Structural Analysis of Point Defects in Solids: An Introduction to Multiple Magnetic Resonance Spectroscopy

375 Pages·1992·7.791 MB·English

by  Professor Dr. Johann-Martin Spaeth, Priv.-Doz. Dr. Jürgen R. Niklas, Professor Ralph H. Bartram Ph. D. (auth.)

43
Springer Series in Solid-State Sciences
Edited by Hans-Joachim Queisser
Springer Series in Solid-State Sciences
Editors: M. Cardona P. Fulde K. von Klitzing H.-J. Queisser
Managing Editor: H. K.V. Lotsch Volumes 1-89 are listed at the end of the book
90 Earlier and Recent Aspects of Superconductivity Editors: J. O. Bednorz and K. A. Muller
91 Electronic Properties of Conjugated Polymers III Basic Models and Applications
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92 Physics and Engineering Applications of Magnetism Editors: Y. Ishikawa and N. Miura
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95 Electronic Materials A New Era in Materials Science
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96 Electron Liquids By A. Isihara
97 Localization and Confinement of Electrons in Semiconductors
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98 Magnetism and the Electronic Structure of Crystals
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99 Electronic Properties of High-T c Superconductors and Related Compounds
Editors: H. Kuzmany, M. Mehring, and J. Fink
100 Electron Correlations in Molecules and Solids By P. Fulde
101 High Magnetic Fields in Semiconductor Physics III
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102 Conjugated Conducting Polymers Editor: H. Kiess
103 Molecular Dynamics Simulations Editor: F. Yonezawa
104 Products of Random Matrices in Statistical Physics
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lOS Self-Trapped Excitons By K. S. Song and R. T. Williams
106 Physics of High-Temperature Superconductors Editors: S. Maekawa and M. Sato
107 Electronic Properties of Polymers Orientation and Dimensionality of Conjugated Systems
Editors: H. Kuzmany, M. Mehring, and S. Roth
108 Site Symmetry in Crystals Theory and Applications
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109 Transport Phenomena in Mesoscopic Systems By H. Fukuyama, T. Ando
I 10 Symmetry and Optical Phenomena in SuperlaUices and Other Heterostructures
By E. L. Ivchenko, O. E. Pikus
III Low-Dimensional Electronic Systems New Concepts
By. O. Bauer, F. Kuchar, H. Heinrich
Johann-Martin Spaeth Jurgen R. Niklas
Ralph H. Bartram
Structural Analysis
of Point Defects
in Solids
An Introduction to Multiple Magnetic
Resonance Spectroscopy
With 165 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
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Budapest
Professor Dr. Johann-Martin Spaeth
Priv.-Doz. Dr. Jiirgen R. Niklas
Fachbereich Physik, Universitiit-Gesamthochschule
Warburger Strasse 100, W-4790 Paderborn, Fed. Rep. of Germany
Professor Ralph H. Bartram, Ph. D.
Department of Physics, University of Connecticut
Storrs, CT 06268, USA
Series Editors:
Professor Dr., Ores. h. c. Manuel Cardona
Professor Dr., Dr. h. c. Peter Fulde
Professor Dr., Dr. h. c. Klaus von Klitzing
Professor Dr., Ores. h. c. Hans-Joachim Queisser
Max-Planck-Institut fur Festkorperforschung, Heisenbergstrasse 1
W -7000 Stuttgart 80, Fed. Rep. of Germany
Managing Editor:
Dr. Helmut K. V. Lotsch
Springer-Verlag, Tiergartenstrasse 17, W -6900 Heidelberg, Fed. Rep. of Germany
ISBN-13 : 978-3-642-84407-2 e-ISBN-13 : 978-3-642-84405-8
DOl: 10.1007/978-3-642-84405-8
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Preface
The investigation of point defects in model systems, such as F centers in
alkali halides, has a venerable history in condensed matter physics. However,
in recent years, the study of defects has acquired a much greater practical
importance for materials science, since defects even in low concentration have
a controlling influence on the bulk properties of solids such as semiconductors
and laser materials. It follows that the demand for reliable methods of defect
structural analysis and of defect engineering has increased enormously.
The advent of multiple magnetic resonance techniques revolutionized the
structural analysis of point defects in solids. The extension and elaboration of
these techniques in recent years have greatly enhanced their discrimination,
reliability and applicability. With the help of modern experimental methods
such as computer controlled experiments and computer aided data acquisi
tion and analysis, these techniques were shown to be applicable to practical
problems in materials science, as well as to the study of model defects. A cor
relation between magnetic resonance spectra and bulk properties of materials
is often achievable with these multiple magnetic resonance techniques.
