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MEMS惯性传感器的设计守则.pdf

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    Cover
    Half-title
    Title
    Copyright
    Contents
    Preface
    Acknowledgments
    Notation
    1 Introduction
    1.1 A short foray through the pre-MEMS history
    1.2 Applications and market
    1.3 The ingredients of inertial MEMS
    References
    2 Transducers
    2.1 Anisotropic material properties, tensors, and rotations
    2.1.1 Stress, strain, and piezoresistivity
    Hooke's law
    Normal stresses
    Shear stresses
    Stress and strain tensors
    The stress--strain relation for anisotropic materials
    The piezoresistance of silicon
    2.1.2 Rotation of coordinate systems
    Coordinate frames
    The rotation tensor
    Transformation of tensors of second order
    2.2 Piezoresistive transducers
    2.2.1 Piezoresistors
    2.2.2 Piezoresistors on silicon
    Thin piezoresistors
    Temperature compensation in piezoresistors
    2.2.3 Piezoresistors on polysilicon
    2.3 Piezoelectric transducers
    2.3.1 The piezoelectric effect
    2.3.2 Piezoelectric equations
    Piezoelectric sensors in MEMS
    2.4 Capacitive transducers
    2.4.1 Electrostatic forces
    2.4.2 Parallel-plate capacitors
    Capacitance sensing
    The pull-in effect
    2.4.3 Tilting-plate capacitors
    Nonlinear distortions
    Instabilities of a singular tilting plate
    Instabilities of the tilting capacitance pair
    2.4.4 Comb capacitors
    Unidirectional linear combs
    Bidirectional actuation
    Radial combs
    Frame-based capacitors
    2.4.5 Levitation
    Comb levitation
    Levitation in drive combs
    Reduction of levitation forces
    References
    3 Non-inertial forces
    3.1 Springs
    3.1.1 Beams
    3.1.2 The stiffness matrix
    3.1.3 The bending equation for beams
    Internal forces and moments
    Differential relations of a bent beams
    3.1.4 Cantilever beams
    Cantilevers under different loads
    Skew beam bending and asymmetric suspensions
    Residual stress in bending beams
    3.1.5 Torsion springs
    Cylindrical torsion bars
    Torsion bars with arbitrary cross-section
    Rectangular bars
    Cylindrical bars
    3.1.6 Stress concentration
    3.1.7 Suspensions
    Parallel and serial spring connections
    Beam chains
    Plate suspension
    3.2 Damping forces
    3.2.1 Fluid-flow models
    Continuous viscous flow
    Viscosity of gases
    Continuous-flow equations
    3.2.2 Slide damping
    Couette flow for slowly moving plates
    Stokes flow for rapidly oscillating plates
    3.2.3 Squeeze damping
    Reynolds' equation
    Low-frequency squeeze damping
    High-frequency squeeze damping
    The impact of perforation
    3.2.4 Drag forces
    3.2.5 Free molecular flow
    3.2.6 Structural damping
    References
    4 MEMS technologies
    4.1 Microfabrication of inertial MEMS
    4.1.1 Basic microelectronic fabrication steps
    Deposition
    Patterning
    Doping
    4.1.2 Etching
    Isotropic wet etching
    Anisotropic wet etching
    Electrochemical etch stop
    4.1.3 Dry etching
    Reactive-ion etching
    Deep reactive-ion etching
    4.2 Wafer bonding
    4.2.1 Zero-level packaging and wafer bonding
    4.2.2 Wafer-bonding processes
    Fusion bonding
    Anodic bonding
    Glass-frit bonding
    Metallic-alloy seal bonding
    Polymer bonding
    Thermocompression bonding
    4.3 Integrated processes
    4.3.1 Bulk micromachining
    4.3.2 Surface micromachining
    A thick polysilicon process
    Cavity sealing using SMM
    4.3.3 SOI-MEMS processes
    MEMS prototyping processes
    4.3.4 CMOS-MEMS
    Pre-CMOS MEMS
    Intra-CMOS MEMS
    Post-CMOS MEMS
    References
    5 First-level packaging
    5.1 FLP packages
    5.2 FLP technologies
    5.2.1 Dicing and die separation
    5.2.2 Die attachment
    Packaging materials
    Die-attachment-induced stress
    5.2.3 Electrical interconnection
    5.2.4 Encapsulation
    Overmolded plastic packages
    Pre-molded plastic packages
    References
    6 Electrical interfaces
    6.1 Sensing electronics – building blocks
    6.1.1 The MOS transistor
    Drain current
    The small-signal model
    6.1.2 Operational and transconductance amplifiers
    A simple transconductance amplifier
