li style="flex:1">Chapter 3 </li><li style="flex:1">Capacitive Strain Sensor Employing a Buckled Beam Mechanical </li></ul>Amplifier ........................................................................................................................ <a href="#0_0">48 </a>3.1. 3.2. Introduction..................................................................................................................... <a href="#0_0">48 </a>Mechanical amplifier ...................................................................................................... <a href="#0_0">49 </a>3.2.1 Background................................................................................................... <a href="#0_0">50 </a>3.2.2 Principle........................................................................................................ <a href="#0_0">51 </a>Analytical modeling........................................................................................................ <a href="#0_0">52 </a>3.3.1 Derivation of the curvature function under an applied force........................ <a href="#0_0">53 </a>3.3. 2 3.3.2 Calculate the mechanical gain ...................................................................... <a href="#0_0">56 </a>3.3.3 Small input force simplification and the structure nominal mechanical gain <a href="#0_0">59 </a>3.3.4 Large deflection compensation..................................................................... <a href="#0_0">60 </a>3.3.5 Calculate the buckling beam equivalent stiffness in x-direction .................. <a href="#0_0">60 </a>Finite-Element-Analysis verification.............................................................................. <a href="#0_0">61 </a>3.4.1 FEA verification of nominal mechanical...................................................... <a href="#0_0">61 </a>3.4.2 FEA verification of equivalent stiffness ....................................................... <a href="#0_0">62 </a>3.4. 3.4.3 FEA verification of mechanical gain corresponding to large displacement input <a href="#0_0">63 </a>3.5. 3.6. Nonlinearity of the buckled beam amplifier ................................................................... <a href="#0_0">65 </a>Fundamental noise analysis ............................................................................................ <a href="#0_0">67 </a>3.6.1 Resistive thermal noise estimation................................................................ <a href="#0_0">68 </a>3.6.2 Mechanical thermal noise (Brownian motion noise) estimation .................. <a href="#0_0">70 </a>The maximum stress of the structure and locations........................................................ <a href="#0_0">73 </a>Device fabrication........................................................................................................... <a href="#0_0">75 </a>Fabricated device ............................................................................................................ <a href="#0_0">77 </a> 3.7. 3.8. 3.9. 3.10. Testing............................................................................................................................. <a href="#0_0">80 </a>3.10.1 Test fixture .................................................................................................... <a href="#0_0">80 </a>3.10.2 Device functionality test under microscope.................................................. <a href="#0_0">83 </a>3.10.3 Capacitive readout circuitry.......................................................................... <a href="#0_0">84 </a>3 3.10.3.1 C/V characteristics using MS3110®.................................................. <a href="#0_0">84 </a>3.10.3.2 C/V characteristics using developed interface electronics................ <a href="#0_0">88 </a>3.11. Conclusions..................................................................................................................... <a href="#0_0">93 </a><ul style="display: flex;"><li style="flex:1">Chapter 4 </li><li style="flex:1">Sensor Backing Design ........................................................................ <a href="#0_0">95 </a></li></ul><ul style="display: flex;"><li style="flex:1">4.1. </li><li style="flex:1">Strain transmission ratio of a solid backing......................................................................