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

Abstract

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 NVcenters with the desired charge state for future ICT and sensor applications.

Ab initio theory of the nitrogen-vacancy center in diamond

“…Extensive tests showed that if the defects are placed at least 7.5 Å far from each other then the degeneracy of the corresponding orbitals is maintained and the constant shift in the KS levels can be well monitored and corrected 117 . In a recent study, the pair of NV center and ionized N s was analyzed in detail with arriving the same conclusion that 7.5 Å distance between the two defects suffices to avoid the splitting of the degeneracy of the corresponding orbitals, and NV center can be well approximated as isolated 166 . These achievements makes possible to directly simulate NV center with correct total energies that is necessary for modeling direct interaction of NV center with surface species 117 .…”

The bulk conversion depth of the NV-center in diamond: computing a charged defect in a neutral slab

“…Comparing the bulk conversion values for the different terminations (HSE06 computations), we get a value of 1.961 eV for the F-terminated surface (average value of the two configurations in the 15th layer), for the H/O/ OH-terminated surface we get 1.959 eV (for the configuration in the 15th layer), and for the N-terminated surface we get 1.963 eV (for the configuration in the 14th layer). This can be compared to the bulk value of 1.962 eV for a 512 atom neutral supercell (containing a NV-center and an electron donor nitrogen atom placed 12.23 Å from the NV-center along the symmetry axis of the supercell in the NV-N configuration) in our previous work [45]. As can be seen, the values are very close to each other, deviating 0.004 eV at most.…”

“…At least when the surfaces are defect free and without its own spin-density. It is also worth reiterating that the donor-N has no spin density at all [45], which is also verification of the success of the charging of the defect-center resulting in a neutral supercell.…”

“…We achieve a neutral supercell by using an additional substitutional N to donate an electron to the NVcenter, thereby giving it a negative charge state. This charging method has been shown to give the correct structure, energetics and spin density of the NVcharge state, and result in zero spin density on the donor-N [45]. This donor-N was placed 7.7-8.1 Å from the NV-center, and at the same depth from the top layer as the NV-center to avoid the creation of an artificial dipole interaction across the layers of the slab.…”

“…We charge the NV-center by an additional donor-N, thereby achieving an uncharged supercell, as described in our previous work. This charging method has been shown to render the correct properties of the NV -(minus) charge state, and result in zero spin density on the additional donor nitrogen [45,46]. A charged system must be treated with great care since the pseudopotential expressions for the total energy are derived in a chargeneutrality condition [47].…”