Ab initio thermodynamics calculation of the relative concentration of NV - and NV0 defects in diamond

Two charge states of nitrogen-vacancy (NV) defects in diamond are modeled using density functional theory. Vibrational properties and the free formation energies of the defects are calculated, with the implementation of the charge-neutrality condition for NV - to determine the chemical potential of the electron as a function of temperature. We find that at temperatures above 600 K the concentration of NV - becomes greater than that of the NV0