<a href="#0_0">95 </a></li></ul>4.1.1 Transmission ratio definition .......................................................................... <a href="#0_0">95 </a>4.1.2 Strain transmission ratio of a solid backing.................................................... <a href="#0_0">96 </a>Transmission ratio of a folded-spring backing................................................................<a href="#0_0">102 </a>4.2.1 Folded-spring backing structure analysis...................................................... <a href="#0_0">103 </a>4.2.2 Anchor location and package gain................................................................ <a href="#0_0">106 </a>4.2.3 Package gain discussions.............................................................................. <a href="#0_0">109 </a>4.2. 4.2.3.1 4.2.3.2 The maximum package gain for piezoresistive sensor design.......... <a href="#0_0">109 </a>The maximum displacement for capacitive sensor design ................<a href="#0_0">111 </a>4.3. 4.4. Overall sensor module backing design ........................................................................... <a href="#0_0">116 </a>Summary and conclusions .............................................................................................. <a href="#0_0">119 </a><ul style="display: flex;"><li style="flex:1">Chapter 5 </li><li style="flex:1">Sensing Structure Design .................................................................... <a href="#0_0">120 </a></li></ul>5.1. 5.2. 5.3. 5.4. Structure modification ....................................................................................................<a href="#0_0">120 </a>Capacitive output sensitivity calculation ........................................................................<a href="#0_0">122 </a>Fringe capacitance effect on comb drive finger design ..................................................<a href="#0_0">124 </a>Nominal capacitance and parasitic capacitance..............................................................<a href="#0_0">126 </a>45.5. 5.6. Series resistance consideration .......................................................................................<a href="#0_0">127 </a>Structure mechanical property ........................................................................................<a href="#0_0">128 </a>5.6.1 Nonlinearity of the buckled beam amplifier................................................. <a href="#0_0">128 </a>5.6.2 Resonance modes and frequencies................................................................ <a href="#0_0">128 </a>5.6.3 Mechanical thermal noise analysis ............................................................... <a href="#0_0">130 </a>Fabrication process .........................................................................................................<a href="#0_0">131 </a>Fabricated device ............................................................................................................<a href="#0_0">135 </a>Summary and conclusions ..............................................................................................<a href="#0_0">136 </a> 5.7. 5.8. 5.9. <ul style="display: flex;"><li style="flex:1">Chapter 6 </li><li style="flex:1">Testing Fixtures and Device Testing ................................................. <a href="#0_0">137 </a></li></ul><ul style="display: flex;"><li style="flex:1">6.1. </li><li style="flex:1">Test fixtures for capacitance output characteristics ........................................................<a href="#0_0">137 </a></li></ul>6.1.1 Four-point strain testing fixture .................................................................... <a href="#0_0">137 </a>6.1.2 Bent cantilever beam testing fixture ............................................................. <a href="#0_0">141 </a>6.1.3 Capacitive strain sensor applying procedure ................................................ <a href="#0_0">144 </a>Package gain & mechanical gain measurement under microscope ................................<a href="#0_0">148 </a>Capacitive output characteristics ....................................................................................<a href="#0_0">151 </a>6.3.1 Interfaced to an off-the-shelf C/V converter................................................. <a href="#0_0">151 </a>6.2. 6.3. 