Comparative study of band-structure calculations for type-II InAs/${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$Sb strained-layer superlattices

Short-period InAs/${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$Sb superlattices may allow strong optical transitions in the long-wavelength infrared (>10 μm) spectral region. Absorption calculations can be difficult, however, because of the strongly type-II interface and because of the large lattice mismatch. We present a comparative study of band-structure calculations for strained-layer type-II InAs/${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$Sb superlattices grown on GaSb. The energy of superlattice band gaps (${\mathit{E}}_{\mathit{g}\mathit{s}}$) and the cutoff wavelengths (${\lambda }_{\mathit{c}}$) are computed in the empirical tight-binding, effective-bond-orbital, and 8×8 k⋅p models. In the empirical tight-binding model (ETBM) the strain is included by scaling the matrix elements according to Harrison’s universal 1/${\mathit{d}}^2$ rule and by appropriately modifying the angular dependence. The bond-orbital model (EBOM) and k⋅p calculations include the strain via the deformation-potential theory. We find in all cases that the superlattice band gap decreases rapidly with increasing x and that the proper inclusion of strain is critical in the ETBM. Our results compare favorably with existing experiments. In addition, we compare directly the results of the EBOM and k⋅p models. Contrary to expectations, the two models give quite different results for InAs/InSb superlattices.