Exciton binding energies in GaAs films on AlxGa1−xAs substrates

Abstract

We use the fractional–dimensional approach (FDA) to study exciton binding energies in GaAs films on [Formula: see text] substrates. In this approach, the Schrödinger equation for a given anisotropic system is solved in a noninteger-dimensional space where the interactions are assumed to occur in an isotropic effective environment. The heavy-hole and light-hole exciton binding energies are calculated as functions of the film thickness and substrate thickness. The numerical results show that both the heavy-hole and light-hole exciton binding energies decrease monotonously as the film thickness increases. When the film thickness and the substrate thickness is relatively small, the change of substrate thickness has comparatively remarkable influence on both heavy-hole and light-hole exciton binding energies. As the substrate thickness increases, both the heavy-hole and light-hole exciton binding energies increase gradually. When the film thickness or the substrate thickness is relatively large, the change of substrate thickness has no significant influence on both heavy-hole and light-hole exciton binding energies.