Albrecht Winnacker The Physics Behind Semiconductor Technology The Physics Behind Semiconductor Technology Albrecht Winnacker The Physics Behind Semiconductor Technology Albrecht Winnacker Centre for Advanced Materials Heidelberg University Heidelberg, Germany Institute Materials for Electronics and Energy Technology University of Erlangen-Nuernberg Erlangen, Germany ISBN 978-3-031-10313-1 ISBN 978-3-031-10314-8 (eBook) https://doi.org/10.1007/978-3-031-10314-8 © Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface This book goes back to a two-semester lecture given at the University of Heidelberg for master’s and advanced bachelor’s students of physics, and it summarizes many aspects of a lecture given to students at the Engineering faculty of the University of Erlangen specializing in the fields of electrical engineering and electronic materials. This dual origin of the book reflects the fact that on the one hand semiconductor technology is certainly an outstanding application of solid state physics, and on the other hand it represents an important sector of materials science and engineering, dealing with processes and devices based on semiconductor materials. So, having a foothold in one of the basic fields of physics, and another one in the engineering fields of materials science and electronics, it operates at the interface between pure and applied science. The distinction made between these two manifestations of science, sometimes resulting in controversial assessments of their respective merits, often overlooks the close interrelation between the two. Basic facts and discoveries of pure science regularly have resulted in technical achievements of high relevance. On the other hand, new technical tools or experimental observations have provided the key to fundamental scientific insights, and technical challenges have initiated basic understanding. So the distinction between pure and applied science is not so much a matter of the objects and topics under consideration, but, as it seems, one of the meanings of “understanding”. Pure science in general and pure physics in particular aim at realizing the complex interplay between cause and effect, while application and engineering rather aim at ensuring “function”, taking care of reliability and yield of technical processes. This textbook somehow has in mind to bridge that gap. Whenever dealing with basic technological processes and facts like the doping of semiconductors, lattice defects, or the field effect transistor, it includes considerations and statements on the underlying basic physical principles in the form of “physics comments”. When dealing with fundamental physics like dispersion relations, carrier statistics, or the two-dimensional electron gas, it immediately includes their most practical consequences like the indirect or direct nature of semiconductors, the question of high-temperature electronics, or the definition of the unit Ohm. v vi Preface In this way, it may help engineering students to get an insight into the basic, sometimes profound, character of the underlying physics, and to help the student of physics to get an impression of the sophistication of engineering and fabrication with their requirements on perfection and reliability. The book is divided into two parts, the first one dealing essentially with materials, their structure, and their function. The second part deals with “devices”, making use of the structure and function of the materials and components. So, in summary, this is not a book on the latest achievements of electronics (in spite of often referring to them); it is a book on “understanding”, in the sense given above, in the sense of physics, and in the sense of engineering. In this way, it may promote mutual respect between the two disciplines. I am deeply grateful to my wife Eva for her continuous support and patience. Heidelberg, Erlangen, Germany Albrecht Winnacker September 2022 Contents Part I Semiconductor Materials: Structure, Processes, Fabrication 1 Crystal Structure and Energy Bands ............................ 3 1.1 The Lattice Structure .................................... 3 1.2 Energy Bands ........................................... 6 1.3 Metals and Insulators .................................... 8 1.4 Electrons and Holes ..................................... 9 1.5 The Origin of Energy Bands according to the Schroedinger Equation ............................................... 10 1.6 Band Structure .......................................... 12 1.7 Direct and Indirect Semiconductors ........................ 17 1.8 Basic Properties of a Semiconductor Material to Be Taken from the Band Structure .................................. 19 1.9 Questions and Answers .................................. 23 2 Transport of Charge Carriers .................................. 25 2.1 Ohm’s Law ............................................. 25 2.2 Mobility and Hall Effect ................................. 30 2.3 Factors Determining the Mobility of Charge Carriers ......... 33 2.4 Saturation Velocity ...................................... 35 2.5 Mobility and Frequency Limit of Devices ................... 35 References .................................................... 37 3 Donors and Acceptors ......................................... 39 3.1 Creation of Free Electrons and Holes by Thermal Excitation .............................................. 39 3.2 Doping of Si ............................................ 41 3.3 The Hydrogen Model of Donors and Acceptors .............. 43 vii viii Contents 3.4 Shallow Donors and Acceptors in Compound Semiconductors ......................................... 46 3.5 Isoelectronic Impurities .................................. 47 3.6 Questions and Answers .................................. 49 4 Carrier Statistics .............................................. 51 4.1 Density of States ........................................ 51 4.2 Free Carrier Concentration in Thermal Equilibrium .......... 53 4.3 The Law of Mass Action ................................. 57 4.4 The Intrinsic Case ....................................... 57 4.5 Semi-insulating Semiconductors ........................... 61 4.6 The Temperature Dependence of Carrier Concentration. Why Si-Electronics Does not Work at Elevated Temperatures ........................................... 64 4.7 Questions and Answers .................................. 67 5 Fabrication of Electronic Silicon ................................ 69 5.1 Silicon Valley, Si-Technology, and Si-Age .................. 69 5.2 The Siemens Process .................................... 