Polar interface vibrations in GaN/AlN quantum dots: Essential effects of crystal anisotropy

The inherent anisotropy of crystal lattices of the nitride semiconductor compounds is found to essentially determine the character of surface polar vibrations of a GaN quantum dot in AlN matrix. The interface phonons are analyzed within the framework of the anisotropic macroscopic dielectric continuum model. Analytical solutions are obtained for surface modes on a quantum dot of oblate spheroidal form. These modes can exist in continuous frequency regions, in contrast to quantized frequencies that are characteristic for isotropic case. The period of spatial oscillations in these modes varies substantially over the dot surface, so that the oscillations can have condensation points at the dot poles. Along with truly localized surface states, there are two other types of phonon modes. First, runaway modes, which freely leave the dot surface through escape roots in equatorial regions. Second, quasistationary (leaky) states, in which the areas of spatial oscillations are separated from the escape root regions by the areas of exponential behavior. The leaky states can provide effective energy relaxation of the confined electrons.