Phonon modes in spherical silicon germanium alloy (SiGe) nanocrystals containing up to 1147 atoms (3.6 nm) have been investigated as a function of the 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 Si to Ge atoms), and location (surface or interior) of clusters of atoms in 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 SiGe alloy reported in the literature. Insights into the behavior of Raman peaks usually identified as Ge-Ge, Si-Si, and Ge-Si optical phonon modes are presented.
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