Influence of Nonparabolicity on the Superlattice Band Structure

The energy spectrum is analysed of the superlattice taking into account the nonparabolicity effect in the host materials. Starting from the Kane theory the dispersion relation is derived for the symmetric superlattice. Moreover the expression for the concentration is given. The expressions derived are general and can be applied even to cases when a potential dependence exists. An extended effective mass is introduced depending both, on the energy and the energy gap as well as on the potential. The numerical results are given for the doping superlattice, assuming a triangular dependence of the potential. It is shown that the model, neglecting the nonparabolicity effects, yields good results for smaller energies and smaller values of the transverse component of the wave vector; in the opposite case, the nonparabolicity effects must be taken into consideration.