Optical Spectroscopy of Inorganic Solids

by Henderson, B.; Imbusch, G. F.

• ISBN13: 9780199298624
• ISBN10: 0199298629
• Format: Paperback
• Copyright: 2006-07-20
• Publisher: Oxford University Press

Summary

The beautiful colors of many inorganic compounds, including minerals and gemstones, as well as the mysterious cold light of luminescence emitted by these materials, have attracted the inquisitiveness of natural philosophers for centuries. The scientific study of such phenomena - the optical spectroscopy of solids - has paid rich dividends in technological advances such as lasers and other optronic devices. This is a book on the art of optical spectroscopy of solids, establishing a theoretical and experimental framework for the subject, which is well illustrated with relevant spectra and experimental data. Chapters 1 to 5 set down the quantum description of atoms, ions and defects in solids, and the interaction of such centers with electromagnetic radiation. Considerations of symmetry and the effects of lattice vibrations on the spectroscopic properties are treated in detail. The physical bases of prominent experimental techniques are presented in Chapter 6 and their application to color centers, dopant rare-earth and transition-metal ions are described in Chapters 7 -9. The spectroscopic behaviors of magnetic ions at high concentration are detailed in Chapter 10, followed by a brief review of the operational features of solid state lasers that rely on the foregoing discussion of their optical characteristics. Finally, Chapter 12 describes the application of magneto-optical double resonance techniques to the elucidation of the optical properties of insulating and semi-conducting materials. The authors emphasize that their own interests have guided the selection of topics from the panoply of available choices. They have written the book with senior undergraduates and postgraduates in mind: it is expected also to be useful to seasoned investigators from solid state physics and engineering from inorganic chemistry, and from materials and geological sciences.

Table of Contents

1 Spectroscopy and electronic structure of inorganic solids	1	(28)
1.1 Historical comments	1	(2)
1.2 The classical optical constants	3	(5)
1.2.1 Resonance models for the optical constants	5	(3)
1.3 Spectroscopy and quantum mechanics	8	(1)
1.4 Atoms and ions in solids	9	(9)
1.5 Optical properties of solids	18	(8)
1.5.1 Interband optical transitions	20	(6)
1.5.2 Bandgap transitions	26	(1)
Appendix 1A Excitons in crystalline solids	26	(3)
2 Energy levels of free atoms and of optical centres in crystals	29	(49)
2.1 Electronic structure of one-electron atoms	29	(6)
2.1.1 Orbital angular momentum	30	(2)
2.1.2 Electron spin	32	(1)
2.1.3 The coupled representation—total angular momentum	32	(1)
2.1.4 Spin-orbit coupling	33	(2)
2.2 Transitions between stationary states	35	(1)
2.3 Multi-electron atoms	36	(9)
2.3.1 The central field Hamiltonian	36	(2)
2.3.2 Exchange symmetry	38	(1)
2.3.3 Classification of wavefunctions of the central field Hamiltonian	39	(1)
2.3.4 Wavefunctions and energy levels for outer electrons	40	(1)
2.3.5 The case of two p electrons	41	(3)
2.3.6 Spin-orbit coupling for multi-electron atoms	44	(1)
2.4 Optical centres in a static crystalline environment	45	(5)
2.4.1 The crystal field	48	(2)
2.5 Energy levels of F-centres and related defects	50	(17)
2.5.1 F-centre models based on square-well potentials	51	(8)
