Pseudopotential Calculations of Electronic Charge Densities in Seven Semiconductors

Electronic charge densities are calculated as a function of position in the unit cell for seven diamond and zinc-blende semiconductors using wave functions derived from pseudopotential band-structure calculations. Detailed plots of the charge density are presented in the (110) plane for each valence band of Ge, GaAs, and ZnSe and for the sum of the valence bands of Ge, GaAs, ZnSe, $\alpha -\mathrm{S}\mathrm{n}$, InSb, CdTe, and Si. Trends in bonding and ionicity are discussed in detail. The covalent-bonding charge is also calculated for these crystals and is plotted against the ionicity scales of Phillips and Van Vechten and of Pauling. It is shown that an extrapolation to zero covalent-bonding charge yields a critical value of the ionicity which separates fourfold-coordinated and sixfold-coordinated diatomic crystals. This value is in agreement with the empirical value obtained by Phillips and Van Vechten.