Understanding MEMS

The continued advancement of MEMS (micro-electro-mechanical systems) complexity, performance, commercial exploitation and market size requires an ever-expanding graduate population with state-of-the-art expertise.

Understanding MEMS: Principles and Applications provides a comprehensive introduction to this complex and multidisciplinary technology that is accessible to senior undergraduate and graduate students from a range of engineering and physical sciences backgrounds.

Fully self-contained, this textbook is designed to help students grasp the key principles and operation of MEMS devices and to inspire advanced study or a career in this field.

Moreover, with the increasing application areas, product categories and functionality of MEMS, industry professionals will also benefit from this consolidated overview, source of relevant equations and extensive solutions to problems.

Key features:

• Details the fundamentals of MEMS, enabling readers to understand the basic governing equations and know how they apply at the micron scale.

• Strong pedagogical emphasis enabling students to understand the fundamentals of MEMS devices.

• Self-contained study aid featuring problems and solutions.

• Book companion website hosts Matlab and PSpice codes and viewgraphs.

Auteur
Luis Castañer, Universitat Politecnica de Cataluña, Barcelona, Spain
Luis Castañer is a Professor at Universitat Politecnica de Cataluña, where he teaches courses focusing on semiconductor devices, analog circuits, photovoltaic systems, solar cells and MEMS.

Contenu

Preface xiii

About the Companion Website xv

1 Scaling of Forces 1

1.1 Scaling of Forces Model 1

1.2 Weight 2

1.2.1 Example: MEMS Accelerometer 2

1.3 Elastic Force 3

1.3.1 Example: AFM Cantilever 4

1.4 Electrostatic Force 4

1.4.1 Example: MEMS RF Switch 6

1.5 Capillary Force 6

1.5.1 Example: Wet Etching Force 8

1.6 Piezoelectric Force 8

1.6.1 Example: Force in Film Embossing 9

1.7 Magnetic Force 10

1.7.1 Example: Compass Magnetometer 10

1.8 Dielectrophoretic Force 11

1.8.1 Example: Nanoparticle in a Spherical Symmetry Electric Field 12

1.9 Summary 13

Problems 13

2 Elasticity 15

2.1 Stress 15

2.2 Strain 18

2.3 Stressstrain Relationship 20

2.3.1 Example: Plane Stress 21

2.4 Strainstress Relationship in Anisotropic Materials 22

2.5 Miller Indices 23

2.5.1 Example: Miller Indices of Typical Planes 24

2.6 Angles of Crystallographic Planes 25

2.6.1 Example 25

2.7 Compliance and Stiffness Matrices for Single-Crystal Silicon 26

2.7.1 Example: Young's Modulus and Poisson Ratio for (100) Silicon 27

2.8 Orthogonal Transformation 29

2.9 Transformation of the Stress State 31

2.9.1 Example: Rotation of the Stress State 31

2.9.2 Example: Matrix Notation for the Rotation of the Stress State 32

2.10 Orthogonal Transformation of the Stiffness Matrix 32

2.10.1 Example: C11 Coefficient in Rotated Axes 33

2.10.2 Example: Young's Modulus and Poisson Ratio in the (111) Direction 34

2.11 Elastic Properties of Selected MEMS Materials 36

Problems 36

3 Bending of Microstructures 37

3.1 Static Equilibrium 37

3.2 Free Body Diagram 38

3.3 Neutral Plane and Curvature 39

3.4 Pure Bending 40

3.4.1 Example: Neutral Plane for a Rectangular Cross-section 41

3.4.2 Example: Cantilever with Point Force at the Tip 42

3.5 Moment of Inertia and Bending Moment 43

3.5.1 Example: Moment of Inertia of a Rectangular Cross-section 43

3.6 Beam Equation 44

3.7 End-loaded Cantilever 45

3.8 Equivalent Stiffness 47

3.9 Beam Equation for Point Load and Distributed Load 48

3.10 Castigliano's Second Theorem 48

3.10.1 Strain Energy in an Elastic Body Subject to Pure Bending 50

3.11 Flexures 51

3.11.1 Fixedfixed Flexure 51

3.11.2 Example: Comparison of Stiffness Constants 53

3.11.3 Example: Folded Flexure 53

3.12 Rectangular Membrane 54

3.13 Simplified Model for a Rectangular Membrane Under Pressure 55

3.13.1 Example: Thin Membrane Subject to Pressure 57

3.14 Edge-clamped Circular Membrane 58

Problems 60

4 Piezoresistance and Piezoelectricity 65

4.1 Electrical Resistance 65

4.1.1 Example: Resistance Value 66

4.2 One-dimensional Piezoresistance Model 67

4.2.1 Example: Gauge Factors 68

4.3 Piezoresistance in Anisotropic Materials 69

4.4 Orthogonal Transformation of Ohm's Law 70

4.5 Piezoresistance Coefficients Transformation 71

4.5.1 Example: Calculation of Rotated Piezoresistive Components 𝜋 11, 𝜋 12 and 𝜋 16 for unit axes X [110], Y [ 110] and Z [001] 72

4.5.2 Analytical Expressions for Some Rotated Piezoresistive Components 74

4.6 Two-dimensional Piezoresistors 74

4.6.1 Example: Accelerometer with Cantilever and Piezoresistive Sensing 76

4.7 Pressure Sensing with Rectangular Membranes 79

4.7.1 Example: Single-resistor Pressure Sensor 82

4.7.2 Example: Pressure Sensors Comparison 85

4.8 Piezoelectricity 86

4.8.1 Relevant Data for Some Piezoelectric Materials 88

4.8.2 Example: Piezoelectric Generator 89 <p...