We investigate the energetics and electronic structure of multiatomic vacancies in hexagonal boron nitride $\left(h\text{-BN}\right)$ based on the local-density approximation in the density-functional theory. We find that the energetics of vacancies strongly depends not only on the environmental condition of boron and nitrogen chemical potentials but also on electron chemical potentials of these systems. Under nitrogen- and electron-rich conditions, the triangular vacancy comprised of one nitrogen and three boron atoms is a geometrically favorable structure. We also find that the atomic structure of vacancies depends on their charge state. In vacancies with nitrogen edges, the distance between the next-nearest-neighbor nitrogen atoms increases on injection with excess electrons. In contrast, the distance between the next-nearest-neighbor boron atoms decreases for vacancies with boron edges on injection with excess electrons. Our detailed analysis of electronic structures of vacancies unravels the origin of the structural modification of vacancies with regard to their charge state.

• Received 10 August 2009

DOI:https://doi.org/10.1103/PhysRevB.80.161404