Point Defects in Semiconductors and Insulators: Determination of Atomic and Electronic Structure from Paramagnetic Hyperfine Interactions

496 Pages·2003·16.72 MB·English

by  Professor Dr. Johann-Martin Spaeth, Professor Dr. Harald Overhof (auth.)

Springer Series in
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51 Point Defects 56 Si02 in Si Microdevices
in Semiconductors ByM.Itsumi
and Insulators
Determination of Atomic 57 Radiation Effects
in Advanced Semiconductor Materials
and Electronic Structure
and Devices
from Paramagnetic Hyperfine
By C. Claeys and E. Simoen
Interactions
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J.-M. Spaeth H.Overhof
Point Defects
in Semiconductors
and Insulators
Determination of Atomic
and Electronic Structure
from Paramagnetic Hyperfine Interactions
With 279 Figures
, Springer
Professor Dr. Johann-Martin Spaeth
Professor Dr. Harald Overhof
Fachbereich Physik
Universităt Paderborn
Warburger StraBe 100
33095 Paderborn
Germany
e-mail:
[email protected]
[email protected]
Series Editors:
Professor R. M. Osgood, Jr.
Microelectronics Science Laboratory, Department of Electrical Engineering
Columbia University, Seeley W. Mudd Building, New York, NY 10027, USA
Professor Robert Huli
University of Virginia, Dept. ofMaterials Science and Engineering, Thornton HalI
Charlottesville, VA 22903-2442, USA
Professor Jiirgen Parisi
Universităt Oldenburg, Fachbereich Physik, Abt. Energie-und Halbleiterforschung
Carl-von-Ossietzky-Strasse 9-11, 26129 Oldenburg, Germany
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Professor Hans-Joachim Queisser
Max-Planck-Institut fiir Festkorperforschung, Abt. Experimentelle Physik
Heisenbergstrasse 1, 70569 Stuttgart, Germany
ISSN 0933-033x
ISBN 978-3-642-62722-4 ISBN 978-3-642-55615-9 (eBook)
DOI 10.1007/978-3-642-55615-9
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Preface
The precedent book with the title "Structural Analysis of Point Defects in
Solids: An introduction to multiple magnetic resonance spectroscopy" ap
peared about 10 years ago. Since then a very active development has oc
curred both with respect to the experimental methods and the theoretical
interpretation of the experimental results. It would therefore not have been
sufficient to simply publish a second edition of the precedent book with cor
rections and a few additions. Furthermore the application of the multiple
magnetic resonance methods has more and more shifted towards materials
science and represents one of the important methods of materials analysis.
Multiple magnetic resonances are used less now for "fundamental" studies
in solid state physics. Therefore a more "pedestrian" access to the meth
ods is called for to help the materials scientist to use them or to appreciate
results obtained by using these methods. We have kept the two introduc
tory chapters on conventional electron paramagnetic resonance (EPR) of the
precedent book which are the base for the multiple resonance methods. The
chapter on optical detection of EPR (ODEPR) was supplemented by sections
on the structural information one can get from "forbidden" transitions as well
as on spatial correlations between defects in the so-called "cross relaxation
spectroscopy". High-field ODEPR/ENDOR was also added. The chapter on
stationary electron nuclear double resonance (ENDOR) was supplemented by
the method of stochastic END OR developed a few years ago in Paderborn
which is now also commercially available. In ENDOR spectroscopy the most
difficult task is the analysis of ENDOR spectra which may contain several
hundred lines. The chapter on the analysis of ENDOR spectra was com
pletely rewritten with the aim to provide a few simple tools how to start and
complete an ENDOR analysis. A completely new chapter is included on the
so-called electrical detection of EPR (EDEPR) and ENDOR (EDENDOR)
in which the paramagnetic and nuclear magnetic resonances are detected via
the electrical conductivity. Although EDEPR has been observed already in
the late sixties, the mechanisms have been better understood only in recent
years. EDEPR/ENDOR spectroscopy has proved to be as sensitive as optical
detection via luminescence and is particularly useful for small semiconduc
tor volumes such as thin epitaxial layers or microelectronic devices and for
very low defect concentrations. Also the chapter on the theoretical interpre-
VI Preface
tation of the measured hyperfine (hf) interactions is completely new. When
the precedent book appeared in 1992, the vast majority of theoretical pa
pers on hf interactions of point defects in solids dealt with point defects in
ionic crystals, mainly color centers, although many experimental data were
already available for defects in semiconductors and the emphasis had already
shifted to semiconductors. The theoretical methods used for the description
of point defects in ionic crystals are hardly useful for deep defects in semi
conductors. These are described by the local densitiy approximations (LDA)
to the Density Functional Theory (DFT) ,which had been applied to deep
defects in semiconductors already in the eighties. The theoretical work using
DFT-based methods, however, concentrated at that time on total energies for
semiconductor defects and on quantities that could be derived from total en
ergies like lattice relaxations and defect reactions. With very few exceptions,
the hf interaction problem had not been tackled. This is why in the precedent
book the general theory was presented with applications predominantly to
defects in ionic crystals. In the meantime the DFT-based methods have been
extended to treat hf interactions. For many deep defects the results have
been shown to be quite reliable when compared with experimental data. The
DFT-based methods proved to be flexible with successful applications ranging
from defects in homopolar crystals like diamond and silicon to defects in 111-V
compound semiconductors and the more ionic II-VI semiconductors as well
as to color centers in ionic crystals. The theory chapter of this book discusses
therefore the DFT methods and how from this theory the hf interactions can
be derived, which is illustrated with several examples. Finally the chapter on
the technical aspects of the optical detection of EPR and ENDOR is retained
from the precedent book and extended to high frequency jhigh field while that
on the technical aspects of ENDOR spectrometers, which are commercially
available, is omitted.