    Models of operational and transconductance amplifiers
    The real Op Amp
    Instrumentation amplifiers
    6.2 Sensor interfaces
    6.2.1 Resistive interfaces
    6.2.2 Piezoelectric interfaces
    6.2.3 Capacitive interfaces
    Principles of capacitive sensing
    Current sensing
    Voltage sensing
    Charge sensing
    Comparison and improvements
    Switched-capacitor sensing
    6.3 Data converters
    6.3.1 Sampling and hold
    6.3.2 Single-sample conversion in the amplitude domain
    6.3.3 Time-domain conversion
    Pulse-width and pulse-density modulation
    Converters
    References
    7 Accelerometers
    7.1 General measurement objectives
    7.2 The spring–mass system
    7.2.1 The transfer functions
    The trade-off between sensitivity and bandwidth
    7.2.2 Accelerometer imperfections
    A simplified accelerometer model with imperfections
    Cross-coupling
    7.2.3 Accelerometer feedback control
    The linearized feedback model
    The signal-to-noise ratio
    Closed-loop dynamics
    7.2.4 Feedback control with nonlinear actuators
    Bidirectional capacitive actuators
    Single-sided actuators
    Linearization and embedded converters
    7.3 Resonant accelerometers
    7.3.1 Resonant beams
    Resonance vibration – exact solution
    Resonance frequencies by the energy method
    7.3.2 Resonant accelerometer systems
    7.4 Beam accelerometers
    7.4.1 Beam dynamics
    The principle of virtual work
    Eigenmode expansion
    Damping and electrostatic forces
    Static deflection
    7.4.2 Model implementation
    The impact of nonlinear damping
    Feedback control
    7.5 Various other accelerometer principles
    7.5.1 Tunneling accelerometers
    7.5.2 Convective and bubble accelerometers
    7.6 From 1D to 6D accelerometers
    7.6.1 1D accelerometers
    Piezoresistive accelerometers
    Capacitive accelerometers
    Piezoelectric accelerometers
    7.6.2 2D and 3D accelerometers
    Parallel implementation
    2D and 3D accelerometers with multi-DOF sensing elements
    7.6.3 6D accelerometers
    References
    8 Gyroscopes
    8.1 Some basic principles
    8.2 Kinematics of gyroscopes
    8.2.1 Platform rotation and angular velocity
    8.2.2 Body rotation in a non-inertial system
    8.2.3 The angular-momentum theorem
    8.2.4 The momentum equation
    8.2.5 The small-angle approximation
    8.3 The performance of gyroscopes
    8.4 Rate-integrating gyroscopes
    8.4.1 Two-DOF gyroscopes
    8.4.2 The principle of angular gyroscopes
    8.4.3 An imperfection model
    8.4.4 Imperfection in angular gyroscopes
    8.4.5 Gyroscope control
    8.5 Rate gyroscopes
    8.5.1 System architecture
    The drive resonator
    Sensing
    8.5.2 Resonance sensing
    8.5.3 Non-resonant sensing
    8.5.4 Noise
    8.5.5 The zero-rate output
    Mechanical bias sources
    Q-bias
    The impact of transducer imperfections
    R-bias
    Other bias sources
    8.5.6 Bias stability
    8.5.7 Acceleration suppression and tuning forks
    Anti-phase-driven identical gyroscopes
    Tuning-fork gyroscopes
    8.5.8 Drive-motion control and spring nonlinearities
    The phase-locked loop
    The amplitude loop
    Spring nonlinearities and the resonator transfer function
    8.6 Gyroscope architectures
    8.6.1 Mode-decoupling architectures
    8.6.2 z-Gyroscopes
    Mode decoupling by frame-based architectures
    Doubly decoupled z-gyroscopes
    8.6.3 In-plane-sensitive gyroscopes
    In-plane-sensitive linear gyroscopes
    Linear–rotatory gyroscopes
    8.6.4 Torsional gyroscopes
    1D torsional gyroscopes
    Decoupled torsional gyroscopes
    8.7 Non-planar MEMS gyroscopes
    8.7.1 Beam gyroscopes
    8.7.2 Quartz tuning forks
    8.7.3 Ring gyroscopes
    8.7.4 Bulk acoustic-wave gyroscopes
    8.8 2D and 3D gyroscopes and ways towards a 6D IMU
    8.8.1 Single-mass multiple-DOF inertial sensors
    Gyroscope-free, single-mass IMUs
    Single-mass, gyroscope-based IMUs
    5D inertial sensors
    8.8.2 2D gyroscopes
    8.8.3 3D gyroscopes
    A fully decoupled 3D gyroscope and extension towards an IMU
    References
    9 Test and calibration
    References
    Concluding remarks
    References
    Index
    This page intentionally left blank
