Finite-size effects on acoustic phonons in GaAs/AlAs superlattices

We present a detailed study of the Raman-scattering spectra by acoustical phonons in finite-size GaAs/AlAs superlattices. The scattering geometry relies on an optical microcavity to enhance the Raman efficiency and to access the $q_z=0\mathrm{}$ forward-scattering contribution. The results are analyzed using a photoelastic model for the Raman efficiency, which takes into account the superlattices finite size, the cavity confined optical field, and the acoustical-phonon displacements including the elastic modulation. The latter are derived from a matrix method implementation of the elastic continuum model for the complex layered structure. The calculations provide a complete description of the main experimental results that include: (i) the observation of low-energy oscillations, (ii) the presence of three main Raman lines in the first folded-phonon spectral region, (iii) the broadening of the Raman peaks, and (iv) the spectral shift of the lines with respect to the infinite superlattice. In addition, the observed asymmetry of the main central peak is understood as due to a $q_z$-nonconservation induced violation of the expected center-zone Raman selection rule. Besides providing a clear observation of the finite-size effects on superlattice acoustical phonons, the reported results demonstrate the use of microcavity geometries to access center-zone minigap excitation in layered structures.