Table Of ContentS
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
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.
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).
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Printed in the Federal Republik of Germany
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
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
Semiconductors for Micro and Nanosystem Technology 7
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
8 Semiconductors for Micro and Nanosystem Technology
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
Semiconductors for Micro and Nanosystem Technology 9
