Solid-State Physics
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Harald Ibach l Hans Lu th Solid-State Physics An Introduction to Principles of Materials Science Fourth Extensively Updated and Enlarged Edition With 286 Figures, 18 Panels and 104 Problems 13
Professor Dr. Harald Ibach Professor Dr. Dr. h.c. Hans Lu th Institut fu r Bio- und Nanosysteme Forschungszentrum Ju lich GmbH, 52425 Ju lich and Rheinisch-Westfälische Technische Hochschule 52062 Aachen, Germany e-mail: h.ibach@fz-juelich.de e-mail: h.lueth@fz-juelich.de Title of the German original edition: H. Ibach, H. Lu th: Festkörperphysik. Einfu hrung in die Grundlagen (Siebente Auflage) # Springer-Verlag Berlin Heidelberg 1981, 1988, 1990, 1995, 1999, 2002, 2009 ISBN 978-3-540-93803-3 e-isbn 978-3-540-93804-0 DOI 10.1007/978-3-540-93804-0 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009926968 # Springer-Verlag Berlin Heidelberg 1993, 1995, 2003, 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: estudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface to the Fourth Edition The Nobel Prize awarded to Albert Fert and our colleague Peter GruÈ nberg has drawn the attention to the remarkable progress that has been achieved in the field of magnetism concerning both its understanding and its applications. Adding a section on the giant magneto resistance (GMR) e ect was therefore necessary. As the GMR-e ect is observed in magnetic thin-film systems, it was natural to combine the treatise on the GMR-e ect with a brief summary of the specific magnetic properties of thin films; and we did so with a new panel. The wealth of phenomena encountered in thin-film magnetism is intimately related to the interplay of various sources of magnetic anisotropy. We therefore had to pay attention to the most common source of magnetic anisotropy, the crystalline anisotropy and to the phenomena that go along with it, such as magnetic hysteresis and domain walls. The GMR-e ect is only one of the many new e ects that one encounters when the dimensions of solids shrink into the nanometer range. For example, the semi-classical approach to electron transport fails in small dimensions, and normal electric current flow is replaced by ballistic or di usive transport giving rise to quantum e ects such as Aharonov-Bohm oscillations, Altshuler-Aronov-Spivak-oscillations, weak localization, and universal conductance fluctuations. A new section on quantum transport is devoted to these phenomena. One of the intellectually most appealing fields in the realm of dielectric properties of matter is that of materials with negative index of refraction. While no natural material with that property exists, composite materials involving lattices of electric and magnetic resonance circuits, so called metamaterials, have been made and exhibit most unusual optical properties. With further progress in the preparation of artificial structures of nanometer dimensions application of metamaterials for optics in the visual range is at hand. We have devoted a new panel to this exciting field. Here, as well as in nearly all other fields of current interest, progress largely depends on the progress in the preparation of nanostructures. We have included a new panel on various preparation techniques. We have also updated the panels on photoemission and neutron di raction. We gratefully acknowledge the many comments and suggestions by colleagues and students that have helped to improve this volume. JuÈ lich and Aachen, February 2009 H. Ibach. H. LuÈth
Preface to the Third Edition Our German textbook ``FestkoÈ rperphysik'' has meanwhile appeared in its 6 th edition, extensively revised and extended in comparison to the latest 2 nd English edition. Presently, the book has been translated into Japanese, Korean and Polish and is used as a standard text in many universities around the world. It is therefore high time to carefully revise the English text and bring it up to par with the latest 6 th German edition. The sections on ``High Temperature Superconductors'' as well as Panel XVI on ``Shubnikov-de Haas Oscillations and Quantum Hall E ect'' are completely revised according to the present deeper understanding of the phenomena. This 3 rd English edition has furthermore been expanded by several chapters to meet the educational requirements for recent fields of research. We let ourselves be guided by the idea that modern teaching of solid state physics emphasizes aspects of material science and its applications, in particular in solid state electronics. Accordingly, deviations from the ideal periodic solid have