Microscopic investigation of phonon modes in SiGe alloy nanocrystals

Phonon modes in spherical silicon germanium alloy $(\text{SiGe})$ nanocrystals containing up to 1147 atoms $(3.6\phantom{\rule{0.3em}{0ex}}\text{nm})$ have been investigated as a function of the $\text{Si}$ concentration. Microscopic details of phonon modes, including phonon frequencies and vibrational amplitudes, phonon density-of-states are calculated directly from the dynamic matrices. In particular, the dependence of phonon frequency on the configuration (such as a different ratio of $\text{Si}$ to $\text{Ge}$ atoms), and location (surface or interior) of clusters of atoms in $\text{SiGe}$ alloy nanocrystals have been investigated. Low frequency surface phonons that are related to the spheroidal and torsional modes of a continuum sphere are identified and their frequency dependence on alloy concentration elucidated. The calculated results are compared with measured Raman spectra in bulk, thin films, and superlattices of $\text{SiGe}$ alloy reported in the literature. Insights into the behavior of Raman peaks usually identified as $\text{Ge}\text{\ensuremath{-}}\text{Ge}$, $\text{Si}\text{\ensuremath{-}}\text{Si}$, and $\text{Ge}\text{\ensuremath{-}}\text{Si}$ optical phonon modes are presented.