On the Models for the Investigation of Charged Defects in Solids: The Case of the VN- Defect in Diamond

Local charged defects in periodic systems are usually investigated by adopting the supercell charge compensated (CC) model, which consists of two main ingredients: (i) the periodic supercell, hopefully large enough to reduce to negligible values the interaction among defects belonging to different cells; (ii) a background of uniform compensating charge that restores the neutrality of the supercell and then avoids the "Coulomb catastrophe". Here, an alternative approach is proposed and compared to CC, the double defect (DD) model, in which another point defect is introduced in the supercell that provides (or accept) the electron to be transferred (subtracted) to the defect of interest. The DD model requires obviously a (much) larger supercell than CC, and the effect of the relative position of the two defects must be explored. A third possible option, the cluster approach, is not discussed here. The two models have been compared with reference to the VN- defect; for DD, the positive compensating charge is provided by a P atom. Three cubic supercells of increasing size (containing 216, 512, and 1000 atoms) and up to eight relative VN--P+ defect-defect positions have been considered. The comparison extends to the equilibrium geometry around the defect, band structure, charge and spin distribution, IR and Raman vibrational spectra, and electron paramagnetic resonance constants. It turns out that the CC and DD models provide very similar results for all of these properties, in particular when the P+ compensating defect is not too close to VN-.