Self-consistent study of confined states in thin GaAs-AlAs superlattices

We have investigated the (GaAs${)}_1$-(AlAs${)}_1$ and (GaAs${)}_4$-(AlAs${)}_4$ superlattice heterostructures in the [001] orientation by using the self-consistent pseudopotential method within the local-density formalism. The stability of the (GaAs${)}_1$-(AlAs${)}_1$ superlattices with respect to the constituent compounds and the electronic energy structure are analyzed. The ordered ${\mathrm{GaAlAs}}_2$ phase is found to be energetically less stable relative to the disproportionation into its constituent binary compounds. Self-consistent charge distribution reveals that the bond charge maximum of the Al—As bond increases at the expense of the Ga—As bond upon superlattice formation. We found (GaAs${)}_1$-(AlAs${)}_1$ is an indirect band-gap material, whereas (GaAs${)}_4$-(AlAs${)}_4$ in a direct band-gap material. The crystal field in (GaAs${)}_4$-(AlAs${)}_4$ gives rise to splitting in the conduction-band minima. Charge distributions of three conduction-band states—one from the Γ and two from the M point of the superlattice Brillouin zone—show a confined character. Their confinement suggests a staggered band lineup, AlAs being the quantum well for the conduction-band electrons. This band lineup is different from that which occurs in superlattices with large periodicity, but is in agreement with the experimental data obtained from very thin GaAs-AlAs superlattices.