Phonon spectra of diamond and zinc-blende semiconductors

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Abstract
We model the phonon spectra of the diamond-structure compounds C, Si, Ge, Sn and the zinc-blende-structure compounds GaP, GaAs, and ZnS. We use a four-parameter valence-force model consisting of first- and second-neighbor forces plus the very important coplanar angle-angle interaction introduced by McMurry et al. Although formally ‘‘fifth neighbor,’’ this interaction follows bond stretching and bond bending in importance. In agreement with the remarkable spread of screening charge along 〈110〉 bond chains this interaction highlights the physical importance of these chains. Two-parameter fits to the spectra are quite successful using only bond bending and bond stretching but with much smaller values of bond bending than found by Martin, who fitted the elastic constants. In zinc-blende compounds two bond-stretching parameters are available corresponding to the two distinct vertex atoms. The extra degree of freedom gives little improvement and produces such wildly different values as to call into question the degree of localization implied by the intuitive picture of bond bending. We introduce long-range Coulomb interactions through a ‘‘bond-tilt’’ model yielding dipole-dipole and quadrupole-quadrupole interactions. These interactions further improve the fits given by the valence-force model, yielding an LO-TO splitting for the zinc-blende compounds. The interactions are manifestly rotationally invariant, satisfying a serious question raised by an earlier model due to Lax. Our models give a different perspective on the physics of covalent phonon spectra which we feel is complementary to the bond-charge models of Martin and Weber. The accuracy of our best fits is comparable.