The MEMS Handbook Introduction & Fundamentals

Table of Contents......Page 10
1: Introduction......Page 13
References......Page 16
2.1 Introduction......Page 18
2.2 The Log Plot......Page 19
2.3 Scaling of Mechanical Systems......Page 20
References......Page 24
3.1 Introduction......Page 25
3.2 Mechanical Property Definitions......Page 26
3.3 Test Methods......Page 27
3.3.1 Specimen and Test Structure Preparation......Page 28
3.3.2 Dimension Measurement......Page 29
3.3.5 Tensile Tests......Page 30
3.3.5.2 Specimen Fixed at One End......Page 31
3.3.5.4 Smaller Specimens......Page 32
3.3.6.1 Out-of-Plane Bending......Page 33
3.3.6.3 In-Plane Bending......Page 34
3.3.6.4 Bending of Larger Specimens......Page 35
3.3.7 Resonant Structure Tests......Page 36
3.3.10 Other Test Methods......Page 38
3.3.13 Creep Tests......Page 39
3.4 Mechanical Properties......Page 40
3.5 Initial Design Values......Page 46
Acknowledgments......Page 47
References......Page 48
4.1 Introduction......Page 57
4.2 Flow Physics......Page 58
4.3 Fluid Modeling......Page 59
4.4 Navier–Stokes Equations......Page 62
4.5 Compressibility......Page 64
4.6 Boundary Conditions......Page 67
4.7 Molecular-Based Models......Page 73
4.8 Liquid Flows......Page 79
4.9 Surface Phenomena......Page 84
4.10 Parting Remarks......Page 88
References......Page 89
5.1.1 Full-System Simulation......Page 93
5.1.2 Computational Complexity of MEMS Flows......Page 95
5.1.3 Coupled-Domain Problems......Page 96
5.1.4 A Prototype Problem......Page 97
5.2 Coupled Circuit-Device Simulation......Page 98
5.3.2 The Fluid Simulator: NepsilonkappaκTalphar......Page 100
5.3.2.1 Formulation for Flow–Structure Interactions......Page 102
5.3.2.2 Grid Velocity Algorithm......Page 104
5.3.3 The Structural Simulator......Page 105
5.4 Circuit-Micro-Fluidic Device Simulation......Page 106
5.4.1 Software Integration......Page 107
5.4.3 Effective Time-Stepping Algorithms......Page 108
5.5.1 Microfluidic System Description......Page 111
5.6 Summary and Discussion......Page 113
References......Page 114
6.1 Introduction......Page 117
6.2 Gas Flows......Page 118
6.2.1 Molecular Magnitudes......Page 120
6.2.2 An Overview of the Direct Simulation Monte Carlo Method......Page 122
6.2.3 Limitations, Error Sources, and Disadvantages of the DSMC Approach......Page 123
6.2.4.1 Microchannel Flows......Page 126
6.2.4.2 Separated Rarefied Gas Flows......Page 131
6.2.5.3 Parallel DSMC Algorithms......Page 132
6.2.6 DSMC Coupling with Continuum Equations......Page 133
6.2.7 Boltzmann Equation Research......Page 134
6.2.9 Lattice Boltzmann Methods......Page 135
6.3.1 Electric Double Layer and Electrokinetic Effects......Page 136
6.3.2 The Electro-Osmotic Flow......Page 137
6.3.4 Treatment of Surfaces......Page 138
References......Page 139
7.1.1 Overview......Page 144
7.1.2 Background......Page 145
7.2.1 Preliminaries......Page 146
7.2.1.1 Slip-Flow Boundary Conditions......Page 147
7.2.2.1 Second-Order Velocity Slip......Page 148
7.2.2.2 A Second-Order Slip Model for the Hard-Sphere Gas......Page 150
7.2.2.3 Oscillatory Shear Flows......Page 153
7.2.2.4 Wave Propagation in Small-Scale Channels......Page 154
7.2.2.5 Reynolds Equation for Thin Films......Page 155
7.2.3.1 The Graetz Problem for Arbitrary Knudsen Numbers......Page 157
7.2.3.2 Viscous Heat Dissipation and the Effect of Slip Flow......Page 158
7.2.3.3 Thermophoretic Force on Small Particles......Page 159
7.3 Simulation Methods Development......Page 161
7.3.1 The Effect of Finite Discretization......Page 162
7.3.2 DSMC Convergence to the Chapman–Enskog Solution in the Kn less than or equal to 1 Limit......Page 163
7.3.3 Forces on Small Spherical Particles......Page 164
7.3.4 Hybrid Continuum–Atomistic Methods......Page 165
7.3.5 Statistical Noise in Low-Speed Flows......Page 166
References......Page 167
8.1 Introduction......Page 171
8.2 History of Burnett Equations......Page 175