6.3.2 Interfaced to a developed low noise C/V converter...................................... <a href="#0_0">153 </a>Temperature behavior .....................................................................................................<a href="#0_0">155 </a>Step response ..................................................................................................................<a href="#0_0">159 </a>Frequency response testing.............................................................................................<a href="#0_0">160 </a> 6.4. 6.5. 6.6. 5 6.6.1 Test fixture .................................................................................................... <a href="#0_0">161 </a>6.6.2 Resonant cantilever beam resonant frequency calculation........................... <a href="#0_0">161 </a>6.6.3 Actuation displacement versus generated strain........................................... <a href="#0_0">163 </a>6.6.4 Test fixture behavior ..................................................................................... <a href="#0_0">163 </a>6.6.5 Sensor Dynamic behavior............................................................................. <a href="#0_0">165 </a><ul style="display: flex;"><li style="flex:1">Conclusions.....................................................................................................................<a href="#0_0">166 </a></li><li style="flex:1">6.7. </li></ul>Bibliography.................................................................................................................. <a href="#0_0">168 </a>6 LIST OF TABLES Table 1.1. Major requirements for the MEMS strain gage module used for a <ul style="display: flex;"><li style="flex:1">rolling-element bearing. </li><li style="flex:1">22 </li></ul><ul style="display: flex;"><li style="flex:1">29 </li><li style="flex:1">Table 2.1. Properties of strain gage conductors. </li></ul><a href="#0_0">Table 2.2.</a><a href="#0_0"> </a><a href="#0_0">Longitudinal and transverse pi</a>ezoresistance coefficients for various <ul style="display: flex;"><li style="flex:1">combination of direction in cubic crystals. </li><li style="flex:1"><a href="#0_0">35 </a></li></ul>35 47 59 Table 2.3. Adiabatic piezoresistance coefficients at room temperature. Table 2.4. Summary of four types of micromachined strain gages. Table 3.1. Properties of hyperbolic cosine and sine function. <a href="#0_0">Table 3.2.</a><a href="#0_0"> </a><a href="#0_0">Com</a>parison of nominal mechanical gains obtained analytically and from FEA. <a href="#0_0">62 </a>Table 3.3. Comparison of structure stiffness obtained analytically and from FEA. Table 3.4. Design values of the buckled beam strain sensor. Table 3.5. Parameters of the test fixture. 63 79 81 <a href="#0_0">Table 4.1.</a><a href="#0_0"> </a><a href="#0_0">Calculated transmission ratio with various bonding adhesive thickness.</a><a href="#0_0"> </a><a href="#0_0">The </a><a href="#0_0">structure is with thickness of 480 µm and ge</a>ometrical dimensions is illustrated in <ul style="display: flex;"><li style="flex:1">Figure 4.6. </li><li style="flex:1"><a href="#0_0">105 </a></li></ul>123 <a href="#0_0">129 </a>141 Table 5.1. Device parameters. <a href="#0_0">Table 5.2. Resonant frequency and shape of each part of the sensing structure. </a>Table 6.1. Parameters of the developed four-point test fixture. 7 <a href="#0_0">Table 6.2. Param</a>eters of the developed bent cantilever beam test fixture. Table 6.3. Beam parameters. <a href="#0_0">143 </a>162 <ul style="display: flex;"><li style="flex:1"><a href="#0_0">162 </a></li><li style="flex:1"><a href="#0_0">Table 6.4. Calculated fundamental resonant frequencies of various beam </a>lengths. </li></ul>8LIST OF FIGURES <ul style="display: flex;"><li style="flex:1">Figure 1.1. Strain definition. </li><li style="flex:1"><a href="#0_0">18 </a></li></ul><a href="#0_0">19 </a><a href="#0_0">25 </a><a href="#0_0">26 </a><a href="#0_0">30 </a> Figure 1.2. Strain-stress relationship for common materials. Figure 2.1. Metallic-foil strain gage. Figure 2.2. The resistance change of a cylindrical conductive wire under strain. Figure 2.3. Wheatstone bridge configuration. Figure 2.4. Piezoresistor under a) longitudinal and b) transverse stress. The small red <ul style="display: flex;"><li style="flex:1">arrow on the resistor points in the direction of the exciting current. </li><li style="flex:1"><a href="#0_0">33 </a></li></ul>Figure 2.5. Variation