Microscopic origin for the orientation dependence of NV centers in chemical-vapor-deposited diamond

First-principles calculation reveals that hydrogen, which is abundant in chemical vapor deposition (CVD), can significantly improve the uniformity of nitrogen-vacancy (NV) centers in diamond. It shows that the formation of NV centers can be described as a multi-step process: first, a substitutional N (NC) is preferentially formed at the surface layer over that of either a carbon vacancy (VC) or an in-pane nitrogen-vacancy-hydrogen (NVH) complex. Second, with the help of H, a VC is preferentially incorporated in the newly formed topmost layer as a nearest neighbor to the NC (now buried in the first sublayer). This NVH complex is even more stable than NC on the same layer. Third, H protects the already formed NV centers by forming low-energy NVHX complexes. These NV centers with their axes pointing along the directions of surface C-H bonds during their incorporation explain the experimental observations by CVD growth on (1 0 0) and (1 1 0) surfaces. Based on the model, we predict that CVD growth on (1 1 1) surface could eliminate the orientation domains to significantly improve the performance of NV centers.