Fig. 1. (Color online) The 21 defect-pairs that can be formed by two point defects in GaN. The color represents their formation energies in the neutral state (in Ga-rich GaN).

Fig. 2. (Color online) Six different structural configurations of the V_N–V_N defect-pair (classified as Group-1). The blue balls show the locations of the two nitrogen vacancies (V_N).

Fig. 3. (Color online) The formation energies of two defect-pairs V_N–V_N and V_Ga–V_N in different charge states as functions of the Fermi level (in Ga-rich GaN), calculated with PBE-relaxed and HSE-relaxed structures.

Fig. 4. (Color online) The formation energies of (a) 6 point defects, (b) 6 defect-pairs that have the same component atoms as point defects, (c) 7 defect-pairs that cannot relax to point defects, as functions of Fermi level in Ga-rich GaN. (d–f) shows the corresponding results in N-rich GaN.

Fig. 5. (Color online) The transition energy levels of the 13 defect-pairs in the band gap of GaN.

Table 1. The formation energies of two defect-pairs V_N–V_N and V_Ga–V_N in the neutral state calculated with PBE-relaxed and HSE-relaxed structures (in Ga-rich GaN). 6 structural configurations with different defect-defect distance (in the unrelaxed initial structure) are considered.

Table 2. The calculated formation energies (in eV) of 21 defect-pairs in Ga-rich and N-rich GaN. For each defect-pair, 6 different structural configurations are considered and the distances (in Å) between the two defect sites are listed (before structural relaxation). The lowest-energy configurations are shown in bold. The symbol * means that the defect-pair becomes a point defect or annihilated after structural relaxation.