An empirical tight-binding method for tetrahedrally coordinated cubic materials is presented and applied to group-IV and III-V semiconductors. The present ${\mathrm{spds}}^{*}$ method extends existing calculations by the inclusion of all five $d$ orbitals per atom in the basis set. On-site energies and two-center integrals between nearest neighbors in the Hamiltonian are fitted to measured energies, pseudopotential results, and the free-electron band structure. We demonstrate excellent agreement with pseudopotential calculations up to about 6 eV above the valence-band maximum even without inclusion of interactions with more distant atoms and three-center integrals. The symmetry character of the Bloch functions at the $X$ point is considerably improved by the inclusion of $d$ orbitals. Density of states, reduced masses, and deformation potentials are correctly reproduced.

• Received 17 July 1997

DOI:https://doi.org/10.1103/PhysRevB.57.6493