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 Si_1−xGe_x 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.