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An Introduction to the Optical Spectroscopy of Inorganic Solids J. Garc´ ıa Sol´ e, L.E. Baus ´ a and D. Jaque Universidad Aut´ onoma de Madrid, Madrid, Spain
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An Introduction to theOptical Spectroscopy
of Inorganic Solids
J. Garca Sole, L.E. Bausa and D. JaqueUniversidad Autonoma de Madrid, Madrid, Spain
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An Introduction to theOptical Spectroscopy
of Inorganic Solids
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An Introduction to theOptical Spectroscopy
of Inorganic Solids
J. Garca Sole, L.E. Bausa and D. JaqueUniversidad Autonoma de Madrid, Madrid, Spain
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Library of Congress Cataloging-in-Publication Data
Garca Sole, J. (Jose)An introduction to the optical spectroscopy of inorganic solids / J. Garca Sole,
and L. E. Bausa, and D. Jaque.p. cm.
Includes index.ISBN 0-470-86885-6 (cloth)ISBN 0-470-86886-4 (pbk.)1. SolidsSpectra. 2. Energy-band theory of solids. 3. Solid state chemistry.
4. Chemistry, Inorganic. 5. Spectrum analysis.I. Bausa, L. E. (Louisa E.) II. Jaque, D. (Daniel) III. Title.
QC176 .8 . O6G25 2005530 .41dc22 2004018408
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0-470-86885 6 (cloth)0-470-86886 4 (paper)
Typeset in 10/12pt Times by TechBooks, New Delhi, IndiaPrinted and bound in Great Britain by TJ International, Padstow, CornwallThis book is printed on acid-free paper responsibly manufactured from sustainable forestryin which at least two trees are planted for each one used for paper production.
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To my wife, Rosario, and my two children, Pepe and Pablo. They are themost important part of my life.
Jose Garca Sole
To Beatriz, Carmen, Fernando and Luis for their love.Luisa Bausa Lopez
To my familyDaniel Jaque Garcia
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Contents
Preface xi
Acknowledgments xv
Some Physical Constants of Interest in Spectroscopy xvii
A Periodic Table of the Elements for Optical Spectroscopy xix
1 Fundamentals 11.1 The Origins of Spectroscopy 11.2 The Electromagnetic Spectrum and Optical Spectroscopy 21.3 Absorption 8
1.3.1 The Absorption Coefficient 81.3.2 The Measurement of Absorption Spectra: The Spectrophotometer 111.3.3 Reflectivity 15
1.4 Luminescence 161.4.1 The Measurement of Photoluminescence: The Spectrofluorimeter 171.4.2 Luminescent Efficiency 201.4.3 Stokes and Anti-Stokes Shifts 221.4.4 Time-Resolved Luminescence 25
1.5 Scattering: The Raman Effect 281.6 Advanced Topic: The Fourier Transform Spectrometer 33Exercises 36References and Further Reading 38
2 Light Sources 392.1 Introduction 39
2.1.1 Thermal Radiation and Plancks Law 392.2 Lamps 41
2.2.1 Tungsten and Quartz Halogen Lamps 42
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viii CONTENTS
2.2.2 Spectral Lamps 422.2.3 Fluorescent Lamps 432.2.4 High-Pressure Discharge Vapor Lamps 442.2.5 Solid State Lamps 44
2.3 The Laser 452.3.1 Lasers as Light Sources in Spectroscopy 452.3.2 The Basic Principles of Lasers 472.3.3 Population Inversion: the Threshold Condition 482.3.4 Pumping Techniques 512.3.5 The Resonator 52
2.4 Types of Lasers 522.4.1 The Excimer Laser 532.4.2 Gas Lasers 552.4.3 Dye Lasers 572.4.4 Semiconductor Lasers 602.4.5 Solid State Lasers 62
2.5 The Tunability of Laser Radiation 642.5.1 Tunable Solid State Lasers 642.5.2 Tunable Coherent Radiation by Frequency-Mixing Techniques 672.5.3 Optical Parametric Oscillation and Amplification 68
2.6 Advanced Topics: Site Selective Spectroscopy and ExcitedState Absorption 712.6.1 Site Selective Spectroscopy 722.6.2 Excited State Absorption 73
Exercises 74References and Further Reading 74
