Vibrational effect on vacancy concentration in diamond: The density-functional-theory calculation

The vacancy concentration of the C-vacancy in diamond has been calculated using the density functional theory (DFT). Supercells containing up to 512 atomic sites are used to model the vacancy system. We calculate the formation energy, phonon density of states (P-h-DOS), and vacancy concentration. The vibrational contribution is considered in the calculation of vacancy concentration. The calculated formation energy is 6.76 eV with the symmetry of D2d. From the phonon calculation, the Ph-DOS is softened on the vacancy side, significantly contributing to the vacancy concentration up to 106 times from that ignoring the vibrational effect.