We would like to express our appreciation to Dr. S. Greulich-Weber and
to Dr. S. Schweizer for many fruitful discussions and for their technical assis
tance with some of the figures and also with the text. We are also indebted
to Dr. U. Gerstmann for many suggestions, for his help with the calculations,
and for a critical reading of the manuscript.
Paderborn, J. -M. Spaeth
September 2002 H.Overhof
Contents
1. Introduction.............................................. 1
1.1 Structure of Point Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Basic Concepts of Defect Structure Determination by EPR .. 4
1.3 Superhyperfine and Electronic Structures of Defects in Solids 9
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. . . . . . . .. 13
2.3 Some Useful Relations for Angular Momentum Operators. . .. 15
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. . . . . . . . . . . . . . . . . .. 46
3.5 Hyperfine Splitting of EPR Spectra. . . . . . . . . . . . . . . . . . . . . .. 53
3.6 Superhyperfine Splitting of EPR Spectra . . . . . . . . . . . . . . . . .. 61
3.7 Inhomogeneous Line Widths of EPR Lines. . . . . . . . . . . . . . . .. 70
4. Optical Detection of Electron Paramagnetic Resonance . .. 75
4.1 Optical Transitions of Defects in Solids. . . . . . . . . . . . . . . . . . .. 76
4.2 Spectral Form of Optical Transitions of Defects in Solids .... 78
4.3 EPR Detected with Magnetic Circular Dichroism
of Absorption Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84
4.4 MCDA Excitation Spectra of ODEPR Lines
(MCDA "Tagged" by EPR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 93
VIII Contents
4.5 Spatially Resolved MCDA and ODEPR Spectra. . . . . . . . . . .. 99
4.6 Measurement of Spin-Lattice Relaxation Time Tl
with MCDA Method .................................... 101
4.7 Determination of Spin State with MCDA Method .......... 103
4.8 EPR of Ground and Excited States Detected
with Optical Pumping .................................. 109
4.9 EPR Optically Detected
in Donor-Acceptor Pair Recombination Luminescence ....... 118
4.10 Optically Detected EPR of Triplet States .................. 125
4.11 ODEPR of Trapped Excitons
with MCDA Method .................................... 129
4.12 Sensitivity of ODEPR Measurements ..................... 131
4.13 Structural Information from Forbidden Transitions
in MCDA-EPR Spectra ................................. 134
4.14 Spatial Correlation Between Defects
by Cross-Relaxation-Spectroscopy ........................ 144
4.15 High-Field ODEPR/ODENDOR ......................... 156
5. Electron Nuclear Double Resonance ...................... 163
5.1 The Resolution Problem, a Simple Model .................. 163
5.2 Type of Information from EPR and NMR Spectra .......... 165
5.3 Indirect Detection of NMR, Double Resonance ............. 167
5.4 Examples of ENDOR Spectra ............................ 174
5.5 Relations Between EPR and ENDOR Spectra,
ENDOR-Induced EPR .................................. 176
5.6 Electron Nuclear Nuclear Triple Resonance (Double ENDOR) 183
5.7 Temperature Dependence and Photo-Excitation
of ENDOR Spectra ..................................... 186
5.7.1 Temperature Dependence of ENDOR Spectra ........ 186
5.7.2 Photo-Excitation of ENDOR Spectra ............... 188
5.8 Stochastic ENDOR ..................................... 190
6. Analysis of END OR Spectra .. ................ , ........... 197
6.1 Qualitative Analysis of ENDOR Spectra ................... 198
6.1.1 Spin Hamiltonian ................................. 198
6.1.2 Simple First Order Solution ....................... 199
6.1.3 Assignment of Nuclei ............................. 201
6.1.4 Angular Dependence of ENDOR Lines .............. 204
6.1.5 Symmetry Considerations, Neighbor Shells .......... 209
6.2 Quantitative Analysis of ENDOR Spectra ................. 212
6.2.1 Higher Order Approximations ...................... 212
6.2.2 Large Anisotropic Hyperfine Interactions ............ 213
6.2.3 Approximation with the Effective Electron Spin Seff .. 223
6.2.4 Second Order Splittings
of the Superhyperfine Structure .................... 226
Contents IX
6.2.5 Sample Alignment ................................ 237
6.2.6 Reconstruction of the EPR Line Shape
from ENDOR Data ............................... 243
6.2.7 Asymmetric Superhyperfine Tensors ................ 247
6.2.8 Selection Rules and ENDOR Line Intensities ......... 250
6.2.9 ENDOR Spectra in the Case of a Large Quadrupole
Interaction and Axial Symmetry ................... 253
6.2.10 Powder ENDOR Spectra .......................... 259
