Strain-shift coefficients for phonons inSi1−xGexepilayers on silicon

The measurement of the strain coefficients for the three longitudinal-optical phonons in strained ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ (0<x<0.35) molecular-beam-epitaxy-grown epilayers on (100) Si is reported. Strain in the epilayers was varied by annealing metastable pseudomorphically grown epilayers at various temperatures and was measured by double-crystal x-ray diffractometry. The strain-shift coefficients for the phonons were obtained from Raman-scattering measurements of the annealed specimens. For all compositions it was found that the Si-Si phonon frequencies vary linearly with strain. The strain-shift coefficient, however, showed a small composition dependence, varying from about -750 ${\mathrm{cm}}^{\mathrm{-}1}$ at x=0.08 to about -950 ${\mathrm{cm}}^{\mathrm{-}1}$ at x=0.35, corresponding to a stress factor τ≊0.4+0.57x+0.13${\mathit{x}}^2$ ${\mathrm{cm}}^{\mathrm{-}1}$/kbar for this vibration. The magnitude of the corresponding coefficients for the Si-Ge and Ge-Ge lines are slightly less than that of the Si-Si line, and vary in a similar way with x.