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E-grāmata: Mechanics of Microsystems [Wiley Online]

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Mechanics of Microsystems

Alberto Corigliano, Raffaele Ardito, Claudia Comi, Attilio Frangi, Aldo Ghisi and Stefano Mariani, Politecnico di Milano, Italy

 

A mechanical approach to microsystems, covering fundamental concepts including MEMS design, modelling and reliability

 

Mechanics of Microsystems takes a mechanical approach to microsystems and covers fundamental concepts including MEMS design, modelling and reliability. The book examines the mechanical behaviour of microsystems from a ‘design for reliability’ point of view and includes examples of applications in industry.

Mechanics of Microsystems is divided into two main parts. The first part recalls basic knowledge related to the microsystems behaviour and offers an overview on microsystems and fundamental design and modelling tools from a mechanical point of view, together with many practical examples of real microsystems. The second part covers the mechanical characterization of materials at the micro-scale and considers the most important reliability issues (fracture, fatigue, stiction, damping phenomena, etc) which are fundamental to fabricate a real working device.

 

 

Key features:

  • Provides an overview of MEMS, with special focus on mechanical-based Microsystems and reliability issues.
  • Includes examples of applications in industry.
  • Accompanied by a website hosting supplementary material.

 

 

The book provides essential reading for researchers and practitioners working with MEMS, as well as graduate students in mechanical, materials and electrical engineering.

