Insight into the nitrogen-vacancy center formation in type-Ib diamond by irradiation and annealing approach

Comprehending the microscopic formation of nitrogen vacancy (NV) centers in nitrogen-doped diamonds is crucial for enhancing the controllable preparation of NV centers and quantum applications. Irradiation followed by annealing simulations for a type-Ib diamond with a 900 ppm concentration of isolated nitrogen is conducted along different orientations and at different annealing temperatures. In these simulations, molecular dynamics (MD) with smoothly connected potential functions are implemented. MD simulations revealed the dynamic formation process of the NV center, which was subsequently verified by first-principles calculations and experiments. The results indicate that vacancies undergo one or multiple migrations by exchanging sites with neighboring atoms. There are three mechanisms for the formation of NV centers: direct irradiation-induced NV formation, irradiation with further annealing to form NV and vacancy migration (VM) during the annealing process. Furthermore, the results show that both VM and NV center formations are affected by orientations. This study clarifies the formation of NV centers across multiple scales and provides a solid foundation for the targeted preparation of NV centers.