Solid-State Spectroscopy

Hans Kuzmany

Solid-State Spectroscopy

An Introduction

Second Edition

123

Prof. Dr. Hans KuzmanyUniversitat WienInst. MaterialphysikStrudlhofgasse 41090 WienAustriahans.kuzmany@univie.ac.atkuzman@ap.univie.ac.at

ISBN 978-3-642-01478-9 e-ISBN 978-3-642-01479-6DOI 10.1007/978-3-642-01479-6Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2009933283

c© Springer-Verlag Berlin Heidelberg 2009This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, 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 publicationor 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. Violationsare liable to prosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does notimply, even in the absence of a specific statement, that such names are exempt from the relevant protectivelaws 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 Second Edition

To write a second edition of a textbook is a very challenging enterprise for theauthor in many aspects. First of all it gives the chance to back up the contentand the text from the previous edition with all the experience he has collectedafter the first edition was distributed and to include the full set of advices andrecommendations he had received from colleagues and students. As importantis the possibility to include new developments in the subject of the book.Solid-state spectroscopy was originally addressed to be most important forour understanding of the solid sate. This promise has been more than fulfilledas in the almost ten years after the publication of the first edition manyimportant technical developments of analytical tools has lead to better oreven new understanding of materials. Good examples of this progress are therapid development of synchrotron radiation as an omnipresent light source,the increasing interest in spintronics which promoted the spectroscopy of spinsystems or the new subject of transport or electron addition spectroscopyin nanostructures. These and many other subjects are now included in thetextbook or were rephrased according to the most recent developments.

Solid-state spectroscopy has still the character of an analytical tool but ina few special cases as for example in the field of luminescence the breakthroughto the market has occurred.

The format of the textbook as it was originally designed was retained in thenew edition. In the first and main part of the book basic concepts of the varioustypes of spectroscopy are described with particular emphasis on the physicalbackground of the methods. The sections on synchrotron radiation, photoemission, and on spin resonance were extended and a new chapter was addedon spectroscopy of nanostructured solids. On the other hand the contributionsfrom positron annihilation and myon spin resonance were shortened in order tolimit the overall text to an acceptable volume. The dedication of the textbookremains as given in the preface of the first English edition and can be inspectedthere.

In the second part of the book which is again formatted as appendices tothe individual chapters, a more detailed presentation is provided to help the

V

VI Preface to the Second Edition

advanced reader or teaching professors in finding the connections to theoreti-cal interpretations. In some cases, where it was demanded from the progressof understanding, parts of the presentations which were originally in the ap-pendices were moved to the main text.

As for the problems new exercises were included to cover the new sub-jects accepted in the second edition. The problem solutions are still availablefrom the author as an extra booklet with the ISBN number 963 463 268 8published by H. Kuzmany, M. Hulman and J. Kurti at the Eotvos Univer-sity in Budapest. New problems are assigned by an upperscale n. They areunfortunately not included in the booklet.

Due to the lack of space many presentations could not be provided insufficient detail to allow for immediate application in research and technology.Therefore to each chapter the list of references for further reading was updatedwith most important recent literature.

Finally it is a great pleasure for me to acknowledge all colleagues whocontributed to the better understanding of this textbook by numerous dis-cussions and recommendations during its preparation. Particularly valuablecontributions came from Prof. H. Grosse, Prof. Th. Pichler, Dr. R. Pfeiffer,Dr. A. Gruneis, Dr. C. Kramberger, and Mag. W. Plank, Universitat Wien,Prof. F. Simon, University of Technology and Economics Budapest, Prof. W.Jantsch, Universitat Linz, and Prof. P. Jarillo-Herero, Massachusetts Instituteof Technology, Boston. I am also very grateful to our technicians A. Stangland Ch. Vlcek for helping to get new and updated illustrations for the text-book. Finally, I very much acknowledge the editor-in-chief Dr. Ascheron fromSpringer Verlag for his continuous stimulations during the preparation of themanuscript and for his patience in receiving it.

