Electronic band structure and nonparabolicity in strained-layer Si-${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ superlattices

We report a pseudopotential calculation of the nonparabolicity of the conduction and valence minibands for Si-${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{\mathrm{x}}$ strained-layer superlattices of period 10–30 Å. We find that the conduction-band nonparabolicity in directions both perpendicular (z) and parallel to the interface planes is several orders of magnitude larger than that for bulk silicon and is comparable in magnitude with the value for bulk GaAs. Along the superlattice axis (z), the conduction-band nonparabolicity is dominated by virtual transitions involving the lowest conduction states and strongly reflects the energy separation between them. Since this separation depends on strain and layer widths, the magnitude of this nonparabolicity can be ‘‘tuned’’ over 2 orders of magnitude. In the valence band, and along the direction parallel to the interface planes in the conduction band, the nonparabolicity is dominated by virtual excitations across the fundamental gap. The effective masses are also presented. A comparison is given of the mechanisms determining band nonparabolicity in Si-${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{\mathrm{x}}$, GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As, and GaAs-${\mathrm{GaAs}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{P}}_{\mathrm{x}}$ superlattices.