Transverse interplanar forces and phonon spectra of strained Si, Ge, and Si/Ge superlattices

We present a first-principles pseudopotential study of the effects of the (001) biaxial strain on the transverse phonon spectra of Si and Ge along the a direction, and of the transverse phonon modes of strained Si/Ge (001) superlattices (SL's). The supercell method is used to calculate the [001] transverse interplanar force constants (IPFC's) of Si and Ge at three strain configurations corresponding to coherent growth on Si1-xGex (001) (with x=0, 0.5, and 1) substrates. IPFC's up to the eighth-nearest-neighboring planes were included. It has been found that (i) the strain-induced frequency shift of the transverse optical (TO) branch is in excellent agreement with the available experimental data and has a weak wave vector dependence. (ii) Both the Si- and Ge-Like TO confined modes in strained Si/Ge (001) SL's are well described relative to the bulk dispersions by an effective confinement length d(eff)=(n+3)a(perpendicular to)/4, where n is the number of monolayers of Si or Ge, and a(perpendicular to)/4 is the corresponding interplanar distance. (iii) The frequencies of the interface modes are about 400 cm(-1) and have a strong dependence on the interfaces coupling in short period SL's.