The stable and metastable configurations of interstitial Mg in GaN and its migration energy barriers are studied from first-principles calculations. In addition to the conventional octahedral (O, global energy minimum) and tetrahedral (T, metastable) interstitial sites, we have discovered two metastable interstitial complexes with formation energy lower than or close to that of the T configuration but higher than O. Except for Mg at O site, which only has $+2$ charge state, all other configurations also permit charge states $+1$ or 0. The minimum migration energy barrier for ${\mathrm{Mg}}^{++}$ between O sites is found to be $1.95\mathrm{eV}$. We further find that, when Fermi energy is close to the conduction band, the migration between O sites via metastable configurations occurs through a recombination-enhanced mechanism in which the charge state changes from $+2$ at O site to 0 at metastable sites by consecutive capture of two electrons during the migration. This process greatly reduces the migration energy barrier to as low as $1.47\mathrm{eV}$. This value is consistent with experiments, and we also discuss the role of intrinsic defects in the migration of Mg.

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• Diffusion
• Interstitials
• III-V semiconductors
• Hybrid functionals