Electron Gas Statistics in Size-Quantized Thin Films With Non-Parabolic Energy Spectra

Abstract

The electron gas statistics in semiconducting thin films with arbitrary isotropic energy spectra was found in this theoretical work. General expressions for the density of states of the charge carriers and for the chemical potential were deduced according to the two-band Kane model approach. The ratio of the expression obtained for the density of states to that of the expression deduced according to the parabolic approach was shown to be a function of the energy. The Fermi energy of the electron gas was observed to be a function of the thin film thickness, the non-parabolic parameter, the concentration and the temperature. In the strong non-parabolic approach the dependency of the Fermi energy on the thin film thickness was shown to exhibit non-monotonic characteristics.