Wien, April 2009 Hans Kuzmany

Preface to the First Edition

The dramatic increase of our knowledge about the solid-state in the last 10–20years has come in great part from new spectroscopic experimental techniques.In this context spectroscopy is used in a broad sense and covers various ex-periments where energy analysis of a particle or electromagnetic radiationis crucial. Accordingly, spectroscopic methods extend in the electromagneticspectrum from radio waves to γ radiation but also include particles after theirinteraction with a solid. Each spectral range has its characteristic techniqueand addresses particular properties of the solid. A fundamental knowledge ofthe various methods is therefore a prerequisite for a successful investigationof problems in a particular area.

The actual motivation for writing this textbook was the lack of any di-dactic review summarizing the methods and applications of spectroscopywith regards to solids. Many of the methods were well known from molec-ular physics but, even there, reliable and comprehensive textbooks are notavailable. Also, spectroscopic problems can be characteristically different inmolecules and crystalline material because of the periodic arrangements ofatoms and molecules in the latter.

The material presented here is a result of several postgraduate courseson “Solid-State Spectroscopy” given by the author over the last few years.The goal of these lectures was to supply a representative selection of spec-troscopic techniques and to describe their field of application. This goal hasbeen retained as the concept of the current textbook. Accordingly, the inten-tion is to provide a broad knowledge of the basic concepts, sufficient to followspecialized lectures or specialized literature later on.

Another source of the subject to be discussed is a textbook written bythe author in 1989 in German and edited by Springer Verlag in 1989. In thistextbook the concept of presentation and didactic strategy was developed butthe elaboration of the material has been performed in much more detail in thecurrent version and the volume of subjects presented has been substantiallyincreased.

VII

VIII Preface to the First Edition

During the formulation of the text particular attention was paid to aphysical understanding of the spectroscopic problems rather than to theirformal description. To improve information transfer from the text the mostimportant results have been framed. This should be of particular help for theapplication-oriented reader. To simplify presentation no vector or tensor nota-tion is employed in general. Only in cases where the physical meaning requiresthe specification of the rank of the variables, bulk letters, or indexed symbolsin script are used for vectors and tensors and bulk letters in Roman for oper-ators. The bulk of the book deals with a description of current spectroscopictechniques and their applications on an introductory level. This is backed upby extensive appendices which contain several useful tables and a considerablenumber of further details, including some mathematical formulations on anadvanced level. In this way a better link could be established with standardtextbooks and to formulations used in spectroscopic research. The book isconstructed, however, to allow reading and understanding without a study ofthe appendices. In this context the latter can be used either as a source ofadditional information for the lecturers or as part of the course work.

The first part of the textbook describes electromagnetic radiation, lightsources such as lasers and synchrotron radiation, and general concepts ofexperimental techniques. The second part concentrates on individual spectro-scopic methods using electromagnetic radiation and particles. The problemscollected at the end of each chapter are designed to further the understandingof the text. Each of them is flagged for its instructive value. Discussion andsolution of the problems is highly recommended. Problems with an asteriskare more difficult and may be considered as an extension of the subject cov-ered by the book. Problems labeled with a superscript a require input fromthe appendix.

During the specification of the problems I strongly benefited from valuablediscussions with colleagues and former students in my group. In this contextI am particularly grateful to Mag. J. Winter, Mag. R. Winkler, and Mag. M.Hulman for their engagement in the discussion of the problems. A bookletwith solutions will be available from the author for interested readers.

The current textbook may be useful as a first text for senior undergraduatestudents. However, it is particularly designed for postgraduates in physics,chemistry, and material science, before they start to work in a special researchfield. With the inclusion of the appendices the value of the book is extended toa more knowledgeable audience such as students working on a thesis, academiclecturers who intend to set up a similar course in solid-state spectroscopy, oreven researchers in the field.

Two years of education in general physics are a prerequisite for under-standing this book. In addition, a basic knowledge of solid-state physics andsome background in the concepts of quantum mechanics will be very helpful.At the end of each chapter references are given for readers who need additionalinformation on specific subjects and recent developments.

