Exact-solutions of 2-band models of graded-gap superlattices

Abstract

We have theoretically investigated two-band models of graded-gap superlattices within the envelope-function approximation. Assuming that the gap varies linearly with spatial coordinate, we are able to find exact solutions of the corresponding Dirac-like equation describing the conduction- and valenceband envelope-functions. The dispersion relation inside allowed miniband of the superlattice may be expressed in terms of confluent hypergeometric functions in a closed form.