Although many multiple resonance techniques have been developed over
the course of a generation, the principles and procedures involved in their
application to structural analysis of point defects have never been collected in
a single volume. The objective of the present book is to make these principles
and procedures, including recent developments, which are, of course, familiar
to the dedicated practitioners of this seemingly arcane discipline, accessible
to a much more comprehensive class of materials scientists. The intention is
to provide the reader with a working knowledge which will enable him either
to apply multiple magnetic resonance spectroscopy to the investigation of
defects in a wide variety of host materials, or at least to appreciate the power
of the method and the implications of its findings.
VI Prefa.ce
We should like to express our appreciation to Dr. F. Lohse for providing
information on ODMR spectroscopy, to Mr. P. Alteheld and Mr. M. Rac for
reading and correcting the manuscript, and to Mrs. E. Henrichs and Mrs.
W. Kriete for their skillful and patient typing of the manuscript. One of the
authors (J.-M. S.) gratefully a.cknowledges a one-semester stipend from the
Volkswagen-Stiftung without which the completion of this book would not
have been possible.
Paderborn J.-M. Spaeth J.R. Niklas
Storrs, March 1992 R.H. Bartram
Table of Contents
1. Introduction ........................ 1
1.1 Structure of Point Defects . . . . . . . . . . . . . . 2
1.2 Basic Concepts of Defect Structure Determination
by Electron Paramagnetic Resonance . . . . . . . . . . . . .. 4
1.3 Superhyperfine and Electronic Structures
of Defects in Solids . . . . . . . . . . . . 8
2. Fundamentals of Electron Paramagnetic Resonance 11
2.1 Magnetic Properties of Electrons and Nuclei . 11
2.2 Electrons and Nuclei in an External Magnetic Field 12
2.3 Some Useful Relations for
Angular Momentum Operators ..... . 14
2.4 Time Dependence of Angular Momentum
Operators and Macroscopic Magnetization 15
2.5 Basic Magnetic Resonance Experiment . 17
2.6 Spin-Lattice Relaxation ........ . 20
2.7 Rate Equations for a Two-Level System 22
2.8 Bloch Equations. . . . . . . . . . . . . . 26
2.9 Conventional Detection of
Electron Paramagnetic Resonance and Its Sensitivity 31
3. Electron Paramagnetic Resonance Spectra 35
3.1 Spin Hamiltonian ......... . 35
3.2 Electron Zeeman Interaction .... . 38
3.3 g-Factor Splitting of EPR Spectra 42
3.4 Fine-Structure Splitting of EPR Spectra 45
3.5 Hyperfine Splitting of EPR Spectra ... 53
3.6 Superhyperfine Splitting of EPR Spectra 62
3.7 Inhomogeneous Line Widths of EPR lines 72
4. Optical Detection of Electron Paramagnetic Resonance 77
4.1 Optical Transitions of Defects in Solids ..... . 78
VIII Table of Contents
4.2 Spectral Form of Optical Transitions of
Defects in Solids ............ . 80
4.3 EPR Detected with
Magnetic Circular Dichroism of Absorption Method 86
4.4 MCDA Excitation Spectra of ODEPR Lines
(MCDA "Tagged" by EPR) .. . . . . . . . . . . . 96
4.5 Spatially Resolved MCDA and ODEPR Spectra . . 102
4.6 Measurement of Spin-Lattice Relaxation Time Tl with MCDA
Method ....................... 105
4.7 Determination of Spin State with MCDA Method 106
4.8 EPR of Ground and Excited States
Detected with Optical Pumping . . . . . . . . . . 112
4.9 EPR Optically Detected in
Donor-Acceptor Pair Recombination Luminescence 122
4.10 Optically Detected EPR of Triplet States. 129
4.11 ODEPR of Trapped Excitons with
MCDA Method ........... . 133
4.12 Sensitivity of ODEPR Measurements 135
5. Electron Nuclear Double Resonance 139
5.1 The Resolution Problem, a Simple Model. 139
5.2 Type of Information from EPR and NMR Spectra. 141
5.3 Indirect Detection of NMR, Double Resonance. 143
5.4 Examples of ENDOR Spectra . . . . . . . . . 150
5.5 Relations Between EPR and ENDOR Spectra,
END OR-Induced EPR . . . . . . . . . . .. ....... 154
5.6 Electron Nuclear Nuclear Triple Resonance
(Double ENDOR) ........... . 160
5.7 Temperature Dependence and
Photo-Excitation of ENDOR Spectra. 163
5.7.1 Temperature Dependence of END OR Spectra 163
5.7.2 Photo-Excitation of ENDOR Spectra. 166
6. Determination of Defect Symmetries from