Preface to the First Edition IX

The subject covered by this textbook extends over a very broad field ofmaterial science. Extended discussions with many specialists were thereforeextremely important. In this context I would like to acknowledge in partic-ular Prof. G. Vogl and Prof. H. Grosse from the Universitat Wien, Prof. M.Mehring from the Universitat Stuttgart, Prof. J. Fink from the Institut furFestkorperphysik und Werkstofforschung in Dresden, and Prof. J. Kurti fromthe Eotvos University in Budapest.

For critical reading and correction of special chapters I acknowledge Doz.B. Sepiol from Wien, and Prof. Kurti and Prof. Mehring from Budapestand Stuttgart, respectively. Also, I am particularly grateful to T. Leitner forhis continuous efforts to get the graphics of the textbook into a computer-compatible shape and for designing the cover plate.

Finally, I acknowledge the Springer Verlag in Heidelberg, in particularDr. Lotsch and Mr. C.-D. Bachem, for their support and efforts during thepreparation of the manuscript.

It has been the idea of this book to provide an overview and an aid for new-comers to the rapidly emerging and colorful field of solid-state spectroscopy.

Wien, January 1998 Hans Kuzmany

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Electromagnetic Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Electromagnetic Waves and Maxwell’s Theory . . . . . . . . . . . . . . 52.2 Radiation from Accelerated Charges . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 The Hertzian Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Emission from Arbitrarily Accelerated Charges . . . . . . . . 14

2.3 Fourier Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.1 Fourier Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.2 Examples of Fourier Transforms . . . . . . . . . . . . . . . . . . . . . 16

2.4 Radiation with a Finite-Frequency Spectrum . . . . . . . . . . . . . . 182.4.1 Damped Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . 182.4.2 Frequency Spectrum for Electromagnetic Waves with

a Finite Radiation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4.3 Frequency Spectrum and Power Spectrum . . . . . . . . . . . 21

2.5 Coherence and Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.1 Periodic and Non-Periodic Electromagnetic Fields . . . . . 232.5.2 Coherent and Non-Coherent Superposition . . . . . . . . . . . 242.5.3 Temporary Coherence and Correlation . . . . . . . . . . . . . . . 252.5.4 The Wiener–Khintchin Theorem . . . . . . . . . . . . . . . . . . . . 28

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3 Light Sources with General Application . . . . . . . . . . . . . . . . . . . 313.1 Black Body Radiation and Gas-Discharge Lamps . . . . . . . . . . . . 313.2 Spectral Lamps, and Shape of Spectral Lines . . . . . . . . . . . . . . 34

3.2.1 Low-Pressure Spectral Lamps . . . . . . . . . . . . . . . . . . . . . . . 353.2.2 Shape of Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3.1 Synchrotron Light Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3.2 Generation and Properties of Synchrotron Radiation . . . 403.3.3 Special Synchrotron Facilities . . . . . . . . . . . . . . . . . . . . . . . 43

XI

XII Contents

3.3.4 Synchrotron Facilities World Wide . . . . . . . . . . . . . . . . . . . 453.3.5 The Fourth Synchrotron Generation . . . . . . . . . . . . . . . . . 47

3.4 Lasers as Radiation Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.4.1 Generation and Properties of Laser Radiation . . . . . . . . . 493.4.2 Continuous-Wave Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.4.3 Semiconductor Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.4.4 Pulsed Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4.5 Tunable Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.6 Free-Electron Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.4.7 New Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4 Spectral Analysis of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.1 Optical Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.1.1 Optical Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.1.2 Polarizers and Phase Plates . . . . . . . . . . . . . . . . . . . . . . . . . 714.1.3 Glass Fibers and Light Pipes . . . . . . . . . . . . . . . . . . . . . . . 73

4.2 Monochromators and Spectrometers . . . . . . . . . . . . . . . . . . . . . . . 754.2.1 Characteristics of Monochromators . . . . . . . . . . . . . . . . . . 754.2.2 The Prism Monochromator . . . . . . . . . . . . . . . . . . . . . . . . 764.2.3 The Grating Monochromator . . . . . . . . . . . . . . . . . . . . . . . 78

