The formation and migration energies of a vacancy in Si and Ge were calculated by using perturbation theory in which the perturbation theory in terms of pseudopotentials was extended by including higher-order terms corresponding to the covalent bonding effect so as to be applicable to IV and III-V covalent semiconductors. Lattice distortions around a vacancy were taken into account. The formation energy of a vacancy was calculated to be 2.74 to 2.84eV for Si and 2.53 to 2.63eV for Ge. The migration energy of a vacancy was 0.38 to 0.50eV for Si and 0.31 to 0.40eV for Ge.

Perturbation Theory of Covalent Crystals. III. Calculation of Formation and Migration Energies of a Vacancy in Si and Ge. T.Soma, A.Morita: Journal of the Physical Society of Japan, 1972, 32[2], 357-64