An Introduction to the Optical Spectroscopy of Inorganic Solids

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1 An Introduction to the Optical Spectroscopy of Inorganic Solids J. García Solé, L.E. Bausá and D. Jaque Universidad Autónoma de Madrid, Madrid, Spain

3 An Introduction to the Optical Spectroscopy of Inorganic Solids

5 An Introduction to the Optical Spectroscopy of Inorganic Solids J. García Solé, L.E. Bausá and D. Jaque Universidad Autónoma de Madrid, Madrid, Spain

6 Copyright C 2005 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on or All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or ed to permreq@wiley.co.uk, or faxed to (+44) Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA , USA Wiley-VCH Verlag GmbH, Boschstr. 12, D Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data García Solé, J. (José) An introduction to the optical spectroscopy of inorganic solids / J. García Solé, and L. E. Bausá, and D. Jaque. p. cm. Includes index. ISBN (cloth) ISBN (pbk.) 1. Solids Spectra. 2. Energy-band theory of solids. 3. Solid state chemistry. 4. Chemistry, Inorganic. 5. Spectrum analysis. I. Bausá, L. E. (Louisa E.) II. Jaque, D. (Daniel) III. Title. QC O6G dc British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN (cloth) (paper) Typeset in 10/12pt Times by TechBooks, New Delhi, India Printed and bound in Great Britain by TJ International, Padstow, Cornwall This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

7 To my wife, Rosario, and my two children, Pepe and Pablo. They are the most important part of my life. José García Solé To Beatriz, Carmen, Fernando and Luis for their love. Luisa Bausá López To my family Daniel Jaque Garcia

9 Contents Preface Acknowledgments Some Physical Constants of Interest in Spectroscopy A Periodic Table of the Elements for Optical Spectroscopy xi xv xvii xix 1 Fundamentals The Origins of Spectroscopy The Electromagnetic Spectrum and Optical Spectroscopy Absorption The Absorption Coefficient The Measurement of Absorption Spectra: The Spectrophotometer Reflectivity Luminescence The Measurement of Photoluminescence: The Spectrofluorimeter Luminescent Efficiency Stokes and Anti-Stokes Shifts Time-Resolved Luminescence Scattering: The Raman Effect Advanced Topic: The Fourier Transform Spectrometer 33 Exercises 36 References and Further Reading 38 2 Light Sources Introduction Thermal Radiation and Planck s Law Lamps Tungsten and Quartz Halogen Lamps 42

10 viii CONTENTS Spectral Lamps Fluorescent Lamps High-Pressure Discharge Vapor Lamps Solid State Lamps The Laser Lasers as Light Sources in Spectroscopy The Basic Principles of Lasers Population Inversion: the Threshold Condition Pumping Techniques The Resonator Types of Lasers The Excimer Laser Gas Lasers Dye Lasers Semiconductor Lasers Solid State Lasers The Tunability of Laser Radiation Tunable Solid State Lasers Tunable Coherent Radiation by Frequency-Mixing Techniques Optical Parametric Oscillation and Amplification Advanced Topics: Site Selective Spectroscopy and Excited State Absorption Site Selective Spectroscopy Excited State Absorption 73 Exercises 74 References and Further Reading 74 3 Monochromators and Detectors Introduction Monochromators Detectors Basic Parameters Types of Detectors The Photomultiplier The Working Principles of a Photomultiplier Noise in Photomultipliers Optimization of the Signal-to-Noise Ratio The Averaging Procedure The Lock-in Amplifier The Photon Counter The Optical Multichannel Analyzer Detection of Pulses Digital Oscilloscopes The Boxcar Integrator 107

11 CONTENTS 3.7 Advanced Topics: The Streak Camera and the Autocorrelator The Streak Camera The Autocorrelator 109 Exercises 111 References and Further Reading 112 ix 4 The Optical Transparency of Solids Introduction Optical Magnitudes and the Dielectric Constant The Lorentz Oscillator Metals Ideal Metal Damping Effects Semiconductors and Insulators The Spectral Shape of the Fundamental Absorption Edge The Absorption Edge for Direct Transitions The Absorption Edge for Indirect Transitions Excitons Weakly Bound (Mott Wannier) Excitons Tightly Bound (Frenkel) Excitons Advanced Topic: The Color of Metals 144 Exercises 146 References and Further Reading Optically Active Centers Introduction Static Interaction Crystalline Field Theory Molecular Orbital Theory Band Intensities The Absorption Probability Allowed Transitions and Selection Rules Polarized Transitions The Probability of Spontaneous Emission The Effect of the Crystal on the Transition Probabilities Oscillator Strength: Smakula s Formula Dynamic Interaction: The Configurational Coordinate Diagram Band Shape: The Huang Rhys Coupling Parameter Nonradiative Transitions Multiphonon Emission Energy Transfer The Concentration Quenching of Luminescence Advanced Topic: The Determination of Quantum Efficiencies 191