4.3 Interferometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.3.1 Multiple-Beam Interference for a Parallel Plate . . . . . . . . 834.3.2 The Fabry–Perot Interferometer . . . . . . . . . . . . . . . . . . . . 854.3.3 The Multipass Fabry–Perot Interferometer . . . . . . . . . . . 87

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5 Detection of Electromagnetic Radiation . . . . . . . . . . . . . . . . . . . 915.1 Signal and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2 Photographic Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.3 Photomultipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.4 Photoelectric Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.4.1 Fundamentals of Photoelectric Detectors . . . . . . . . . . . . . 975.4.2 Photoconduction Detectors . . . . . . . . . . . . . . . . . . . . . . . . 985.4.3 Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.4.4 Detector Arrays and Imagers . . . . . . . . . . . . . . . . . . . . . . . 102

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6 The Dielectric Response Functions . . . . . . . . . . . . . . . . . . . . . . . . 1076.1 Optical Constants, and Kramers–Kronig Relations . . . . . . . . . . 108

6.1.1 Optical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.1.2 Reflection and Transmission . . . . . . . . . . . . . . . . . . . . . . . . 1106.1.3 Kramers–Kronig Dispersion Relations . . . . . . . . . . . . . . . 111

6.2 Physical Origin of Contributions to the Dielectric Function . . . 1136.3 Model Dielectric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Contents XIII

6.3.1 Dielectric Function for Harmonic Oscillators . . . . . . . . . 1146.3.2 The Dielectric Function for Free Carriers . . . . . . . . . . . . . 1196.3.3 Dielectric Functions for Combined Free Carrier and

Oscillator Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.3.4 Oscillator Strength and Sum Rules . . . . . . . . . . . . . . . . . . 123

6.4 Experimental Determination of Dielectric Functions(Ellipsometry) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7 Spectroscopy in the Visible and Near-Visible SpectralRange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297.1 Quantum-Mechanical Description of Optical Absorption . . . . . 1297.2 Absorption from Extended States in Semiconductors . . . . . . . . 131

7.2.1 The Physical Background and the Shape of theAbsorption in Semiconductors . . . . . . . . . . . . . . . . . . . . . . 132

7.2.2 Direct and Allowed Transitions at the Absorption Edge 1347.2.3 Forbidden Transitions and Phonon-Assisted Transitions 1357.2.4 Absorption from Higher Transitions . . . . . . . . . . . . . . . . . 137

7.3 Absorption from Localized States . . . . . . . . . . . . . . . . . . . . . . . . . 1387.3.1 Absorption of Extended and Localized Excitons . . . . . . 1387.3.2 Absorption by Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.4 Theoretical Description of Absorption by Localized States . . . 1417.5 Crystal Field and Ligand Field Induced Absorption . . . . . . . . . 1467.6 Luminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7.6.1 Luminescence from Semiconductors . . . . . . . . . . . . . . . . . 1507.6.2 Luminescence from Point Defects in Insulators . . . . . . . 154

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

8 Symmetry and Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1618.1 Symmetry of Molecules and Crystals . . . . . . . . . . . . . . . . . . . . . . 161

8.1.1 Formal Definition and Description of Symmetry . . . . . . 1618.1.2 The Mathematical Description of Symmetry

Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1648.1.3 Transformation Behavior of Physical Properties . . . . . . 165

8.2 Representation of Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668.3 Classification of Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1718.4 Infinitely Extended Ensembles and Space Groups . . . . . . . . . . . 1748.5 Quantum-Mechanical Selection Rules . . . . . . . . . . . . . . . . . . . . . . 176Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

9 Light Scattering Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1839.1 Instrumentation and Setup for Light Scattering Experiments . 1839.2 Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

