Resonant MEMS: Fundamentals, Implementation, and Application(Advanced Micro and Nanosystems)

Part of the AMN book series, this book covers the principles, modeling and implementation as well as applications of resonant MEMS from a unified viewpoint. It starts out with the fundamental equations and phenomena that govern the behavior of resonant MEMS and then gives a detailed overview of their implementation in capacitive, piezoelectric, thermal and organic devices, complemented by chapters addressing the packaging of the devices and their stability. The last part of the book is devoted to the cutting-edge applications of resonant MEMS such as inertial, chemical and biosensors, fluid properties sensors, timing devices and energy harvesting systems.

Table of Contents:
Series editor’s preface XV Preface XVII About the Volume Editors IX List of Contributors XXI Part I: Fundamentals 1 1 Fundamental Theory of Resonant MEMS Devices 3 Stephen M. Heinrich and Isabelle Dufour 1.1 Introduction 3 1.2 Nomenclature 4 1.3 Single-Degree-of-Freedom (SDOF) Systems 5 1.3.1 Free Vibration 6 1.3.2 Harmonically Forced Vibration 8 1.3.3 Contributions to Quality Factor from Multiple Sources 13 1.4 Continuous Systems Modeling: Microcantilever Beam Example 14 1.4.1 Modeling Assumptions 15 1.4.2 Boundary Value Problem for a Vibrating Microcantilever 16 1.4.3 Free-Vibration Response of Microcantilever 17 1.4.4 Steady-State Response of a Harmonically Excited Microcantilever 19 1.5 Formulas for Undamped Natural Frequencies 22 1.5.1 Simple Deformations (Axial, Bending, Twisting) of 1D Structural Members: Cantilevers and Doubly Clamped Members (“Bridges”) 23 1.5.1.1 Axial Vibrations (Along x-Axis) 23 1.5.1.2 Torsional Vibrations (Based on h ⪡ b) (Twist About x-Axis) 24 1.5.1.3 Flexural (Bending) Vibrations 24 1.5.2 Transverse Deflection of 2D Structures: Circular and Square Plates with Free and Clamped Supports 25 1.5.3 Transverse Deflection of 1D Membrane Structures (“Strings”) 25 1.5.4 Transverse Deflection of 2D Membrane Structures: Circular and Square Membranes under Uniform Tension and Supported along Periphery 26 1.5.5 In-Plane Deformation of Slender Circular Rings 26 1.5.5.1 Extensional Modes 26 1.5.5.2 In-Plane Bending Modes 26 1.6 Summary 27 Acknowledgment 27 References 27 2 Frequency Response of Cantilever Beams Immersed in Viscous Fluids 29 Cornelis Anthony van Eysden and John Elie Sader 2.1 Introduction 29 2.2 Low Order Modes 30 2.2.1 Flexural Oscillation 30 2.2.2 Torsional Oscillation 36 2.2.3 In-Plane Flexural Oscillation 37 2.2.4 Extensional Oscillation 37 2.3 Arbitrary Mode Order 38 2.3.1 Incompressible Flows 38 2.3.2 Compressible Flows 46 2.3.2.1 Scaling Analysis 47 2.3.2.2 Numerical Results 48 References 51 3 Damping in Resonant MEMS 55 Shirin Ghaffari and Thomas William Kenny 3.1 Introduction 55 3.2 Air Damping 56 3.3 Surface Damping 59 3.4 Anchor Damping 61 3.5 Electrical Damping 63 3.6 Thermoelastic Dissipation (TED) 64 3.7 Akhiezer Effect (AKE) 66 References 69 4 Parametrically Excited Micro- and Nanosystems 73 Jeffrey F. Rhoads, Congzhong Guo, and Gary K. Fedder 4.1 Introduction 73 4.2 Sources of Parametric Excitation in MEMS and NEMS 74 4.2.1 Parametric Excitation via Electrostatic Transduction 75 4.2.2 Other Sources of Parametric Excitation 77 4.3 Modeling the Underlying Dynamics–Variants of the Mathieu Equation 77 4.4 Perturbation