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

Abstract

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.

Thermal conductivity and inelastic X-ray scattering measurements on SiGeSn polycrystalline alloy

“…The LVM peak positions for the Si 1-x Ge x sample ranged from 11.4-12.9 meV and are 12.1 meV on average. These values are comparable with that reported for single-crystalline Si 1-x Ge x , 2) indicating the Gerelated local structure proposed for the single-crystalline Si 1-x Ge x is also formed in the polycrystalline Si 1-x Ge x . In contrast to the LVM for the Si 1-x Ge x sample, the energy peak position shifted towards lower energy, namely lower frequency, in the case of Si 1-x-y Ge x Sn y .…”

“…In Si 1-x Ge x , the LVM is produced at the Ge-Ge pairs or Ge atom clusters, which are surrounded by Si atoms. 2) On the other hand, we previously reported that the EXAFS measurement on a single-crystalline Ge-rich Si 1-x-y Ge x Sn y alloy revealed that a Sn atom locates at the second nearest neighbor of a Si atom to form a Si-Ge-Sn local structure. 22) Stochastically, this local structure hardly forms spontaneously when all atoms distribute randomly.…”

“…The parameters used, such as interatomic distance and equations, have been described elsewhere. 2,24)…”

“…1) On the other hand, we measured the phonon dispersion curves of single-crystalline Si 1-x Ge x having Ge content in the range of 16% ∼ 72% by means of the inelastic X-ray scattering (IXS) technique. 2,3) The IXS results, compared with theoretical calculation results of the phonon dispersion curves, indicated the presence of a local vibration mode (LVM), which should originate from a Gerelated local structure formed in the Si 1-x Ge x crystals. The LVM was found to be independent of wavenumber.…”

BCS-BEC crossover of ultracold ions driven by density-dependent short-range interactions in a quantum plasma

“…Moreover, it is shown that the resulting quantum ion-acoustic waves exhibit distinct dispersion relations across the BCS-BEC crossover, which provide a direct route to probe the changing scattering length, as well as the BCS and BEC states. It would deserve an experimental measurement of a phonon dispersion [89] varying continuously from BCS to BEC state.…”