Series Preface xiii
Preface xv
Acknowledgements xvii
Notation xix
About the Companion Website xxiii
1 Introduction
1(8)
1.1 Microsystems
1(2)
1.2 Microsystems Fabrication
3(2)
1.3 Mechanics in Microsystems
5(1)
1.4 Book Contents
6(3)
References
7(2)
Part I Fundamentals
9(82)
2 Fundamentals of Mechanics and Coupled Problems
11(62)
2.1 Introduction
11(1)
2.2 Kinematics and Dynamics of Material Points and Rigid Bodies
12(13)
2.2.1 Basic Notions of Kinematics and Motion Composition
12(3)
2.2.2 Basic Notions of Dynamics and Relative Dynamics
15(2)
2.2.3 One-Degree-of-Freedom Oscillator
17(5)
2.2.4 Rigid-Body Kinematics and Dynamics
22(3)
2.3 Solid Mechanics
25(18)
2.3.1 Linear Elastic Problem for Deformable Solids
26(9)
2.3.2 Linear Elastic Problem for Beams
35(8)
2.4 Fluid Mechanics
43(6)
2.4.1 Navier--Stokes Equations
43(5)
2.4.2 Fluid--Structure Interaction
48(1)
2.5 Electrostatics and Electromechanics
49(11)
2.5.1 Basic Notions of Electrostatics
49(5)
2.5.2 Simple Electromechanical Problem
54(4)
2.5.3 General Electromechanical Coupled Problem
58(2)
2.6 Piezoelectric Materials in Microsystems
60(4)
2.6.1 Piezoelectric Materials
60(2)
2.6.2 Piezoelectric Modelling
62(2)
2.7 Heat Conduction and Thermomechanics
64(9)
2.7.1 Heat Problem
64(3)
2.7.2 Thermomechanical Coupled Problem
67(3)
References
70(3)
3 Modelling of Linear and Nonlinear Mechanical Response
73(18)
3.1 Introduction
73(1)
3.2 Fundamental Principles
74(2)
3.2.1 Principle of Virtual Power
74(1)
3.2.2 Total Potential Energy Principle
74(1)
3.2.3 Hamilton's Principle
75(1)
3.2.4 Specialization of the Principle of Virtual Powers to Beams
76(1)
3.3 Approximation Techniques and Weighted Residuals Approach
76(3)
3.4 Exact and Approximate Solutions for Dynamic Problems
79(5)
3.4.1 Free Flexural Linear Vibrations of a Single-span Beam
79(1)
3.4.2 Nonlinear Vibration of an Axially Loaded Beam
80(4)
3.5 Example of Application: Bistable Elements
84(7)
References
90(1)
Part II Devices
91(114)
4 Accelerometers
93(16)
4.1 Introduction
93(1)
4.2 Capacitive Accelerometers
94(4)
4.2.1 In-Plane Sensing
94(2)
4.2.2 Out-of-Plane Sensing
96(2)
4.3 Resonant Accelerometers
98(3)
4.3.1 Resonating Proof Mass
98(1)
4.3.2 Resonating Elements Coupled to the Proof Mass
99(2)
4.4 Examples
101(6)
4.4.1 Three-Axis Capacitive Accelerometer
101(3)
4.4.2 Out-of-Plane Resonant Accelerometer
104(1)
4.4.3 In-Plane Resonant Accelerometer
105(2)
4.5 Design Problems and Reliability Issues
107(2)
References
107(2)
5 Coriolis-Based Gyroscopes
109(12)
5.1 Introduction
109(1)
5.2 Basic Working Principle
109(4)
5.2.1 Sensitivity of Coriolis Vibratory Gyroscopes
112(1)
5.3 Lumped-Mass Gyroscopes
113(5)
5.3.1 Symmetric and Decoupled Gyroscope
113(1)
5.3.2 Tuning-Fork Gyroscope
114(1)
5.3.3 Three-Axis Gyroscope
115(1)
5.3.4 Gyroscopes with Resonant Sensing
115(3)
5.4 Disc and Ring Gyroscopes
118(1)
5.5 Design Problems and Reliability Issues
118(3)
References
119(2)
6 Resonators
121(10)
6.1 Introduction
121(2)
6.2 Electrostatically Actuated Resonators
123(2)
6.3 Piezoelectric Resonators
125(1)
6.4 Nonlinearity Issues
126(5)
References
128(3)
7 Micromirrors and Parametric Resonance
131(16)
7.1 Introduction
131(1)
7.2 Electrostatic Resonant Micromirror
132(15)
7.2.1 Numerical Simulations with a Continuation Approach
136(4)
7.2.2 Experimental Set-Up
140(5)
References
145(2)
8 Vibrating Lorentz Force Magnetometers
147(14)
8.1 Introduction
147(1)
8.2 Vibrating Lorentz Force Magnetometers
148(608)
8.2.1 Classical Devices
148(3)
8.2.2 Improved Design
151(4)
8.2.3 Further Improvements
155(1)
8.3 Topology or Geometry Optimization
156(3)
References
159(2)
9 Mechanical Energy Harvesters
161(24)
9.1 Introduction
161(1)
9.2 Inertial Energy Harvesters
162(12)
9.2.1 Classification of Resonant Energy Harvesters
162(3)
9.2.2 Mechanical Model of a Simple Piezoelectric Harvester
165(9)
9.3 Frequency Upconversion and Bistability
174(2)
9.4 Fluid-Structure Interaction Energy Harvesters
176(9)
9.4.1 Synopsis of Aeroelastic Phenomena
177(2)
9.4.2 Energy Harvesting through Vortex-Induced Vibration
179(1)
9.4.3 Energy Harvesting through Flutter Instability
180(1)
References
181(4)
10 Micropumps
185(20)
10.1 Introduction
185(1)
10.2 Modelling Issues for Diaphragm Micropumps
186(2)
10.3 Modelling of Electrostatic Actuator
188(8)
10.3.1 Simplified Electromechanical Model
188(4)
10.3.2 Reliability Issues
192(4)
10.4 Multiphysics Model of an Electrostatic Micropump