9.2.1 Fundamentals of Raman Scattering . . . . . . . . . . . . . . . . . 185

XIV Contents

9.2.2 Classical Determination of Scattering Intensity andRaman Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

9.2.3 Longitudinal and Transversal Optical Modes . . . . . . . . . 1939.2.4 Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.2.5 A Simple Quantum-Mechanical Theory of Raman

Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.2.6 Temperature Dependence of Raman Scattering . . . . . . . 2019.2.7 Raman Scattering from Disordered Structures . . . . . . . . . 2029.2.8 Resonance Raman Scattering and Electronic Raman

Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2049.2.9 Raman Scattering in the Time Domain . . . . . . . . . . . . . . . 208

9.3 Brillouin Scattering and Rayleigh Scattering . . . . . . . . . . . . . . . 2109.3.1 Fundamentals of Brillouin Scattering . . . . . . . . . . . . . . . . 2109.3.2 Experimental Results of Brillouin Scattering . . . . . . . . . 2139.3.3 Rayleigh Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

10 Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21710.1 Radiation Sources, Optical Components, and Detectors . . . . . 21810.2 Dispersive Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 22310.3 Fourier Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

10.3.1 Basic Principles of Fourier Spectroscopy . . . . . . . . . . . . . 22610.3.2 Operating Conditions for Fourier Spectrometers . . . . . . 22910.3.3 Fourier-Transform Raman Spectroscopy . . . . . . . . . . . . . 233

10.4 Intensities for Infrared Absorption . . . . . . . . . . . . . . . . . . . . . . . . 23410.4.1 Absorption for Electronic Transitions . . . . . . . . . . . . . . . . 23510.4.2 Absorption for Vibronic Transitions . . . . . . . . . . . . . . . . . 235

10.5 Examples from Solid-State Spectroscopy . . . . . . . . . . . . . . . . . . . 23610.5.1 Investigations on Molecules and Polycrystalline

Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23710.5.2 Infrared Absorption and Reflection from Crystals . . . . . . 23810.5.3 Attenuated Total Reflection . . . . . . . . . . . . . . . . . . . . . . . . 24110.5.4 Applications in Semiconductor Physics . . . . . . . . . . . . . . 24310.5.5 Properties of Metals in the Infrared . . . . . . . . . . . . . . . . . 246

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

11 Magnetic Resonance Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . 25111.1 Magnetic Moments of Atoms and Nuclei . . . . . . . . . . . . . . . . . . . 251

11.1.1 Orientation of Magnetic Moments in a Field, andZeeman Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

11.1.2 Magnetic Moments in Solids . . . . . . . . . . . . . . . . . . . . . . . 25511.2 Magnetic Moments in a Magnetic Field . . . . . . . . . . . . . . . . . . . . 257

11.2.1 Motion of Magnetic Moments and Bloch Equations . . . 25711.2.2 The Larmor Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

11.3 Basic Concepts of Spin Resonance . . . . . . . . . . . . . . . . . . . . . . . . 259

Contents XV

11.3.1 Induction into a Sensor Coil . . . . . . . . . . . . . . . . . . . . . . . . 26011.3.2 Free Induction Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26311.3.3 Tuning the Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26311.3.4 Susceptibility and Absorption of Power in CW

Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26411.3.5 Resonance Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26611.3.6 The Resonance Excitation as an Absorption Process . . 267

11.4 Relaxation Times and Linewidths for Magnetic Resonance . . . 26911.4.1 Dipole-Dipole Interaction and Transversal Relaxation

Time T2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26911.4.2 Shape of Resonance Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 27211.4.3 The Spin-Lattice Relaxation T1 . . . . . . . . . . . . . . . . . . . . . 273

11.5 The Effective Spin Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . 27511.6 Electron Spin Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

11.6.1 Zeeman Splitting and Crystal Field Effects . . . . . . . . . . . 27611.6.2 Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27811.6.3 Spin-Orbit Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28111.6.4 Free Carrier Spin Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 284

