Compositional dependence of Raman frequencies in ternaryGe1−x−ySixSnyalloys

Abstract

The Ge-Ge, Si-Si, and Si-Ge Raman frequencies in ${\mathrm{Ge}}_{1\ensuremath{-}x\ensuremath{-}y}{\mathrm{Si}}_{x}{\mathrm{Sn}}_{y}$ alloys were measured for $x\ensuremath{\leqslant}0.2$ and $y\ensuremath{\leqslant}0.1$. The Ge-Ge and Si-Si mode frequencies are found to be linear functions of composition over the measured range. The coefficients obtained from linear fits to the experimental data are similar to those measured in binary alloys incorporating Si, Ge, or Sn, suggesting that the linear behavior extends over the entire range of possible compositions $(x,y)$ to include the binary alloys as special cases. The linear coefficients are shown to follow a universal behavior that results from the scaling of phonon dispersion curves in Si, Ge, and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$.