END OR Angular Dependences ..... . 169
6.1 Definition of Neighbor Shells .... . 170
6.2 Neighbor Shells and Transformation of
Interaction Tensors . . . . . . . . . 171
6.3 Interaction Tensor Symmetries and
ENDOR Angular Dependence. 173
6.4 Neighbor Shell Symmetries and
ENDOR Angular Dependences. 175
6.4.1 Simple Example. 175
6.4.2 General Case . . . . . . 178
Table of Contents IX
6.4.3 Defect Structure and Symmetry Matrices . 182
6.5 Low Symmetry Defects in
Higher Symmetry Environments . 194
6.6 Ways to Distinguish Between
High and Low Symmetry Defects 200
6.7 Role of EPR Spectrum for an ENDOR Analysis 204
6.8 Solution of the Spin Hamiltonian 207
6.8.1 Concept of Effective Spin. . . 207
6.8.2 Nuclear Spin Hamiltonian . . 208
6.8.3 Calculation of Effective Spin . 214
6.8.4 Mutual Interactions Between Neighbor Nuclei 215
6.8.5 Large hf or shf Interaction for One Nucleus. . 218
6.8.6 Numerical Calculation of EPR Angular Dependences 218
6.8.7 Fitting of Free Parameters in a Simulated
ENDOR Angular Dependence. . . . . . . . . . 220
6.8.8 Examples of Results Obtained from Analysis of
ENDOR Angular Dependences 222
6.9 Software Treatment of ENDOR Spectra. . . . . . . . . 225
7. Theoretical Interpretation of Superhyperfine and
Quadrupole Interactions . . . . . . . 231
7.1 Structures of Point Defects ... 231
7.1.1 Impurities in Insulators. 232
7.1.2 Color Centers ..... . 233
7.1.3 Defects in Semiconductors 233
7.2 Origin of Zeeman, Hyperfine and
Quadrupole Interactions . . . . . 234
7.2.1 Origin of the Hamiltonian 234
7.2.2 Wigner-Eckart Theorem 236
7.2.3 Zeeman Interaction ... 236
7.2.4 Hyperfine Interaction .. 237
7.2.5 Quadrupole Interaction. 238
7.2.6 Total Hamiltonian ... 239
...
7.3 Central Ion Hyperfine Structure ... 239
7.3.1 Free Ion Electronic Structure 240
7.3.2 Crystal Field Splitting ... . 243
7.3.3 Spin Hamiltonian ...... . 244
7.4 Covalency and Superhyperfine Interaction 247
7.4.1 Molecular Orbitals and Configuration Mixing 248
7.4.2 Superhyperfine Interaction .. . 249
7.4.3 Ligand Core Polarization ... . 253
7.4.4 Ligand Quadrupole Interaction 254
7.4.5 Pseudopotentials ..... 256
7.4.6 Lattice Dynamical Effects ... 258
X Table of Contents
7.5 Orthogonalized Envelope Functions . . . . . . . . . . . 258
7.5.1 Wannier's Theorem and Effectiv~Mass Theory 259
7.5.2 Continuum Models . . . . . . . . . . . . . . . . 260
7.5.3 Point-Ion Model and Ion-Size Corrections . . . 261
7.5.4 Green's Function Method for Deep-Level Impurities. 262
7.5.5 Orthogonalization to Core Orbitals . . . . . . . . .. 263
7.6 Simple Approximations and Illustrations for
Interpretation of shf and Quadrupole Interactions 264
7.6.1 Point Dipole-Dipole Interaction . . . . . . 265
7.6.2 Calculation of Isotropic shf Constants with
Orthogonalized Envelope Function ..... 270
7.6.3 Transferred shf Interactions ... . . . . . . 271
7.6.4 Calculation of Anisotropic shf Constant b with
Orthogonalized Envelope Function ..... 273
7.6.5 Dynamical Contributions to shf Interactions 275
7.6.6 Quadrupole Interactions . 277
8. Technology of ENDOR Spectrometers 281
8.1 Experimental Constraints for Conventional ENDOR . 282
8.1.1 Modulation Frequency 282
8.1.2 Sensitivity.................... 282
8.1.3 Temperature................... 282
8.1.4 Microwave and Radio-Frequency Field Intensities 283
8.1.5 Microwave and END OR Frequency 284
8.1.6 Static Magnetic Field. . . 285
8.1. 7 Modulation of Parameters . . . 285
8.2 ENDOR Spectrometer Design . . . . . 286
8.3 Components of ENDOR Spectrometer 291
8.3.1 Signal Pre-Amplifier 291
8.3.2 Microwave Detector. . . . . 292
8.3.3 Microwave Sources . . . . . 297
8.3.4 ENDOR Microwave Cavities 301
8.3.5 Radio-Frequency Generators. 306
9. Experimental Aspects of Optic~fly Detected EPR and ENDOR 309
9.1 Sensitivity Considerations . . . . . . . . . . . . . . 309
9.1.1 Magnetic Circular Dichroism of Absorption. 310
9.1.2 Optically Detected EPR . . . . . . . . . . 311
9.2 ODMR Spectrometers Monitoring Light Emission . 312
9.3 ODMR Spectrometers Monitoring
Magnetic Circular Properties of Absorption and Emission. 314
9.3.1 General Description of the Spectrometer . . 314
9.3.2 Measurement of
Magnetic Circular Dichroism of Absorption. . . . . . . 316