Optical Characterization of Solids

462 Pages·2002·13.204 MB·English

by  Professor Daniela Dragoman, Professor Mircea Dragoman (auth.)

Daniela Dragoman Mircea Dragoman
Optical Characterization of Solids
Springer-Verlag Berlin Heidelberg GmbH
ONLINE LIBRARY
Physics and Astronomy
http://www.springer.de/phys/
D. Dragoman M. Dragoman
Optical Characterization
of Solids
With 184 Figures
i
Springer
Professor Daniela Dragoman
University of Bucharest, Physics Department
P.O. Box MG-ll
76900 Bucharest, Romania
e-mail: [email protected]
Professor Mircea Dragoman
National Institute for Research and Development in Microtechnologies (IMT)
P.O. Box 38-160
72225 Bucharest, Romania
e-mails:[email protected]@yahoo.com
library of Congress Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek -CIP-Einheitsaufnahme
Dragoman. Daniela:
Optical characterization of solids 1 D. Dragoman; M. Dragoman. -Berlin; Heidelberg; New York;
Barcelona; Hong Kong; London; Milan; Paris; Thkyo : Springer. 2002
(Physics and astronomy online library)
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ISBN 978-3-642-07521-6 ISBN 978-3-662-04870-2 (eBook)
DOl 10.1007/978-3-662-04870-2
© Springer-Verlag Berlin Heidelberg 2002
Originally published by Springer-Verlag Berlin Heidelberg New York in 2002.
Softcover reprint of the hardcover 1st edition 2002
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Preface
The interaction between the electromagnetic field and matter is an essential issue
in modem physics. The physical concepts describing the field-matter interaction
are of paramount importance, being at the origin of quantum mechanics and
quantum field theories. On the other hand, the field-matter interaction is the main
tool used nowadays to investigate the structure and properties of matter at the
microscopic level.
The subject of this book is the characterization of the solid-state through the
interaction with the electromagnetic field. The main properties of different types
of solids, such as dielectrics, semiconductors, disordered materials, impurified
solids, low-dimensional structures, nanostructures, metals or superconductors, are
revealed through their interaction with the electromagnetic field whose
wavelength lies within the optical spectrum. Therefore, the book is focused on the
investigation of the main properties of different types of solids that are obtained
through light emission, absorption or scattering.
There is already an immense literature dedicated to light-solid-state
interactions or, in other words, the optical spectroscopy of solids, due to its major
role in understanding the physics and properties of the solid-state. This literature is
continuously growing and flourishing, due also to the paramount importance of
solid-state devices in the development of any conceivable area of technology,
including the booming information technology. However, this literature is mainly
written emphasizing a certain type of materials (semiconductors, high-temperature
superconductors, etc.) or a certain type of optical spectroscopy method (Raman
scattering, luminescence, etc.). We have tried a new, hybrid and at the same time
unifying approach.
The theory of light-solid interaction based on light absorption, emission and
scattering is very complex, being mainly based on quantum mechanical concepts,
although sometimes semi-classical approaches are still satisfactory. A simple
question comes immediately to mind: how can we relate the results of the theory
of light-solid interactions with the properties of solids? In other words, how can
one determine basic solid characteristics such as electronic band structure or
important quantitative parameters such as the effective mass of an electron or a
hole, the magnitude of electron-phonon coupling, the exciton lifetime, etc., from
the absorption, emission or the scattering of light in a solid? There is no simple or
VI Preface
direct answer to this straightforward question. We hope that the reader will be able
to fmd an answer to this question after reading this book, which is a first attempt
to unify disparate theories and experimental facts in a single and coherent way,
able to connect light-matter interaction theories with solid-state characteristics
and parameters. The practical significance of this view is of great importance for
all readers who work in the area of solid-state physics, electronics, optoelectronics
or nanoscience.
The book can be read by anyone with some elementary knowledge of solid
state physics. Chapters I and 2 provide the reader with all basic information
needed to understand later chapters. The book is inspired by a course presented by
one of us (D.D) at the University of Bucharest, Physics Faculty, Solid State
Department, at the Master in Science level. Therefore, although rigorous, the
mathematical treatment is presented in quite a simple and straightforward manner.
The book style is somewhere between a pedagogical and a review-like style, our
focus being on the physical explanations.
