Polycrystalline SnO2 films fabricated by thermal evaporation of tin and isothermal oxidation at 500 degrees C in pure oxygen have been studied by atomic force microscopy and scanning tunnelling microscopy. Topographic images revealed that individual grains have a polyhedral microstructure consisting of facets intersecting at depressions surrounded by terrace-step features. These may be the result of the anisotropic oxidation of tin. Ambient tunnelling current-voltage characteristics measured from individual grains ate strongly rectifying, suggesting that the Fermi level is being pinned by surface states within the bandgap. The surface states are due mainly to chemisorbed oxygen species from air.