Raman scattering in germanium-silicon alloys under hydrostatic pressure

Abstract

The pressure dependence of vibrational Raman scattering in polycrystalline ${\mathrm{Ge}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Si}}_{\mathit{x}}$ alloys is studied up to \ensuremath{\sim}100 kbar across the compositional range, and the mode Gr\"uneisen parameters \ensuremath{\gamma} for the Si-Si, Ge-Ge, and Ge-Si optical phonons are determined from the Raman shifts. ${\ensuremath{\gamma}}_{\mathrm{Si}\mathrm{\ensuremath{-}}\mathrm{Si}}$ increases with the Ge fraction of the alloy and ${\ensuremath{\gamma}}_{\mathrm{Ge}\mathrm{\ensuremath{-}}\mathrm{Ge}}$ increases with the Si fraction. The dependence of the Raman shift on x and pressure is described by a modified cellular isodisplacement model of optical phonons. In particular, the predicted dependence of the Ge-Si mode frequency on alloy composition at ambient pressure is found to agree much better with experiment when the variation of the average Ge-Si bond length with alloy composition is included in this model.