Evolution of intrinsic vacancies and prolonged lifetimes of vacancy clusters in black phosphorene

Due to the relatively low formation energies and highly mobile characteristics of atomic vacancies in phosphorene, understanding their evolution becomes crucial for its structural integrity, chemical activities and applications. Herein, by combining first-principles calculations and kinetic Monte Carlo simulation, we investigate the time evolution and formation of atomic vacancy clusters from isolated monovacancies (MVs), aiming to uncover the mechanisms of diffusion, annihilation, and reaction of these atomic vacancies. We find that while isolated MVs possess a highly mobile characteristic, they react and form MV pairs which possess much lower mobility and high stability under ambient conditions. We also show that the disappearance of MVs at the edge is quite slow due to the relatively high energy barrier, and as a result, around 80% of MVs remain even after two years under ambient conditions. Our findings on one hand provide useful information for the structural repairing of phosphorene through chemical functionalization of these vacancy clusters, and on the other hand, suggest that these rather stable vacancy clusters may be used as activated catalysts.