Excitons in a GaAs Film on AlxGa1-xAs Influenced by the Thickness of the Substrate.

Within the framework of the fractional-dimensional approach, exciton binding energies in GaAs films on AlxGa1-xAs substrates are investigated theoretically. In this scheme, the real anisotropic "exciton + film" semiconductor system is mapped into an effective fractional-dimensional isotropic space. For different aluminum contents and film thicknesses, the exciton binding energies are obtained as functions of the substrate thickness. The numerical results shown that, for different aluminum contents and film thicknesses, the exciton binding energies in GaAs films on AlxGa1-xAs substrates all exhibit their maxima as the substrate thickness increases. It is also shown that the binding energies of heavy-hole and light-hole excitons both have their maxima as the substrate thickness increases. [ABSTRACT FROM AUTHOR]