Dielectric Screening Model for Lattice Vibrations of Diamond-Structure Crystals

The phonon dispersion curves of Si are calculated from the dielectric screening theory using approximations based on Phillips's bond-charge model for covalent crystals. The off-diagonal ($K\ne K^{\prime }$) elements of the inverse dielectric function ${\epsilon }^{-1\mathrm{}}(\mathrm{q}+\mathrm{K}, \mathrm{q}+{\mathrm{K}}^{\prime })$ are essential in the calculation for a nonmetal; here their effect is approximated by the interactions involving the bond charges. The diagonal part is calculated within the pseudopotential framework. One adjustable parameter, which affects only the LA modes, is used. The results are generally in good agreement with experiment (of order 10% except for the low acoustic modes for which the maximum error is 36%). The calculation suggests a two-parameter model for the forces, which can readily be applied to all crystals with the diamond structure. In agreement with the assumptions of bond-charge model, it is found that the major deviations from homology of the dispersion curves of the different elements are explained by the decreasing importance of the bond-charge forces as the dielectric constant increases.