Perturbation Theory of Covalent Crystals. II. Lattice Vibration Spectra in Si and Ge

Phonon dispersion curves for Si and Ge are calculated by using the perturbation theory developed in our previous paper, where the perturbation theory based on pseudopotentials has been extended by taking into account higher order terms corresponding to the covalent bond effect so as to be applicable to IV and III-V covalent semiconductors. The resulting phonon dispersion curves are qualitatively in good agreement with experiment in spite of introducing no adjustable parameter and explain the crossing of LO and TO curves along the [100] direction and the minimum in [110] II optic mode near the zone boundary.