We had no desire to write a book on solid-state theory, which would have
been a hopeless project due to the immensity of theories and concepts applicable
to various types of materials and interactions, so that a balance had to be found
between theory and the practical methods for characterizing the parameters of
different materials. Throughout the book many exotic types of materials have been
introduced without a detailed definition and associated mathematical model. The
mention of the fact that a material belongs to a specific category was made only to
help interested readers to go deeper in the study of that material. We could not
have insisted on rigorous models for all materials; however, we have always
specified the parameter under scrutiny and the physical basis of its determination
through optical means. Frequently, in the area of light-matter interaction the
mathematical treatments and models are so complex that many times the physical
insights become obscure. Therefore, we have not insisted on mathematical details,
the theoretical treatment serving mainly for the introduction and explanation of the
fundamental physical effects involved in the light-matter interaction. This
approach is partially justified because many experimental results are not compared
with rigorous and sophisticated mathematical models but with simplified
phenomenological models or simple mathematical fitting formulas. We have
provided in the entire book, whenever possible, simple formulas helping to
elucidate the main subject of this book, i.e. the connection between light-solid
interactions and solid-state characteristics and properties.
The same criterion was applied in the design of the figures. Almost always
the figures do not reproduce exactly the experimental details, but are only sketches
of main trends and typical situations encountered in practice. We have chosen this
manner of illustrating the book since we considered the figures as graphical
supports of physical explanations rather than raw scientific data. Although in most
cases we refer to specific experiments, on specific materials, these examples are
chosen to evidence a concept or a trend typical for a larger category of materials,
the figures underlining this character of the examples. On the other hand, even for
Preface VII
the same material, the experimental results can differ because of the fabrication
method of the sample, because of the method used for optical characterization,
environmental conditions, etc.; no two experimental results are alike. However,
the phenomenon under investigation is still present, except for some details; its
characteristics have to be extracted from experimental data, so the trends rather
than details are important in the description of the way in which the parameters of
the samples are obtained through light-matter interactions.
Chapter J reviews the main elementary excitations encountered in the solid
state such as phonons, excitons, coupled and collective excitations. It is important
to read this chapter because· these excitations are referred to throughout the
remainder of the book, their behavior on interaction with the electromagnetic field
being in direct relation with many solid-state properties.
Chapter 2 deals with the main physical effects of light-solid interaction and
constitutes the main theoretical foundation of the book. The calculations are
presented in detail and explained in such a way that the reader should be able to
follow them easily. Also, the main experimental methods are reviewed here in
depth, together with the physical effect that has originated them. We have not
provided very detailed set-ups, many of them are only block schemes or simplified
versions. The reason is that an actual set-up is done with what is available in a
certain laboratory. However, the block scheme is the same in any experimental
arrangement. This chapter is about one quarter of the entire book and must be read
carefully by graduated students and young researchers before tackling the subjects
of the following chapters.
The next six chapters of the book are dedicated to different types of solid
state materials that interact with optical fields and so reveal their properties. The
connection between different solid-state properties and the light-solid interaction
theories and experimental facts are discussed in detail.
Chapter 3 is dedicated to doped solids, exemplified through different types
of ions introduced in crystalline hosts. The optical properties of rare-earth ions,
transition-metal ions, diluted magnetic semiconductors, manganites, color-centers,
filled-shell ions and donors and acceptors in semiconductors are presented.
Chapter 4 is focused on bulk solids, such as semiconductors or metals, and
their optical properties. A special emphasis is put here on new materials, for
example GaN or metal nanoparticles, and on special physical phenomena such as
anharmonic, isotope or many-body effects. The relaxation phenomena in bulk
solids are presented extensively, considering the excitons, carriers and phonons
relaxation behavior at excitation with ultrashort pulses.
Chapter 5 reviews briefly the optical properties of interfaces and thin films,
whereas Chapter 6 is dedicated to the optical characterization and parameter
determination of low-dimensional structures. These micro- and nanostructures are
the subject of numerous recent studies due to their unique electronic and optical
properties, not encountered in any other type of solid, and with important
applications in electronics and optoelectronics. Therefore, this chapter constitutes
a substantial part of the book. Optical properties of low-dimensional
VIII Preface
semiconductors, in particular optical absorption, luminescence, and scattering are
explained in detail, followed by optical characterization methods. Emphasis is put
on confinement effects, electronic structure and internal fields, excitons,
biexcitons, coupled excitations and microcavities, relaxation phenomena and
many-body effects. This long chapter ends with optical properties of coupled
quantum wells, superlattices and nanoparticles. The newly developed carbon
nanotubes, with huge and still not fully exploited applications in electronics, are
also mentioned briefly.
