Native point defects and impurities in hexagonal boron nitride

Hexagonal BN ($h$-BN) is attracting a lot of attention for two-dimensional electronics and as a host for single-photon emitters. We study the properties of native defects and impurities in $h$-BN using density functional theory with a hybrid functional. Native vacancy and antisite defects have high formation energies, and are unlikely to form under thermodynamic equilibrium for typical growth conditions. Self-interstitials can have low formation energies when the Fermi level is near the band edges, and may form as charge compensating centers; however, their low migration barriers render them highly mobile, and they are unlikely to be present as isolated defects. The defect chemistry of $h$-BN is most likely dominated by defects involving carbon, oxygen, and hydrogen impurities. Substitutional carbon and oxygen, as well as interstitial hydrogen and boron vacancy–hydrogen complexes, are low-energy defects in $h$-BN. Based on our results, we can rule out several proposed sources for defect-related luminescence in $h$-BN. In particular, we find that the frequently observed 4.1 eV emission cannot be associated with recombination at ${\mathrm{C}}_{\mathrm{N}}$, as has been commonly assumed. We suggest alternative assignments for the origins of this emission, with ${\mathrm{C}}_{\mathrm{B}}$ as a candidate. We also discuss possible defect origins for the recently observed single-photon emission in $h$-BN, identifying interstitials or their complexes as plausible centers.

Figure 1

(a) Top-down view of the in-plane honeycomb structure of $h$-BN. Boron atoms are indicated by green spheres, nitrogen are grey. (b) Side view showing the interlayer spacing and AA′ stacking sequence. (c) Electronic band structure plotted along a high-symmetry path in the Brillouin zone. The energy of the highest occupied valence state is set to zero.

Figure 2

Charge-state transition levels [Eq. (2)] for point defects in $h$-BN.

Figure 3

Formation energies of native point defects in $h$-BN as a function of Fermi level under (a) N-rich and (b) N-poor conditions. The slope of each line segment corresponds to the charge state according to Eq. (1). Kinks in the curve correspond to to charge-state transition levels [Eq. (2) and Fig. 2].

Figure 4

Calculated potential energy surfaces for migration of the neutral boron vacancy (blue squares) and the neutral nitrogen vacancy (red diamonds) in $h$-BN. The curves are drawn as a guide to the eye.

Figure 5

Calculated potential energy surfaces for migration of the neutral boron interstitial (blue squares) and the neutral nitrogen interstitial (red diamonds) in $h$-BN. The curves are drawn as a guide to the eye.

Figure 6

Formation energies of impurity-related defect centers in $h$-BN as a function of Fermi level in N-rich and N-poor conditions for [(a) and (b)] C impurities, [(c) and (d)] O impurities, and [(e) and (f)] H impurities. The slope of each line segment corresponds to the charge state according to Eq. (1); kinks in the curves correspond to charge-state transition levels [Eq. (2)].

Figure 7

Charge-state transition levels [Eq. (2)] for impurity-related defect species in $h$-BN. Defect levels related to C are shown in orange, due to oxygen in blue, and hydrogen in red.