Valley-mixing effects in short-period superlattices

The subband structure of (GaAs${)}_{\mathrm{N}}$/(AlAs${)}_{\mathrm{M}}$ along the growth direction [001] through the center of the Brillouin zone and through the zone-boundary point at (100) is calculated using a second-neighbor tight-binding method using the parameters fitted to the conduction valleys of the bulk materials. The parentage of the states in the bulk Γ and X valleys is traced. A striking general feature of the valley mixing depending sensitively on N and M is explained in terms of the symmetry of the superlattice. This result forms a basis for exploring the lack of perfection of the interface.