Electronic structure of tin dioxide surfaces

We present the results of a theoretical study of the surface electronic structure of the ideal (110), (001), and (100) faces of tin dioxide, a semiconductor crystallizing with the bulk rutile structure. The surface electronic structure is determined using a scattering-theoretic method in which the bulk electronic structure is described by a tight-binding Hamiltonian including first- and second-nearest-neighbor interactions. The results are obtained in terms of surface bound states, surface resonances, and surface densities of states, which are wavevector, layer, atom, and orbital resolved. All this information allows a detailed discussion of the origin, the nature, and the localization of the obtained surface features. Common trends are found for the three faces. The optical band gap is found to be nearly free of surface states. The dominant features are backbond states in the lower valence-band region and Sn $s$-derived states in the lower conduction-band region. We find one of each for the (001) and (100) faces and two of each for the (110) face which contains two tin atoms per surface unit cell. The upper valence-band region leads only to weak, O $p$-derived resonances. All these features are governed by the relatively strong ionicity of Sn${\mathrm{O}}_2$. The differences in the results obtained for the three faces are interpreted in terms of the coordination of the surface cations.