Theory of Lattice Raman Scattering in Insulators

Abstract

The theory of Raman scattering by phonons in perfect insulator crystals is developed here. The Hamiltonian for the interacting system of electrons, phonons, and photons is written in second-quantized form, and a canonical transformation is performed to remove the lowest-order interactions. In the resulting transformed Hamiltonian, the terms causing Raman scattering can be identified. The basic electron-system eigenstates are taken in the Wannier exciton representation, including bound and continuum states. The frequency dependence of the components of the Raman tensor is obtained for single-phonon and two-phonon overtone scattering. As a function of incident photon energy, the Raman tensor has poles at energies corresponding to creation of quasiparticles (e.g., virtual excitons). This produces a particularly important effect in resonance Raman scattering, where the creation of virtual excitons dominates the scattering process. Some numerical estimates for single and overtone resonant-Raman-scattering efficiencies are given for CdS and GaAs, and are compared with available experiments. The use of the resonance Raman effect as a probe of quasiparticles is suggested.