Splitting of the states derived from the bulkXminima in GaAs-AlAs superlattices

We have carried out full-scale pseudopotential calculations on (GaAs${)}_{\mathrm{n}}$-(AlAs${)}_{\mathrm{n}}$ superlattices (n>2) to determine the relative alignment of the superlattice conduction states derived from the secondary bulk X minima. These are states characterized by contributions from the bulk minima oriented along the growth axis 〈001〉 ($X_z$) and states characterized by the bulk (010) ($X_y$) and (100) ($X_x$) minima that lie in the plane of the interfaces. We present the splitting in energy of $X_z$ and $X_x$,$X_y$ levels for 2<n<15 and report that the lowest superlattice state is related to $X_z$. We discuss the origin of this splitting, determine the oscillator strengths of optical transitions to the valence band, and compare with experimental data. We argue that the position of the $X_x$,$X_y$ levels may be used to assess the quality of the interface at the microscopic level.