Gallium nitride has been extensively used in light-emitting diodes, high-frequency and high-voltage transistors, and lasers. [1][2][3][4] Design of these devices with high performance usually requires good n-type or p-type conductivity with high concentrations of free carriers. Although good n-type conductivity can be easily achieved in GaN, [5] good p-type doping is more difficult to achieved due to the difficulty in activation of p-type dopants. Mg is the most effective p-type dopant in GaN [6][7][8] because Mg Ga (Mg replacing Ga) is a relatively shallow acceptor and can produce hole carriers. However, the Mg Ga acceptors may form dopant-defect complexes with donor defects such as V N (nitrogen vacancy) or other dopants such as H (e.g., the H interstitial H i ). [9,10] The formed complexes, Mg Ga -V N and Mg Ga -H i , are chargecompensated and thus cannot be ionized to produce electron or hole carriers, so the donor-acceptor-compensated complexes impose a limit on the increase of hole concentration. [10][11][12] As V N has low formation energy and thus high concentration if GaN is doped into p-type with a low Fermi level [12,13] and hydrogen is an unavoidable dopant during different GaN growth processes such as metal-organic chemical-vapor deposition (MOCVD), hydride vapor-phase epitaxy (HVPE), and ammonia-based molecular-beam epitaxy (MBE), [14][15][16] the donor defects or dopants that can compensate the Mg Ga acceptors can be very abundant. Therefore, the donor-acceptor complexes are also abundant, causing severe compensation in GaN. To activate the Mg Ga acceptor, high-temperature annealing or electron-beam irradiation processes were introduced to dissociate complexes such as Mg Ga -H i . [8,16] Given the severe influences, the Mg-related dopant-defect complexes have attracted intensive attention in the past 20 years and interesting complexes have been reported apart from Mg Ga -V N and Mg Ga -H i . [17][18][19] Because the H dopants can also replace N, forming a H N substitutional defect (a defect complex V N -H i in which H is on the interstitial site near the N vacancy site), [20] which is also an effective donor and can compensate the acceptors, [21,22] the pioneering work of Lee et al. through both first-principles calculations and experimental observations showed that the Mg Ga -H N (Mg Ga -V N -H i ) complexes exist and are key components for understanding the Mg acceptor activation and passivation processes. [17] Furthermore, the Mg interstitial (Mg i ) can also compensate Mg Ga and form the Mg Ga -Mg i complex. [12] These complexes have been proposed as the origins of various bands (peaks) in the photoluminescence (PL) spectra of Mg-doped GaN layers; for example, Mg Ga -H N produces the ultraviolet peak, [17] Mg Ga -V N is responsible for the red luminescence (RL) band, [11] and Mg Ga -Mg i is responsible for the blue band. [23] Although the Mg-related dopant-defect complexes have been studied for two decades, it is still an open question whether all the low-energy and high-concentration Mg-relate...