12 x CONTENTS Exercises 195 References and Further Reading Applications: Rare Earth and Transition Metal Ions, and Color Centers Introduction Rare Earth Ions Trivalent Rare Earth Ions: The Dieke Diagram Divalent Rare Earth Ions Nonradiative Transitions in Rare Earth Ions: The Energy-Gap Law Transition Metal Ions d 1 Ions d n Ions: Sugano Tanabe Diagrams Color centers Advanced Topics: The Judd and Ofelt Formalism, and Optical Cooling of Solids The Judd and Ofelt Formalism Optical Cooling of Solids 228 Exercises 231 References and Further Reading Group Theory and Spectroscopy Introduction Symmetry Operations and Classes Representations: The Character Table Reduction in Symmetry and The Splitting of Energy Levels Selection Rules for Optical Transitions Illustrative Examples Advanced Topic: The Application to Optical Transitions of Kramers Ions 256 Exercises 260 References and Further Reading 262 Appendix A1 The Joint Density of States 263 Appendix A2 The Effect of an Octahedral Field on a d 1 Valence Electron 266 Appendix A3 The Calculation of the Probability of Spontaneous Emission by Means of Einstein s Thermodynamic Treatment 271 Appendix A4 The Determination of Smakula s Formula 274 Index 277

13 Preface This book treats the most basic aspects to be initiated into the field of the optical spectroscopy of solids, so that a student with some background in quantum physics, optics, and solid state physics may be able to interpret simple optical spectra (absorption, reflectivity, emission, scattering, etc.) and learn about the main basic instrumentation used in this field. The term optical spectroscopy refers only to the range of interacting electromagnetic radiation lying within the so-called optical range ; a range that includes the visible and a small part of the ultraviolet and infrared spectral regions, at about nm. We improperly label this radiation as light, while this term only strictly refers to that radiation which can be detected by the human eye. The term solids includes metals, semiconductors and insulators. Although most of the material treated in this book concerns the spectroscopy of centers embedded in inorganic materials, the principles described here are also applicable to molecules and atoms in the gaseous and/or the liquid state. Although a number of excellent books covering the field of optical spectroscopy are available, they are mostly extensive books, due to their systematic and formal contents. Thus, we aimed to write this book for a number of specific reasons: (i) Members of several scientific communities (analytical chemistry, solid state physics, photonics, etc.) may be interested in a simple introductory book, since the basic concepts of spectroscopy and the instrumentation treated in this text apply to solid as well as to molecular systems. (ii) An introductory book is appropriate because a number of optical spectroscopic techniques are used in many laboratories for material characterization. (iii) Spectroscopy is a topic that is now included in several courses for undergraduate and postgraduate students. (iv) The research area of optical materials is, at present, an activity within the modern and more general area of photonics. A great variety of optical materials are based on inorganic materials activated with optically active ions (centers).

14 xii PREFACE Any experiment involving optical spectroscopy consists of a light source, a sample, and a detection recording system. According to this scheme, this book is organized as follows. The book starts with a short introduction to the fundamentals of optical spectroscopy, (Chapter 1) describing the basic standard equipment needed to measure optical spectra and the main optical magnitudes (the absorption coefficient, transmittance, reflectance, and luminescence efficiency) that can be measured with this equipment. The next two chapters (Chapters 2 and 3) are devoted to the main characteristics and the basic working principles of the general instrumentation used in optical spectroscopy. These include the light sources (lamp and lasers) used to excite the crystals, as well as the instrumentation used to detect and analyze the reflected, transmitted, scattered, or emitted light. Chapter 4, presents details of the absorption and reflectivity spectra of pure crystals. The first part of this chapter connects the optical magnitudes that can be measured by spectrophotometers with the dielectric constant. We then consider how the valence electrons of the solid units (atoms or ions) respond to the electromagnetic field of the optical radiation. This establishes a frequency dependence of the dielectric constant, so that the absorption and reflectivity spectrum (the transparency) of a solid can be predicted. The last part of this chapter focuses on the main features of the spectra associated with metals, insulators, and semiconductors. The absorption edge and excitonic structure of band gap (semiconductors or insulator) materials are also treated. Chapters 5 and 6 deal with the spectra of optically active centers. The term optically active center corresponds to a dopant ion and its environment (or to a color center), which produces absorption and/or emission bands that are different to those of the pure crystalline host. This is the case for a large variety of optical materials, such as phosphors, solid state lasers, and amplifiers. In Chapter 5, we discuss in a simple way static (crystalline field) and dynamic (coordinate configuration model) effects on the optically active centers and how they affect their spectra (the peak position, and the shape and intensity of optical bands). We also introduce nonradiative depopulation mechanisms (multiphonon emission and energy transfer) in order to understand the ability of a particular center to emit light; in other words, the competition between the mechanisms of radiative de-excitation and nonradiative de-excitation. Chapter 6 is devoted to discussing the main optical properties of transition metal ions (3d n outer electronic configuration), trivalent rare earth ions (4f n 5s 2 5p 6 outer electronic configuration), and color centers, based on the concepts introduced in Chapter 5. These are the usual centers in solid state lasers and in various phosphors. In addition, these centers are very interesting from a didactic viewpoint. We introduce the Tanabe Sugano and Dieke diagrams and their application to the interpretation of the main spectral features of transition metal ion and trivalent rare earth ion spectra, respectively. Color centers are also introduced in this chapter, special attention being devoted to the spectra of the simplest F centers in alkali halides.

15 PREFACE Chapter 7 is a very simple introduction to group theory and its usefulness to interpreting the optical spectra of active centers. The purpose of this chapter is to present some basic concepts, for non-specialists in group theory, so they can evaluate its potential and, hopefully the feasibility of applying it to simple problems, such as the determination and labeling of the energy levels of an active center by means of the character table of its symmetry group. Finally, the book includes a collection of illustrative examples and a variety of specifically selected spectra. A number of these spectra correspond to systems that have actually been investigated in our laboratory. José García Solé Luisa Bausá Daniel Jaque Madrid, June 2004 xiii

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