Résumé
The resonant inelastic light scattering by acoustic vibration modes in spherical germanium nanocrystals is studied theoretically. The Raman-Brillouin efficiency is calculated using quantum perturbation theory and assuming deformation-potential interaction between the confined electronic states and the nanocrystal vibration modes. The electronic states are described using the effective mass approximation. The vibration modes are calculated, on one hand, using an atomistic approach based on the Stillinger-Weber interaction potential and, on the other hand, using elasticity theory (Lamb's model). Both models are compared depending on the nanocrystal size and on the surface boundary conditions. By projecting the Stillinger-Weber vibration modes on Lamb's modes, we are able to discuss the validity of the elasticity theory and to determine the origin of the low-frequency Raman-Brillouin scattering.