Interaction of the N vacancy with H and Mg acceptors in $p$-type GaN

Results from recent experimental studies suggest that the N vacancy (V$_{N})$ may compensate Mg acceptors in GaN in addition to the compensation arising from H introduced during growth. To investigate this possibility further, density-functional-theory calculations were performed to determine the interactions of V$_{N}$ with H, Mg, and the MgH center in GaN, and modeling was performed to determine the state populations at elevated temperatures. The results indicate that V$_{N}$H and MgV$_{N}$H complexes with H inside the vacancy are highly stable in $p$-type GaN and act to compensate or passivate Mg acceptors. Furthermore, barriers for formation of these complexes were investigated and the results indicate that they can readily form at temperatures $>$ 400\r{ } C, which is well below temperatures typically used for GaN growth. Overall, the results indicate that the V$_{N}$ compensation behavior suggested by experiments arises not from isolated V$_{N}$, but rather from V$_{N}$H and MgV$_{N}$H complexes with H located inside the vacancy.