196(2)
10.5 Piezoelectric Micropumps
198(7)
10.5.1 Modelling of the Actuator
198(3)
10.5.2 Complete Multiphysics Model
201(1)
References
202(3)
Part III Reliability and Dissipative Phenomena
205(188)
11 Mechanical Characterization at the Microscale
207(38)
11.1 Introduction
207(2)
11.2 Mechanical Characterization of Polysilicon as a Structural Material for Microsystems
209(6)
11.2.1 Polysilicon as a Structural Material for Microsystems
209(1)
11.2.2 Testing Methodologies
210(1)
11.2.3 Quasi-Static Testing
211(3)
11.2.4 High-Frequency Testing
214(1)
11.3 Weibull Approach
215(4)
11.4 On-Chip Testing Methodology for Experimental Determination of Elastic Stiffness and Nominal Strength
219(26)
11.4.1 On-Chip Bending Test through a Comb-Finger Rotational Electrostatic Actuator
220(5)
11.4.2 On-Chip Bending Test through a Parallel-Plate Electrostatic Actuator
225(4)
11.4.3 On-Chip Tensile Test through an Electrothermomechanical Actuator
229(4)
11.4.4 On-Chip Test for Thick Polysilicon Films
233(7)
References
240(5)
12 Fracture and Fatigue in Microsystems
245(26)
12.1 Introduction
245(1)
12.2 Fracture Mechanics: An Overview
245(4)
12.3 MEMS Failure Modes due to Cracking
249(7)
12.3.1 Cracking and Delamination at Package Level
249(1)
12.3.2 Cracking at Silicon Film Level
250(6)
12.4 Fatigue in Microsystems
256(15)
12.4.1 An Introduction to Fatigue in Mechanics
256(3)
12.4.2 Polysilicon Fatigue
259(2)
12.4.3 Fatigue in Metals at the Microscale
261(2)
12.4.4 Fatigue Testing at the Microscale
263(3)
References
266(5)
13 Accidental Drop Impact
271(20)
13.1 Introduction
271(1)
13.2 Single-Degree-of-Freedom Response to Drops
272(4)
13.3 Estimation of the Acceleration Peak Induced by an Accidental Drop
276(1)
13.4 A Multiscale Approach to Drop Impact Events
277(3)
13.4.1 Macroscale Level
277(2)
13.4.2 Mesoscale Level
279(1)
13.4.3 Microscale Level
279(1)
13.5 Results: Drop-Induced Failure of Inertial MEMS
280(11)
References
287(4)
14 Fabrication-Induced Residual Stresses and Relevant Failures
291(22)
14.1 Main Sources of Residual Stresses in Microsystems
291(1)
14.2 The Stoney Formula and its Modifications
292(7)
14.3 Experimental Methods for the Evaluation of Residual Stresses
299(5)
14.4 Delamination, Buckling and Cracks in Thin Films due to Residual Stresses
304(9)
References
310(3)
15 Damping in Microsystems
313(38)
15.1 Introduction
313(1)
15.2 Gas Damping in the Continuum Regime with Slip Boundary Conditions
314(6)
15.2.1 Experimental Validation at Ambient Pressure
317(1)
15.2.2 Effects of Decreasing Working Pressure
318(2)
15.3 Gas Damping in the Rarefied Regime
320(5)
15.3.1 Evaluation of Damping at Low Pressure using Kinetic Models
321(2)
15.3.2 Linearization of the BGK Model
323(1)
15.3.3 Numerical Implementation
324(1)
15.3 A Application to MEMS
325(3)
15.4 Gas Damping in the Free-Molecule Regime
328(7)
15.4.1 Boundary Integral Equation Approach
328(2)
15.4.2 Experimental Validations
330(5)
15.5 Solid Damping: Thermoelasticity
335(3)
15.6 Solid Damping: Anchor Losses
338(8)
15.6.1 Analytical Estimation of Dissipation
339(3)
15.6.2 Numerical Estimation of Anchor Losses
342(4)
15.7 Solid Damping: Additional unknown Sources -- Surface Losses
346(5)
15.7.1 Solid Damping: Deviations from Thermoelasticity
346(1)
15.7.2 Solid Damping: Losses in Piezoresonators
346(2)
References
348(3)
16 Surface Interactions
351(42)
16.1 Introduction
352(1)
16.2 Spontaneous Adhesion or Stiction
352(1)
16.3 Adhesion Sources
353(9)
16.3.1 Capillary Attraction
353(3)
16.3.2 Van der Waals Interactions
356(2)
16.3.3 Casimir Forces
358(1)
16.3.4 Hydrogen Bonds
359(1)
16.3.5 Electrostatic Forces
360(2)
16.4 Experimental Characterization
362(12)
16.4.1 Experiments by Mastrangelo and Hsu
362(1)
16.4.2 Experiments by the Sandia Group
362(3)
16.4.3 Experiments by the Virginia Group
365(2)
16.4.4 Peel Experiments
367(1)
16.4.5 Pull-in Experiments
368(4)
16.4.6 Tests for Sidewall Adhesion
372(2)
16.5 Modelling and Simulation
374(6)
16.5.1 Lennard-Jones Potential
374(1)
16.5.2 Tribological Models: Hertz, JKR, DMT
375(2)
16.5.3 Computation of Adhesion Energy
377(3)
16.6 Recent Advances
380(13)
16.6.1 Finite Element Analysis of Adhesion between Rough Surfaces
380(3)
16.6.2 Accelerated Numerical Techniques
383(4)
References
387(6)
Index 393
Alberto Corigliano, Raffaele Ardito, Claudia Comi, Attilio Frangi, Aldo Ghisi, and Stefano Mariani Politecnico di Milano, Italy

