Multistability of interstitial magnesium and its carrier recombined migration in gallium nitride

We present density-functional-theory calculations which provide a microscopic picture of the recombination-enhanced migration of interstitial Mg in GaN. We determine stable structures and migration pathways with accurate HSE approximation to the exchange-correlation energy, and also computed recombination rates using the obtained energy spectrum and wavefunctions. It is found that the migration between the most stable octahedral sites (Mg$_{\textrm{O}}$) via newly found interstitial complex structure shows the lowest migration energy in which one or two electrons are captured during the migration, that the most stable charge state of 2+ changes to 1+ or neutral, and that by this recombination of carriers the migration barrier is significantly reduced. Starting from Mg$_{\textrm{O}}^{2+}$, Mg captures an electron becoming the 1+ charge state and overcomes the barrier of 1.65 eV, much reduced from 2.23 eV in case of the migration with the 2+ charge state kept. Moreover, further electron capture is realized accompanied by substantial structural relaxation, thus Mg becoming neutral. Detailed HSE calculations for this second capture show that the migration barrier is 1.55 eV, thus clarifying the important role of the carrier recombination for Mg migration in GaN. These findings are corroborated by the present quantitative calculations of recombination rates based on electronic Hamiltonian constructed from our DFT-obtained energy spectrum. The timescale of the recombination is clarified to be in or under the timescale of the migration with typical electron density and the enhancement is expected to be significant.