Light and Matter Id / Licht Und Materie Id: Infrared and Raman Spectra of Non-Metals

ISBN-13: 9783642464355 / Angielski / Miękka / 2012 / 602 str.

H. Bilz; D. Strauch; R. K. Wehner

Opis

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.

Spis treści

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.