Perturbation Theory of Covalent Crystals. III. Calculation of Formation and Migration Energies of a Vacancy in Si and Ge

The formation and migration energies of a vacancy in Si and Ge are calculated by using the perturbation theory developed in the authors' previous paper, in which the perturbation theory in terms of pseudopotentials has been extended by including higher order terms corresponding to the covalent bonding effect so as to be applicable to IV and III-V covalent semiconductors. In calculations, lattice distortions around a vacancy are taken into account. The formation energy of a vacancy is calculated to be 2.74∼2.84 eV for Si and 2.53∼2.63 eV for Ge. The migration energy of a vacancy is 0.38∼0.50 eV for Si and 0.31∼0.40 eV for Ge. Experimental data are discussed in comparison with these theoretical values.