2.5.2 Continuum models for defects	59	(4)
2.5.3 Continuum models of vacancy aggregate centres	63	(4)
2.6 Crystal field states of a single 3d electron	67	(11)
2.6.1 (3d)¹ electronic configuration in an octahedral crystal field	67	(7)
2.6.2 The distorted octahedron: lower-symmetry crystal fields	74	(2)
2.6.3 (3d)¹ electronic configuration in a tetrahedral crystal field	76	(2)
3 Symmetry and group representation theory	78	(68)
3.1 Fundamentals of group theory	78	(42)
3.1.1 Symmetry and symmetry operators	78	(1)
3.1.2 Group theory and quantum mechanics I	79	(4)
3.1.3 Properties of groups and sets	83	(1)
3.1.4 Group representations	84	(9)
3.1.5 Group theory and quantum mechanics II	93	(2)
3.1.6 Product spaces and product representations	95	(2)
3.1.7 Theorems on matrix elements	97	(2)
3.1.8 Reduction in symmetry and splitting of energy levels	99	(4)
3.1.9 The full rotation group	103	(7)
3.1.10 The octahedral double group, O'	110	(1)
3.1.11 Other point symmetry groups	111	(3)
3.1.12 Decomposition of irreducible representations of the full rotation group	114	(3)
3.1.13 Splitting due to spin–orbit coupling	117	(3)
3.2 Multi-(3d) electron systems	120	(14)
3.2.1 Two-(3d) electron wavefunctions	122	(4)
3.2.2 Energy levels of (3d)n electron systems in an octahedral field	126	(3)
3.2.3 Energy levels of (3d)n electron systems in a tetrahedral field	129	(3)
3.2.4 Lower-symmetry fields and spin–orbit coupling	132	(2)
Appendix 3A Clebsch–Gordan coefficients for basis functions of the full rotation group	134	(5)
Appendix 3B Clebsch–Gordon coefficients for octahedral basis functions	139	(7)
4 Radiative transition rates and selection rules	146	(37)
4.1 Time-dependent perturbation theory	146	(4)
4.2 The radiation field	150	(3)
4.3 Interaction between the electronic centre and the radiation field	153	(5)
4.3.1 The electromagnetic interaction Hamiltonian	154	(3)
4.3.2 Local field correction in solids	157	(1)
4.4 Spontaneous and stimulated optical transitions	158	(14)
4.4.1 Einstein A and B coefficients	158	(2)
4.4.2 Calculation of the spontaneous transition probability	160	(2)
4.4.3 The absorption coefficient	162	(4)
4.4.4 The lifetime and natural linewidth of transitions	166	(6)
4.5 Selection rules and oscillator strengths in optical centres	172	(9)
4.5.1 Oscillator strengths for optical transitions	172	(2)
4.5.2 Selection rules and the Wigner–Eckhart theorem	174	(7)
Appendix 4A Electric and magnetic dipole operators for RCP and LCP radiation	181	(2)
5 Electronic centres in a vibrating crystalline environment	183	(75)
5.1 General considerations	183	(1)
5.2 Lattice vibrations	184	(8)
5.2.1 The linear harmonic oscillator	184	(1)
5.2.2 The linear monatomic chain	185	(7)
5.3 The coupled electron–lattice system	192	(5)
5.4 Radiative transitions using the configurational coordinate model	197	(21)
5.4.1 Absorption transitions	199	(9)
5.4.2 Emission transitions	208	(1)
5.4.3 Vibronic coupling and electronic degeneracy	209	(4)
5.4.4 Observed bandshapes	213	(5)
5.4.5 Deficiencies of the configurational coordinate model	218	(1)
5.5 The electron–lattice interaction in the weak coupling limit	218	(7)
5.5.1 Radiative transitions in the weak coupling limit	221	(4)
5.6 Vibronic processes in broad bands	225	(3)
5.7 Phonon-induced relaxation processes	228	(14)
5.7.1 Direct relaxation between adjacent levels	228	(3)
5.7.2 Raman and Orbach relaxation processes	231	(3)
5.7.3 Intrinsic Raman broadening processes	234	(1)
