Role of interface states in band structures of short-period (GaAs${)}_{\mathit{n}}$/(${\mathrm{Ge}}_2$${)}_{\mathit{n}}$ [001] superlattices under a zero-field model

We have calculated the band structures of the (GaAs${)}_{\mathit{n}}$/(${\mathrm{Ge}}_2$ ${)}_{\mathit{n}}$ [001] superlattices (SL’s) with n=1–10 giving special attention to the role of the interface states at the Ga-Ge and As-Ge polar interfaces. The calculations are performed by means of a semiempirical tight-binding method with an ${\mathit{sp}}^3$ ${\mathit{s}}^{\mathrm{*}}$ basis. The presence of the electric field in the SL is totally ignored, i.e., ‘‘the zero-field model.’’ For the (GaAs${)}_{10}$/(${\mathrm{Ge}}_2$ ${)}_{10}$ [001] SL, the band gap is 0.85 eV, with the conduction-band minimum at the X point, into which the fcc L point is folded. The states at the conduction- and valence-band edges are confined two dimensionally in the Ge layers. Furthermore, we have found two interface bands in the lower and upper regions of the gap. The states of the lower interface band are located at the Ga-Ge interface, while those of the upper interface band are located at the As-Ge interface. The energies of the interface states depend on the parameters representing the Ga-Ge and As-Ge bond lengths and the valence-band discontinuity between GaAs and Ge, but the interface states do not disappear from the gap with reasonable choices of the parameters. By decreasing the SL period n, the energy gap between the confined band-edge states increases (1.07 eV at the X point for n=2) due to the quantum confinement effect. A sudden shrinkage in the band gap (${\mathit{E}}_{\mathit{g}}$=0.16 eV at the R point) is obtained for n=1. The origin of the band-gap shrinkage is related to the fact that the overlap of the interface states becomes so large that they combine as band states.