The dependence of the surface structure, composition, and electronic properties of three low index $\mathrm{Sn}{\mathrm{O}}_{2}$ surfaces on the annealing temperature in vacuum has been investigated experimentally by low energy ${\mathrm{He}}^{+}$ ion scattering spectroscopy (LEIS), low energy electron diffraction (LEED), scanning tunneling microscopy (STM), and angle resolved valence band photoemission (ARUPS) using synchrotron radiation. Transitions from stoichiometric to reduced surface phases have been observed at $440--520\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, $610--660\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and $560--660\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for the $\mathrm{Sn}{\mathrm{O}}_{2}$ (110), (100), and (101) surfaces, respectively. Density functional theory has been employed to assess the oxidation state and stability of different surface structures and compositions at various oxygen chemical potentials. The reduction of the $\mathrm{Sn}{\mathrm{O}}_{2}$ surfaces is facilitated by the dual valency of Sn, and for all three surfaces a transition from Sn(IV) to Sn(II) is observed. For the (100) and (101) surfaces, theory supports the experimental observations that the phase transitions are accomplished by removal of bridging oxygen atoms from a stoichiometric $\mathrm{Sn}{\mathrm{O}}_{2}$ surface, leaving a SnO surface layer with a $1\ifmmode\times\else\texttimes\fi{}1$ periodicity. For the (110) surface the lowest energy surface under reducing conditions was predicted for a model with a SnO surface layer with all bridging oxygen and every second row of in-plane oxygen atoms removed. Ab initio atomistic thermodynamic calculations predict the phase transition conditions for the (101) surface, but there are significant differences with the experimentally observed transition temperatures for the (110) and (100) surfaces. This discrepancy between experiment and thermodynamic equilibrium calculations is likely because of a dominant role of kinetic processes in the experiment. The reduction of surface Sn atoms from a Sn(IV) to a Sn(II) valence state results in filling of the $\mathrm{Sn}\text{\ensuremath{-}}5s$ states and, consequently, the formation of Sn derived surface states for all three investigated surfaces. The dispersion of the surface states for the reduced (101) surface was determined and found to be in good agreement with the DFT results. For the (110) surface, the $4\ifmmode\times\else\texttimes\fi{}1$ reconstruction that forms after sputter and annealing cycles was also investigated. For this surface, states that span almost the entire band gap were observed. Resonant photoemission spectroscopy identified all the surface states on the reduced $\mathrm{Sn}{\mathrm{O}}_{2}$ surfaces as Sn derived.
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