Consistent anharmonic-shell-model calculation for the Raman mode in silicon

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Abstract
We show that a previous failure to describe the frequency shift Δ and linewidth Γ of the optical zone-center mode in silicon with an anharmonic shell model arises from the neglect of the electronic polarizability effects in the perturbative treatment of the anharmonic interactions. We consider cubic anharmonic shell-shell interactions between nearest-neighbor atoms in a shell model used in the past for silicon. We apply an anharmonic perturbation theory which properly takes into account the adiabatic constraint for the shell’s polarization. We obtain Δ and Γ as functions of temperature in good agreement with experimental data.