11.7 Nuclear Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28411.7.1 The Chemical Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28511.7.2 Pulsed Nuclear Magnetic Resonance . . . . . . . . . . . . . . . . 28711.7.3 Magic-Angle Spinning NMR . . . . . . . . . . . . . . . . . . . . . . . . 28911.7.4 Cross Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29011.7.5 Electron-Nuclear Double Resonance . . . . . . . . . . . . . . . . . 29211.7.6 Knight Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29211.7.7 Two-Dimensional NMR and NMR Tomography . . . . . . . 293

11.8 Nuclear Quadrupole Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

12 Ultraviolet and X-Ray Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 29712.1 Instrumentation for Ultraviolet and X-Ray Spectroscopy . . . . . 298

12.1.1 X-Ray Sources and X-Ray Optics . . . . . . . . . . . . . . . . . . . 29812.1.2 X-Ray and Electron Spectrometers . . . . . . . . . . . . . . . . . . 30212.1.3 X-Ray and Electron Detectors . . . . . . . . . . . . . . . . . . . . . . 305

12.2 X-Ray Absorption and X-Ray Fluorescence . . . . . . . . . . . . . . . . . 30712.3 X-Ray and UV Electron Spectroscopy . . . . . . . . . . . . . . . . . . . . . 311

12.3.1 Auger Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31112.3.2 Basic Principles of Photoelectron Spectroscopy . . . . . . . 31212.3.3 X-Ray Photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31412.3.4 Ultraviolet Photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . 316

12.4 Angle-Resolved Photoemission (ARPES) . . . . . . . . . . . . . . . . . . . 31912.4.1 Basic Concepts of Angle-Resolved Photoemission . . . . . . 31912.4.2 Band Structure of 3D Crystals . . . . . . . . . . . . . . . . . . . . . . 32212.4.3 Direct Recording for ε(k) . . . . . . . . . . . . . . . . . . . . . . . . . . 323

12.5 Inverse Photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

XVI Contents

12.6 X-Ray Absorption Fine Structure . . . . . . . . . . . . . . . . . . . . . . . . . 32712.7 Inelastic Scattering of X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

13 Spectroscopy with γ Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33313.1 Moßbauer Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

13.1.1 Fundamentals of Moßbauer Spectroscopy . . . . . . . . . . . . 33313.1.2 Experimental Set Up and Instrumentation for

Moßbauer Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 33613.1.3 Results of Moßbauer Spectroscopy . . . . . . . . . . . . . . . . . . 33913.1.4 Moßbauer Spectroscopy in the Time Domain . . . . . . . . . 341

13.2 Perturbed Angular Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 34113.2.1 Basic Description of the Perturbed Angular Correlation 34113.2.2 Experimental Results from Perturbed Angular

Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

14 Generalized Form of Response Functions . . . . . . . . . . . . . . . . . . 34914.1 The Momentum Dependence of the Dielectric Function . . . . . . 34914.2 Excitations of the Electronic System . . . . . . . . . . . . . . . . . . . . . . 352

14.2.1 Plasmons and Plasmon Dispersion . . . . . . . . . . . . . . . . . . 35314.2.2 Single-Particle Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . 35314.2.3 Combination of the Dielectric Response . . . . . . . . . . . . . 354

14.3 Generalized Response Functions and Correlation Functionsin Linear Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35614.3.1 Linear Response Theory and Kramers–Kronig

Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35614.3.2 The General Response Function . . . . . . . . . . . . . . . . . . . . 35714.3.3 Dynamic Form Factor and Correlation Functions . . . . . 36014.3.4 The Generalized Dielectric Function for Charged

Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

15 Spectroscopy with Electrons, Positrons and Muons . . . . . . . 36715.1 Electron Energy Loss Spectroscopy (EELS) . . . . . . . . . . . . . . . . 368

15.1.1 Electron Energy Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36915.1.2 Spectrometers and Detectors . . . . . . . . . . . . . . . . . . . . . . . 37215.1.3 Applications of Electron Energy-Loss Spectroscopy . . . . 373

