Volume-dependence of phonon frequencies and mode Grüneisen parameters for Si and Ge

The volume-dependence of phonon frequencies for Si and Ge is studied using higher-order perturbation and local Heine-Abarenkov model pseudopotential. The obtained mode Grüneisen parameters at atmospheric pressure are in good agreement with the experimental data. The mode Grüneisen parameters obtained for the Raman, TO, LO and LA modes increase slightly with decreasing volume. The other TA mode Grüneisen parameters decrease strongly as function of the volume strain, and give important contribution to the anharmonic properties of Si and Ge. The pressure dependence of phonon frequencies for Raman and some modes at the zone boundaries are estimated over the whole region of the compressed volume before the pressure induced covalent-metallic phase transition.