Determination of the nitrogen vacancy as a shallow compensating center in GaN doped with divalent metals

We report accurate energetics of defects introduced in GaN on doping with divalent metals, focussing on the technologically important case of Mg doping, using a model which takes into consideration both the effect of hole localisation and dipolar polarisation of the host material, and includes a well-defined reference level. Defect formation and ionisation energies show that divalent dopants are counterbalanced in GaN by nitrogen vacancies and not by holes, which explains both the difficulty in achieving p-type conductivity in GaN and the associated major spectroscopic features, including the ubiquitous 3.46 eV photoluminescence line, a characteristic of all lightly divalent metal-doped GaN materials that has also been shown to occur in pure GaN samples. Our results give a comprehensive explanation for the observed behaviour of GaN doped with low concentrations of divalent metals in good agreement with relevant experiment.