gained more weight in the text: we now consider phase diagrams of alloys, some basics of defect physics and amorphous solids. Because of the importance of strained layer systems in device physics, inclusion of the fundamentals of crystal elasticity theory seems (again) necessary, so a new chapter is devoted to this topic. The additional chapter on the excitation spectrum of a superconductor is intended to further the understanding of modern research on superconductor/normal conductor interfaces as well as on applications in superconductor electronics. For similar reasons, sections on the metal/semiconductor Schottky-contact and on the basic concepts of important semiconductor devices have been included in the new edition. With all of these additions we have tried to maintain the spirit of the book, namely to put the phenomena into a general frame of an atomistically founded understanding of solid state physics. We thank Dr. Klaus Dahmen, Dr. Arno FoÈ rster, Dr. Margret Giesen, Dr. Michel Marso, Prof. Dr. Angela Rizzi and Dr. Thomas SchaÈ pers for discussions on special topics and many suggestions for improving the presentation. We express our thanks to Dr. H. J. Koelsch, Dr. T. Schneider and Mr. C.-D. Bachem of Springer-Verlag for the pleasant collaboration. JuÈ lich and Aachen, January 2003 H. Ibach. H. LuÈth
Preface to the Second Edition Our German textbook ``FestkoÈrperphysik'' has become rather popular among German-speaking students, and is currently produced in its 4 th edition. Its English version has already been adopted by many universities in the United States and other countries. This new 2 nd edition corresponds to the 4 th edition in German. In addition to correcting some typographical errors and making small improvements in the presentation, in the present edition some chapters have been revised or extended. Panel V, for example, has been extended to include a description of angle-resolved photoemission and its importance for the study of electronic band structures. Section 10.10 on high-temperature superconductors has been completely rewritten. This active field of research continues to progress rapidly and many new results have emerged since the publication of the first edition. These results shed new light on much of the fundamental physics. The new version of Sect. 10.10 has been developed in discussions with colleagues who are themselves engaged in superconductivity research. We thank, in particular, Professor C. Calandra from the University of Modena and Dr. R. WoÈ rdenweber of the Institute of Thin Film and Ion Technology at the Research Centre JuÈ lich. The revision of the problems was done with the help of Dr. W. Daum, Dr. A. FoÈ rster, A. Leuther and Ch. Ohler. We would like to thank them for their e orts. We also thank Dr. Margret Giesen for numerous improvements to the manuscript as well as Dr. Angela Lahee for the competent translation of the revised or new sections. JuÈ lich and Aachen, April 1995 H. Ibach. H. LuÈth
Preface to the First Edition In recent decades solid state physics has seen many dramatic new developments and has become one of the largest independent branches of physics. It has simultaneously expanded into many new areas, playing a vital role in fields that were once the domain of the engineering and chemical sciences. A consequence of this explosive development is that no single university lecturer can today be expected to have a detailed knowledge of all aspects of this vast subject; likewise, it is impossible to conceive of a course that could o er students a comprehensive understanding of the entire discipline and its many applications. In view of this situation, it is particularly valuable to have a textbook that gives a concise account of the essential elements of the physics of solids. In this book the fundamental aspects of solid state physics are presented according to the scheme: Chemical bonding, structure, lattice dynamics, and electronic properties. We believe that this sequence is the optimum choice for tutorial purposes. It enables the more di cult concepts to be introduced at a point where a basic understanding of fundamental ideas has already been achieved through the study of simple models and examples. In addition to this carefully structured exposition of classical solid state theory based on the periodic solid and the one-electron approximation, the book also includes comprehensive descriptions of the most active areas in modern research: magnetism, superconductivity and semiconductor physics. The chapter on magnetism discusses the exchange coupling of both localized