Analysis 79 4.5 Linear, Steady-State Behaviors 80 4.6 Sources of Nonlinearity and Nonlinear Steady-State Behaviors 81 4.7 Complex Dynamics in Parametrically Excited Micro/Nanosystems 84 4.8 Combined Parametric and Direct Excitations 85 4.9 Select Applications 85 4.9.1 Resonant Mass Sensing 85 4.9.2 Inertial Sensing 86 4.9.3 Micromirror Actuation 87 4.9.4 Bifurcation Control 88 4.10 Some Parting Thoughts 89 Acknowledgment 89 References 89 5 Finite ElementModeling of Resonators 97 Reza Abdolvand, Jonathan Gonzales, and Gavin Ho 5.1 Introduction to Finite Element Analysis 97 5.1.1 Mathematical Fundamentals 97 5.1.1.1 Static Problems 98 5.1.1.2 Dynamic Problems (Modal Analysis) 100 5.1.2 Practical Implementation 101 5.1.2.1 Set Up 102 5.1.2.2 Processing 103 5.1.2.3 Post-processing 103 5.2 Application of FEA in MEMS Resonator Design 104 5.2.1 Modal Analysis 104 5.2.1.1 Mode Shape Analysis for Design Optimization 104 5.2.1.2 Modeling Process-Induced Variation 108 5.2.2 Loss Analysis 110 5.2.2.1 Anchor Loss 110 5.2.2.2 Thermoelastic Damping 112 5.2.3 Frequency Response Analysis 113 5.2.3.1 Spurious Mode Identification and Rejection 113 5.2.3.2 Filter Design 115 5.3 Summary 116 References 116 Part II: Implementation 119 6 Capacitive Resonators 121 Gary K. Fedder 6.1 Introduction 121 6.2 Capacitive Transduction 122 6.3 Electromechanical Actuation 123 6.3.1 Electromechanical Force Derivation 123 6.3.2 Voltage Dependent Force Components 124 6.4 Capacitive Sensing and Motional Capacitor Topologies 127 6.4.1 Parallel-Moving Plates 127 6.4.2 Perpendicular Moving Plates 129 6.4.3 Electrostatic Spring Softening and Snap-In 132 6.4.4 Angular Moving Plates 134 6.5 Electrical Isolation 135 6.6 Capacitive Resonator Circuit Models 136 6.7 Capacitive Interfaces 138 6.7.1 Transimpedance Amplifier 138 6.7.2 High-Impedance Voltage Detection 142 6.7.3 Switched-Capacitor Detection 142 6.8 Conclusion 143 Acknowledgment 144 References 144 7 Piezoelectric Resonant MEMS 147 Gianluca Piazza 7.1 Introduction to Piezoelectric Resonant MEMS 147 7.2 Fundamentals of Piezoelectricity and Piezoelectric Resonators 149 7.3 Thin Film Piezoelectric Materials for Resonant MEMS 152 7.4 Equivalent Electrical Circuit of Piezoelectric Resonant MEMS 153 7.4.1 One-Port Piezoelectric Resonators 156 7.4.2 Two-Port Piezoelectric Resonators 157 7.4.3 Resonator Figure of Merit 158 7.5 Examples of Piezoelectric Resonant MEMS: Vibrations in Beams, Membranes, and Plates 158 7.5.1 Flexural Vibrations 159 7.5.2 Width-Extensional Vibrations 163 7.5.3 Thickness-Extensional and Shear Vibrations 166 7.6 Conclusions 168 References 169 8 Electrothermal Excitation of Resonant MEMS 173 Oliver Brand and Siavash Pourkamali 8.1 Basic Principles 173 8.1.1 Fundamental Equations for Electro-Thermo-Mechanical Transduction 173 8.1.2 Time Constants and Frequency Dependencies 175 8.2 Actuator Implementations 178 8.2.1 Thin-Film/Surface Actuators 179 8.2.2 Bulk Actuators 184 8.3 Piezoresistive Sensing 185 8.3.1 Fundamental Equations for Piezoresistive Sensing 185 8.3.2 Piezoresistor Implementations 187 8.3.3 Self-SustainedThermal-Piezoresistive Oscillators 189 8.4 Modeling and Optimization of Single-Port Thermal-Piezoresistive Resonators 193 8.4.1 Thermo-Electro-Mechanical Modeling 193 8.4.2 Resonator Equivalent Electrical Circuit and Optimization 195 8.5 Examples ofThermally Actuated Resonant MEMS 197 