Surface optical phonons in a triaxial ellipsoidal quantum dot

The surface optical phonon eigenmodes in ellipsoidal quantum dots were calculated using the dielectric-continuum model. The problem is exactly solvable in terms of ellipsoidal coordinates and the eigenmodes are written in terms of Lame polynomials. A study of the mode frequency dependence on the shape of the dots is carried out. This represents a generalization over earlier work on spheres and spheroids. Differences in the results obtained using an optically active and an optically passive host is presented. The size independence of the mode frequencies for a quantum dot of arbitrary shape is proven.