8.3 Governing Equations......Page 176
8.4 Wall-Boundary Conditions......Page 181
8.5 Linearized Stability Analysis of Burnett Equations......Page 182
8.6 Numerical Method......Page 183
8.7.1 Application to Hypersonic Shock Structure......Page 184
8.7.2 Application to Two-Dimensional Hypersonic Blunt Body Flow......Page 186
8.7.3 Application to Axisymmetric Hypersonic Blunt Body Flow......Page 187
8.7.4 Application to NACA 0012 Airfoil......Page 192
8.7.5 Subsonic Flow in a Microchannel......Page 193
8.7.6 Supersonic Flow in a Microchannel......Page 198
8.8 Conclusions......Page 202
References......Page 203
9.1 Introduction......Page 206
9.2 3-D Compressible Viscous MHD Equations......Page 207
9.3 LBGK Equation and Equilibrium Particle Distribution Function fi0 for MHD Flow Equations......Page 208
9.5 Solution of Coupled LBGK Equations for Particle Distribution Functions......Page 209
9.6.1 Analytical and Numerical Solutions......Page 210
9.6.2 LBGK Solution Procedure......Page 213
Acknowledgments......Page 214
References......Page 215
10.1 Introduction......Page 216
10.1.1 Unique Aspects of Liquids in Microchannels......Page 217
10.1.2 Continuum Hydrodynamics of Pressure-Driven Flow in Channels......Page 220
10.1.3 Hydraulic Diameter......Page 221
10.1.4 Flow in Round Capillaries......Page 222
10.1.6 Transition to Turbulent Flow......Page 223
10.1.7 Noncircular Channels......Page 224
10.1.8 Experimental Studies of Flow-Through Microchannels......Page 225
10.1.9 Proposed Explanations for Measured Behavior......Page 228
10.1.10 Measurements of Velocity in Microchannels......Page 229
10.1.12 Capacitive Effects......Page 231
10.2 Electrokinetics Background......Page 233
10.2.1 Electrical Double Layers......Page 234
10.2.2 EOF with Finite EDL......Page 236
10.2.3 Thin EDL Electroosmotic Flow......Page 238
10.2.4 Electrophoresis......Page 239
10.2.5 Similarity between Electric and Velocity Fields for Electroosmosis and Electrophoresis......Page 240
10.2.6 Electrokinetic Microchips......Page 243
10.2.7 Engineering Considerations: Flow Rate and Pressure of Simple Electroosmotic Flows......Page 245
10.2.8 Electroosmotic Pumps......Page 246
10.2.10.1 Field Amplified Sample Stacking (FASS)......Page 247
10.2.10.5 Electrothermal Flows......Page 248
10.2.10.6 Electrokinetic Flow Instabilities......Page 249
10.2.11 Practical Considerations......Page 259
10.3 Summary and Conclusions......Page 260
References......Page 261
11.1 Introduction......Page 269
11.2.1 The Cube-Square Law......Page 270
11.2.2 Applicability of the Continuum Hypothesis......Page 271
11.3 Governing Equations for Lubrication......Page 272
11.4 Couette-Flow Damping......Page 273
11.4.1 Limit of Molecular Flow......Page 274
11.5.1 Derivation of Governing Equations......Page 275
11.6 Lubrication in Rotating Devices......Page 277
11.7.2 Minimum Etchable Clearance......Page 279
11.8 Thrust Bearings......Page 280
11.9.1.1 Static Journal Bearing Behavior......Page 282
11.9.1.2 Journal Bearing Stability......Page 284
11.9.3 Side Pressurization......Page 286
11.9.4 Hydrostatic Operation......Page 287
11.10.1 Cross-Wafer Uniformity......Page 290
11.10.3 Material Properties......Page 291
11.11 Tribology and Wear......Page 292
11.11.2 The Tribology of Silicon......Page 293
References......Page 294
12.1 Introduction......Page 297
12.2 The Evolution Equation for a Liquid Film on a Solid Surface......Page 306
12.3.1 Constant Surface Tension and Gravity......Page 311
12.3.2 van der Waals Forces and Constant Surface Tension......Page 313
12.3.2.1 Homogeneous Substrates......Page 315
12.3.2.2 Heterogeneous Substrates......Page 320
12.3.2.3 Flow on a Rotating Disc......Page 322
12.4.1 Thermocapillarity, Surface Tension, and Gravity......Page 324
12.4.2 Liquid Film on a Thick Substrate......Page 329
12.5.1 Interfacial Conditions......Page 331
12.5.2 Evaporation/Condensation Only......Page 333
