Fig. 2: Formation energies of the trivacancy defect and energy barriers between its different configurations.

a Formation energy of the trivacancy in h-BN in three different configurations as a function of the Fermi energy. The charge states of 0P and 1B (blue and green lines) are +1q (rising slope), 0q (horizontal), −1q, and −2q (falling slopes). The charge states of 2N (red line) are −1q to −3q. The vertical dotted line indicates the position of the Fermi energy if the h-BN layer is contacted by graphene. b Energy barrier between the planar (0P) and 1B configurations for the neutral charge state under different electric fields. A positive (blue lines) sign indicates that the field points upwards in Fig. 1a. A negative sign (green lines) indicates a field in the opposite direction. The black dashed line marks the zero energy. c Energy barrier heights from b as a function of the field strength. The blue line refers to the forward barrier (0P-to-1B), the red one to the backward path (1B-to-0P). The symbols are the computed values, while the dashed lines represent a linear fit. d Energy barrier between the 0P and 1B configurations for the neutral and the ±1q charge state.