Angus Rockett The materials Science of Semiconductors 2 Springer
The Materials Science of semiconductors
The Materials Science of Semiconductors
Angus rockett The Materials science of semiconductors Springer
Angus Rockett The Materials Science of Semiconductors
Angus Rockett University of Illinois 201a Materials Science and Engineering Building 1304 West Green Street Urbana IL 61801 Library of Congress Control Number. 2007932591 ISBN978-0-387-25653-5 e-lSBN978-0-387-68650-9 Printed on acid-free paper. All rights reserved. This work may not be translated or copied in whole or in part without the written onnection with any form of information storage and retrieval, electronic adaptation, computer software, publication of trade names, trademarks, service marks and similar terms, even if they are not identified as h, is not to be taken expression of opinion as to whether or not they are subject to proprietary 987654321
Angus Rockett University of Illinois 201a Materials Science and Engineering Building 1304 West Green Street Urbana, IL 61801 USA ISBN 978-0-387-25653-5 e-ISBN 978-0-387-68650-9 Printed on acid-free paper. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com Library of Congress Control Number: 2007932591 © 2008 Springer Science+Business Media, LLC
Dedication To my parents, for thei To my family for their love an questions, and of course, their enthusiasm
Dedication To my parents, for their teaching, To my family for their love and encouragement, and to the students in my class for their suggestions, comments questions, and of course, their enthusiasm
PREFACE OBJECTIVES The primary purpose of this book is to convey insight into why semiconductors are the way they are, either because of how their atoms bond with one another, because of mistakes in their structure, or because of how they are produced or processed he approach is to explore both the science of how atoms interact and to connect the results to real materials properties, and to show the engineering concepts that can be used to produce or improve a semiconductor by design. Along with this I hope how some applications for the topics under discussion so that one may see how the concepts are applied in the laboratory The intended audience of this book is senior undergraduate students and graduate students early in their careers or with limited background in the subject. I intend this book to be equally useful to those teaching in electrical engineering, materials science, or even chemical engineering or physics curricula, although the book is written for a materials science audience primarily. To try to maintain the focus on materials concepts the details of many of the derivations and equations are left out of he book. Likewise I have not delved into the details of electrical engineering topics in as much detail as an electrical engineer might wish. It is assumed that students are familiar with these topics from earlier course The core prerequisite subjects assumed for use of this book are basic chemistry physics, and electrical circuits. The most essential topics from an intermediate level in these subjects are reviewed. Students taking my class are assumed to have had a condensed matter physics course and a semiconductor device theory course with significantly more detail than is covered in Chapters 2 and 3. Furthermore they are assumed to have had some organic chemistry(at least at the Freshman undergraduate level)and general materials science courses with significantly more information than provide in the review in Chapter 4. In spite of these expectations my audience usually includes graduate students lacking background in at least one of these topics to the material in this book includes more than 25 years ductor materials science and processing. My primary research over the past 18 years has concerned the fundamental materials science of the semiconductor CulnSe2 and related compounds. This material is a fascinating study in all of the topics of materials science rolled into a single field. As such, the results appear from time to time in the book as illustrations. Given rising concems about energy world wide, the book also makes reference to solar cells, properly
PREFACE OBJECTIVES The primary purpose of this book is to convey insight into why semiconductors are the way they are, either because of how their atoms bond with one another, because of mistakes in their structure, or because of how they are produced or processed. The approach is to explore both the science of how atoms interact and to connect the results to real materials properties, and to show the engineering concepts that can be used to produce or improve a semiconductor by design. Along with this I hope to show some applications for the topics under discussion so that one may see how the concepts are applied in the laboratory. The intended audience of this book is senior undergraduate students and graduate students early in their careers or with limited background in the subject. I intend this book to be equally useful to those teaching in electrical engineering, materials science, or even chemical engineering or physics curricula, although the book is written for a materials science audience primarily. To try to maintain the focus on materials concepts the details of many of the derivations and equations are left out of the book. Likewise I have not delved into the details of electrical engineering topics in as much detail as an electrical engineer might wish. It is assumed that students are familiar with these