First-principles calculations, based upon density-functional theory, ultra-soft pseudopotentials and plane-wave basis sets, were used to investigate the energetics, relaxed positions and electronic structures of O vacancies on the (110) surface. Three types of vacancy were studied, which were obtained by removing bridging, in-plane and sub-bridging O atoms. Calculations were performed for a range of vacancy concentrations, and for various geometries at given concentrations, in order to investigate interactions between the vacancies. At low and intermediate concentrations, it was found that the bridging vacancy was the most stable; in agreement with experiment. At high concentrations, corresponding to a strongly reduced surface, the formation energies of bridging and in-plane vacancies were almost the same; so that both types were expected to occur in thermal equilibrium. In all of the situations studied, the relaxation of the ions which surrounded the vacancies was small, and typically of the order of 0.01nm or less. Other results showed that the electronic density of states in the gap region was affected by the various types of defects.

The Energetics and Structure of Oxygen Vacancies on the SnO2 (11O) Surface. J.Oviedo, M.J.Gillan: Surface Science, 2000, 467[1-3], 35-48