Binding energies and envelope functions of light-hole excitons in GaAs/${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs strained quantum wells

We calculate the binding energies and envelope functions of light-hole excitons in GaAs/${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs strained single quantum wells with various In concentrations, band offsets, and layer thickness. We use a variational method with a set of Gaussian-type functions as a trial wave function instead of a predetermined rigid function form. The binding energy and overlap integral of the light-hole exciton in the type-II configuration reach maximum, then approach the bulk values with a decrease in the ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-layer thickness. In addition, the calculated results suggest that there is no stable type-II light-hole exciton under some condition. The band-offset dependence of the exciton binding energy indicates the smooth decrease of its value with the spatial configuration change of the light-hole potential from type-I structure to a type-II one via the flat light-hole potential. It is noted that the binding energy is considerably enhanced in the flat light-hole potential. © 1996 The American Physical Society.