Daniela Dragoman Mircea Dragoman Optical Characterization of Solids

Transcription

1 Daniela Dragoman Mircea Dragoman Optical Characterization of Solids

2 Springer-Verlag Berlin Heidelberg GmbH Physics and Astronomy ONLINE LIBRARY

3 D. Dragoman M. Dragoman Optical Characterization of Solids With 184 Figures i Springer

4 Professor Daniela Dragoman University of Bucharest, Physics Department P.O. Box MG-ll Bucharest, Romania Professor Mircea Dragoman National Institute for Research and Development in Microtechnologies (IMT) P.O. Box Bucharest, Romania 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 (Physics and astronomy online library) 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 microillm or in other ways. 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 in its current version. and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law. ISBN ISBN (ebook) DOl / Springer-Verlag Berlin Heidelberg 2002 Originally published by Springer-Verlag Berlin Heidelberg New York in Softcover reprint of the hardcover 1st edition 2002 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. Typesetting: Camera-ready copy from authors Cover concept: design & production GmbH. Heidelberg Printed on acid-free paper SPIN: /3020 CU

5 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

6 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 solidstate 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

7 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 solidstate 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

8 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 , 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

9 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, May 2001 Daniela Dragoman, Mircea Dragoman

10 Contents 1. Elementary Excitations in Solids Energy Band Structure in Crystalline Materials k P Method Numerical Methods of Electron Energy Band Calculation la Phonons la.l Bose-Einstein Statistics la.2 Fermi-Dirac Statistics Plasmons Magnetic Excitations Magnons Excitons Frenkel Excitons Wannier-Mott Excitons Interactions Between Excitons A Bound Excitons and Excitonic Complexes Polarons Polaritons References Optical Transitions The Quantization of the Electromagnetic Radiation Transition Probabilities Optical Properties of Crystalline Materials Mechanisms for Spectral Line Broadening Lorentzian Broadening of Spectral Lines Gaussian Broadening of Spectral Line Voigt Profile Multipolar Contributions to the Interaction Hamiltonian Optical Constants of Solids Kramers-Kronig Relations Drude-Lorentz Theory of the Electrically Charged Oscillators Sum Rule... 54

11 XII Contents Microscopic Origin of Absorption Absorption Mechanisms Band-to-Band Light Absorption: Direct and Allowed Absorption Band-to-Band Direct, Forbidden Transitions Band-to-Band Indirect, Allowed Transitions Band-to-Band Indirect, Forbidden Transitions Effects That Can Appear at Band-to-Band Absorption Intraband Absorption Absorption on Free Carriers Absorption on Wannier-Mott Excitons Indirect Excitonic Absorption Biexciton Production Through Photon Absorption Light Absorption on Phonons Optical Properties of Solids in External Magnetic Fields Energy Levels in Magnetic Field Interaction of Electromagnetic Radiation with a System in a Magnetic Field Light Interaction with Metals in Magnetic Field Phenomena at Low Frequencies The Shubnikov-de Haas Effect Photoluminescence Inelastic Light Scattering Raman Scattering Brillouin Scattering Nonlinear Optical Response of Solids Nonlinear Raman Effect Stimulated Raman Effect Inverse Raman Scattering Hyper-Raman Effect Coherent Anti-Stokes Raman Scattering (CARS) Optical Methods for the Characterization of Light-Matter Interaction Transmission/Reflection Spectroscopy Modulated Reflectance and Transmittance Pump-Probe Spectroscopy Amplitude and Phase Spectroscopy Photoluminescence Light Scattering Four-Wave Mixing Optical Bloch Equations Quantum Beats and Polarization Beats Spectral Hole Burning

12 Contents XIII Fluorescence Line Narrowing Magneto-Optical Kerr Effect Line Identification References Optical Properties ofimpurities in Solids Electronic Structure ofisolated Atoms Ions in Crystals Frank-Condon Principle for Defects with Large Orbits Jahn-Teller Effect Interactions Between Ions Spatial Migration Optical Properties of the Rare-Earth Ions J udd-ofelt Theory of One and Two Photon Transitions Optical Spectra of Rare-Earth Ions Interaction Processes for Rare-Earth Ions Transition Metal Ions Optical Properties of Transition Metal Ions Iron-Group Ion Pairs Diluted Magnetic Semiconductors Manganites Color Centers Filled-Shell Ions Optical Properties of Donors and Acceptors in Semiconductors References Bulk Materials Electronic Structure Excitons in Bulk Semiconductors Anharmonic Effects Isotope Effects Effects Due to Alloying Deformation Potentials Optical Determination of Magnetic Properties Rotational Spectra of Solids Many-Body Effects Coupled Excitations Relaxation Phenomena in Bulk Semiconductors Exciton Relaxation Carrier Relaxation Phonon Relaxation Optical Properties of Metals Phase Transitions References

13 XIV Contents 5. Optical Properties of Interfaces and Thin Films Surface Effects Thin Films Magnetic Thin Films References Low-Dimensional Structures Low-Dimensional Semiconductor Heterostructures l.l Quantum Well Excitons Optical Properties of Low-Dimensional Semiconductor Heterostructures Intraband Absorption Excitonic Absorption Luminescence Scattering in Low-Dimensional Heterostructures Intersubband Optical Transitions Depolarization Shift and Coulomb Renormalization Radiative Intraband Transitions in Heterostructures Collective Excitations Nonlinear Optics Optical Characterization of Low-Dimensional Semiconductor Heterostructures Confinement Effects Optical Determination Electronic Structure Parameters Determination of Internal Electric Fields Diffusion Optical Properties of Excitons Biexcitons Magnetic Properties Collective Excitations Coupled Excitations Quantum Microcavities Relaxation Phenomena in Low Dimensional Structures Many-Body Effects Coupled Quantum Wells Carbon Nanotubes Optical Properties of Superlattices Band Structure Excitons in Superlattices Other Parameters Nanoparticies References

14 Contents XV 7. Optical Properties of Disordered Materials Disordered Alloys Disordered Superiattices Rough Surfaces Po1ycrystalline and Nanocrystalline Materials Continuous-Network Structures Optical Properties of Amorphous Materials Theory of Electronic States in Amorphous Semiconductors General Optical Properties of Amorphous Semiconductors Tetrahedrally Coordinated Amorphous Semiconductors Chalcogenide Glasses Other Amorphous Materials References Optical Properties of High-Temperature Superconductors High-Temperature Superconductors Optical Methods for HTS Investigation Anisotropy of Optical Response Observation of Superconducting Transition Symmetry of Superconducting Gap Non-BCS Behavior BCS-Like Behavior HTS Dynamics Pseudogap References Index Index of Materials