3 Monochromators and Detectors 773.1 Introduction 773.2 Monochromators 773.3 Detectors 82
3.3.1 Basic Parameters 833.3.2 Types of Detectors 84
3.4 The Photomultiplier 933.4.1 The Working Principles of a Photomultiplier 933.4.2 Noise in Photomultipliers 97
3.5 Optimization of the Signal-to-Noise Ratio 1013.5.1 The Averaging Procedure 1013.5.2 The Lock-in Amplifier 1013.5.3 The Photon Counter 1033.5.4 The Optical Multichannel Analyzer 104
3.6 Detection of Pulses 1063.6.1 Digital Oscilloscopes 1073.6.2 The Boxcar Integrator 107
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CONTENTS ix
3.7 Advanced Topics: The Streak Camera and the Autocorrelator 1083.7.1 The Streak Camera 1083.7.2 The Autocorrelator 109
Exercises 111References and Further Reading 112
4 The Optical Transparency of Solids 1134.1 Introduction 1134.2 Optical Magnitudes and the Dielectric Constant 1134.3 The Lorentz Oscillator 1164.4 Metals 122
4.4.1 Ideal Metal 1234.4.2 Damping Effects 126
4.5 Semiconductors and Insulators 1274.6 The Spectral Shape of the Fundamental Absorption Edge 131
4.6.1 The Absorption Edge for Direct Transitions 1334.6.2 The Absorption Edge for Indirect Transitions 135
4.7 Excitons 1394.7.1 Weakly Bound (MottWannier) Excitons 1404.7.2 Tightly Bound (Frenkel) Excitons 143
4.8 Advanced Topic: The Color of Metals 144Exercises 146References and Further Reading 149
5 Optically Active Centers 1515.1 Introduction 1515.2 Static Interaction 152
5.2.1 Crystalline Field Theory 1535.2.2 Molecular Orbital Theory 159
5.3 Band Intensities 1615.3.1 The Absorption Probability 1615.3.2 Allowed Transitions and Selection Rules 1635.3.3 Polarized Transitions 1655.3.4 The Probability of Spontaneous Emission 1665.3.5 The Effect of the Crystal on the Transition Probabilities 1675.3.6 Oscillator Strength: Smakulas Formula 168
5.4 Dynamic Interaction: The Configurational Coordinate Diagram 1705.5 Band Shape: The HuangRhys Coupling Parameter 1755.6 Nonradiative Transitions 181
5.6.1 Multiphonon Emission 1825.6.2 Energy Transfer 1835.6.3 The Concentration Quenching of Luminescence 188
5.7 Advanced Topic: The Determination of Quantum Efficiencies 191
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Exercises 195References and Further Reading 197
6 Applications: Rare Earth and Transition Metal Ions, andColor Centers 1996.1 Introduction 1996.2 Rare Earth Ions 200
6.2.1 Trivalent Rare Earth Ions: The Dieke Diagram 2006.2.2 Divalent Rare Earth Ions 205
6.3 Nonradiative Transitions in Rare Earth Ions: The Energy-Gap Law 2066.4 Transition Metal Ions 210
6.4.1 3d1 Ions 2116.4.2 3dn Ions: SuganoTanabe Diagrams 212
6.5 Color centers 2206.6 Advanced Topics: The Judd and Ofelt Formalism, and
Optical Cooling of Solids 2246.6.1 The Judd and Ofelt Formalism 2256.6.2 Optical Cooling of Solids 228
Exercises 231References and Further Reading 233
7 Group Theory and Spectroscopy 2357.1 Introduction 2357.2 Symmetry Operations and Classes 2367.3 Representations: The Character Table 2407.4 Reduction in Symmetry and The Splitting of Energy Levels 2447.5 Selection Rules for Optical Transitions 2517.6 Illustrative Examples 2537.7 Advanced Topic: The Application to Optical Transitions of
Kramers Ions 256Exercises 260References and Further Reading 262
Appendix A1 The Joint Density of States 263Appendix A2 The Effect of an Octahedral Field on a d1 Valence
Electron 266Appendix A3 The Calculation of the Probability of Spontaneous
Emission by Means of Einsteins ThermodynamicTreatment 271
Appendix A4 The Determination of Smakulas Formula 274
Index 277
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Preface
This book treats the most basic aspects to be initiated into the field of the optical spec-troscopy 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 instrumentationused in this field.