70 5.3 Crystal Growth of Silicon ................................ 73 5.4 The Float Zone Process as a Purification Method ............ 75 5.5 Wafering ............................................... 75 5.6 Electronic Silicon, a Material of Extreme Purity and Crystalline Perfection ................................ 77 5.7 Questions and Answers .................................. 79 6 Lattice Defects ................................................ 81 6.1 Intrinsic and Extrinsic Defects ............................ 81 6.2 Point Defects ........................................... 82 6.3 Line Defects (Dislocations) ............................... 85 6.4 The Role of Dislocations in Electronic Materials ............. 86 6.5 Two-Dimensional Defects ................................ 88 6.6 Three-Dimensional Defects ............................... 89 6.7 Questions and Answers .................................. 94 References .................................................... 94 7 Compound Semiconductors .................................... 95 7.1 Introduction, Some History ............................... 95 7.2 The Potential of III-V-Compounds ......................... 99 7.3 Growth of GaAs and InP by the LEC and VGF Process ....... 102 7.4 “New” Compound Semiconductors: SiC, AlN, and GaN ...... 104 7.5 Epitaxy ................................................ 108 7.6 Questions and Answers .................................. 112 References .................................................... 113 Contents ix 8 Amorphous Semiconductors ................................... 115 8.1 Short-Range Order and Band Structure ..................... 115 8.2 On the Distinction Between Direct and Indirect Semiconductors in Amorphous Semiconductors ............. 119 8.3 Variable Range Hopping Conduction ....................... 121 8.4 The Problem of Doping in a-Si ............................ 122 8.5 Applications of a-Si:H ................................... 124 8.6 Questions and Answers .................................. 125 References .................................................... 126 Part II Devices 9 The pn-Junction .............................................. 129 9.1 pn-Junction Without External Voltage ...................... 129 9.2 pn-Junction with External Voltage ......................... 134 9.3 Breakthrough Voltage .................................... 139 9.4 Thickness of Depletion Layers ............................ 140 9.5 Questions and Answers .................................. 140 10 Solar Cells .................................................... 143 10.1 The Sun, a Gigantic Energy Source ........................ 143 10.2 The Solar Cell, a pn-Junction Device ....................... 144 10.3 Operating Principle of the Solar Cell in Detail ............... 148 10.4 The Optimum Bandgap for a Solar Cell Material ............. 151 10.5 Thin Film Solar Cells .................................... 153 10.6 Cheaper Silicon for Photovoltaics .......................... 154 10.7 Questions and Answers .................................. 157 References .................................................... 158 11 Light Emitting Diodes (LEDs) .................................. 159 11.1 The Light Emitting Process in Semiconductors .............. 159 11.2 The Linewidth of LEDs .................................. 161 11.3 Radiative and Nonradiative Processes ...................... 163 11.4 External and Internal Quantum Efficiency ................... 165 11.5 LEDs for All Colors ..................................... 166 11.6 The Story of the Blue LED ............................... 168 11.7 White LEDs ............................................ 170 11.8 UV LEDs .............................................. 172 11.9 Brightness of LEDs ...................................... 173 11.10 Questions and Answers .................................. 177 References .................................................... 178 x Contents 12 Semiconductor Lasers ......................................... 179 12.1 The Laser Principle ...................................... 179 12.2 Light Amplification and Lasing ........................... 185 12.3 Double Heterojunction Laser ............................. 189 12.4 Lasers for Optical Data Storage and Optical Data Transmission ........................................... 192 12.5 Laser Materials for Optical Data Transmission, an Example of Bandgap Engineering ....................... 194 12.6 Questions and Answers .................................. 197 References .................................................... 198 13 Transistors ................................................... 199 13.1 The Bipolar Transistor ................................... 200 13.2 Field Effect Transistor ................................... 204 13.3 A MOSFET Problem Related to Miniaturization of Modern Electronics: High k-dielectrics ................... 211 13.4 The Two-Dimensional Electron Gas, Realized inaMOSFET .......................................... 214 13.5 Questions and Answers .................................. 219 Reference ..................................................... 220 14 Integrated Circuits ............................................ 221 14.1 Moore’s Law ........................................... 221 14.2 Photolithography: Components and Steps of Fabrication ...... 223 14.3 Exposure in the Photolithography .......................... 227 14.4 Some Important Constituents of Integrated Circuits .......... 228 14.5 Light Sources for Photolithography ........................ 230 14.6 Resolution Enhancement Techniques ....................... 234 14.7 Some Concluding Remarks on the Present Situation of Chip Technology ..................................... 235 14.8 Questions and Answers .................................. 236 References .................................................... 237 15 Organic Electronics ........................................... 239 15.1 Organic Materials for Electronics, a Totally Different Approach .............................................. 239 15.2 Conjugated Double Bonds ................................ 240 15.3 Band Structure and Conductivity in Polymers ............... 241 15.4 Polymer Conductivity by “Doping” ........................ 243 15.5 Conductivity of Polymers by Charge Carrier Injection ........ 246 15.6 Charge Carrier Transport ................................. 247 15.7 Organic Light-Emitting Diodes (OLEDs) ................... 248 15.8 Organic Solar Cells ...................................... 255 15.9 Questions and Answers .................................. 257 References .................................................... 259