Charged dopants in neutral supercells through substitutional donor (acceptor): nitrogen donor charging of the nitrogen-vacancy center in diamond

Charged defects are traditionally computed by adding (subtracting) electrons for negative (positive) impurities. When using periodic boundary conditions this results in artificially charged supercells that also require a compensating background charge of the opposite sign, which makes slab supercells problematic because of an arbitrary dependence on the vacuum thickness. In this work, we test the method of using neutral supercells through the use of a substitutional electron donor (acceptor) to describe charged systems. We use density functional theory (DFT) to compare the effects of charging the well-studied NV-center in diamond by a substitutional donor nitrogen. We investigate the influence of the donor-N on the NV-center properties as a function of the distance between them, and find that they converge toward those obtained when adding an electron. We analyze the spin density and conclude that the donor-N has a zero magnetic moment, and thus, will not be seen in electron spin resonance. We validate our DFT energies through comparison to GW simulations. Charging the NV-center with a substitutional donor-N enables accurate calculations of slabs, without the ambiguity of using charged supercells. Implantation of donor-N atoms opens up the possibility to engineer NV-centers with the desired charge state for future ICT and sensor applications.