Tight-binding study of the hole subband structure properties of p-type delta-doped quantum wells in Si by using a Thomas-Fermi-Dirac potential

Abstract

We present the hole subband structure of p-type delta-doped single, double, multiple and superlattice quantum wells in Si. We use the first neighbors sp3s ∗ tight-binding approximation including spin for the hole level structure analysis. The parameters of the tightbinding hamiltonian were taken from Klimeck et al. [Klimeck G, Bowen R C, Boykin T B, Salazar-Lazaro C, Cwik T A and Stoica A 2000 Superlattice. Microst. 27 77], first neighbors parameters that give realiable results for the valence band of Si. The calculations are based on a scheme previously proposed and applied to delta-doped quantum well systems [Vlaev S J and Gaggero-Sager L M 1998 Phys. Rev. B 58 1142]. The scheme relies on the incorporation of the delta-doped quantum well potential in the diagonal terms of the tight-binding hamiltonian. We give a detail description of the delta-doped quantum well structures, this is, we study the hole subband structure behavior as a function of the impurity density, the interwell distance of the doped planes and the superlattice period. We also compare our results with the available theoretical and experimental data, obtaining a reasonable agreement.