Abstract |
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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 [1] and Density-Functional Perturbation Theory [2], 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 [3] 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 [4]. The approach is then generalized to second-order Raman scattering in the spirit of Ref. [5]. The comparison of the simulations with experimental measurements [6] shows that the Random-Phase Approximation (i.e. neglecting excitonic effects) is able to capture the main changes in frequency-dependence relative intensities. References [1] R. M. Martin, 'Electronic Structure', Cambridge University Press (2004). [2] M. Veithen, X. Gonze and Ph. Ghosez, Phys. Rev. B 71, 125107 (2005). [3] G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74, 601 (2002). [4] Y. Gillet, M. Giantomassi, X. Gonze, Phys. Rev. B 88, 094305 (2013). [5] C. Ambrosch-Draxl et al, Phys. Rev. B 65, 064501 (2002) [6] J. B. Renucci, R. N. Tyte and M. Cardona. Phys. Rev. B 11, 3885 (1975). |