Phonons in GaP quantum dots

The phonon structure of GaP quantum dots is studied using an atomistic potential model. The dot eigenmodes are obtained from a direct diagonalization of the dynamical matrix and classified using an efficient dual-space analysis method. Our calculations provide a theoretical explanantion for several experimental observations. (1) Depending on the spatial localization, the phonon modes of dots are either dot-interior (bulklike) or surfacelike. (2) The frequencies of the dot-interior modes can be qualitatively described by the “truncated crystal method” using a single branch and a single wave vector of the bulk-phonon dispersion. In contrast, the surface modes cannot be described by this model. (3) The dot-interior modes have a dominant bulk parentage from a specific part of the Brillouin zone, while the surface modes do not. (4) The frequencies of the bulklike $\Gamma$-derived longitudinal optical (LO) and transverse optical (TO) phonon modes are found to decrease with decreasing dot size. This decrease reflects the downward dispersion of the bulk optical-phonon branches away from the $\Gamma$ point. (5) The surface modes located between the bulk TO- and LO-phonon bands have a significant bulk $\Gamma$ character, and are thus Raman detectable. (6) The dot-interior modes exhibit only a slight LO/TO mode mixing, while the surfacelike modes show a strong mode mixing.