and delocalized electrons, and will even guide the reader to the point when he or she can appreciate modern thin-film experiments. The standard picture of superconductivity is elucidated by means of a simplified presentation of BCS theory. A section is also devoted to the novel high-temperature superconductors. This field, however, remains in such a state of flux that it was necessary to confine the treatment to some selected experimental results and a few central ideas about this fascinating phenomenon. The chapter on semiconductors contains, in addition to a general introduction to these materials and their properties, detailed descriptions of semiconductor heterostructures, superlattices, epitaxy, and the quantum Hall e ect. In solid state physics, the interaction between theory and experiment has always played, and continues to play, a vital role. We have thus attempted throughout this book to steer a middle course in which both theory and experiment are adequately represented. Where a theoretical approach is
Preface to the First Edition ix helpful and not too cumbersome, we have not hesitated in challenging the reader with the necessary abstract concepts. Furthermore, we have tried to include theoretical methods and concepts, for example, those of group theory, that are indispensible for an understanding of contemporary original publications dealing with solid state theory. The concise presentation of the essential theoretical aspects is complemented by the inclusion of selected experimental methods and examples, summarized in the form of self-contained panels. These o er the reader the opportunity to test and consolidate the material already studied and may prove helpful in stimulating further study in areas of particular interest. Students will also benefit significantly from working through the extensive series of problems that relate to each chapter. These examples are not restricted to calculations based on the methods described in the text; in many cases they lead into areas that lie outside the scope of the main presentation. All of the examples have been put to the test in our own lecture courses. Nonetheless, the student may often need a helping hand or some preparatory instruction from a lecturer. The problems will be useful to both students and lecturers; they are designed to stimulate further study and to illustrate the connections between di erent disciplines. This book is a translation of the third edition of the original German text. The authors consider it their immensely good fortune to have been supported by Dr. Angela Lahee in the translation and editing of this work. We are also grateful to numerous colleagues who over the years have o ered valuable suggestions about the presentation of the book or have supplied the experimental material described herein. For her critical reading of parts of the manuscript and the page proofs we thank in particular Dr. Angela Rizzi. Other valuable contributions were made by Dr. W. Daum, Mr. Ch. Stuhlman, Dr. M. Wuttig and Mr. G. Bogdanyi. The figures were prepared with great care and patience by Mrs. U. Marx-Birmans and Mr. H. Mattke. The German manuscript was typed by Mrs. D. KruÈ ger, Mrs. JuÈ rss-nysten and Mrs. G. O ermann. We express our thanks to Dr. H. Lotsch and Mr. C.-D. Bachem of Springer-Verlag for the pleasant collaboration. JuÈ lich, January 1991 H. Ibach. H. LuÈth
Contents 1 Chemical Bonding in Solids... 1 1.1 The Periodic Table of the Elements... 1 1.2 Covalent Bonding... 4 1.3 Ionic Bonding... 9 1.4 Metallic Bonding... 13 1.5The Hydrogen Bond... 15 1.6 The van der Waals Bond... 15 Problems... 16 2 Structure of Solid Matter... 21 2.1 The Crystal Lattice... 22 2.2 Point Symmetry... 25 2.3 The 32 Crystal Classes (Point Groups)... 27 2.4 The Significance of Symmetry... 28 2.5Simple Crystal Structures... 31 2.6 Phase Diagrams of Alloys... 36 2.7 Defects in Solids... 45 Problems... 48 3 Di raction from Periodic Structures... 51 3.1 General Theory of Di raction... 51 3.2 Periodic Structures and the Reciprocal Lattice... 57 3.3 The Scattering Conditions for Periodic Structures..... 58 3.4 The Bragg Interpretation of the Laue Condition...... 60 3.5Brillouin Zones... 63 3.6 The Structure Factor... 64 3.7 Methods of Structure Analysis... 67 Problems... 70 Panel I: Di raction Experiments with Various Particles...... 72 Panel II: X-Ray Interferometry and X-Ray Topography..... 78 4 Dynamics of Atoms in Crystals... 83 4.1 The Potential... 84 4.2 The Equation of Motion... 85 4.3 The Diatomic Linear Chain... 86
