Electronic materials science eugene a irene 1st edition

www.elsolucionario.org ELECTRONIC MATERIALS SCIENCE www.elsolucionario.org ELECTRONIC MATERIALS SCIENCE Eugene A Irene University of North Carolina Chapel Hill, North Carolina A John Wiley & Sons, Inc., Publication Copyright © 2005 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008 Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services please contact our Customer Care Department within the U.S at 877-762-2974, outside the U.S at 317-572-3993 or fax 317-5724002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print, however, may not be available in electronic format Library of Congress Cataloging-in-Publication Data: Irene, Eugene A Electronic materials science / Eugene A Irene p cm Includes bibliographical references and index ISBN 0-471-69597-1 (cloth) Electronics—Materials Electronic apparatus and appliances—Materials TK7871.I74 2005 621.381—dc22 2004016686 Printed in the United States of America 10 I Title CONTENTS Preface xi Introduction to Electronic Materials Science 1.1 Introduction / 1.2 Structure and Diffraction / 1.3 Defects / 1.4 Diffusion / 1.5 Phase Equilibria / 1.6 Mechanical Properties / 1.7 Electronic Structure / 1.8 Electronic Properties and Devices / 1.9 Electronic Materials Science / Structure of Solids 2.1 Introduction / 2.2 Order / 10 2.3 The Lattice / 12 2.4 Crystal Structure / 16 2.5 Notation / 17 2.5.1 Naming Planes / 17 2.5.2 Lattice Directions / 19 2.6 Lattice Geometry / 21 2.6.1 Planar Spacing Formulas / 21 2.6.2 Close Packing / 22 2.7 The Wigner-Seitz Cell / 24 v www.elsolucionario.org vi CONTENTS 2.8 Crystal Structures / 25 2.8.1 Structures for Elements / 25 2.8.2 Structures for Compounds / 26 2.8.3 Solid Solutions / 28 Related Reading / 29 Exercises / 29 Diffraction 3.1 Introduction / 31 3.2 Phase Difference and Bragg’s Law / 33 3.3 The Scattering Problem / 37 3.3.1 Coherent Scattering from an Electron / 38 3.3.2 Coherent Scattering from an Atom / 40 3.3.3 Coherent Scattering from a Unit Cell / 40 3.3.4 Structure Factor Calculations / 43 3.4 Reciprocal Space, RESP / 45 3.4.1 Why Reciprocal Space? / 45 3.4.2 Definition of RESP / 46 3.4.3 Definition of Reciprocal Lattice Vector / 48 3.4.4 The Ewald Construction / 50 3.5 Diffraction Techniques / 53 3.5.1 Rotating Crystal Method / 53 3.5.2 Powder Method / 53 3.5.3 Laue Method / 55 3.6 Wave Vector Representation / 55 31 Related Reading / 58 Exercises / 58 Defects in Solids 4.1 Introduction / 61 4.2 Why Do Defects Form? / 62 4.2.1 Review of Some Thermodynamics Ideas / 62 4.3 Point Defects / 66 4.4 The Statistics of Point Defects / 67 4.5 Line Defects—Dislocations / 71 4.5.1 Edge Dislocations / 73 4.5.2 Screw Dislocations / 74 4.5.3 Burger’s Vector and the Burger Circuit / 76 4.5.4 Dislocation Motion / 77 61 CONTENTS 4.6 Planar Defects / 77 4.6.1 Grain Boundaries / 77 4.6.2 Twin Boundaries / 78 4.7 Three-Dimensional Defects / 79 vii Related Reading / 79 Exercises / 80 Diffusion in Solids 5.1 Introduction to Diffusion Equations / 81 5.2 Atomistic Theory of Diffusion: Fick’s Laws and a Theory for the Diffussion Construct D / 83 5.3 Random Walk Problem / 87 5.3.1 Random Walk Calculations / 89 5.3.2 Relation of D to Random Walk / 89 5.3.3 Self-Diffusion Vacancy Mechanism in a FCC Crystal / 90 5.3.4 Activation Energy for Diffusion / 91 5.4 Other Mass Transport Mechanisms / 91 5.4.1 Permeability versus Diffusion / 91 5.4.2 Convection versus Diffusion / 94 5.5 Mathematics of Diffusion / 94 5.5.1 Steady State Diffusion—Fick’s First Law / 95 5.5.2 Non–Steady State Diffusion—Fick’s Second Law / 97 81 Related Reading / 108 Exercises / 108 Phase Equilibria 6.1 Introduction / 111 6.2 The Gibbs Phase Rule / 111 6.2.1 Definitions / 111 6.2.2 Equilibrium Among Phases—The Phase Rule / 113 6.2.3 Applications of the Phase Rule / 115 6.2.4 Construction of Phase Diagrams: Theory and Experiment / 116 6.2.5 The Tie Line Principle / 120 6.2.6 The Lever Rule / 121 6.2.7 Examples of Phase Equilibria / 125 6.3 Nucleation and Growth of Phases / 130 6.3.1 Thermodynamics of Phase Transformations / 130 6.3.2 Nucleation / 133 Related Reading / 137 Exercises / 138 111 viii CONTENTS Mechanical Properties of Solids—Elasticity 7.1 Introduction / 139 7.2 Elasticity Relationships / 141 7.2.1 True versus Engineering Strain / 143 7.2.2 Nature of Elasticity and Young’s Modulus / 144 7.3 An Analysis of Stress by the Equation of Motion / 147 7.4 Hooke’s Law for Pure Dilatation and Pure Shear / 150 7.5 Poisson’s Ratio / 151 7.6 Relationships Among E, e, and v / 151 7.7 Relationships Among E, G, and n / 153 7.8 Resolving the Normal Forces / 156 139 Related Reading / 157 Exercises / 158 Mechanical Properties of Solids—Plasticity 8.1 Introduction / 161 8.2 Plasticity Observations / 161 8.3 Role of Dislocations / 163 8.4 Deformation of Noncrystalline Materials / 175 8.4.1 Thermal Behavior of Amorphous Solids / 175 8.4.2 Time-Dependent Deformation of Amorphous Materials / 177 8.4.3 Models for Network Solids / 179 8.4.4 Elastomers / 183 161 Related Reading / 186 Exercises / 186 Electronic Structure of Solids 9.1 