Phonon spectra of strained Si and Ge

Abstract

Phonon spectra of Si and Ge grown pseudomorphically on [001]-oriented ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ substrates are studied theoretically. In the case of Si or Ge grown on a [001]-oriented substrate, the frequency shift induced by the biaxial strain for the LO-phonon mode is found to be nearly rigid along the [001] direction, whereas for the TO-phonon mode the frequency shift is wave-vector dependent. Frequency shifts of the LA- and TA-phonon modes also show a wave-vector dependence. Raman spectra of strained Si/Ge superlattices are calculated with strained force constants and a good agreement with experimental Raman spectra is obtained.