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More About This Title Resonant MEMS - Fundamentals, Implementation, andApplication
English
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.
English
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.
English
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