Chapter 7 is dedicated to disordered solids, in particular to the optical
properties of disordered structures, such as disordered alloys and rough surfaces,
and disordered materials, such as polycrystalline and different amorphous states.
The last chapter, Chapter 8, deals with optical methods for the investigation
of high-temperature superconductors (HTS). Since there is no satisfactory theory
to explain the HTS behavior, the optical investigation is used to test the new
theories on HTS, giving extremely valuable information about the symmetry of
the superconducting gap, the BCS or non-BCS behavior of HTS, and the
pseudogap. The book keeps pace with the most recent developments in the field,
including the unexpected discovery in March 200 I of the superconducting MgB2
intermetallic compound.
We have written this book with the goal of giving a comprehensive view of
the determination of solid parameters through the interaction with optical fields.
The reader is helped in his efforts to understand the main issues of the book by
some hundreds of references listed at the end of each chapter. The references were
selected from the most recent publications on the basis of their direct relevance to
the main issues of the book; of course, not all studies could be included and there
are most probably other papers worth mentioning, which are not referred to here.
On the other hand, some important subjects could have been missed because they
have not made a significant progress during 1996-2001, which is the period from
which we have gathered the material of the book. This is unavoidable. We have
always respected the point of view of the authors with respect to the models and
the interpretation of various experiments. We are conscious that at least some of
these models and interpretations are still under debate, and that other versions
have appeared regarding the same subject. Therefore, it is possible that some
members of the scientific community are not entirely happy with our presentation;
others will be unhappy with a different interpretation - this is how science
progress.
We hope that this book will be a helpful instrument for graduated students,
Ph.D. students and researchers in the area of solid-state physics, materials,
nanoscience, electronics, optics and optoelectronics.
We would like to thank to all the librarians of the National Atomic Physics
Institute Library-Bucharest, especially Mrs. Stela Emilia Mihalcea and Mrs.
Natalita Feroiu for their continuous efforts to provide us with hundreds of
references in a very short time. For the same reasons we are indebted to the
Preface IX
librarians of Univ. of Bucharest, Physics Faculty, especially to Mrs. Laura
Vlaescu.
We would like to thank to Dr. Claus Ascheron and Dr. Angela Lahee from
Springer Verlag for their continuous trust and support regarding our scientific
work. Their sincere encouragement and confidence has helped us to overcome the
difficulties naturally encountered in writing books with thorny subjects like this
one.
Bucharest, Daniela Dragoman,
May 2001 Mircea Dragoman
Contents
1. Elementary Excitations in Solids ......................................... .
1.1 Energy Band Structure in Crystalline Materials................. .......... 2
1.2 k· P Method .................................................................... 11
1.3 Numerical Methods of Electron Energy Band Calculation. .. ... ... .... 14
lA Phonons.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... . . . . . . . . . . . . . . ..... 16
lA.l Bose-Einstein Statistics............................................. 19
lA.2 Fermi-Dirac Statistics............................................... 19
1.5 Plasmons ........................................................................ 20
1.6 Magnetic Excitations ........................................................... 22
1.6.1 Magnons ............................................................... 24
1.7 Excitons. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26
1.7.1 Frenkel Excitons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... . .. 26
1.7.2 Wannier-Mott Excitons ............................................. 27
1.7.3 Interactions Between Excitons ..................................... 30
1.7A Bound Excitons and Excitonic Complexes ....................... 31
1.8 Polarons ........................................................................ 31
1.9 Polaritons ....................................................................... 35
References ........................................................................... 36
2. Optical Transitions ........................................................... 37
2.1 The Quantization of the Electromagnetic Radiation ...................... 37
2.2 Transition Probabilities ...................................................... 39
2.2.1 Optical Properties of Crystalline Materials ....................... 42
2.2.2 Mechanisms for Spectral Line Broadening ....................... 44
2.2.2.1 Lorentzian Broadening of Spectral Lines ................ 44
2.2.2.2 Gaussian Broadening of Spectral Line ................... 45
2.2.2.3 Voigt Profile ................................................. 46
2.2.3 Multipolar Contributions to the Interaction Hamiltonian ....... 46
2.3 Optical Constants of Solids .................................................. 47
2.3.1 Kramers-Kronig Relations .......................................... 50
2.3.2 Drude-Lorentz Theory of the Electrically
Charged Oscillators... ... ... ... ... ... ... ... ... ... ... ... .. . ... ... ...... 51
2.3.3 Sum Rule .............................................................. 54