The term optical spectroscopy refers only to the range of interacting electro-magnetic radiation lying within the so-called optical range; a range that includesthe visible and a small part of the ultraviolet and infrared spectral regions, at about2003000 nm. We improperly label this radiation as light, while this term onlystrictly refers to that radiation which can be detected by the human eye. The termsolids includes metals, semiconductors and insulators. Although most of the mate-rial treated in this book concerns the spectroscopy of centers embedded in inorganicmaterials, the principles described here are also applicable to molecules and atoms inthe gaseous and/or the liquid state.
Although a number of excellent books covering the field of optical spectroscopyare available, they are mostly extensive books, due to their systematic and formalcontents. Thus, we aimed to write this book for a number of specific reasons:
(i) Members of several scientific communities (analytical chemistry, solid statephysics, photonics, etc.) may be interested in a simple introductory book, sincethe basic concepts of spectroscopy and the instrumentation treated in this textapply to solid as well as to molecular systems.
(ii) An introductory book is appropriate because a number of optical spectroscopictechniques are used in many laboratories for material characterization.
(iii) Spectroscopy is a topic that is now included in several courses for undergraduateand postgraduate students.
(iv) The research area of optical materials is, at present, an activity within the modernand more general area of photonics. A great variety of optical materials are basedon inorganic materials activated with optically active ions (centers).
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xii PREFACE
Any experiment involving optical spectroscopy consists of a light source, a sample,and a detectionrecording system. According to this scheme, this book is organizedas follows.
The book starts with a short introduction to the fundamentals of optical spec-troscopy, (Chapter 1) describing the basic standard equipment needed to measureoptical spectra and the main optical magnitudes (the absorption coefficient, trans-mittance, reflectance, and luminescence efficiency) that can be measured with thisequipment. The next two chapters (Chapters 2 and 3) are devoted to the main char-acteristics and the basic working principles of the general instrumentation used inoptical spectroscopy. These include the light sources (lamp and lasers) used to excitethe 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 byspectrophotometers with the dielectric constant. We then consider how the valenceelectrons of the solid units (atoms or ions) respond to the electromagnetic fieldof the optical radiation. This establishes a frequency dependence of the dielectricconstant, so that the absorption and reflectivity spectrum (the transparency) of a solidcan be predicted. The last part of this chapter focuses on the main features of thespectra associated with metals, insulators, and semiconductors. The absorption edgeand excitonic structure of band gap (semiconductors or insulator) materials are alsotreated.
Chapters 5 and 6 deal with the spectra of optically active centers. The termoptically active center corresponds to a dopant ion and its environment (or to a colorcenter), which produces absorption and/or emission bands that are different to thoseof 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 theyaffect their spectra (the peak position, and the shape and intensity of optical bands).We also introduce nonradiative depopulation mechanisms (multiphonon emission andenergy 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-excitationand nonradiative de-excitation.
Chapter 6 is devoted to discussing the main optical properties of transition metalions (3dn outer electronic configuration), trivalent rare earth ions (4fn5s25p6 outerelectronic configuration), and color centers, based on the concepts introduced inChapter 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 introducethe TanabeSugano and Dieke diagrams and their application to the interpretation ofthe main spectral features of transition metal ion and trivalent rare earth ion spectra,respectively. Color centers are also introduced in this chapter, special attention beingdevoted to the spectra of the simplest F centers in alkali halides.
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PREFACE xiii
Chapter 7 is a very simple introduction to group theory and its usefulness tointerpreting the optical spectra of active centers. The purpose of this chapter is topresent some basic concepts, for non-specialists in group theory, so they can evaluateits potential and, hopefully the feasibility of applying it to simple problems, such asthe determination and labeling of the energy levels of an active center by means ofthe character table of its symmetry group.
Finally, the book includes a collection of illustrative examples and a variety ofspecifically selected spectra. A number of these spectra correspond to systems thathave actually been investigated in our laboratory.
Jose Garca SoleLuisa Bausa
Daniel JaqueMadrid, June 2004