References 199 9 Nanoelectromechanical Systems (NEMS) 203 Liviu Nicu, Vaida Auzelyte, Luis Guillermo Villanueva, Nuria Barniol, Francesc Perez-Murano,Warner J. Venstra, Herre S. J. van der Zant, Gabriel Abadal, Veronica Savu, and Jürgen Brugger 9.1 Introduction 203 9.1.1 Fundamental Studies 203 9.1.2 Transduction at the Nanoscale 206 9.1.3 Materials, Fabrication, and System Integration 208 9.1.4 Electronics 211 9.1.5 Nonlinear MEMS/NEMS Applications 212 9.2 Carbon-Based NEMS 215 9.3 Toward Functional Bio-NEMS 219 9.3.1 NEMS-Based Energy Harvesting: an Emerging Field 220 9.4 Summary and Outlook 222 References 224 10 Organic Resonant MEMS Devices 233 Sylvan Schmid 10.1 Introduction 233 10.2 Device Designs 235 10.2.1 Conductive Polymer with Electrostatic Actuation 235 10.2.2 Dielectric Polymer with Polarization Force Actuation 236 10.2.3 Superparamagnetic Nanoparticle Composite with Magnetic Actuation 238 10.2.4 Metallized Polymer with Lorentz Force Actuation 239 10.3 Quality Factor of Polymeric Micromechanical Resonators 242 10.3.1 Quality Factor in Viscous Environment 242 10.3.2 Quality Factor of Relaxed Resonators in Vacuum 242 10.3.3 Quality Factor of Unrelaxed Resonators in Vacuum 243 10.4 Applications 247 10.4.1 Humidity Sensor 247 10.4.2 Vibrational Energy Harvesting 252 10.4.3 Artificial Cochlea 253 References 256 11 Devices with Embedded Channels 261 Thomas P. Burg 11.1 Introduction 261 11.2 Theory 263 11.2.1 Effects of Fluid Density and Flow 263 11.2.2 Effects of Viscosity on the Quality Factor 267 11.2.3 Effect of Surface Reactions 269 11.2.4 Single Particle Measurements 271 11.3 Device Technology 273 11.3.1 Fabrication 273 11.3.2 Packaging Considerations 275 11.4 Applications 279 11.4.1 Measurements of Fluid Density and Mass Flow 279 11.4.2 Single Particle and Single Cell Measurements 279 11.4.3 Surface-Based Measurements 280 11.5 Conclusion 282 References 283 12 Hermetic Packaging for Resonant MEMS 287 Matthew William Messana, Andrew Bradley Graham, and Thomas William Kenny 12.1 Introduction 287 12.2 Overview of Packaging Types 289 12.3 Die-Level Vacuum-Can Packaging 291 12.4 Wafer Bonding for Device Packaging 293 12.5 Thin Film Encapsulation-Based Packaging 296 12.6 Getters 298 12.7 The “Stanford epi-Seal Process” for Packaging of MEMS Resonators 299 12.8 Conclusion 302 References 302 13 Compensation, Tuning, and Trimming of MEMS Resonators 305 Roozbeh Tabrizian and Farrokh Ayazi 13.1 Introduction 306 13.2 Compensation Techniques in MEMS Resonators 306 13.2.1 Compensation for Thermal Effects 306 13.2.1.1 Engineering the Geometry 307 13.2.1.2 Doping 307 13.2.1.3 Composite Resonators 309 13.2.2 Compensation for Manufacturing Uncertainties 313 13.2.3 Compensation and Control of Quality Factor 315 13.2.4 Compensation for Polarization Voltage 317 13.3 Tuning Methods in MEMS Resonators 317 13.3.1 Device Level Tuning 317 13.3.1.1 Electrostatic Tuning 318 13.3.1.2 Thermal Tuning 318 13.3.1.3 Piezoelectric Tuning 319 13.3.2 System-Level Tuning 320 13.4 Trimming Methods 321 References 322 Part III: Application 327 14 MEMS Inertial Sensors 329 Diego Emilio Serrano and Farrokh Ayazi 14.1 Introduction 329 14.2 Accelerometers 329 14.2.1 Principles of Operation 330 14.2.2 Quasi-Static Accelerometers 331 14.2.2.1 Squeeze-Film Damping 332 14.2.2.2 Electromechanical Transduction in Accelerometers 333 14.2.2.3 Mechanical Noise in