Electronic Band Structure in the Sodium Iodide Crystal

The electronic band structure of sodium iodide has been calculated by using the tight-binding method for the valence bands and an empirical method for the lowest conduction bands. Functions for the ${\mathrm{I}}^{-}$ and ${\mathrm{Na}}^{+}$ ions have been obtained by solving the Hartree-Fock-Slater modified equation. The $5p$ and $5s$ ${\mathrm{I}}^{-}$ functions are allowed to mix at appropriate points in the Brillouin zone. The lattice parameter is varied and yields results for shifts in energy which agree with those observed when the lattice temperature is changed. Spin-orbit interactions are included and yield results for the $5p$ bands which are in agreement with experiment. Effective masses for electrons and holes are calculated at the points $\Gamma$, L, and $X$ in the valence and conduction bands.