XII Contents 4.4 Scattering from Time-Varying Structures ± Phonon Spectroscopy... 91 4.5Elastic Properties of Crystals... 94 Problems... 104 Panel III: Raman Spectroscopy... 107 5 Thermal Properties... 113 5.1 The Density of States... 113 5.2 The Thermal Energy of a Harmonic Oscillator...... 116 5.3 The Specific Heat Capacity... 118 5.4 E ects Due to Anharmonicity... 120 5.5 Thermal Expansion... 121 5.6 Heat Conduction by Phonons... 124 Problems... 129 Panel IV: Experiments at Low Temperatures... 131 6 ``Free'' Electrons in Solids... 135 6.1 The Free-Electron Gas in an Infinite Square-Well Potential... 136 6.2 The Fermi Gas at T =0K... 140 6.3 Fermi Statistics... 142 6.4 The Specific Heat Capacity of Electrons in Metals.... 145 6.5Electrostatic Screening in a Fermi Gas ± The Mott Transition... 150 6.6 Thermionic Emission of Electrons from Metals...... 152 Problems... 156 7 The Electronic Bandstructure of Solids... 159 7.1 General Symmetry Properties... 159 7.2 The Nearly Free-Electron Approximation... 163 7.3 The Tight-Binding Approximation... 167 7.4 Examples of Bandstructures... 173 7.5The Density of States... 177 7.6 Density of States in Non-Crystalline Solids... 179 Problems... 182 Panel V: Photoemission Spectroscopy... 184 8 Magnetism... 191 8.1 Diamagnetism and Paramagnetism... 191 8.2 The Exchange Interaction... 196 8.3 Exchange Interaction Between Free Electrons... 199 8.4 The Band Model of Ferromagnetism... 201 8.5The Temperature Behavior of a Ferromagnet in the Band Model... 205 8.6 Ferromagnetic Coupling for Localized Electrons..... 209
Contents XIII 8.7 Antiferromagnetism... 211 8.8 Spin Waves... 215 8.9 Crystalline Anisotropy... 219 Problems... 225 Panel VI: Magnetostatic Spin Waves... 227 Panel VII: Magnetism in Thin-Film Systems and GMR-E ect... 233 9 Motion of Electrons and Transport Phenomena... 241 9.1 Motion of Electrons in Bands and the E ective Mass... 241 9.2 Currents in Bands and Holes... 245 9.3 Scattering of Electrons in Bands... 247 9.4 The Boltzmann Equation and Relaxation Time... 251 9.5The Electrical Conductivity of Metals... 255 9.6 Thermoelectric E ects... 261 9.7 The Wiedemann-Franz Law... 264 9.8 Electrical Conductivity of Localized Electrons... 266 9.9 Quantum Transport in Nanostructures... 268 Problems... 282 Panel VIII: Quantum Oscillations and the Topology of Fermi Surfaces... 285 10 Superconductivity... 291 10.1 Some Fundamental Phenomena Associated with Superconductivity... 291 10.2 Phenomenological Description by Means of the London Equations... 296 10.3 Instability of the ``Fermi Sea'' and Cooper Pairs...... 299 10.4 The BCS Ground State... 304 10.5The Excitation Spectrum of a Superconductor... 312 10.6 Consequences of the BCS Theory and Comparison with Experimental Results... 317 10.7 Supercurrents and Critical Currents... 321 10.8 Coherence of the BCS Ground State and the Meissner-Ochsenfeld E ect... 324 10.9 Quantization of Magnetic Flux... 329 10.10 Type II Superconductors... 333 10.11 ``High-Temperature'' Superconductors... 340 Problems... 349 Panel IX: One-Electron Tunneling in Superconductor Junctions... 352 Panel X: Cooper-Pair Tunneling ± The Josephson E ect..... 362 11 Dielectric Properties of Materials... 371 11.1 The Dielectric Function... 371 11.2 Absorption of Electromagnetic Radiation... 374 11.3 The Dielectric Function for a Harmonic Oscillator.... 377
XIV Contents 11.4 Longitudinal and Transverse Normal Modes... 379 11.5Surface Waves on a Dielectric... 382 11.6 Reflectivity of a Dielectric Half-Space... 384 11.7 The Local Field... 385 11.8 The Polarization Catastrophe and Ferroelectrics..... 387 11.9 The Free-Electron Gas... 389 11.10 Interband Transitions... 391 11.11 Excitons... 398 11.12 Dielectric Energy Losses of Electrons... 400 Problems... 403 Panel XI: Novel Optical Materials... 407 Panel XII: Infrared Spectroscopy... 414 Panel XIII: The Frustrated Total Reflection Method... 417 12 Semiconductors... 419 12.1 Data of a Number of Important Semiconductors..... 420 12.2 Charge Carrier Density in Intrinsic Semiconductors... 424 12.3 Doping of Semiconductors... 428 12.4 Carrier Densities in Doped Semiconductors... 432 12.5Conductivity of Semiconductors... 437 12.6 The p±n Junction and the Metal/Semiconductor SchottkyContact... 443 12.7 Semiconductor Heterostructures and Superlattices.... 459 12.8 Important Semiconductor Devices... 472 Problems... 486 Panel XIV: The Hall E ect... 489 Panel XV: Cyclotron Resonance in Semiconductors... 492 Panel XVI: Shubnikov-de Haas Oscillations and Quantum HallE ect... 495 Panel XVII: Semiconductor Epitaxy... 504 Panel XVIII: Preparation of Nanostructures... 510 References... 517 Index... 527