Theory of disorder-induced acoustic-phonon Raman scattering in quantum wells and superlattices

We present a theory of resonant Raman scattering by acoustic phonons in semiconductor quantum wells and superlattices for the case when translational invariance along as well as perpendicular to the growth direction is perturbed due to layer thickness fluctuations and interface roughness, both with and without an applied magnetic field. The breakdown of crystal momentum conservation along the growth direction (${\mathit{q}}_{\mathit{z}}$) leads to scattering from individual layers and folded acoustic phonons from the whole mini-Brillouin zone contribute to a continuous emission background of geminate recombination. The Raman intensity is evaluated from the phonon displacement field. It is proportional to the difference in the amplitudes of pairs of counterpropagating waves constituting each mode. This dependence causes characteristic intensity variations (peaks and dips) superimposed on the emission continuum at energies of gaps of the folded phonon dispersion. Interface roughness also allows for elastic scattering of photoexcited intermediate electronic states in the Raman process into states with nonzero crystal momentum (${\mathit{q}}_{\mathrm{\parallel }}$) perpendicular to the growth direction. This momentum can be compensated by acoustic phonons in higher-order Raman processes. Due to this effect internal gaps of the phonon dispersion, e.g., at anticrossings of longitudinal and transverse acoustic branches for ${\mathit{q}}_{\mathrm{\parallel }}$≠0, acquire enough strength to appear in the spectrum as additional structure.