topics from earlier courses. The core prerequisite subjects assumed for use of this book are basic chemistry, physics, and electrical circuits. The most essential topics from an intermediate level in these subjects are reviewed. Students taking my class are assumed to have had a condensed matter physics course and a semiconductor device theory course with significantly more detail than is covered in Chapters 2 and 3. Furthermore they are assumed to have had some organic chemistry (at least at the Freshman undergraduate level) and general materials science courses with significantly more information than I provide in the review in Chapter 4. In spite of these expectations my audience usually includes graduate students lacking background in at least one of these topics. My background that applies to the material in this book includes more than 25 years doing research in semiconductor materials science and processing. My primary research over the past 18 years has concerned the fundamental materials science of the semiconductor CuInSe2 and related compounds. This material is a fascinating study in all of the topics of materials science rolled into a single field. As such, the results appear from time to time in the book as illustrations. Given rising concerns about energy world wide, the book also makes reference to solar cells, properly
Preface known as photovoltaic devices, in several application sections. This also reflects my long study of that field TOPICS AND USE OF THE BOOK I have taught a class based on the material that is presented in this book for many years. I get through most of the topics, excluding detailed discussions of the applications, in one semester. Each chapter typically gets about three hours of lecture, although Chapters 6, 7, 9, and 12 often receive four to five lectures and Chapter I gets one hour. My students have generally been a mixture of senior undergraduate and graduate students. One of the common features of these students is that many, especially the graduate students, lack a strong background in some one of the underlying prerequisite subjects such as condensed matter physics, principles of electronic devices. or materials science. Therefore the book includes a brief review of these topics in Chapters 2-4 and I cover these subjects very quickly in the class. Even for the students with a background in all of these areas I usually find it helpful to review selected topics from these chapters. In presenting review topics I ope that the book can be useful to a student body that completely lacks a detailed background if the instructor is willing to go through this material One of the challenges in writing the book is that its intended audience does not have nuch background in quantum mechanics. Therefore, I cannot practically go into details about how the wave function interactions in Chapter 5 are calculated that lead to the matrix element values in the lCAo matrix(or into details of corrections to the lCao that are used in real calculations today. I have attempted to present the material in such a way that a student without this background can understand the important take-home messages of the subject even if they are unfamiliar with how the values are derived Of course, if one is doing tight binding theory these matrix elements may be considered fitting parameters, so what I am doing in Chapter 5 is not so much less sophisticated than tight binding theory anyway. One may also note that I have taken two approaches to the question of how atomic orbitals contribute to miconductor band structures in Chapter 5, one almost purely visual the Harrison diagram approach-and one semiquantitative, covering the basic approach of lCAo theory. Hence, hopefully the student will have different ways of remembering the lationships among orbitals, bonds, and bands. It is useful when covering the Aterial to also make connections to the material in Chapter 2 on nearly free electron Chapters 6 and 7 are the core of the materials science in the book. They talk about how to engineer a semiconductor material to achieve given properties through modification of its structure and chemistry. Hence, they spend a considerable time on defects and how and why they form. Most of the preceding chapters are building up to these two in hopes that when the student gets here they will say to themselves"of course it should work this way, considering how the atoms are changing and how forming
viii known as photovoltaic devices, in several application sections. This also reflects my long study of that field. TOPICS AND USE OF THE BOOK I have taught a class based on the material that is presented in this book for many years. I get through most of the topics, excluding detailed discussions of the applications, in one semester. Each chapter typically gets about three hours of lecture, although Chapters 6, 7, 9, and 12 often receive four to five lectures and Chapter 1 gets one hour. My students have generally been a mixture of senior undergraduate and graduate students. One of the common features of these students is that many, especially the graduate students, lack a strong background in some one of the underlying prerequisite subjects such as condensed matter physics, principles of electronic devices, or materials science. Therefore the book includes a brief review of these topics in Chapters 2-4 and I cover these subjects very quickly in the class. Even for the students with a background in all of these areas I usually find it helpful to review selected topics from these