Alberto Corigliano is a Professor of Solid and Structural Mechanics at the Department of Civil and Environmental Engineering of Politecnico di Milano, Italy. A. Corigliano has authored and co-authored more than 240 scientific publications in fields related to solid and structural mechanics at various scales, including 2 book chapters in Microsystems area, and 7 patents on Microsystems. During his research activity, A. Corigliano covered a wide range of subjects in the fields of structural and materials mechanics, with particular reference to theoretical and computational problems relevant to non-linear material responses.

Raffaele Ardito is an Associate Professor of Solid and Structural Mechanics at the Department of Civil and Environmental Engineering of Politecnico di Milano, Italy. He graduated in 2000 (cum laude) at the Politecnico di Milano in Civil Engineering and he received the Ph.D. degree, cum laude, in 2004. From 2004 to 2006 he was a research fellow at the National Institute for Nuclear Physics, joining an international research group with focus on solid mechanics in cryogenic conditions. He spent, in 2008 and 2010, two periods of research at the Research Laboratory of Electronics, Massachusetts Institute of Technology, as visiting scientist. His scientific contributions to the field of MEMS focus on theoretical and computational aspects of adhesion and multi-physics behavior.

Claudia Comi is a Professor of Solid and Structural Mechanics at the Department of Civil and Environmental Engineering of Politecnico di Milano, Italy. C. Comi has authored and co-authored more than 140 scientific publications in various fields of solid and structural mechanics and 4 patents on Microsystems. Her main research interests concern theoretical and computational mechanics of materials and structures. Her research activities focus on damage and quasi-brittle fracture modelling, on instability phenomena and nonlocal models for elastoplastic and damaging one-phase and multi-phase materials, including functionally graded materials, and on design and reliability of MEMS.

Attilio Frangi is a Professor of Solid and Structural Mechanics at the Department of Civil and Environmental Engineering of Politecnico di Milano, Italy. A. Frangi has authored and co-authored more than 150 scientific publications on issues of computational mechanics and micromechanics and 5 patents on Microsystems. He has co-edited one scientific monograph on the multi-physics simulation of MEMS and NEMS. The research interests of A. Frangi in the field of MEMS include: the design of new devices; the theoretical and numerical analysis of multi-physics phenomena; the analysis of non-linear phenomena in the dynamical response of MOEMS.

Aldo Ghisi is an Assistant Professor of Solid and Structural Mechanics at the Department of Civil and Environmental Engineering of Politecnico di Milano, Italy. A. Ghisi has authored and co-authored more than 70 scientific publications on various subjects related to materials and structural mechanics. His research areas include multi-physics phenomena in micro/nano structures, particularly related to mechanical simulation of drop impacts, fatigue in polysilicon, gas-solid interaction, study of wafer-to-wafer bonding. Besides microsystems, he is also involved in the numerical and experimental study of metallic alloys for cryogenic applications and in dam engineering.

Stefano Mariani is an Associate Professor of Solid and Structural Mechanics at the Department of Civil and Environmental Engineering of Politecnico di Milano, Italy. S. Mariani has authored and co-authored about 170 scientific publications. His main research interests are: numerical simulations of ductile fracture in metals and quasi-brittle fracture in heterogeneous and functionally graded materials; extended finite element methods; calibration of constitutive models via extended and sigma-point Kalman filters; multi-scale solution methods for dynamic delamination in layered composites; reliability of MEMS subject to shocks and drops; structural health monitoring of composite structures through MEMS sensors.
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