Accelerometers 334 14.2.3 Resonant Accelerometers 334 14.2.3.1 Electrostatic Spring-Softening 335 14.2.3.2 Acceleration Sensitivity in Resonant Accelerometers 336 14.3 Gyroscopes 336 14.3.1 Principles of Operation 337 14.3.1.1 Vibratory Gyroscopes 337 14.3.1.2 Mode-Split versus Mode-Matched Gyroscopes 339 14.3.2 Bulk-AcousticWave (BAW) Gyroscopes 341 14.3.2.1 Angular Gain 342 14.3.2.2 Zero-Rate Output 343 14.3.2.3 ZRO Cancelation 345 14.3.2.4 Electromechanical Transduction in Gyroscopes 345 14.3.2.5 Electrostatic Mode Matching and Mode Alignment 346 14.3.3 Mechanical Noise in Mode-Matched Gyroscopes 347 14.4 Multi-degree-of-Freedom Inertial Measurement Units 348 14.4.1 System-in-Package IMUs 348 14.4.2 Single-Die IMUs 349 14.4.3 Future Trends in Sensor Integration 351 References 352 15 Resonant MEMS Chemical Sensors 355 Luke A. Beardslee, Oliver Brand, and Fabien Josse 15.1 Introduction 355 15.2 Modeling of Resonant Microcantilever Chemical Sensors 357 15.2.1 Generalized Resonant Frequency 360 15.3 Effects of Chemical Analyte Sorption into the Coating 361 15.3.1 Resonant Frequency 361 15.3.2 Quality Factor 363 15.4 Figures of Merit 364 15.5 Chemically Sensitive Layers 368 15.6 Packaging 371 15.7 Gas-Phase Chemical Sensors 374 15.8 Liquid-Phase Chemical Sensors 377 15.8.1 Cantilevers 379 15.8.2 Microdisk Resonators 380 15.8.3 AcousticWave Sensors 381 15.8.4 Resonators with Encapsulated Channels 383 References 383 16 Biosensors 391 Blake N. Johnson and Raj Mutharasan 16.1 Introduction 391 16.2 Design Considerations: Length Scale, Geometry, and Materials 392 16.2.1 Fabrication Materials 392 16.2.2 Single-Layer Geometry 402 16.2.3 Multi-Layer Geometry 403 16.2.4 Length Scales 403 16.3 Surface Functionalization: Preparation, Passivation, and Bio-recognition 404 16.3.1 Antibody-Based Bio-recognition 405 16.3.2 Nucleic Acid-Based Bio-recognition 405 16.3.3 Alternative Bio-recognition Agents 407 16.4 Biosensing Application Formats 408 16.4.1 Dip-Dry-Measure Method 408 16.4.2 Continuous Flow Method 408 16.5 Application Case Studies 409 16.5.1 Whole Cells: Pathogens and Parasites 409 16.5.1.1 Foodborne Pathogen: Escherichia coli O157:H7 409 16.5.1.2 Foodborne Pathogen: Listeria monocytogenes 411 16.5.1.3 Waterborne Parasite: Cryptosporidium parvum 413 16.5.1.4 Waterborne Parasite: Giardia lamblia 413 16.5.2 Proteins: Biomarkers and Toxins 414 16.5.2.1 Prostate Cancer Biomarker: Prostate Specific Antigen 414 16.5.2.2 Prostate Cancer Biomarker: Alpha-methylacyl-CoA Racemase (AMACR) 414 16.5.2.3 Toxin in SourceWater: Microcystin 415 16.5.2.4 Toxin in Food Matrices: Staphylococcal enterotoxin B 415 16.5.3 Virus 416 16.5.4 Nucleic Acids: Biomarkers and Genes Associated with Toxin Production 416 16.5.4.1 RNA-Based Biomarkers: MicroRNA 416 16.5.4.2 Gene Signature of a Virus 417 16.5.4.3 Toxin-Associated Genes for Pathogen Detection without DNA Amplification 417 16.6 Conclusions and Future Trends 418 Acknowledgment 419 References 419 17 Fluid Property Sensors 427 Erwin K. Reichel, Martin Heinisch, and Bernhard Jakoby 17.1 Introduction 427 17.2 Definition of Fluid Properties 429 17.2.1 Rheological Properties 429 17.2.2 Time-Harmonic Deformation 431 17.2.3 Classical Methods for Measuring Fluid Properties 431 17.2.4 Miniaturized Rheometers 432 17.3 Resonator Sensors 433 17.3.1 Excitation and Readout 433 17.3.2 Eigenmode Decomposition 433 17.3.3 Electrical