Phonon Dispersion Curves by Raman Scattering in SiC, Polytypes $3C$, $4H$, $6H$, $15R$, and $21R$

Phonon dispersion curves for SiC have been constructed from first-order Raman scattering data. The method used is a new one that exploits the existence of polytypes. Excitation by an argon ion laser made possible the observation of nine one-phonon lines in $4H \mathrm{SiC}$, 16 lines in $15R$, and 14 lines in $21R$. The symmetry type of each phonon mode was determined by polarization analysis, and the modes were further classified by the use of a standard large zone. The three groups of one-phonon lines, together with 15 lines previously reported for $6H \mathrm{SiC}$, were then all assigned to their positions in a single large-zone plot, to yield a set of SiC phonon dispersion curves comparable with those obtained for other materials by neutron diffraction. The results verify the existence of a common phonon spectrum for all SiC polytypes in the axial direction. Longitudinal and transverse acoustic velocities are obtained from the dispersion curves, and are in good agreement with experimental values. Thus, optic modes in polytypes give information on acoustic properties. All SiC polytypes have in common a set of strong modes in which the Si and C sublattices vibrate against each other. The anisotropy of one of these modes varies with polytype in the same way as the $\frac{c}{a}$ axial ratios. Both the anisotropy and the $\frac{c}{a}$ ratio are related empirically to the percentage of hexagonal planes in the polytype stacking arrangement.