Theory of incompletely isovalent delta-doped semiconductors

In order to calculate the dependence of the electronic structure of single delta-doped layers on the area concentration c of isovalent impurities, the averaged t-matrix approximation (ATA) is applied to the case of a few impurities within a layer, and generalized to the case of a few missing impurities in an otherwise completely filled layer. In this way, exact results for the limits c --> 0 and c --> 1 are obtained. An interpolation between these limits results in Green's functions which allow the calculation of c-dependent electronic properties. In the case of GaAs:In, the top of the heavy-hole subband is calculated for a short-range (delta-like) difference between the host atom (Ga) and the impurity (In) potentials on the basis of a parabolic host band structure as well as by applying a three-band Hamiltonian. The comparison with the results from a virtual-crystal approximation proves the latter to describe the subbands well, provided that single impurities do not bind charge carriers. The subband dispersion for heavy holes, calculated for AlAs:Ga on the basis of a realistic ten-band Hamiltonian, shows a camel-back structure caused by the warping of the host heavy-hole band. This structure is proved to result in a pronounced high-energy peak of the subband density of states, in contrast to its step-like behaviour in the case of parabolic bands.