Modeling MEMS and NEMS

Modeling MEMS and NEMS

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Features

  • Develops the ability to construct, analyze, and interpret mathematical models for microscale devices
  • Constructs a series of models in increasing complexity for a range of thermal, elastic, electrostatic, and magnetically driven devices
  • Clarifies the origins of numerical difficulties and suggests techniques to overcome them
  • Provides additional background material o in an appendix
  • Includes a companion Web site at www.modelingmemsandnems.com that provides a wealth of supplemental material
  • Summary

    Designing small structures necessitates an a priori understanding of various device behaviors. The way to gain such understanding is to construct, analyze, and interpret the proper mathematical model.

    Through such models, Modeling MEMS and NEMS illuminates microscale and nanoscale phenomena, thereby facilitating the design and optimization of micro- and nanoscale devices. After some introductory material, a review of continuum mechanics, and a study of scaling, the book is organized around phenomena. Each chapter addresses a sequence of real devices that share a common feature. The authors abstract that feature from the devices and present the mathematical tools needed to model it. They construct, analyze, and interpret a series of models of increasing complexity, then at the end of the chapter, they return to one of the devices described, apply the model to it, and interpret the analysis.

    In the beginning, the world of microdevices was dominated by experimental work and the development of fabrication techniques. As it matures, optimization and innovative designs are moving to the forefront. Modeling MEMS and NEMS not only provides the practical background and tools needed to design and optimize microdevices but it also helps develop the intuitive understanding that can lead to developing new and better designs and devices.

    Table of Contents

    INTRODUCTION
    MEMS and NEMS
    A Capsule History of MEMS and NEMS
    Dimensional Analysis and Scaling
    Exercises
    A REFRESHER ON CONTINUUM MECHANICS
    Introduction
    The Continuum Hypothesis
    Heat Conduction
    Elasticity
    Linear Thermoelasticity
    Fluid Dynamics
    Electromagnetism
    Numerical Methods for Continuum Mechanics
    SMALL IS DIFFERENT
    The Backyard
    Scaling
    Systems
    Exercises
    THERMALLY DRIVEN SYSTEMS
    Introduction
    Thermally Driven Devices
    From PDE to ODE: Lumped Models
    Joule Heating of a Cylinder
    Analysis of Thermal Data Storage
    Exercises
    MODELING ELASTIC STRUCTURES
    Introduction
    Examples of Elastic Structures in MEMS/NEMS
    The Mass on a Spring
    Membranes
    Beams
    Plates
    The Capacitive Pressure Sensor
    Exercises
    MODELING COUPLED THERMAL-ELASTIC SYSTEMS
    Introduction
    Devices and Phenomena in Thermal-Elastic Systems
    Modeling Thermopneumatic Systems
    The Thermoelastic Rod Revisited
    Modeling Thermoelastic V-Beam Actuators
    Modeling Thermal Bimorph Actuators
    Modeling Bimetallic Thermal Actuators
    Exercises
    MODELING ELECTROSTATIC-ELASTIC SYSTEMS
    Introduction
    Devices Using Electrostatic Actuation
    The Mass-Spring Model
    Modeling General Electrostatic-Elastic Systems
    Electrostatic-Elastic Systems - Membrane Theory
    Electrostatic-Elastic Systems - Beam and Plate Theory
    Analysis of Capacitive Control Schemes
    Exercises
    MODELING MAGNETICALLY ACTUATED SYSTEMS
    Introduction
    Magnetically Driven Devices
    Mass-Spring Models
    A Simple Membrane Micropump Model
    A Small-Aspect Ratio Model
    Exercises
    MICROFLUIDICS
    Introduction
    Microfluidic Devices
    More Fluidic Scaling
    Modeling Squeeze Film Damping
    Exercises
    BEYOND CONTINUUM THEORY
    Introduction
    Limits of Contiuum Mechanics
    Devices and Systems Beyond Continuum Theory
    Exercises
    REFERENCES
    APPENDICES
    Mathematical Results
    Physical Constants
    INDEX

    Each chapter also contains Related Reading and Notes sections.

    Editorial Reviews

    "Researchers in MEMS and NEMS … are likely to find much of interest [in this book], … and to date there is no other book on MEMS and NEMS that is focused on the modeling process to the same extent. Graduate students of MEMS and NEMS will find the book to be between useful and indispensable. … [This] is a thought-provoking book for those with interests in modeling and is likely to have a longevity well beyond the usual half-life of a textbook."
    - SIAM Review, Vol. 46, No. 1

    "Although the exposition is primarily intended for the engineering community … applied mathematicians can also get a lot of inspiration [from this book]. … The large number of exercises makes it suitable … also as a textbook for graduate students … ."
    - EMS Newsletter



    "…whether or not the next small thing turns out to be the next big thing, the topic offers interesting science to be explored, and here is a good book to guide you through it. …very broad scope … Generous references are given … Elasticity and heat transfer are perhaps the domains that are most prominent, although there is plenty of insight and interest in other areas, and the choice of core problems is excellent. …

    "Researchers in MEMS and NEMS, where modeling and simulation are increasingly recognized as important first steps in design, are likely to find much of interest … and to date there is no other book on MEMS and NEMS that is focused on the modeling process to the same extent. … Graduate students of MEMS and NEMS will find the book to be between useful and indispensable … well suited to a graduate course …

    "The writing style is very clear and lively, producing a readable--even vibrant--text. But above all, it is a thought-provoking book for those with interest in modeling and is likely to have a longevity well beyond the usual half-life of a textbook."
    - SIAM Review, March 2004

    "Starting from the deep principles of physical scaling and dimensional analysis, Pelesko and Bernstein introduce a wide range of MEMS and NEMS devices to motivate their review of the essential continuum mathematical physics of coupled-domain micro-scaled devices. Their book is bound to become the standard text for modelers of MEMS and NEMS, as well as an essential volume on the bookshelves of all MEMS and NEMS designers. Given the book's sophisticated, yet straightforward, approach to the fundamental physics of several energy domains (thermal, elastic, electrostatic, magnetic, and fluid) the volume can be recommended as the basis for general courses in applied science and engineering."
    - Seldon B. Crary, President and CEO, Crary Group, Inc., Palo Alto, California, USA and Copenhagen, Denmark

     
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