15.2 Tunneling Spectroscopy (TS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37615.2.1 The Tunneling Effect in Solids . . . . . . . . . . . . . . . . . . . . . . 37715.2.2 The Tunneling Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37915.2.3 Tunneling Spectroscopy in Superconductors . . . . . . . . . . 38415.2.4 Scanning Tunneling Spectroscopy . . . . . . . . . . . . . . . . . . . 389

15.3 Positrons Annihilation Spectroscopy (PAS). . . . . . . . . . . . . . . . . 38915.3.1 Positron Sources and Spectrometer . . . . . . . . . . . . . . . . . 392

Contents XVII

15.3.2 Experimental Results from Positron AnnihilationSpectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

15.4 Muon Spin Rotation (μSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39415.4.1 Muons and Muon Spin Rotation . . . . . . . . . . . . . . . . . . . . 39515.4.2 Influence of Internal Fields . . . . . . . . . . . . . . . . . . . . . . . . . 39715.4.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

16 Spectroscopy of Mesoscopic and Nanoscopic Solids . . . . . . . . 40116.1 Classical Nanoscopic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

16.1.1 Optical Properties of Small Metallic Particles in theClassical Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

16.1.2 Coulomb Oscillations and Coulomb Diamonds forClassical and for Quantized Nanostructures . . . . . . . . . . . 403

16.2 Spectroscopy in Systems with Size Quantization . . . . . . . . . . . 40916.2.1 Size Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40916.2.2 Spectroscopy in Quasi-Metallic Quantum Dots . . . . . . . . 41016.2.3 Spectroscopy in Semiconducting Quantum Dots . . . . . . . 41216.2.4 Landau Levels and Quantum Hall Effect . . . . . . . . . . . . . 417

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

17 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42317.1 Neutrons and Neutron Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

17.1.1 Neutrons for Scattering Experiments . . . . . . . . . . . . . . . . 42417.1.2 Thermal Neutron Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 42517.1.3 Cold and Hot Neutron Sources . . . . . . . . . . . . . . . . . . . . . 427

17.2 Neutron Spectrometer and Detectors . . . . . . . . . . . . . . . . . . . . . . 42817.2.1 Neutron Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42817.2.2 Neutron Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

17.3 The Process of Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . 43017.3.1 The Scattering Cross Section . . . . . . . . . . . . . . . . . . . . . . . 43017.3.2 Coherent and Incoherent Scattering in the Born

Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43117.3.3 Inelastic Neutron Scattering and Scattering Geometry . 433

17.4 Response Function and Correlation Function for InelasticNeutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

17.5 Results from Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 437Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

18 Spectroscopy with Atoms and Ions . . . . . . . . . . . . . . . . . . . . . . . . 44118.1 Instrumentation for Atom and Ion Spectroscopy . . . . . . . . . . . 442

18.1.1 Ion Beam Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44218.1.2 Accelerators and Beam Handling . . . . . . . . . . . . . . . . . . . 44318.1.3 Analyzer and Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

18.2 Energy Loss and Penetration of Heavy Particles in Solids . . . 445

XVIII Contents

18.3 Backscattering Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44618.3.1 Rutherford Backscattering Spectroscopy . . . . . . . . . . . . 44818.3.2 Elastic Recoil Detection Spectroscopy . . . . . . . . . . . . . . 449

18.4 Secondary Ion Mass Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . 450Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

A To Chapter 1, Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

B To Chapter 2, Electromagnetic Radiation . . . . . . . . . . . . . . . . . 455B.1 Photometric Radiation Equivalent . . . . . . . . . . . . . . . . . . . . . . . . . 455B.2 The Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455B.3 Potentials for the Electromagnetic Field . . . . . . . . . . . . . . . . . . . 456B.4 Expansion of the Potential in Multipole Moments . . . . . . . . . . . 456B.5 Time-Retarded Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457B.6 Radiation from an Arbitrarily Accelerated Charge . . . . . . . . . . 458B.7 Fourier Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459B.8 The δ Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

B.8.1 Representations of the δ function . . . . . . . . . . . . . . . . . . . . 461B.8.2 Some Properties of the δ Function . . . . . . . . . . . . . . . . . . . 462

