Light and Matter Id / Licht und Materie Id, Softcover reprint of the original 1st ed. 1984 Infrared and Raman Spectra of Non-Metals Optik / Optics Series

The dynamical properties of solids have recently attracted renewed interest in connection with the increasing understanding of phase transitions and re­ lated phenomena. In particular, soft modes or, more generally, phonon 'anom­ alies' seem to play an important role in structural and electronic phase tran­ sitions, such as ferroelectric or superconducting transitions. The understanding of the mechanisms responsible for the occurrence of unusually low frequencies in phonon spectra requires a detailed analysis of the microscopic forces governing the lattice vibrations. Of particular importance is the influence of the electron­ lattice interaction in the adiabatic approximation which in many cases is the origin of peculiarities in the phonon self-energy. In this work the vibrational spectra of pure non-metals and of those con­ taining point defects are investigated. ' In these materials the interrelation be­ tween the pseudo-harmonic forces (determining the phonon dispersion re­ lations) and the non-linear anharmonic and electron-phonon forces (as they act in infrared and Raman spectra) is most obvious and can be quantitatively analysed in terms of appropriate models. The main task is to arrive at a physically correct treatment of electronic degrees of freedom, as for example in an electronic 'shell' model, which leads to the description of phonon spectra in terms of long-range polarizabilities and short-range deformabilities. The pur­ pose of our review is to stimulate further investigations which, we hope, will result in explicit relations between the parameters of the semi-microscopic models and the matrix elements from the electronic band structure.

Vibrational Infrared and Raman Spectra of Non-Metals.- A. Introduction.- 1. Historical survey.- 2. Outline of the theory of infrared absorption and Raman scattering.- a) Macroscopic aspects.- b) Microscopic aspects.- B. Phonons in insulators.- 3. General properties of phonons.- a) Dynamic and thermodynamic stability of solids.- b) The adiabatic approximation.- c) Force constants.- d) Symmetry properties of phonons.- e) The pseudo-harmonic approximation.- 4. Ionic crystals.- a) The rigid-ion model.- b) Dipole models.- c) The breathing shell model.- d) Ionic deformabilities.- e) Non-central and many-body forces and the elastic properties of crystals.- 5. Covalent crystals.- a) Formal force constants and general properties.- b) Dipole models.- c) Bond-charge models.- d) Valence force fields.- e) Crystals of partially ionic and partially covalent character.- f) Sum rule of lattice vibrations.- 6. Microscopic theory, models, and macroscopic quantities.- a) Overlap theory.- b) The dielectric function method.- c) The direct ‘frozen-in’ phonon approach.- d) Charges and polarizabilities of ions and bonds.- e) Electric fields and effective charges in ionic solids.- f) Fields and charges in covalent solids.- g) The microscopic description of charges and fields.- C. Interaction of photons with matter.- 7. Theory of interaction of photons with particles.- a) Non-relativistic theory of inelastic scattering.- b) Gauge invariance in electromagnetic interaction.- c) Dielectric constant of electrons.- d) Light scattering by electrons.- e) Interaction of photons with electrons and ions.- f) Polaritons in the harmonic approximation.- 8. Infrared absorption and dielectric response.- a) Dielectric susceptibility.- b) Absorption of radiation (fluctuation-dissipation theorem).- c) Frequence-dependence and thermodynamic definitions of the susceptibility, sum rules.- d) Static susceptibility.- 9. Raman scattering of light.- a) Introduction.- b) Quantum theory of spontaneous Raman scattering.- c) Adiabatic representation.- d) Polarizability theory.- e) Green function theory of Raman scattering.- f) The ?4 law.- g) Polariton picture of light scattering.- h) Resonant Raman scattering (RRS).- i) Rayleigh, Brillouin, and Hyper-Raman scattering.- D. Expansion theory of susceptibilities and polarizabilities.- 10. General lattice potential.- a) The undeformed lattice.- b) The lattice in a static electric field and under deformation.- 11. Lattice dipole moment.- a) The undeformed lattice.- b) The lattice in a static electric field and under deformation.- 12. Lattice and electronic susceptibility.- a) Formal expansion of the susceptibility.- b) The harmonic approximation.- c) Anharmonic susceptibility.- d) The anharmonic dispersion oscillator.- e) The damping function.- f) The renormalized dipole moment.- g) The general form of the lattice susceptibility.- h) Coupling of dispersion oscillators.- i) Anharmonic coupling parameters.- j) The susceptibility under external pressure and in a static field.- 13. Lattice polarizability and Raman scattering.- a) Formal expansion of the electronic susceptibility.- b) Harmonic approximation.- c) Anharmonie treatment.- d) Raman scattering in cubic crystals.- e) Raman coupling parameters.- f) Effects of static fields and external pressure.- E. Interpretation of experimental spectra.- 14. Model theory of infrared absorption and Raman scattering.- a) General features of infrared and Raman processes.- b) Microscopic and model treatment of electron-phonon interaction.- c) Shell model treatment of Raman scattering.- d) Bond charge and bond polarizability in infrared and Raman processes.- 15. Infrared spectra of ionic crystals.- a) Qualitative classification of infrared spectra.- b) The infrared spectra of alkali halides: anharmonic effects.- c) Critical point analysis.- d) Density of states approximation.- e) The effect of short-range cubic anharmonicity.- f) The effect of quartic and higher anharmonicity.- g) Coulomb anharmonicity.