chapters. In presenting review topics I hope that the book can be useful to a student body that completely lacks a detailed background if the instructor is willing to go through this material. One of the challenges in writing the book is that its intended audience does not have much background in quantum mechanics. Therefore, I cannot practically go into details about how the wave function interactions in Chapter 5 are calculated that lead to the matrix element values in the LCAO matrix (or into details of corrections to the LCAO that are used in real calculations today. I have attempted to present the material in such a way that a student without this background can understand the important take-home messages of the subject even if they are unfamiliar with how the values are derived. Of course, if one is doing tight binding theory these matrix elements may be considered fitting parameters, so what I am doing in Chapter 5 is not so much less sophisticated than tight binding theory anyway. One may also note that I have taken two approaches to the question of how atomic orbitals contribute to semiconductor band structures in Chapter 5, one almost purely visual – the Harrison diagram approach – and one semiquantitative, covering the basic approach of LCAO theory. Hence, hopefully the student will have different ways of remembering the relationships among orbitals, bonds, and bands. It is useful when covering the material to also make connections to the material in Chapter 2 on nearly free electron behaviors. Chapters 6 and 7 are the core of the materials science in the book. They talk about how to engineer a semiconductor material to achieve given properties through modification of its structure and chemistry. Hence, they spend a considerable time on defects and how and why they form. Most of the preceding chapters are building up to these two in hopes that when the student gets here they will say to themselves “of course it should work this way, considering how the atoms are changing and how the bonds are forming.” Preface
Preface Chapters 8 and 9 cover less commonly applied materials of great value and interest in applications. Especially in the case of Chapter 9 the organic materials appear ikely to increase greatly in range of application in the near future. Amorphous inorganic materials described in Chapter 8 are valueable to understand and preview of what one might expect for the organics in some respects. Many of the issues such as Coulomb blockades at contacts are the same Finally Chapters 10-12 cover some of the major methods of processing thin films When I teach this class this material is covered between the material in Chapter 4 and the material in Chapter 5 but it could just as well be covered last. I put it in the middle because it provides a change of pace in the type of discussion I am presenting. When I was first developing this course together with a second course on dielectrics, metalizations, and other materials and processes used above the semi- conductor surface I tried to separate the course into a materials course and a process- ing course. This did not work well because the two subjects are so heavily intertwined It is hard to see why there would be problems in the materials without understanding heir processing but it is equally hard to see why one should bother with complex processes unless one has an idea of how the material one is producing responds to defects. Likewise, it is difficult to see why a non-equilibrium process such as evaporation should be important to deposition of an alloy unless one sees how phase separation and defects affect the alloy property Of course the biggest problem with writing a book of this type is that the field, especially the organic materials topics, are progressing so rapidly that the book will be somewhat obsolete as soon as it is in print. To improve the longevity of the material covered I have attempted to stick with fundamental concepts and not deal with what I perceive to be passing fads. With luck I will have reason to add some of ACKNOWLEDGEMENTS I wish to thank the many students who have suffered through the use of this book in draft form in my class and for all of their input. It has been an invaluable help. I also wish to thank the various colleages whose work I use to illustrate concepts in the book and whose contributions have been some of the most important in the fie I have tried to recognize them by name in the presentation of their figures. Finall I wish to thank the staff at Kluwer who have been so patient. I hope their long wait pays off. University of Illinois, 2007
ix Chapters 8 and 9 cover less commonly applied materials of great value and interest in applications. Especially in the case of Chapter 9 the organic materials appear likely to increase greatly in range of application in the near future. Amorphous inorganic materials described in Chapter 8 are valueable to understand and preview of what one might expect for the organics in some respects. Many of the issues such as Coulomb blockades at contacts are the same. Finally Chapters 10-12 cover some of the major methods of processing thin films. When I teach this class this material is covered between the material in Chapter 4 and the material in Chapter 5 but it could just as well be covered last. I put it in the middle because it provides a change of pace in the type of discussion I am presenting. When I was first developing this course together with a second course on dielectrics, metalizations, and other materials and