Carbon dependence of Raman mode frequencies in ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}\mathrm{-}\mathit{y}}$${\mathrm{Ge}}_{\mathit{x}}$${\mathrm{C}}_{\mathit{y}}$ alloys

The frequencies of the Si-Si, Si-Ge, and Ge-Ge Raman modes in ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}\mathrm{-}\mathit{y}}$ ${\mathrm{Ge}}_{\mathit{x}}$ ${\mathrm{C}}_{\mathit{y}}$ alloys with y⩽0.03 have been measured. All frequencies are found to increase as a function of the carbon concentration. Within experimental error, this dependence is linear with a large slope, which can be explained qualitatively in terms of the large bond distortions caused by the lattice mismatch between ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ and diamond. Good numerical agreement with theoretical predictions is obtained if the mode frequencies are plotted as a function of the substitutional carbon fraction determined from Rutherford backscattering studies. For the ‘‘Si-Si’’ mode, the magnitude of the carbon contribution to the bond-distortion dependence of the Raman frequency shift is found to be 15 times larger than the Ge contribution. This disagrees with the 8-to-1 strain compensation ratio predicted form Vegard’s law, but agrees well with theoretical predictions of this ratio. © 1996 The American Physical Society.