5.7.4 Linewidths of zero-phonon transitions	235	(2)
5.7.5 Experimental studies of line broadening	237	(1)
5.7.6 Phonon-induced line shifts	238	(4)
5.8 Non-radiative transitions involving multiphonon emission	242	(16)
5.8.1 Non-radiative transitions on F-centres	245	(2)
5.8.2 Non-radiative transitions on dopant ions	247	(11)
6 Experimental techniques	258	(57)
6.1 Optical absorption spectroscopy	258	(5)
6.1.1 Experimental considerations	259	(1)
6.1.2 Absorption coefficient and oscillator strengths	260	(3)
6.2 Luminescence measurements	263	(11)
6.2.1 Phase-sensitive detection	264	(3)
6,2.2 Excitation spectroscopy	267	(4)
6.2.3 Radiative lifetime measurements	271	(3)
6.3 Polarized absorption and luminescence	274	(4)
6.3.1 General considerations	274	(2)
6.3.2 Application to cubic crystals	276	(2)
6.3.3 Non-cubic crystals	278	(1)
6.4 Perturbation spectroscopy	278	(7)
6.4.1 Piezospectroscopy	280	(2)
6.4.2 The Zeeman effect	282	(3)
6.4.3 Electric field effects	285	(1)
6.5 Method of moments in optical spectroscopy	285	(5)
6.5.1 Moments of a vibronically broadened band	287	(1)
6.5.2 Application to perturbation spectroscopy	288	(2)
6.6 Optically detected magnetic resonance (ODMR)	290	(11)
6.6.1 Basic features of ESR and ENDOR	291	(2)
6.6.2 The ODMR experiment	293	(2)
6.6.3 Magnetic circular dichroism (MCD)	295	(4)
6.6.4 Advantages of ODMR spectroscopy	299	(2)
6.7 Laser spectroscopy	301	(10)
6.7.1 Developments in tunable lasers	301	(1)
6.7.2 Scattering experiments	302	(2)
6.7.3 Optical hole burning and fluorescence line narrowing spectro-scopies	304	(7)
6.8 Picosecond spectroscopy of solids	311	(4)
7 Colour centres in ionic crystals	315	(72)
7.1 Models of colour centres	315	(2)
7.2 Single vacancy centres in alkali halides	317	(18)
7.2.1 F+-centres	317	(2)
7.2.2 ESR of F-centres	319	(2)
7.2.3 Optical absorption by F-centres	321	(1)
7.2.4 Electron–phonon interaction at F-centres	322	(3)
7.2.5 Excited states of the F-centres	325	(3)
7.2.6 Uniaxial stress, Stark and Zeeman spectroscopy	328	(6)
7.2.7 F- -centres	334	(1)
7.3 Single vacancy centres in other crystals	335	(8)
7.3.1 One-electron centres	335	(5)
7.3.2 Two-electron centres in oxides	340	(3)
7.4 Vacancy aggregate centres	343	(34)
7.4.1 Kinetics of aggregation	346	(2)
7,4.2 Positions and shapes of F2-, F3-, and F4-bands	348	(5)
7.4.3 Uniaxial stress and Stark eflects for orthorhombic centres	353	(4)
7.4.4 Perturbation spectroscopy of trigonal centres	357	(12)
7.4.5 F-centre aggregates in other crystals	369	(2)
7.4.6 FA-centres	371	(6)
7.5 Optical properties of trapped hole centres	377	(10)
7.5.1 Self-trapped hole or [X-2]-centre	377	(5)
7.5.2 V-centre—the antimorph of the F-centre	382	(2)
7.5.3 Interstitial trapped hole centres	384	(1)
7.5.4 Impurity-related hole centres	385	(2)
8 Spectroscopy of lanthanide (rare-earth) and actinide ions in solids	387	(21)
8.1 Energy levels and eigenstates of the 4fn electrons	388	(6)
8.2 Selection rules for radiative transitions on rare-earth ions	394	(2)
8.3 Specific trivalent rare-earth ions	396	(7)
8.4 Emission from divalent rare-earth ions	403	(1)
8.5 Charge transfer absorption bands	404	(1)
8.6 Defect site spectroscopy	404	(1)
8.7 Spectroscopy of actinide ions	405	(1)
8.8 Rare-earth ions in glass	406	(2)
9 Optical spectroscopy of transition metal ions in solids	408	(37)
9.1 Energy levels and radiative transitions on transition metal ions	409	(1)
9.2 Non-radiative transitions on transition metal ions in solids	409	(1)
