Theoretical study of oxygen-deficientSnO2(110)surfaces

Theoretical consideration of recently proposed ordered stoichiometric and oxygen-deficient (110) surfaces of ${\mathrm{SnO}}_2$ crystal with $1\times 1,$ $1\times 2,$ $2\times 1,$ and $1\times 4$ symmetries have been done. We use a first-principles density-functional method and plane-wave basis, combined with pseudopotentials to calculate surface electronic structures, surface geometries, and energetics. Calculated surface formation energies suggest that stability of the oxygen-deficient surfaces decrease with increasing oxygen deficiency. At oxygen-deficient $1\times 2$ and $1\times 4$ surfaces tin atoms similar to those in SnO crystal were found to appear. In all cases, the highest occupied orbitals were considerably localized at the sites of surface oxygen vacancies. The $2\times 1$ added row surface structures were found to be relatively stable and associated with the decrease of the band gap due to jagged surface. Also, ultraviolet optical absorption coefficients for different surface structures were determined by using the electric dipole approximation with a scissor correction.