Equivalent Circuit 434 17.3.4 Damping 435 17.3.5 Fluid-Structure Interaction 436 17.4 Examples of Resonant Sensors for Fluid Properties 438 17.4.1 Microacoustic Devices 440 17.4.2 MEMS Devices 441 17.4.2.1 Cantilever Devices 441 17.4.2.2 U-Shaped Cantilevers 445 17.4.2.3 Tuning Forks 445 17.4.2.4 Doubly-Clamped Beam Devices 445 17.4.2.5 In-Plane Resonators 445 17.4.2.6 Other Principles 445 17.4.3 Comparison 446 17.5 Conclusions 446 References 446 18 Energy Harvesting Devices 451 Stephen P. Beeby 18.1 Introduction 451 18.2 Generic Harvester Structures 452 18.2.1 Inertial Energy Harvesters 453 18.2.2 Direct Force Energy Harvesters 456 18.2.3 Broadband Energy Harvesters 457 18.2.4 Frequency Conversion 460 18.3 MEMS Energy Harvester Transduction Mechanisms 461 18.3.1 Piezoelectric Transduction 462 18.3.2 Electromagnetic Transduction 464 18.3.3 Electrostatic Transduction 465 18.3.4 Other Transducer Materials 467 18.4 Review and Comparison of MEMS Energy Harvesting Devices 468 18.5 Conclusions 471 References 472 Index 475

About the Author :
Oliver Brand is Professor of Bioengineering and Microelectronics/Microsystems at Georgia Institute of Technology, Atlanta, USA. He received his diploma degree in Physics from Technical University Karlsruhe, Germany, in 1990, and his PhD from ETH Zurich, Switzerland, in 1994. Between 1995 and 2002, he held research and teaching positions at the Georgia Institute of Technology (1995-1997) and ETH Zurich (1997-2002). Oliver Brand's research interest lies in the areas of CMOS-based micro- and nanosystems, MEMS fabrication technologies, and microsystem packaging. Isabelle Dufour is Professor of Electrical Engineering at the University of Bordeaux, France. She received the PhD and habilitation degrees in Engineering Sciences from the University of Paris-Sud, Orsay, France, in 1993 and 2000, respectively. Isabelle Dufour was a CNRS research fellow from 1994 to 2007, first in Cachan working on the modeling of electrostatic actuators such as micromotors and micropumps and after 2000 in Bordeaux working on microcantilever-based chemical sensors. Her research interests are mainly in the areas of sensors for chemical detection, rheological measurements and materials characterization. Stephen M. Heinrich is Professor of Civil Engineering at Marquette University, Wisconsin, USA. He earned his MSc and PhD degrees from the University of Illinois after which he joined the faculty at Marquette University. Stephen Heinrich's research is focused on structural mechanics applications in microelectronics packaging and the development of new analytical models for predicting and enhancing the performance of cantilever-based chemical sensors. The work performed by Stephen Heinrich and his colleagues has resulted in over 100 publications and presentations and three best-paper awards from IEEE and ASME. Fabien Josse is Professor in the Department of Electrical and Computer Engineering and the Department of Biomedical Engineering at Marquette University, Wisconsin, USA. He received the MSc and PhD degrees in Electrical Engineering from the University of Maine, and belongs to the Marquette University faculty since 1982. His research interests include solid state sensors, acoustic wave sensors and MEMS devices for liquid-phase biochemical sensor applications, investigation of novel sensor platforms, and smart sensor systems.