processes used above the semiconductor surface I tried to separate the course into a materials course and a processing course. This did not work well because the two subjects are so heavily intertwined. It is hard to see why there would be problems in the materials without understanding their processing but it is equally hard to see why one should bother with complex processes unless one has an idea of how the material one is producing responds to defects. Likewise, it is difficult to see why a non-equilibrium process such as evaporation should be important to deposition of an alloy unless one sees how phase separation and defects affect the alloy property. Of course the biggest problem with writing a book of this type is that the field, especially the organic materials topics, are progressing so rapidly that the book will be somewhat obsolete as soon as it is in print. To improve the longevity of the material covered I have attempted to stick with fundamental concepts and not deal with what I perceive to be passing fads. With luck I will have reason to add some of these topics to future editions. ACKNOWLEDGEMENTS I wish to thank the many students who have suffered through the use of this book in draft form in my class and for all of their input. It has been an invaluable help. I also wish to thank the various colleages whose work I use to illustrate concepts in the book and whose contributions have been some of the most important in the field. I have tried to recognize them by name in the presentation of their figures. Finally, I wish to thank the staff at Kluwer who have been so patient. I hope their long wait pays off. Angus Rockett Preface University of Illinois, 2007
TABLE OF CONTENTS PREFACE Objectives Topics and use of the book 1. AN ENVIRONMENT OF CHALLENGES I Overview 1.2 A history of modern electronic devices 1. 3 An issue of scale 1.4 Defining electronic materials 112713 1.5 Purity 1.6 Performance 1.7 Summary poin 8 Homework problems 1.9 Suggested readings references 2. THE PHYSICS OF SOLIDS 21 2.1 Electronic band structures of solids 2.1.1 Free electrons in solid 23 2.1.2 Free electrons in a periodic potential 2.1.3 Nearly free electrons 2.1.4 Energy vs. momentum in 3d 2.1.5 Electrons and holes 32 2.1.6 Direct and indirect semiconductors 2.1.7 Effective mass 2.1.8 Density of states 2.2 Intrinsic and extrinsic semiconductors 2.2.1 Intrinsic semiconductors 2.2.2 Extrinsic semiconductors 2.3 Properties and the band structure 2.3.1 Resistance, capacitance, and inductance 2.3.2 Optical properties 02443 2.3.3 Thermal properties 2. 4 Quantum wells and confined carriers
TABLE OF CONTENTS PREFACE VII Objectives ...............................................................................................................vii Topics and use of the book ................................................................................... viii Acknowledgements..................................................................................................ix 1 1.1 Overview ...........................................................................................................1 1.2 A history of modern electronic devices.............................................................2 1.3 An issue of scale................................................................................................7 1.4 Defining electronic materials ..........................................................................11 1.5 Purity................................................................................................................13 1.6 Performance.....................................................................................................14 1.7 Summary points...............................................................................................17 1.8 Homework problems .......................................................................................18 1.9 Suggested readings & references.....................................................................19 21 2.1 Electronic band structures of solids.................................................................21 2.1.1 Free electrons in solids..........................................................................23 2.1.2 Free electrons in a periodic potential ....................................................24 2.1.3 Nearly free electrons .............................................................................25 2.1.4 Energy vs. momentum in 3d .................................................................28 2.1.5 Electrons and holes ...............................................................................32 2.1.6 Direct and indirect semiconductors.......................................................35 2.1.7 Effective mass .......................................................................................37 2.1.8 Density of states ....................................................................................38 2.2 Intrinsic and extrinsic semiconductors ............................................................40 2.2.1 Intrinsic semiconductors .......................................................................40 2.2.2 Extrinsic semiconductors ......................................................................42 2.3 Properties and the band structure ....................................................................44 2.3.1 Resistance, capacitance, and inductance...............................................44 2.3.2 Optical properties ..................................................................................53 2.4 Quantum wells and confined carriers..............................................................59 2.3.3 Thermal properties ................................................................................54 1. AN ENVIRONMENT OF CHALLENGES 2. THE PHYSICS OF SOLIDS