12.5.3 Evaporation/Condensation, Vapor Recoil, Capillarity, and Thermocapillarity......Page 334
12.5.4 Flow on a Rotating Disc......Page 336
12.6 Closing Remarks......Page 338
References......Page 339
13.1 Introduction......Page 346
13.2 Fundamentals......Page 347
13.3 The Bretherton Problem for Pressure-Driven Bubble/Drop Transport......Page 349
13.3.1 Corrections to the Bretherton Results for Pressure-Driven Flow......Page 350
13.4 Bubble Transport by Electrokinetic Flow......Page 353
13.5 Future Directions......Page 356
References......Page 357
14.1 Introduction......Page 359
14.2.1 Mathematical Preliminaries......Page 360
14.2.2 Control System Analysis and Design......Page 363
14.2.2.1 Proportional–Integral–Derivative (PID) Control......Page 365
14.2.2.2 The Root Locus Design Method......Page 366
14.2.2.3 Frequency Response Design Methods......Page 369
14.2.2.4 Lead–Lag Compensation......Page 373
14.3 “Modern” Control......Page 375
14.3.1 Pole Placement......Page 376
14.3.2 The Linear Quadratic Regulator (LQR)......Page 378
14.3.3 Basic Robust Control......Page 380
14.4 Nonlinear Control......Page 382
14.4.1 SISO Feedback Linearization......Page 383
14.4.2 MIMO Full-State Feedback Linearization......Page 386
14.4.3 Control Applications of Lyapunov Stability Theory......Page 387
References......Page 388
15: Model-Based Flow Control for Distributed Architectures......Page 391
15.1 Introduction......Page 392
15.2 Linearization: Life in a Small Neighborhood......Page 393
15.3 Linear Stabilization: Leveraging Modern Linear Control Theory......Page 396
15.3.1 The Hinfinity Approach to Control Design......Page 397
15.3.2 Advantages of Modern Control Design for Non-Normal Systems......Page 400
15.3.3 Effectiveness of Control Feedback at Particular Wavenumber Pairs......Page 403
15.4.1 Centralized Approach......Page 404
15.4.2 Decentralized Approach......Page 405
15.5 Localization: Relaxing Nonphysical Assumptions......Page 406
15.6 Compensator Reduction: Eliminating Unnecessary Complexity......Page 408
15.6.2 Physical-Space Compensator Reduction......Page 409
15.7 Extrapolation: Linear Control of Nonlinear Systems......Page 410
15.8 Generalization: Extending to Spatially Developing Flows......Page 413
15.9 Nonlinear Optimization: Local Solutions for Full Navier–Stokes......Page 415
15.9.1.1 Governing Equation......Page 416
15.9.1.2 Cost Functional......Page 417
15.9.1.3 Gradient of Cost Functional......Page 418
15.9.1.5 Statement of Adjoint Identity......Page 419
15.9.1.6 Definition of Adjoint Field......Page 420
15.9.1.8 Gradient Update to Control......Page 421
15.9.2 Continuous Adjoint vs. Discrete Adjoint......Page 422
15.10 Robustification: Appealing to Murphy’s Law......Page 423
15.10.1 Well-Posedness......Page 424
15.12 Decomposition: Simulation-Based System Modeling......Page 425
15.13 Global Stabilization: Conservatively Enhancing Stability......Page 426
15.15 Performance Limitation: Identifying Ideal Control Targets......Page 427
15.16 Implementation: Evaluating Engineering Trade-Offs......Page 428
15.18 The Future: A Renaissance......Page 430
Acknowledgments......Page 432
References......Page 433
16.1 Introduction......Page 435
16.2.1 Background......Page 436
16.2.2 Feedforward ANN......Page 437
16.2.3 Training......Page 438
16.2.4.5 Training Cutoff......Page 439
16.2.6 Heat Exchanger Application......Page 440
16.2.6.2 Thermal Neurocontrol......Page 441
16.2.6.2.1 Stabilization of Feedback Loop......Page 442
16.2.6.2.2 Adaptive Neurocontrol......Page 0
16.2.6.2.3 Optimal Control......Page 443
16.3 Genetic Algorithms......Page 446
16.3.1 Procedure......Page 447
16.3.3 Other Applications......Page 451
16.4.2 Example Implementation of Fuzzy Control......Page 452
16.4.3.2 Fuzzy vs. Crisp Sets......Page 459
16.4.3.3 Operations on Fuzzy Sets......Page 461
16.4.4 Fuzzy Logic......Page 462
16.4.5 Alternative Inference Systems......Page 464
16.5 Conclusions......Page 465
References......Page 466