of the coefficient π11 in n-type layers with temperature and surface <ul style="display: flex;"><li style="flex:1">concentration. </li><li style="flex:1"><a href="#0_0">36 </a></li></ul><a href="#0_0">38 </a><a href="#0_0">39 </a><a href="#0_0">40 </a><a href="#0_0">42 </a><a href="#0_0">44 </a><a href="#0_0">45 </a><a href="#0_0">50 </a><a href="#0_0">52 </a><a href="#0_0">52 </a> Figure 2.6. A resonant beam subjected to a strain load, ε. Figure 2.7. Resonator excitation and detection diagram. Figure 2.8. Electrostatic excitation and capacitive detection. Figure 2.9. The diagram of a capacitive strain sensor. Figure 2.10. Capacitive strain sensor configuration. Figure 2.11. High sensitivity of a capacitive strain sensor. Figure 3.1. The diagram of a capacitive strain sensor. Figure 3.2. Principle of the buckled beam amplification scheme. Figure 3.3. A buckled beam strain sensor with differential output. 9<ul style="display: flex;"><li style="flex:1">Figure 3.4. (a) Simplified structure. (b) Forces acting on the beam. </li><li style="flex:1"><a href="#0_0">54 </a></li></ul><a href="#0_0">57 </a> Figure 3.5. Beam modeling for calculating Δx. Figure 3.6. Comparison of mechanical gain obtained analytically and by FEA with l=300 μm , w=1 μm , and h=30 μm with the maximum applied strain of ± 2000 με . <a href="#0_0">65 </a> Figure 3.7. Finite Element Analysis result of relationship between nonlinearity, mechanical <ul style="display: flex;"><li style="flex:1">gain, and the maximum strain. </li><li style="flex:1"><a href="#0_0">67 </a></li></ul><a href="#0_0">68 </a><a href="#0_0">69 </a><a href="#0_0">72 </a> Figure 3.8. Device electrical model. Figure 3.9. The diagram of the front amplifier architecture of the interface electronics. Figure 3.10. Device resonant behavior simulation. Figure 3.11. FEA analysis of the structure under the maximum strain indicates that the <ul style="display: flex;"><li style="flex:1">location of maximum stress is near the anchor. </li><li style="flex:1"><a href="#0_0">74 </a></li></ul><a href="#0_0">75 </a><a href="#0_0">78 </a> Figure 3.12. Major fabrication steps. Figure 3.13. An SEM picture of a buckled beam capacitive strain sensor. Figure 3.14. Description of the test strip and bent-beam test fixture. (a) Top view of the 4-inch device wafer and a test strip. (b) Cross-section view a test strip mounted on <ul style="display: flex;"><li style="flex:1">a bent-beam test fixture. </li><li style="flex:1"><a href="#0_0">81 </a></li></ul><ul style="display: flex;"><li style="flex:1"><a href="#0_0">82 </a></li><li style="flex:1">Figure 3.15. A picture of the bent-beam test fixture. </li></ul>Figure 3.16. Microphotographs of sensor comb drive fingers before and after an applied <ul style="display: flex;"><li style="flex:1">tensile strain. </li><li style="flex:1"><a href="#0_0">83 </a></li></ul>10 Figure 3.17. A computer illustration of the bent-beam test fixture. Figure 3.18. Coupled-field finite-element analysis of the structure under applied strain. Figure 3.19. Measured capacitance change as a function of applied strain. Figure 3.20. Strain sensor electronic interface architecture. Figure 3.21. Sensing electronics die photo [40]. <a href="#0_0">85 </a><a href="#0_0">86 </a><a href="#0_0">87 </a><a href="#0_0">89 </a><a href="#0_0">90 </a><a href="#0_0">92 </a><a href="#0_0">92 </a><a href="#0_0">93 </a><a href="#0_0">96 </a><a href="#0_0">98 </a><a href="#0_0">100 </a> Figure 3.22. System testing board. Figure 3.23. Output voltage vs. input strain. Figure 3.24. Output noise spectral density. Figure 4.1. Strain transfer mechanism. Figure 4.2. Sensor substrate geometric dimensions. Figure 4.3. FEA results on bonding adhesive thickness effect on transmission ratio. Figure 4.4. Measured capacitance change as function of the applied strain using the <ul style="display: flex;"><li style="flex:1">four-point test fixture </li><li style="flex:1"><a href="#0_0">101 </a></li></ul><ul style="display: flex;"><li style="flex:1"><a href="#0_0">102 </a></li><li style="flex:1">Figure 4.5.The structure of a folded-spring backing for the capacitive strain sensor. </li></ul>Figure 4.6. Top view of a folded-spring backing and the geometrical dimensions used. The structure has a thickness of 480 μm . <a href="#0_0">103 </a>

Package Consideration in Capacitive Sensor Design

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