We present the density-functional theory (DFT) calculations which provide us with microscopic atomic reaction processes of the Mg acceptor migration in GaN through the vacancy-mediated diffusion processes. For the exchange-correlation energy, we adopt a hybrid approximation in which the exchange energy is treated partly by the exact Hartree-Fock expression and hereby reproduces the experimentally observed band gap. We identify all the possible elementary processes of the Mg migration through the vacancy mechanism and obtain the corresponding energy profiles, thus determining the migration energies along various crystallographic directions in wurtzite GaN. We find clear anisotropic migration behavior corroborated by a substantial difference in the migration energies. We find that the rate-limiting process of the long-range Mg diffusion via the vacancy mechanism is not the Mg hopping process but the Ga hopping process to the nearby vacant site. This finding infers the similarity between the Mg diffusion and self-diffusion. Further calculations of the formation energies of the relevant point defects and their migration barriers computed in this paper, as well as the relevant energetics for the interstitial mechanism explored previously in our calculations, infer that the interstitial mechanism is important in the Mg diffusion under, at least, equilibrium conditions. However, the vacancy mechanism is also found to be important under the experimental condition in which relevant defects, Ga vacancies, are injected.

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• Diffusion
• Dopants
• First-principles calculations
• Semiconductors
• Wide band gap systems