First-principles study of frequency-dependent Resonant Raman scattering

Raman spectroscopy is a widely used technique for materials characterization. The dependence of the Raman intensity on the frequency of the incident light is well known: a resonance phenomenon appears when the exciting light has frequency close to electronic transitions. Unlike for molecules and for graphene, the theoretical prediction of the frequency-dependent Raman response of crystalline systems has remained a challenge. Indeed, many Raman calculations are nowadays done in the static limit (vanishing light frequency), using Density-Functional Theory and Density-Functional Perturbation Theory, thus neglecting frequency-dependence and excitonic effects. In this work, we present a finite difference method to obtain the frequency-dependent Raman intensity. Excitonic effects, included by solving the Bethe-Salpeter Equation are crucial to describe accurately the enhancement of the absolute first-order Raman intensity of silicon for laser photon energies corresponding to the gap of the material [1]. The approach is then generalized to second-order Raman scattering. The comparison of the simulations with experimental measurements shows that the Random-Phase Approximation (i.e. neglecting excitonic effects) is able to capture the main changes in frequency-dependence relative intensities. [1] Y. Gillet, M. Giantomassi, X. Gonze, Phys. Rev. B 88, 094305 (2013)