- h) Absorption at very low frequencies.- i) Non-linear dipole moments.- j) The effect of ionic polarizability.- k) Final states interactions of phonons: anharmonic broadening and bound states.- 1) Line widths of dispersion oscillators and temperaturedependence.- m) Discussion of other diatomic ionic crystals.- n) Cubic crystals with three and more ions in a cell.- 16. Infrared spectra of covalent crystals.- a) General features of the spectra.- b) Spectra of crystals with diamond structure.- c) Covalent crystals with linear dipole moments.- 17. Infrared spectra of crystals with mixed ionic and covalent character.- a) The concurrence of anharmonicity and non-linear dipole moments.- b) Spectra of crystals with zincblende structure.- c) Spectra of perovskites.- d) Spectra of low-symmetry crystals.- e) Spectra of amorphous semiconductors.- 18. Raman scattering from ionic crystals.- a) Raman spectra of cubic ionic crystals.- b) Other diatomic ionic crystals.- c) Perovskites.- d) Other ionic crystals.- e) Photoelasticity and Raman scattering.- f) First-order Raman scattering.- 19. Raman spectra of covalent and partially ionic crystals.- a) Spectra of diamond and its homologues.- b) Spectra of III–V and II–VI compounds.- F. Lattices with point defects.- 20. Types of defects and their effects.- a) Introductory remarks.- b) Point defects, vacancies.- c) Defect-induced infrared and Raman spectra.- d) Localized modes, gap modes.- e) Resonant modes.- f) Off-center and molecular defects: Tunnelling motion.- g) Internal vibrations of molecular defects.- h) Interstitials.- i) Effects of defect clusters and defect concentration.- j) Dislocations, surfaces.- 21. Information contained in defect-induced spectra.- 22. Lattice dynamics of impure lattices.- a) Introduction: Molecular model — the nature of perturbations due to a defect.- b) Lattice distortions — method of lattice statics.- c) Equation of motion of the perturbed lattice.- d) Symmetry considerations.- e) Lifshitz method for the solution of the equation of motion — localization of perturbations.- 23. The Green function of the harmonic perturbed lattice.- a) Real Green function and T matrix.- b) The complex Green function.- c) Resonances: Localized and resonant modes.- d) Eigenvalue treatment of the Green function and T matrix in the impurity space.- 24. Properties of the perturbed harmonic lattice Green function.- a) Kramers-Kronig transform.- b) Normalization of the perturbed resonance-mode eigenvectors: An effective mass of the resonance vibration.- c) Approximate form of the Green function and of the T matrix near a resonance frequency: Width and intensity.- 25. Applications of Green functions: Phonon spectra in perturbed crystals.- a) Phonon density of states.- b) Dielectric susceptibility.- c) Raman scattering.- d) Resonance Raman scattering.- 26. Dynamics of lattices with interstitial or molecular defects.- a) Formulation of the problem.- b) Standard procedure — application to interstitials.- c) Formalism modified for molecular defects.- 27. Shell-model treatment of the dynamics of perturbed lattices and the model theory of infrared-absorption and Ramanscattering spectra.- a) The use of shell models.- b) Effective force constants.- c) Shell-model extension of the Lifshitz formalism.- d) Shell-model interpretation of the effective charge.- e) The higher-order dipole moments.- f) Shell-model interpretation of the Raman scattering intensity.- 28. Concentration effects.- a) Introduction: Diagrammatic expansion.- b) Low-concentration single-site scattering approximation.- c) Self-consistent approximation.- d) Coherent-potential approximation (CPA).- e) Applications.- 29. Mixed crystals.- a) One-and two-mode behaviour.- b) Theoretical models.- c) Changes in the lattice constant and Ivey relation.- 30. Anharmonic effects in perturbed crystals.- a) Introduction: Resonance modes in analogy to the Reststrahlen or Raman oscillator.- b) Qualitative aspects of the anharmonic self-energy in perturbed crystals.- c) Diagonal and off-diagonal elements of the perturbed self-energy.- d) Low-order contributions to the self-energy.- e) Approximate form of the anharmonic Green function.- f) Intensity of resonances.- g) Anharmonic shift of resonance-mode frequencies.- h) Isotope effects.- i) Anharmonic width of resonances.- j) Multi-phonon spectra, sidebands, overtones.- k) Higher-order effects.- 31. Phonon frequency shift from bulk and local strain due to temperature variation, pressure, and lattice distortion in defective crystals.- a) Equilibrium positions.- b) Low-concentration approximation.- c) Relation between lattice and elasticity theory.- d) Static distortions.- e) Pressure-induced frequency shift.- f) Thermal expansion.- 32. Finite crystals.- a) Introduction.- b) Continuum theory of finite crystals.- c) Lattice dynamics of finite crystals.- 33. Present and future problems in lattices with defects.- G. Dynamical theory of interacting phonon systems.- 34. Basic concepts.- a) Introductory comments.- b) Normal coordinates and lattice Hamiltonian.- c) Equilibrium correlation and Green functions.- d) Double-time Green functions: Harmonic approximation.- e) Double-time Green functions: Spectral representations.- 35. Functional methods.- a) Non-equilibrium Green functions.- b) Generalized thermodynamic potentials and cluster expansion.- 36. Phonon dynamics.- a) Basic equations of motion.- b) Equilibrium positions.- c) The renormalized harmonic approximation.- d) Dyson equation with dispersive interactions.- 37. Vertex renormalization.- a) Vertex part integral equations.- b) Self-energy with vertex corrections.- 38. Simple approximations and results.- a) Self-energy and retarded Green functions.- b) Free energy.- H. Appendices.- 39. Tables of elastic and dielectric constants.- 40. Tables of selection rules, etc..- References.