Valley mixing in short-period superlattices and the interface matrix

Energy levels of short-period GaAs/AlAs superlattices are calculated both in an ${\mathit{sps}}^{\mathrm{*}}$ tight-binding model and in an effective-mass approximation. Mixing between Γ and X conduction-band valleys is shown to be successfully described by a current-conserving interface matrix giving boundary conditions among envelope functions and their derivatives at a heterointerface. Two parameters characterizing the mixing are determined.