Introduction / 187 9.2 Waves, Electrons, and the Wave Function / 187 9.2.1 Representation of Waves / 187 9.2.2 Matter Waves / 189 9.2.3 Superposition / 190 9.2.4 Electron Waves / 195 9.3 Quantum Mechanics / 196 9.3.1 Normalization / 197 9.3.2 Dispersion of Electron Waves and the SE / 197 9.3.3 Classical and QM Wave Equations / 199 9.3.4 Solutions to the SE / 200 187 www.elsolucionario.org 292 JUNCTIONS AND DEVICES AND THE NANOSCALE or high stresses lead to interfacial defects, the resulting quantum well devices will not be operable One of the most important materials systems for fabricating quantum wells is GaAs as the narrow gap material (Eg = 1.4 eV, ao = 0.565 nm) and GaxAlyAs with a larger band gap (AlAs = 2.4 eV, ao = 0.566 nm) So the GaAlAs alloy has a gap somewhere in between 1.4 and 2.4, depending on the values for x and y The junction resulting from these two dissimilar materials is called a heterojunction, and this term indicates different materials across the junction Later for optical device fabrication it will be useful to use x = 0.7, y = 0.3, since this alloy has the largest GaAlAs gap (2 eV) and can effect quantum confinement while retaining a direct gap band structure that is useful for optical devices, as was mentioned in Chapter 9, Section 9.5 Figure 11.20a shows a quantum well formed using GaAs as the narrow gap material (Eg = 1.4 eV) and GaxAlyAs (2 eV) Figure 11.20b shows separated semiconductors corresponding to narrow and wide gap materials When these materials are joined as in Figure 11.20a, the result is shown in Figure 11.20c where the dissimilar band gaps lead to the band offsets, DEc (barrier for electrons) and DEv (barrier for holes) The offsets result when the Fermi levels equilibrate, as was discussed earlier in Chapter 11 If the original values of EF for the materials are close, then there is little band banding, and the ideal quantum well structure depicted can be approximated The actual energy levels are determined by the size of the well (l) and the offsets (the strength of the confinement) The quantum well structure is fabricated from three layers in a sandwich structure Modern film making techniques such as molecular beam epitaxy (MBE) usually use atomic beams to form elemental or compound layers on a substrate Different layers can be produced with different atoms or the same atoms in differing proportions (alloys), and the layers can be repeated In effect different alternating nanometer thick layers can be alternated virtually indefinitely Such an array of repeating quantum wells is called a superlattice, and the superlattice structure can be used in many device applications MBE systems are operated in ultra-high vacuum systems and are therefore large, complicated, expensive, and time-consuming to keep in operation However, a variety of high-quality MBE systems are commercially available and extensively used in the scientific and engineering areas of electronic materials One important application of the superlattice is to enhance the performance of photodetectors Recall Section 11.3.2.2 above and Figure 11.13 which shows that a photocell is a PN junction in which an incident photon creates electron hole pairs that are separated across the depletion width of the junction The current flow derives from the carriers that are essentially produced by absorption of the incident light A photodetector is the same kind of device, but it is used to sense light and measure its intensity, rather then produce a usable current or potential Figure 11.21a shows a superlattice structure comprised of multiple quantum wells that were shown in Figure 11.20c Figure 11.21b shows the multiple quantum well structure inserted in between a P and N semiconductor, and with an external electric field applied From this figure it is seen that photoinduced carriers generated as a result of light incident on the device can gain sufficient energy from the applied field to overcome the barriers (DEc the barrier for electrons and DEv the barrier for holes) between quantum wells The accelerated carriers can create additional carriers by impact ionization Impact ionization is the process by which carriers are produced from the energetic collisions of already produced carriers This creates an avalanche effect that enhances the original signal from the original photoproduced carriers The photocell enhanced by the impact ionization via the superlattice is called an avalanche photocell (or photodiode) By judicious choice of the materials that com- 11.4 NANOSTRUCTURES AND NANODEVICES 293 a) b) e P - } DE c } h + DE v N Figure 11.21 (a) Multiple quantum wells forming a superlattice; (b) the superlattice in (a) with an applied forward bias The band offsets and direction for electron and hole motion are indicated prise the superlattice junctions, the band offset values, DEc and DEv, can be engineered so that one carrier amplifies via avalanche at a greater rate than the other thereby improving the signal to noise ratio of the device Also, with the proper values of the applied field and sufficiently thin quantum (