    Inertial MEMS Principles and Practice A practical and systematic overview of the design, fabrication, and testing of MEMS-based inertial sensors, this comprehensive and rigorous guide shows you how to analyze and transform application requirements into practical designs, and helps you to avoid potential pitfalls and to cut design time. With this book you’ll soon be up to speed on the relevant basics, includ- ing MEMS technologies, packaging, kinematics and mechanics, and transducers. You’ll also get a thorough evaluation of different approaches and architectures for design and an overview of key aspects of testing and calibration. Unique insights into the practical difficulties of making sensors for real-world applications make this up-to-date description of the state of the art in inertial MEMS an ideal resource for professional engineers in industry, managers, and application engineers, as well as for students looking for a complete introduction to the area. Volker Kempe has more than 40 years of experience in research and devel- opment in both academia and industry. He led the microelectronics engineering department at Austria Mikro Systems for over 10 years. In 2003 he co-founded, and became Vice President of, SensorDynamics AG, and his current interests focus on the functionality, technology, and application of inertial MEMS.
    Inertial MEMS Principles and Practice Volker Kempe Sensor Dynamics AG, Austria
    c a m b r i d g e u n i v e r s i t y p r e s s Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521766586 C° Cambridge university Press 2011 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2011 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Kempe, Volker. Inertial MEMS : principles and practice / Volker Kempe. p. cm. Includes bibliographical references and index. ISBN 978-0-521-76658-6 (hardback) 1. Microelectromechanical systems. TK7875.K46 629.04′5 – dc22 2010037668 2011 2. Inertial navigation systems. 3. BioMEMS. I. Title. ISBN 978-0-521-76658-6 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
    Contents Preface Acknowledgments Notation page xiii xv xvi 1 2 Introduction 1.1 A short foray through the pre-MEMS history 1.2 Applications and market 1.3 The ingredients of inertial MEMS References Transducers 2.1 Anisotropic material properties, tensors, and rotations 2.1.1 Stress, strain, and piezoresistivity Hooke’s law Normal stresses Shear stresses Stress and strain tensors The stress–strain relation for anisotropic materials The piezoresistance of silicon 2.1.2 Rotation of coordinate systems Coordinate frames The rotation tensor Transformation of tensors of second order 2.2 Piezoresistive transducers 2.2.1 Piezoresistors 2.2.2 Piezoresistors on silicon Thin piezoresistors Temperature compensation in piezoresistors 2.2.3 Piezoresistors on polysilicon 2.3 Piezoelectric transducers 2.3.1 The piezoelectric effect 2.3.2 Piezoelectric equations Piezoelectric sensors in MEMS 1 1 6 9 11 13 13 14 14 14 15 17 21 24 25 26 27 30 33 33 34 35 36 38 39 39 42 43
    vi Contents 2.4 Capacitive transducers 2.4.1 Electrostatic forces 2.4.2 Parallel-plate capacitors Capacitance sensing The pull-in effect 2.4.3 Tilting-plate capacitors Nonlinear distortions Instabilities of a singular tilting plate Instabilities of the tilting capacitance pair 2.4.4 Comb capacitors Unidirectional linear combs Bidirectional actuation Radial combs Frame-based capacitors 2.4.5 Levitation Comb levitation Levitation in drive combs Reduction of levitation forces References 3 Non-inertial forces 3.1 Springs 3.1.1 Beams 3.1.2 The stiffness matrix 3.1.3 The bending equation for beams Internal forces and moments Differential relations of a bent beams 3.1.4 Cantilever beams Cantilevers under different loads Skew beam bending and asymmetric suspensions Residual stress in bending beams 3.1.5 Torsion springs Cylindrical torsion bars Torsion bars with arbitrary cross-section Rectangular bars Cylindrical bars 3.1.6 Stress concentration 3.1.7 Suspensions Parallel and serial spring connections Beam chains Plate suspension 3.2 Damping forces 3.2.1 Fluid-flow models 47 49 51 51 53 55 56 58 58 62 62 65 66 67 69 69 71 73 75 79 79 80 81 82 83 83 87 87 90 93 96 96 97 100 101 101 103 103 104 105 108 108
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