Phonon dispersion curves of GaAs-AlAs superlattices grown in the [111] and [110] directions

Phonon dispersion curves of GaAs-AlAs superlattices grown in the [111] and [110] directions are studied within a rigid-ion model which takes into account both the short-range interaction and the long-range Coulomb interaction. The anisotropic behavior of the optical phonons at the zone center and the interface modes are studied in detail and are compared with those for GaAs-AlAs superlattices grown along the [100] direction. It is shown that the interface modes at finite wave vectors for superlattices grown along different directions are substantially different and depends sensitively on whether the dynamic matrix has reflection symmetry.