ISBN: 3-540-67582-5
TITLE: Mechanical Microsensors
AUTHOR: Elwenspoek, Miko; Wiegerink, Remco
TOC:

1. Introduction 1
2. MEMS 5
2.1 Miniaturisation and Systems 5
2.2 Examples for MEMS 6
2.2.1 Bubble Jet 7
2.2.2 Actuators 9
2.2.3 Micropumps 10
2.3 Small and Large: Scaling 13
2.3.1 Electromagnetic Forces 13
2.3.2 Coulomb Friction 16
2.3.3 Mechanical Strength 16
2.3.4 Dynamic Properties 17
2.4 Available Fabrication Technology 20
2.4.1 Technologies Based on Lithography 20
2.4.1.1 Silicon Micromachining 21
2.4.1.2 LIGA 22
2.4.2 Miniaturisation of Conventional Technologies 23
3. Introduction into Silicon Micromachining 24
3.1 Photolithography 24
3.2 Thin Film Deposition and Doping 25
3.2.1 Silicon Dioxide 26
3.2.2 Chemical Vapour Deposition 27
3.2.3 Evaporation 29
3.2.4 Sputterdeposition 31
3.2.5 Doping 31
3.3 Wet Chemical Etching 32
3.3.1 Isotropic Etching 32
3.3.2 Anisotropic Etching 34
3.3.3 Etch Stop 36
3.4 Waferbonding 40
3.4.1 Anodic Bonding 41
3.4.2 Silicon Fusion Bonding 43
3.5 Plasma Etching 45
3.5.1 Plasma 45
3.5.2 Anisotropic Plasma Etching Modes 47
3.5.3 Configurations 48
3.5.4 Black Silicon Method 53
3.6 Surface Micromachining 55
3.6.1 Thin Film Stress 56
3.6.2 Sticking 57
4. Mechanics of Membranes and Beams 59
4.1 Dynamics of the Mass Spring System 59
4.2 Strings 63
4.3 Beams 65
4.3.1 Stress and Strain 65
4.3.2 Bending Energy 66
4.3.3 Radius of Curvature 67
4.3.4 Lagrange Function of a Flexible Beam 70
4.3.5 Differential Equation for Beams 70
4.3.6 Boundary Conditions for Beams 72
4.3.7 Examples 73
4.3.8 Mechanical Stability 75
4.3.9 Transversal Vibration of Beams 77
4.4 Diaphragms and Membranes 80
4.4.1 Circular Diaphragms 80
4.4.2 Square Membranes 82
Appendix 4.1: Buckling of Bridges 84
5. Principles of Measuring Mechanical Quantities:
Transduction of Deformation 85
5.1 Metal Strain Gauges 85
5.2 Semiconductor Strain Gauges 86
5.2.1 Piezoresistive Effect in Single Crystalline Silicon 87
5.2.2 Piezoresistive Effect in Polysilicon Thin Films 88
5.2.3 Transduction from Deformation to Resistance 89
5.3 Capacitive Transducers 90
5.3.1 Electromechanics 90
5.3.2 Diaphragm Pressure Sensors 94
6. Force and Pressure Sensors 97
6.1 Force Sensors 98
6.1.1 Load Cells 101
6.2 Pressure Sensors 106
6.2.1 Piezoresistive Pressure Sensors 107
6.2.2 Capacitive Pressure Sensors 112
6.2.3 Force Compensation Pressure Sensors 119
6.2.4 Resonant Pressure Sensors 121
6.2.5 Miniature Microphones 126
6.2.6 Tactile Imaging Arrays 130
7. Acceleration and Angular Rate Sensors 132
7.1 Acceleration Sensors 133
7.1.1 Introduction 133
7.1.2 Bulk Micromachined Accelerometers 134
7.1.3 Surface Micromachined Accelerometers 138
7.1.4 Force Feedback 143
7.2 Angular Rate Sensors 145
8. Flow sensors 153
8.1 The Laminar Boundary Layer 153
8.1.1 The Navier-Stokes Equations 153
8.1.2 Heat Transport 157
8.1.3 Hydrodynamic Boundary Layer 158
8.1.4 Thermal Boundary Layer 163
8.1.5 Skin Friction and Heat Transfer 166
8.2 Heat Transport in the Limit of Very Small Reynolds Numbers 168
8.3 Thermal Flow Sensors 173
8.3.1 Anemometer Type Flow Sensors 174
8.3.2 Two-Wire Anemometers 181
8.3.3 Calorimetric Type Flow Sensors 183
8.3.4 Sound Intensity Sensors - The Microflown 188
8.3.5 Time of Flight Sensors 194
8.4 Skin Friction Sensors 195
8.5 "Dry Fluid Flow" Sensors 200
8.6 "Wet Fluid Flow" Sensors 205
9. Resonant Sensors 209
9.1 Basic Principles and Physics 209
9.1.1 Introduction 209
9.1.2 The Differential Equation of a Prismatic Microbridge 211
9.1.3 Solving the Homogeneous, Undamped Problem using Laplace Transforms 212
9.1.4 Solving the Inhomogeneous Problem by Modal Analysis 215
9.1.5 Response to Axial Loads 217
9.1.6 Quality Factor 219
9.1.7 Nonlinear Large-Amplitude Effects 220
9.2 Excitation and Detection Mechanisms 222
9.2.1 Electrostatic Excitation and Capacitive Detection 223
9.2.2 Magnetic Excitation and Detection 223
9.2.3 Piezoelectric Excitation and Detection 223
9.2.4 Electrothermal Excitation and Piezoresistive Detection 224
9.2.5 Optothermal Excitation and Optical Detection 224
9.2.6 Dielectric Excitation and Detection 225
9.3 Examples and Applications 225
10. Electronic Interfacing 229
10.1 Piezoresistive Sensors 230
10.1.1 Wheatstone Bridge Configurations 230
10.1.2 Amplification of the Bridge Output Voltage 233
10.1.3 Noise and Offset 235
10.1.4 Feedback Control Loops 236
10.1.5 Interfacing with Digital Systems 237
10.1.5.1 Analog-to-Digital Conversion 237
10.1.5.2 Voltage to Frequency Converters 240
10.2 Capacitive Sensors 240
10.2.1 Impedance Bridges 241
10.2.2 Capacitance Controlled Oscillators 245
10.3 Resonant Sensors 248
10.3.1 Frequency Dependent Behavior of Resonant Sensors 248
10.3.2 Realizing an Oscillator 249
10.3.3 One-Port Versus Two-Port Resonators 251
10.3.4 Oscillator Based on One-Port Electrostatically Driven Beam Resonator 251
10.3.5 Oscillator Based on Two-Port Electrodynamically Driven H-shaped Resonator 257
11. Packaging 259
11.1 Packaging Techniques 260
11.1.1 Standard Packages 260
11.1.2 Chip Mounting Methods 262
11.1.2 Wafer Level Packaging 263
11.1.3 Interconnection Techniques 265
11.1.4 Multichip Modules 267
11.1.5 Encapsulation Processes 269
11.2 Stress Reduction 269
11.3 Pressure Sensors 270
11.4 Inertial Sensors 272
11.5 Thermal Flow Sensors 272
References 274
Index 291
END
