Band Structure of Spinel-Type Semiconductors

The band structure of Cd${\mathrm{In}}_2$ ${\mathrm{S}}_4$ has been approximately calculated by applying the model potential of Heine, Abarenkov, and Animalu to a model of nearly-free electrons. Extensive use has been made of group theory, which enabled us to classify the electronic states in the band model of the real crystal. At $\Gamma$, the point of highest symmetry in the Brillouin zone, a fairly good picture of the sequence of valence-band states could be established by treating the periodic potential as a first-order perturbation. At points of lower symmetry, such as $X$ and $L$, a considerably larger number of states of equal symmetry appear, the mixing of which has to be taken into account; thus, for such points, a first-order calculation is insufficient. From a tight-binding model it was possible to interpret the upper $\Gamma$-point valence-band levels in terms of sulfur $s$ and $p$ orbitals.