C To Chapter 3, Light Sources with General Application . . . . . 465C.1 Moments of Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465C.2 Convolution of Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465C.3 Fano Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466C.4 Electron Motion in Special Synchrotron Facilities: Wiggler

and Undulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467C.5 Stimulated Emission of Laser Radiation . . . . . . . . . . . . . . . . . . . 468

D To Chapter 4, Spectral Analysis of Light . . . . . . . . . . . . . . . . . . 471D.1 Multiple Beam Interference for a Plane-Parallel Plate . . . . . . . 471

E To Chapter 6, The Dielectric Function . . . . . . . . . . . . . . . . . . . . 473E.1 Reflection and Transmission at an Interface for Arbitrary

Incidence (Fresnel Equations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473E.2 Reflection and Transmission Through Plane and Parallel

Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474E.3 Kramers–Kronig Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 475

F To Chapter 7, Spectroscopy in the Visible andNear-Visible Spectral Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477F.1 Matrix Elements and First-Order Perturbation Theory . . . . . . 477F.2 Transitions Induced by Electromagnetic Radiation . . . . . . . . . . 478F.3 Matrix Elements in Dipole Representation . . . . . . . . . . . . . . . . . 480F.4 Quantum Mechanics of the Harmonic Oscillator . . . . . . . . . . . . 481F.5 Diodes for Blue Luminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

Contents XIX

G To Chapter 8, Symmetry and Selection Rules . . . . . . . . . . . . . 485G.1 Character Tables of Point Groups . . . . . . . . . . . . . . . . . . . . . . . . . 485G.2 Some More Elements of Representation Theory . . . . . . . . . . . . . 492G.3 Representation of Groups by Displacement Coordinates . . . . . . 493G.4 Vibrational Species of Rhombohedric CaCO3 . . . . . . . . . . . . . . . 494

H To Chapter 9, Light Scattering Spectroscopy . . . . . . . . . . . . . . 497H.1 Raman Tensors for the 32 Point Groups . . . . . . . . . . . . . . . . . . . 497H.2 Averaging of Raman-Tensor Components . . . . . . . . . . . . . . . . . . 499

I To Chapter 10, Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . 503I.1 Line-Shape Function from the Fluctuation-Dissipation

Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

J To Chapter 11, Magnetic Resonance Spectroscopy . . . . . . . . 505J.1 g-Factor for the Free Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505J.2 Transformation of Velocities Between Laboratory System

and Rotating System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506J.3 Exchange Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507J.4 Line Shape for Powder Spectra in Magnetic Resonance . . . . . . . 507J.5 Pauli Spin Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508J.6 Spin-Orbit Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

K To Chapter 13, Spectroscopy with γ Rays . . . . . . . . . . . . . . . . . 511K.1 Oscillator Models for Recoil-Free Emission of γ Radiation . . . . 511

L To Chapter 14, Generalized Dielectric Function . . . . . . . . . . . 513L.1 The Kramers–Kronig Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 513L.2 Evaluation of Expectation Value for Particle Density . . . . . . . . 514L.3 The Fluctuation-Dissipation Theorem . . . . . . . . . . . . . . . . . . . . . 515L.4 The Generalized Dielectric Function for Charged Particles . . . . 516L.5 Random Phase Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

M To Chapter 16, Spectroscopy of Mesoscopic andNanoscopic Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519M.1 Appendix: Basic Concepts of Mie Theory . . . . . . . . . . . . . . . . . . 519M.2 Appendix: Field Effect Transistors . . . . . . . . . . . . . . . . . . . . . . . . . 521M.3 Appendix: Quantum Wells, Quantum Wires, and Dots . . . . . . . 522M.4 Appendix: Size Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

M.4.1 Size Quantization in Rectangular Boxes . . . . . . . . . . . . . . 524M.4.2 Size Quantization for Spherical Boxes . . . . . . . . . . . . . . . . 526

N To Chapter 17, Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . 529N.1 Coherent and Incoherent Scattering for Hydrogen and

Deuterium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

XX Contents

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547