Electronic structure of zinc-blende-structure semiconductor heterostructures

We present an extended k⋅p model to calculate the electronic structure of any direct-band-gap semiconductor heterostructure with either normal or with inverted bulk band structure. The full Hamiltonian is block diagonalized in sets of time-reversed states by an appropriated unitary transformation which separates the degenerate spin states into two blocks. The model takes into account the full degeneracy of the eight lowest Bloch states at the Γ point, the subband mixing and coupling, the warping, and the derived boundary conditions at the interface. The anisotropy is treated in perturbation theory. Subbands in quantum wells of ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As/GaAs, of semimagnetic ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te/CdTe, and of narrow-band-gap lattice-matched ${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}$As/${\mathrm{Al}}_{0.48}$${\mathrm{In}}_{0.52}$As are calculated as a function of the dimension and composition of the heterostructure. These examples show the effect of conduction-band–valence-band coupling, subband mixing, and the inclusion of the split-off band in the energy dispersions. Extensive comparison with experimental data and other theoretical approaches is presented.