Electronic properties of cubic crystals with an average of five valence electrons per atom

The electronic structure of cubic crystals with an average of five electrons per atom is analyzed using the linear combination of atomic orbitals (LCAO) method. Only nearest-neighbor interactions are taken into account. The electronic energies are given in closed form for all possible cases. As an example the energy bands and the density of states (DOS) of cubic SnTe are studied in detail. The interaction parameters are determined from pseudopotential band-structure calculations. The LCAO band structure with nearest-neighbor interactions represents a good fit for the pseudopotential valence-band structure. It is found that sp hybridization plays an important role in forming the characteristics of the bands. The sp hybridization is also responsible for the instability of the cubic structure. The DOS is analyzed in terms of critical points. The effect of sp hybridization on the DOS is found to be important. It produces a peak in the upper-valence-band DOS. The energy of the main reflectivity peak of the cubic and rhombohedral compounds with an average of five electrons per atom is calculated and found to compare well with experiment. This energy depends mainly upon the ionic energy, contrary to the case with tetrahedral crystals, where it depends symmetrically upon the ionic and homopolar energies.