Exciton linewidth limited by polar optic-phonon scattering in a short-period superlattice: Anisotropic-effective-medium model

We have treated a short-period superlattice, with the period small compared to the exciton Bohr radius, as an anisotropic effective bulk medium. The effective mass along the growth direction is calculated from the miniband dispersion relations. We have proposed trial wave functions for both the bound and scattering states for the electron-hole relative motion based on this model and derived expressions for linewidths for the polar optic-phonon scattering. Numerical values are given for GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As systems and are compared with the values in bulk GaAs and in GaAs quantum wells.