Solid State Physics
An Introduction
Third Edition
Philip Hofmann
Author
Prof. Philip Hofmann Aarhus University Department of Physics and Astronomy Ny Munkegade 120 8000 Aarhus C Denmark
Solution manual for instructors available from www.wiley-vch.de/ISBN9783527414109
Cover Image: Band structure of aluminum determined by angle‐resolved photoemission spectroscopy. Data taken from Physical Review B 66, 245422 (2002).
All books published by WILEY‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, 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.
Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d‐nb.de>.
© 2022 WILEY‐VCH GmbH, Boschstraße 12, 69469 Weinheim, Germany
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 a 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.
Print ISBN: 978‐3‐527‐41410‐9 ePDF ISBN: 978‐3‐527‐83725‐0 ePub ISBN: 978‐3‐527‐83726‐7
Cover Design: FORMGEBER, Mannheim, Germany
Preface to the First Edition
This book emerged from a course on solid state physics for third‐year students of physics and nanoscience, but it should also be useful for students of related fields such as chemistry and engineering. The aim is to provide a bachelor‐level survey over the whole field without going into too much detail. With this in mind, a lot of emphasis is put on a didactic presentation and little on stringent mathematical derivations or completeness. For a more in‐depth treatment, the reader is referred to the many excellent advanced solid state physics books. A few are listed in the Appendix.
To follow this text, a basic university‐level physics course is required as well as some working knowledge of chemistry, quantum mechanics, and statistical physics. A course in classical electrodynamics is of advantage but not strictly necessary.
Some remarks on how to use this book: Every chapter is accompanied by a set of “discussion” questions and problems. The intention of the questions is to give the student a tool for testing his/her understanding of the subject. Some of the questions can only be answered with knowledge of later chapters. These are marked by an asterisk. Some of the problems are more of a challenge in that they are more difficult mathematically or conceptually or both. These problems are also marked by an asterisk. Not all the information necessary for solving the problems is given here. For standard data, for example, the density of gold or the atomic weight of copper, the reader is referred to the excellent resources available on the World Wide Web.
Finally, I would like to thank the people who have helped me with many discussions and suggestions. In particular, I would like to mention my colleagues Arne Nylandsted Larsen, Ivan Steensgaard, Maria Fuglsang Jensen, Justin Wells, and many others involved in teaching the course in Aarhus.
Preface to the Second Edition
The second edition of this book is slightly enlarged in some subject areas and improved throughout. The enlargement comprises subjects that turned out to be too essential to be missing, even in a basic introduction such as this one. One example is the tight‐binding model for electronic states in solids, which is now added in its simplest form. Other enlargements reflect recent developments in the field that should at least be mentioned in the text and explained on a very basic level, such as graphene and topological insulators.
I decided to support the first edition by online material for subjects that were either crucial for the understanding of this text but not familiar to all readers, or not central enough to be included in the book but still of interest. This turned out to be a good concept, and the new edition is therefore supported by an extended number of such notes; they are referred to in the text. The notes can be found on my website www.philiphofmann.net.
The didactic presentation has been improved, based on the experience of many people with the first edition. The most severe changes have been made in the chapter on magnetism but minor adjustments have been made throughout the book. In these changes, didactic presentation was given a higher priority than elegance or conformity to standard notation, for example, in the figures on Pauli paramagnetism or band ferromagnetism.
Every chapter now contains a “Further Reading” section at the end. Since these sections are supposed to be independent of each other, you will find that the same books are mentioned several times.
I thank the many students and instructors who participated in the last few years' Solid State Physics course at Aarhus University, as well as many colleagues for their criticism and suggestions. Special thanks go to NL architects for permitting me to use the flipper‐bridge picture in Figure 11.3, to Justin Wells for suggesting the analogy to the topological insulators, to James Kermode for Figure 3.7, and to Arne Nylandsted Larsen and Antonija Grubišić Čabo for advice on the sections on solar cells and magnetism, respectively.
Preface to the Third Edition
The third edition of this book introduces numerous improvements throughout the text, in particular in the description of covalent bonding in Chapter 2 and in the discussion of the Bloch theorem and the nearly‐free electron model in Chapter 6.
The most significant changes are related to the problem sections in each chapter. In addition to the “traditional” type of problems that require an analytical solution, I have now included a number of problems that need to be solved numerically. Their complexity varies from plotting a simple function to calculating the carrier densities in a semiconductor. By introducing this new type of problems I hope to strengthen the students' computational skills, to overcome the restriction of being able to calculate solely what can be approximated using a simple model, and to impart upon students the capability to “play” with model parameters in order to explore what might happen in different physical situations. Moreover, exercises such as 4.4 and 6.10 are intended to help students understand the way phonon dispersions or electronic states