giáo trình tiếng anh về Bán dẫn trong công nghệ vi điện tử và công nghệ nano
S emiconductors for Micro and Nanotechnology— An Introduction for Engineers S emiconductors for Micro and Nanotechnology— An Introduction for Engineers Jan G. Korvink and Andreas Greiner Authors: Prof. Dr. Jan G. Korvink Dr. Andreas Greiner IMTEK-Institute for Microsystem IMTEK-Institute for Microsystem Technology Technology Faculty for Applied Sciences Faculty for Applied Sciences Albert Ludwig University Freiburg Albert Ludwig University Freiburg D-79110 Freiburg D-79110 Freiburg Germany Germany . Library of Congress Card No.: applied for. British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Die Deutsche Bibliothek — CIP-Cataloguing-in-Publication Data A catalogue record for this book is available from Die Deutsche Bibliothek. ISBN 3-527-30257-3 © WILEY-VCH Verlag GmbH, Weinheim 2002 Printed on acid-free paper All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form — by photoprinting, microfilm, or any other means — nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printing: Strauss Offsetdruck GmbH, Mörlenbach Bookbinding: Litges & Dopf Buchbinderei GmbH, Heppenheim Printed in the Federal Republik of Germany This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Dedicated to Micheline Pfister, Maria Cristina Vecchi, Sean and Nicolas Vogel, Sarah Maria Greiner and in fond memory of und im Gedenken an Gerrit Jörgen Korvink Gertrud Maria Greiner Semiconductors for Micro and Nanosystem Technology 7 Contents Contents 7 Preface 13 Chapter 1 Introduction 15 The System Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Popular Definitions and Acronyms . . . . . . . . . . . . . . . . . . 19 Semiconductors versus Conductors and Insulators . . . . . . . . 19 The Diode Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 The Transistor Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Passive Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Microsystems: MEMS, MOEMS, NEMS, POEMS, etc. . . . . . 21 Sources of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Summary for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 References for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . 25 8 Semiconductors for Micro and Nanosystem Technology Chapter 2 The Crystal Lattice System 27 Observed Lattice Property Data . . . . . . . . . . . . . . . . . . . . 29 Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Silicon Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Silicon Nitride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Gallium Arsenide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Symmetries of Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Elastic Properties: The Stressed Uniform Lattice . . . . . . . 48 Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 The Vibrating Uniform Lattice . . . . . . . . . . . . . . . . . . . . . 64 Normal Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Phonons, Specific Heat, Thermal Expansion . . . . . . . . . . . . . 81 Modifications to the Uniform Bulk Lattice . . . . . . . . . . . . 88 Summary for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 References for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . 92 Chapter 3 The Electronic System 95 Quantum Mechanics of Single Electrons . . . . . . . . . . . . . 96 Wavefunctions and their Interpretation . . . . . . . . . . . . . . . . . 97 The Schrödinger Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Free and Bound Electrons, Dimensionality Effects . . . . 106 Finite and Infinite Potential Boxes . . . . . . . . . . . . . . . . . . . . 106 Continuous Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Periodic Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 115 Potential Barriers and Tunneling . . . . . . . . . . . . . . . . . . . . . 115 The Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 The Hydrogen Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Transitions Between Electronic States . . . . . . . . . . . . . . . . . 127 Fermion number operators and number states . . . . . . . . . . 130 Periodic Potentials in Crystal . . . . . . . . . . . . . . . . . . . . . 132 The Bloch Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Formation of Band Structure . . . . . . . . . . . . . . . . . . . . . . . . 133 Types of Band Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Effective Mass Approximation . . . . . . . . . . . . . . . . . . . . . . . 139 Summary for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 140 References for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . 141 Semiconductors for Micro and Nanosystem Technology 9 Chapter 4 The Electromagnetic System 143 Basic Equations of Electrodynamics . . . . . . . . . . . . . . . 144 Time-Dependent Potentials . . . . . . . . . . . . . . . . . . . . . . . . .149 Quasi-Static and Static Electric and Magnetic Fields . . . . .151 Basic Description of Light . . . . . . . . . . . . . . . . . . . . . . . 158 The Harmonic Electromagnetic Plane Wave . . . . . . . . . . . .158 The Electromagnetic Gaussian Wave Packet . . . . . . . . . . . . 160 Light as Particles: Photons . . . . . . . . . . . . . . . . . . . . . . . . .162 Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Example: The Homogeneous Glass Fiber . . . . . . . . . . . . . .166 Summary for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 167 References for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . 168 Chapter 5 Statistics 169 Systems and Ensembles . . . . . . . . . . . . . . . . . . . . . . . . . 170 Microcanonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174 Grand Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . .176 Particle Statistics: Counting Particles . . . . . . . . . . . . . . . 178 Maxwell-Boltzmann Statistics . . . . . . . . . . . . . . . . . . . . . . .178 Bose-Einstein Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . .180 Fermi-Dirac Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181 Quasi Particles and Statistics . . . . . . . . . . . . . . . . . . . . . . . .182 Applications of the Bose-Einstein Distributions . . . . . . . 183 Electron Distribution Functions . . . . . . . . . . . . . . . . . . . 184 Intrinsic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . .184 Extrinsic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . .187 Summary for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 190 References for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . 190 Chapter 6 Transport Theory 191 The Semi-Classical Boltzmann Transport Equation . . . . 192 The Streaming Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193 The Scattering Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .195 The BTE for Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Balance Equations for Distribution Function Moments . . .197