Orientation as a key parameter in the valence-subband-structure engineering of quantum wells

The quantum well spectra orientation dependence of cubic semiconductors is studied through a simplification of the valence-subband dispersion relation, applicable for the three symmetrically oriented (perpendicular to the lattice symmetry axes) quantum wells. The semianalytical treatment which is based on the Kohn-Luttinger formalism, incorporates the effect of strain, and is generalized for gapless semiconductors as well as for III-V compounds. The rectangular and hexagonal in-plane symmetries of the 〈011〉 and 〈111〉 films, respectively, are studied by calculating the full subband dispersion in these orientations for GaAs, InAs, Ge, HgTe, and α-Sn. The rectangular symmetry of 〈011〉 films can result in spectral saddle points at ${\mathrm{k}}_{\mathrm{\parallel }}$=0. Orientation is also found to be an important parameter in tailoring surface state branches in gapless semiconductors.