Raman-Brillouin light scattering in low-dimensional systems: Photoelastic model versus quantum model
Raman-Brillouin scattering by acoustic phonons in a free-standing nanosized silicon film is studied theoretically. Two well-known models are used to describe the inelastic light scattering. (i) The Raman-Brillouin quantum model in which the electronic states, and their interactions with light and sound, are taken into account explicitly. In this model, an effective Raman-Brillouin electronic density is introduced; it is very useful for analyzing experimental data when a large number of electronic states are involved as intermediate states in the light scattering process. Its spatial distribution depends on the optical excitation and electronic transitions of the system, and is directly connected to spectral features of the Raman-Brillouin scattering. In particular, diagonal and off-diagonal electronic densities are introduced in order to point out that diagonal electron-vibration matrix elements are relevant for inelastic light scattering in nanosized objects, whereas only off-diagonal matrix elements are allowed for bulk materials. (ii) The photoelastic model is compared to the Raman-Brillouin quantum model and is discussed in terms of validity of the steplike profile of the photoelastic coefficient usually adopted in simulations of the Raman-Brillouin spectra of thin films and superlattices. It is shown that the use of trapezoidlike, rather than steplike, profiles of the photoelastic coefficient is more realistic.