6.2.11 Final Results Obtainable from the Analysis
of ENDOR Spectra ............................... 261
7. Electrical Detection
of Electron Paramagnetic Resonance. . . . . . . . . . . . . . . . . . . . . . 265
7.1 Experimental Methods to Detect EDEPR ................. 266
7.2 Experimental Observation of EDEPR ..................... 269
7.3 The Donor-Acceptor Pair Recombination Model ............ 282
7.4 On the Role of the Electron Irradiation
for the Donor EPR in Silicon ............................ 286
7.5 Spatial Resolution and Low Frequency EDEPR ............ 289
7.6 Electrical Detection of ENDOR .......................... 293
7.7 Concentration and Temperature Dependence
of the EDEPR Signals .................................. 295
7.8 Further Spin-Dependent Recombination Models ............ 304
7.8.1 The Lepine Model ................................ 304
7.8.2 The Model of Kaplan, Solomon and Matt ........... 305
7.8.3 The Spin-Dependent SRH Model ................... 306
8. Theoretical ab initio Calculations
of Hyperfine Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
8.1 Electron States in Solids ................................ 310
8.1.1 Born-Oppenheimer Approximation ................ 311
8.1.2 Hartree and Harlree-Fock Approximations .......... 312
8.1.3 Density Functional Theory
and Local Density Approximation .................. 314
8.1.4 Computational Methods
for Energy Band Calculations ...................... 320
8.2 Computational Methods for Deep Point Defects ............ 324
8.2.1 Cluster Methods ................................. 325
8.2.2 The Supercell Method ............................ 325
8.2.3 Green's Function Methods ......................... 328
8.2.4 The Band Gap Problem and the Scissor Operator . . . . 332
8.3 Hyperfine Interactions .................................. 334
8.3.1 Non-relativistic Hyperfine Interactions .............. 335
8.3.2 Scalar Relativistic Hyperfine Interactions ............ 336
8.3.3 Magnetization Density for Many-Electron States ..... 338
X Contents
8.3.4 The Jahn-Teller Effect ............................ 341
8.3.5 The Core Polarization ............................ 343
8.3.6 Electrical Quadrupole Interaction .................. 347
8.3.7 The Empirical LCAO Scheme ...................... 349
8.3.8 The Envelope Function Method .................... 351
8.3.9 Point Dipole-Dipole Interaction .................... 352
8.4 Deep Point Defects
in Semiconductors and Insulators ......................... 353
8.4.1 Substitutional Donors with Llz = 1 ................. 354
8.4.2 Substitutional Donors with Llz = 2 ................. 355
8.4.3 Interstitial Deep. Donors .......................... 363
8.4.4 Shallow Acceptors with Llz = -1 ................... 367
8.4.5 Deep Acceptors with Llz = -2 ..................... 368
8.4.6 Vacancies ....................................... 370
8.4.7 Point Defects in Ionic Solids ....................... 377
8.4.8 3d Transition Metal Defects ....................... 384
8.4.9 Interstitial 3d TM Defects ......................... 393
8.5 Shallow Defects:
The Effective Mass Approximation and Beyond ............ 399
8.5.1 The EMA Formalism ............................. 400
8.5.2 Simplest Case: Nondegenerate Band Edge ........... 401
8.5.3 Conduction Band with Several Equivalent Minima .... 405
8.5.4 Pseudopotential Calculations ...................... 407
8.5.5 Degenerate Valence Bands ......................... 411
8.6 Conclusions ............................................ 411
9. Experimental Aspects
of Optically Detected EPR and ENDOR .................. 415
9.1 Sensitivity Considerations ............................... 415
9.1.1 Magnetic Circular Dichroism of Absorption .......... 416
9.1.2 Optically Detected EPR ........................... 417
9.2 ODMR Spectrometers Monitoring Light Emission .......... 418
9.3 ODMR Spectrometers Monitoring Magnetic Circular
Properties of Absorption and Emission .................... 420
9.3.1 General Description of the Spectrometer ............ 420
9.3.2 Measurement of Magnetic Circular Dichroism
of Absorption .................................... 422
9.3.3 Measurement of Magnetic Circular Polarization
of Emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
9.4 Experimental Details of the Components of an MCDA/MCPE
ODMR Spectrometer ................................... 426
9.4.1 Light Sources .................................... 426
9.4.2 Monochromators ................................. 427
9.4.3 Imaging Systems ................................. 427
9.4.4 Linear Polarizers ................................. 427