Acoustic waves in (0 0 1) anisotropic polytype heterostructures

We have studied the acoustic waves of (0 0 1) polytype heterostructures formed by slabs of cubic crystals. We have considered symmetric and asymmetric heterostructures formed by AlN, GaN and InN in the zinc-blende structure due to the potential applications of these materials. The anisotropy of the materials has been taken into account and the different propagation directions ranging from the [1 0 0] to the [1 1 0] have been considered. We obtain the dispersion relations for different propagation directions. The coupling between the spatial components of the elastic displacements is different for symmetry and general propagation directions. The spatial localization of the modes in the heterostructures has also been obtained.