Lattice dynamics of SiC polytypes within the bond-charge model

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Abstract
We present a phemomenological approach to the lattice-dynamical properties of various SiC polytypes. A generalized bond-charge model is applied to the cubic and hexagonal polytypes 3C, 6H, 4H, and 2H. The long-range microscopic electric field of ions and bond charges is fully taken into account via an Ewald technique. The short-range elastic interactions are described by bending and stretching forces between ions and bond changes. The force constants and effective charges are fit to phonon frequencies known from Raman and luminescence measurements. The reliability of the model is tested not only for the frequencies but also for the eigenvectors by comparison with results of ab initio calculations for 3C- and 2H-SiC. We show that the anisotropy in the uniaxial hexagonal polytypes is mainly due to the nonanalyticity of the Coulomb forces. The corresponding frequency splittings are related to slight changes of the bond charges in dependence on the bond orientation. Differences in the elastic forces parallel and nonparallel to the hexagonal axis are only necessary to stabilize the zone-boundary phonons. The trends of the resulting frequencies and density of states are discussed versus the percentage hexagonality. Consequences of the different phonon dispersions for the elastic properties of the 3C, 6H, 4H, and 2H polytypes are considered. We speculate about possible mechanisms of polytype stabilization by the lattice vibrations.