Theory of Brillouin Scattering from Surface Acoustic Phonons in Supported Films

The theory of the Brillouin scattering from the surface of a semi-infinite medium, developped previously, is extended to coated surfaces of cubic materials. The Brillouin cross-section is optained for any scattering geometry and for p and s polarization of the incident and scattered light. The formulae for the cross section contain contributions from ripple and elastooptic scattering mechanisms for the film as well as for the substrate. The theory is applied to silica film deposited on crystalline silicon and the behaviour od the cross-section against the film thickbess is investigated. We find that there are strong interference effects among the various contributions to the cross-section, so that the intensity of the spectral lines dramatically oscillates by changing the thickness. Although in general the ripple scattering mechanissm is the dominant one it is found that the elastooptic coupling in the silica film is not negligeable and sometimes is even prevailing. The discrete phonon spectrum (Rayleigh, Sezawa, Lamb modes) and the continuous spectrum (resonances, mixed modes) are both studied.