Energy levels of strainedInxGa1−xAs-GaAs superlattices

The complete k⋅p Hamiltonian with strain is solved numerically to obtain the energies and wave functions of ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-GaAs superlattices. The electron, heavy-hole, light-hole, and split-off bands are treated in a unified description in which the only adjustable parameters are the respective zone-center effective masses in each material. It is shown that the theory accurately reproduces the spectra of a wide range of published samples for valence-band offsets ranging from 0.3 to 0.6. It is also found that the transition energies are relatively insensitive to the valence-band offset over a wide range of offsets. The electron–light-hole exciton energy is fitted more closely at the lower offset values, and suggests a valence-band offset close to 0.4. At this offset, the light holes exhibit borderline type-II behavior, and are only slightly localized in the GaAs layers.