9.3 Spectroscopy of Cr³+ (3d3) ions	410	(22)
9.3.1 Energy levels of Cr³+ ions	410	(5)
9.3.2 Spectroscopy of Cr³+ ions in magnesium and aluminium oxides	415	(13)
9.3.3 Luminescence from Cr³ +ions in other crystalline hosts	428	(2)
9.3.4 Spectroscopy of other 3dn dopant ions	430	(2)
9.4 A survey of other transition metal ions	432	(10)
9.4.1 The 3c¹ configuration	432	(1)
9.4.2 The 3d² configuration	432	(1)
9.4.3 The 3d4 configuration	433	(2)
9.4.4 The 3d5 configuration	435	(2)
9.4.5 The 3d6 configuration	437	(1)
9.4.6 The 3d7 configuration	437	(2)
9.4.7 The 3d8 configuration	439	(3)
9.4.8 The 3d9 configuration	442	(1)
9.5 Transition metal ions in glass	442	(3)
10 Spectroscopy at high dopant concentrations	445	(60)
10.1 Energy transfer between optically active ions	445	(28)
10.1.1 Theoretical analysis of energy transfer	445	(6)
10.1.2 Statistical aspects of energy transfer	451	(9)
10.1.3 Experimental studies of energy transfer	460	(6)
10.1.4 Intraline (D–D) transfer	466	(6)
10.1.5 Transient grating experiments	472	(1)
10.1.6 Radiative transfer	473	(1)
10.2 Cooperative behaviour, upconversion schemes	473	(2)
10.3 Multicentre complexes	475	(6)
10.3.1 Exchange-coupled ion pairs	475	(6)
10.4 Fully concentrated materials	481	(24)
10.4.1 Electronic states in fully concentrated materials: exciton states	482	(6)
10.4.2 Absorption spectra of fully concentrated materials	488	(7)
10.4.3 Luminescence from fully concentrated materials	495	(10)
11 Solid state lasers	505	(41)
11.1 Basic laser phenomena	505	(7)
11.1.1 Population inversion and laser gain	506	(1)
11.1.2 Threshold gain in a laser cavity	507	(2)
11.1.3 The laser output	509	(1)
11.1.4 Multilevel laser systems	510	(2)
11.2 Optically pumped three-level lasers	512	(3)
11.2.1 The ruby laser	514	(1)
11.3 Optically pumped four-level lasers	515	(5)
11.3.1 Nd³+ lasers	518	(2)
11.3.2 Other rare-earth ion lasers	520	(1)
11.4 Tunable vibronic lasers	520	(20)
11.4.1 Colour-centre lasers	522	(2)
11.4.2 FA- and FB-centre lasers	524	(2)
11.4.3 F+2-centre lasers	526	(6)
11.4.4 Tl°-centre lasers	532	(1)
11.4.5 Transition metal ion lasers	533	(7)
11.5 Production of ultra-short pulses	540	(6)
12 Optical detection of magnetic resonance	546	(81)
12.1 ODMR of 3d³ ions	547	(16)
12.1.1 Energy levels and optical transitions of 3d³ ions	548	(6)
12.1.2 Optical detection of spin–lattice relaxation	554	(1)
12.1.3 ODMR of 3d³ ions in magnesium oxide	555	(8)
12.2 ODMR in the triplet state of defects in insulators	563	(17)
12.2.1 The F-centre in calcium oxide	565	(7)
12.2.2 Centres related to the F-centre in calcium oxide	572	(3)
12.2.3 Triplet states of divacancy centres	575	(5)
12.3 Some phosphor ions in alkali halides	580	(11)
12.3.1 Triplet states of impurity centres	579	(8)
12.3.2 Tl°-centres in alkali halides	587	(4)
12.4 Exciton recombination in crystals	591	(14)
12.4.1 Excitons in semiconductors	593	(2)
12.4.2 Triplet excitons in compound semiconductors	595	(8)
12.4.3 Ionic crystals	603	(2)
12.5 Donor–acceptor recombination in semiconductors	605	(7)
12.5.1 Shallow donor–shallow acceptor pairs	608	(2)
12.5.2 Shallow acceptors in gallium phosphide	610	(2)
12.6 Spin memory effects in ODMR	612	(7)
12.6.1 Spin memory and magnetic circular dichroism of F-centres	616	(3)
12.7 Optical–microwave coherence spectroscopy	619	(8)
12.7.1 Phase coherence in ODMR	620	(2)
12.7.2 Transient nutation in triplet state defects	622	(2)
12.7.3 Optically detected spin echoes	624	(3)
References	627	(14)
Index	641