Anomalous low energy phonon dispersion in bulk silicon-germanium observed by inelastic x-ray scattering

We report on an anomalous mode distinct from both optical and acoustic modes in phonon dispersion curves of bulk Si1-xGex alloy with x taking the values of 0.16, 0.32, 0.45, and 0.72. The anomalous mode at approximately 13 meV was observed directly using inelastic x-ray scattering along the Γ-X ([00q]) direction. The phonon dispersion relations of the anomalous mode indicate that there was no momentum dependence, similar to those of the longitudinal and transverse optical modes (Ge-Ge, Si-Ge, and Si-Si modes). In contrast to the acoustic and optical phonon modes, the energy of the anomalous mode shows no Ge fraction dependence. The molecular dynamics simulation corroborates that the Ge-Ge pairs or Ge atom clusters, which are surrounded by Si atoms, provide the anomalous mode, which is unique to the alloy structure. It has been suggested that such a localized vibration mode with no propagation significantly affects the acoustic modes, leading to low thermal conductivity in the SiGe alloy.