Table of contents 2.5 Summary points 2.6 Homework 2. 7 Suggested readings references 3. OVERVIEW OF ELECTRONIC DEVICES 3.1 Diffusion and drift of carriers 3. 1.1 Chemical potential 3.1.2 Carrier motion in a chemical potential gra 3.2 Simple diodes 444万7 3.2. 1 The junction contact potential 3.2.2 Biased junctions 3.2.3 Non-ideal diode behaviors 3 Schottky barriers and ohmic contacts 3.3.1 Ideal metal/semiconductor junctions 3.3.2 Real schottky diode 3.4 Semiconductor heterojunctions 3.4. 1 Heterojunctions at equilibrium 3.4.2 Heterojunctions as diodes 109 3.5 Transistors l11 3.5.2 Field-effect transistors 3.6 Light-emitting devices 119 3.6.1 Light-emitting diodes 3.6.2 Laser diodes 124 3.7S 3.8 Homework problems 3.9 Suggested readings references. 4. ASPECTS OF MATERIALS SCIENCE 141 4.1 Structures of materials 4. 1. 1 Crystal lattices 4.1.2 The reciprocal lattice 4.2 Basic thermodynamics of materials 4.3 Phase diagrams 4.4 Kinetics 4 4.1 Reaction kinetics 4.4.2 Nucleation 4.4.3 Atomic transport. 4.5 Organic molecules 4.6 Applications 4.6.1 A basis for phase transformations 178
73 3.1 Diffusion and drift of carriers..........................................................................74 3.1.1 Chemical potential ................................................................................74 3.1.2 Carrier motion in a chemical potential gradient....................................74 3.2 Simple diodes ..................................................................................................75 3.2.1 The junction contact potential...............................................................77 3.2.2 Biased junctions ....................................................................................81 3.3 Schottky barriers and ohmic contacts..............................................................96 3.3.1 Ideal metal/semiconductor junctions ....................................................96 3.3.2 Real schottky diodes ...........................................................................101 3.4 Semiconductor heterojunctions .....................................................................102 3.4.1 Heterojunctions at equilibrium............................................................103 3.4.2 Heterojunctions as diodes ...................................................................109 3.5 Transistors .....................................................................................................111 3.5.1 Bipolar junction transistors .................................................................111 3.5.2 Field-effect transistors.........................................................................114 3.6 Light-emitting devices...................................................................................119 3.6.1 Light-emitting diodes..........................................................................120 3.6.2 Laser diodes.........................................................................................124 3.7 Summary........................................................................................................134 3.8 Homework problems .....................................................................................136 3.9 Suggested readings & references...................................................................139 141 4.1 Structures of materials...................................................................................141 4.1.1 Crystal lattices.....................................................................................142 4.2 Basic thermodynamics of materials...............................................................151 4.3 Phase diagrams ..............................................................................................155 4.4 Kinetics..........................................................................................................163 4.4.1 Reaction kinetics .................................................................................164 4.4.2 Nucleation ...........................................................................................166 4.4.3 Atomic transport..................................................................................170 4.5 Organic molecules .........................................................................................172 4.6 Applications...................................................................................................178 4.6.1 A basis for phase transformations.......................................................178 xii Table of Contents 2.5 Summary points...............................................................................................67 2.6 Homework .......................................................................................................69 2.7 Suggested readings & references.....................................................................71 3. OVERVIEW OF ELECTRONIC DEVICES 3.2.3 Non-ideal diode behaviors ....................................................................88 4. ASPECTS OF MATERIALS SCIENCE 4.1.2 The reciprocal lattice...........................................................................148
