Interplanar forces and phonon spectra of strained Si and Ge:Ab initiocalculations and applications to Si/Ge superlattices

Abstract

We have studied the effects of biaxial strain in the (001) plane on the interplanar force constants and phonon spectra of bulk Si and Ge for longitudinal propagation along the [001] direction. The results are in good agreement with the available experimental data; moreover, we give predictions for the strain dependence of the bulk dispersions along the \ensuremath{\Delta} line. We provide a practical and accurate way of calculating phonon spectra along [001] for strained [001]-oriented Si/Ge superlattices (SL's), with strain configuration corresponding to growth on arbitrary ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ substrates. The importance of a correct treatment of strain effects for the understanding of SL phonon physics and for SL characterization is illustrated with results for two prototype superlattices lattice matched to Si and Ge.