Subband energy in two-band δ-doped semiconductors

We study electron dynamics in a two-band δ-doped semiconductor within the envelope-function approximation. Using a simple parametrization of the confining potential arising from the ionized donors in the δ -doping layer, we are able to find exact solutions of the Dirac-type equation describing the coupling of host bands. As an application we then consider Si δ -doped GaAs. In particular we find that the ground subband energy scales as a power law of the Si concentration per unit area in a wide range of doping levels. In addition, the coupling of host bands leads to a depression of the subband energy due to nonparabolicity effects.