Obtaining a nonrelativistic dispersion equation for crystals with sphalerite structure

Abstract

The secular determinant in which all thekp interactions are taken exactly into account in the group of four valence and six conduction bands (with the exception of the$\Gamma _{15_{_C } } - \Gamma _{12_C }$ interaction) is examined. An exact analytical expansion is made of this determinant and a tenth degree dispersion equation is obtained. The equation is reduced to compact form permitting its easy reduction to an algebraic equation. It agrees with the eleventh degree dispersion equation obtained earlier for the diamond structure. Neglecting indirect interactions with respect to the upper valence bands, these valence bands are in agreement for both structures.