Band structure and its temperature dependence for type-III ${\mathrm{H}\mathrm{g}\mathrm{T}\mathrm{e}/\mathrm{H}\mathrm{g}}_{1-x}{\mathrm{Cd}}_x\mathrm{Te}$ superlattices and their semimetal constituent

Intersubband transitions in ${\mathrm{H}\mathrm{g}\mathrm{T}\mathrm{e}/\mathrm{H}\mathrm{g}}_{1-x}{\mathrm{Cd}}_x\mathrm{Te}$ superlattices and their dependence on temperature have been investigated for a large number of superlattices with widely different parameters. It has been shown by means of the envelope function approximation using the full $8\times 8$ Kane Hamiltonian, that the valence band offset is primarily responsible for the separation between the $H1-E1\mathrm{}$ and $L1-E1\mathrm{}$ intersubband transition energies of semiconducting ${\mathrm{H}\mathrm{g}\mathrm{T}\mathrm{e}/\mathrm{H}\mathrm{g}}_{1-x}{\mathrm{Cd}}_x\mathrm{Te}$ superlattices with a normal band structure. To a good approximation, all other relevant superlattice parameters have little or no effect on this energy difference. This leads to an unequivocal determination of the valence band offset between HgTe and CdTe Λ which is $570\pm 60\mathrm{meV}$ at 5 K for both the (001) and the $\mathrm{}\left(112\right)\mathrm{}\mathrm{B}$ orientations. The temperature dependence of both intersubband transition energies can only be explained by the following conditions: Λ is also temperature dependent as expressed by $d\Lambda /dT=-0.40\pm 0.04\mathrm{m}\mathrm{e}\mathrm{V}/\mathrm{K};$ the anisotropic heavy hole effective mass has a significant temperature dependence; and $E_g(\mathrm{HgTe},300\mathrm{}\mathrm{K})=-160\pm 5\mathrm{meV}$ which is appreciably lower than the extrapolated values found in the literature.