The energetics and structure of oxygen vacancies on the SnO2(110) surface

First-principles calculations based on density-functional theory, ultra-soft pseudopotentials and plane-wave basis sets are used to investigate the energetics, relaxed ionic positions and electronic structure of oxygen vacancies on the SnO2(110) surface. We study three types of vacancy, obtained by removing bridging, in-plane and sub-bridging oxygen atoms, and calculations are made for a range of vacancy concentrations, and for different geometries at some concentrations, in order to probe interactions between the vacancies. At low and intermediate concentrations, we find that the bridging vacancy is most stable, in agreement with experiment. At high concentrations, corresponding to a strongly reduced surface, the formation energies of bridging and in-plane vacancies are almost the same, so that both types should occur in thermal equilibrium. In all situations examined, the relaxation of ions surrounding the vacancies is small — typically 0.1 Å or less. We present results showing how the electronic density of states in the gap region is affected by the different kinds of defects, and we discuss the relation with measured ultraviolet photoelectron spectra.