Concentration of point defects at metal-oxide surfaces: case study of MgO (100)

We calculate from first principles the concentration of neutral and charged oxygen vacancies on a doped MgO (100) surface at realistic ($T$, $p_{\rm O_2}$) conditions. Vacancy formation energies are computed using hybrid density-functional theory with parameters of the exchange-correlation functional adjusted according to a basic consistency requirement on the Kohn-Sham and $G_0W_0$ defect transition levels. The parameters are validated by CCSD(T) calculations of formation energies for neutral vacancies using embedded cluster models. Gibbs free energies of formation are obtained using the {\em ab initio} atomistic thermodynamics approach.\footnote{K. Reuter and M. Scheffler, Phys. Rev. B \textbf{65}, 035406 (2001); C. M. Weinert and M. Scheffler, Mat. Sci. Forum \textbf{10-12}, 25 (1986); M. Scheffler and J. Dabrowski, Phil. Mag. A \textbf{58}, 107 (1988)} We demonstrate that the concentration of surface vacancies is significantly increased due to band bending and Fermi level pinning at the surface, resulting in lower formation energies of charged vacancies.