Exact Solutions of Two-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 valence-band envelope-functions. The dispersion relation inside allowed miniband of the superlattice may be expressed in terms of confluent hypergeometric functions in a closed form.

arXiv comment7 pages in REVTeX 3.0. 1 Figure on request to F. D-A ([email protected]). FM-UCM-32