Fractional-dimensional approach for excitons in GaAsfilms on Al_xGa_1-xAs substrates

Binding energies of excitons in GaAs films on Al_xGa_1-xAs substrates are studied theoretically with the fractional-dimensional approach. In this approach, the real anisotropic “exciton+film” semiconductor system is mapped into an effective fractional-dimensional isotropic space. For different aluminum concentrations and substrate thicknesses, the exciton binding energies are obtained as a function of the film thickness. The numerical results show that, for different aluminum concentrations and substrate thicknesses, the exciton binding energies in GaAs films on Al_xGa_1-xAs substrates all exhibit their maxima with increasing film thickness. It is also shown that the binding energies of heavy-hole and light-hole excitons both have their maxima with increasing film thickness.