Stability of vacancy defects in MgO: The role of charge neutrality

The energetics and electronic structure of a series of neutral and charged oxygen and magnesium vacancy defects (F, ${\mathit{F}}^{+}$, ${\mathit{F}}^{2+}$, V, ${\mathit{V}}^{\mathrm{-}}$, ${\mathit{V}}^{2\mathrm{-}}$, and P centers) in MgO have been computed using the stationary total-energy functional. We find that contrary to the charge-compensation model for anion-cation defect pairs in ionic materials it is energetically unfavorable for an isolated neutral oxygen vacancy (F center) to transfer electrons to an isolated neutral magnesium vacancy (V center), and form isolated ${\mathit{F}}^{2+}$ and ${\mathit{V}}^{2\mathrm{-}}$ centers. Charge compensation is unfavorable because additional electrons at the V center induce new occupied states in the gap, which increase the energy of the defect. This result is consistent with the interpretation of spectroscopic experiments on MgO, in which the ground-state defects are either neutral or singly charged. The computed formation energies of both the F and V centers are larger than the cohesive energy of MgO per formula unit, but the binding energy of the defects in the P center configuration is 12.16 eV. This attraction between the F and V centers is enhanced when the defects carry a net charge. The position of the vacancy defect state in the fundamental energy gap of MgO is found to be in qualitative agreement with a model for optical absorption and emission, and is used as a simple model for the formation energies of the defects. The contribution of the band-structure energy to the stationary functional is found to account for more than 90% of the defect energies. This component of the defect formation energy is computed directly, using the recursion method, rather than as the difference between the total energies of our 8000-atom cluster with and without the defect.