Theory of First-Order Raman Scattering by Crystals of the Diamond Structure Containing Substitutional Impurities

Abstract

The Raman effect that we consider here is the inelastic scattering of light by the lattice vibrations due to the fluctuations in the crystal electronic polarizability induced by the lattice vibrations. There is conservation of energy, i.e. in a first order scattering process, the frequency ω_s of the scattered radiation differs from the frequency ω_i of the incident radiation by the frequency of one phonon. In perfect crystals, there is also conservation of momentum due to the translational symmetry of the crystal. In actual experiments, the Bragg condition is generally satisfied and since the magnitude of the wave vector of the light in the crystal is very small compared to the maximum magnitude of the phonon wave vector, only the phonons of essentially zero wave vector k̰≃0 are involved in first order scattering. Actually, a good approximation in the description of Raman scattering consists in replacing the small wave vector of light by zero and we shall do so in what follows.