Vacancy migration in hexagonal boron nitride

Activation energies and reaction paths for diffusion and nucleation of mono- and divacancy defects in hexagonal boron nitride layers are theoretically investigated. Migration paths are derived using the nudged elastic band method combined with density-functional-based techniques. We find a different behavior for migration of single boron and nitrogen vacancies with the existence of intermediate metastable states along the migration paths. The temperature dependence of entropic and vibrational contributions to the free Gibbs energies is explicitly taken in account. A rich phase diagram for vacancy migration is then obtained. Boron vacancies are first thermally activated and can migrate to form more stable BN divacancies. At high temperatures, the divacancies can further be activated. In the contrary, nitrogen vacancy migration is energetically unfavorable within all the temperature range below the melting point of h-BN.

Figure 1

(Color online) Schematic numbering of atoms in a h-BN sheet. In a boron vacancy migration process, atom 5 moves to occupy the vacancy site left by atom 1 (red arrow). The same process occurs for a nitrogen vacancy migration (yellow arrow).

Figure 2

(Color online) Upper part: structural configuration along the reaction path for a boron vacancy migration. Lower part: energy evolution along the reaction path. The zero temperature activation energy is the energy associated with the saddle point configuration of picture (b). Along the reaction path, the system passes through the two equivalent metastable states of pictures (c) and (e).

Figure 3

(Color online) Upper part: structural configuration along the reaction path for a nitrogen vacancy migration. Lower part: energy evolution along the reaction path.

Figure 4

(Color online) (a) Relaxed structure of a BN divacancy. The yellow arrow represents divacancy migration via movement of the nitrogen atom 1. (b) final structure of the vacancy after migration. Graph: energy evolution along the reaction path for divacancy motion involving a nitrogen (●) or a boron (∎) atom.

Figure 5

Temperature dependence of the migration activation barrier for a boron vacancy [i for Fig. 2b and ii for Fig. 2d], nitrogen vacancy [v for Fig. 3b and vi for Fig. 3d], and BN divacancy (iii moving the nitrogen atom and iv moving the boron atom). The bold lines represent the effective migration barriers for the different vacancies.

Figure 6

Temperature dependence of diffusion coefficient (i) for a boron vacancy and (ii) for a BN divacancy. The discontinuity at A corresponds to the switch in highest saddle point as shown in Fig. 5. The nitrogen vacancy diffusion coefficient has values lower then ${10}^{-10}{\mathrm{\AA }}^2∕\mathrm{s}$ in all the temperature range considered in the graph.