Thermodynamics of electric-field assisted formation of NV centers in diamond

The nitrogen-vacancy (NV) center in diamond is a widely studied solid-state spin defect, owing to its long spin coherence time even at room temperature and their potentials for quantum information and sensing applications. Traditionally, these defects are formed using ion implantation and electron irradiation, followed by thermal annealing, requiring high temperature for material processing followed by randomly oriented NV centers. However, challenges remain in spatial localization of NV centers with controlled orientation with high energy cost for synthesis. Here, we computationally investigate a new strategy to spatially localize and preferentially orient NV centers in diamond based on electric-field assisted thermal annealing. To model this process from first principles, we use enhanced sampling simulations with ab initio molecular dynamics based on density functional theory to compute the free energy landscape of NV center formation via carbon vacancy migration in diamond, over a range of temperatures and electric fields. We find that the presence of external electric fields can selectively lower NV center formation energy. Our study enables us to construct a thermodynamic phase diagram of NV center formation, which provides insights into the design of controllable synthesis of NV centers.