Exciton binding energies in semiconductor superlattices: An anisotropic-effective-medium approach

Excitons in a semiconductor superlattice are studied via an envelope-function approach on the scale of the superlattice period. The superlattice is modeled as an anisotropic medium characterized by effective masses parallel and perpendicular to the plane of the layers. The perpendicular mass is shown to depend on the miniband dispersion and the resultant anisotropic exciton problem is solved variationally. An analytic expression for the ground-state binding energy is obtained and evaluated for a variety of structures in the GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As system.