Validity of the effective-mass approximation for shallow impurity states in narrow superlattices

Abstract

The applicability of effective-mass theory to the calculation of impurity binding energies is discussed. A numerical test calculation is first performed in the case of one single band. A new two-dimensional effective-mass approximation is then proposed, valid for a small and a moderately small (up to 15) number of planes, allowing determination of impurity states derived from any subband. It is then shown that Bastard's model yields accurate binding energies for the lower states where it is applicable. Finally tunneling effects between quantum wells are considered showing that they have a nonnegligible influence in the experimental conditions.