Influence of extended defects on the formation energy, hyperfine structure, and zero-field splitting of NV centers in diamond

We present a density-functional theory analysis of nitrogen-vacancy (NV) centers in diamond, which are located in the vicinity of extended defects, namely, intrinsic stacking faults, extrinsic stacking faults, and coherent twin boundaries on {111} planes in diamond crystals. Several sites for NV centers close to the extended defects are energetically preferred with respect to the bulk crystal. This indicates that NV centers may be enriched at extended defects. We report the hyperfine structure and zero-field splitting parameters of the NV centers at the extended defects, which typically deviate by about 10% but in some cases up to 90% from their bulk values. Furthermore, we find that the influence of the extended defects on the NV centers is of short range: NV centers that are about three double layers (corresponding to $\approx 6\text{Å}$) away from defect planes already show bulklike behavior.

Figure 1

Illustration of the atomic structure in the vicinity of the intrinsic stacking fault (ISF), the extrinsic stacking fault (ESF), and the coherent twin boundary (CTB). For later reference we assign numbers to all double layers. The yellow spheres represent the carbon atoms. In the left panel an axial NV center in layer $n=-1$ at position aA is shown and the middle panel includes a basal NV center in position aC. The position of the carbon vacancy is indicated by a large blue sphere and the nitrogen atom is represented by a small gray sphere. The horizontal dashed green line serves as a guide for the eye and indicates the center of the region where local hexagonal ordering is present, such as ABA or ACA. The respective double layers are highlighted with red labels. Note that the results displayed in the following figures will not be strictly symmetric with respect to this line because the NV defect complex has a defined orientation but no symmetry center between the N atom and the C vacancy.

Figure 2

Formation energies of NV centers with either axial or basal orientation in vicinity of an ISF, ESF, and CTB. Values are given in eV and are relative to the formation energy $E_{\mathrm{form}}^{\left(0\right)}$ of NV centers in the bulklike region.

Figure 3

Longitudinal component $D$ of the ZFS of a ${\mathrm{NV}}^{-}$ center for different positions relative to the ISF, ESF, and CTB. Values are given with respect to the value $D_0$ of bulk diamond.

Figure 4

Transversal component E of the ZFS (in MHz) for a NV center with basal orientation at different positions relative to the ISF, the ESF, and the CTB.

Figure 5

Hyperfine structure constants $A_{ii}$ for ${}^{14}\mathrm{N}$ for the different positions at the ISF with either axial or basal orientation of the NV center. The $A_{ii}$ values are normalized by the corresponding values $A_{ii}^{\left(0\right)}$ of bulk diamond.

Figure 6

Hyperfine structure constants $A_{11}$ (lower panel) and $A_{33}$ (upper panel) for ${}^{13}\mathrm{C}$ for the various positions relative to the ISF with either axial or basal orientation of the NV center. For the basally oriented NV centers two carbon atoms lie in a common layer. Their values are denoted “pair.” The third carbon atom residing in the layer above the vacancy is denoted “single.”