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 G-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 G point. ~5! The surface modes located between the bulk TOand LO-phonon bands have a significant bulk G 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. @S0163-1829~99!12203-3#