Temperature- and oxygen partial pressure-dependent electrical conductivity in nanoporous rutile and anatase

The dependence of the electrical conductivity (σ) of sintered nanoporous ${\mathrm{TiO}}_{\mathrm{2}}$ (rutile and anatase) layers on temperature (T) and partial pressure of oxygen ${\mathrm{(p}}_{{\mathrm{O}}_{\mathrm{2}}})$ has been studied by impedance spectroscopy for T up to 450 °C and $p_{{\mathrm{O}}_{\mathrm{2}}}$ up to ${10}^{\text{−5}} \mathrm{mbar}.$ The diameter of the ${\mathrm{TiO}}_{\mathrm{2}}$ nanoparticles was changed between 5 and 60 nm. σ is thermally activated with $E_A\text{=0.85\hspace{0.05em}}\mathrm{eV}$ independent of the absolute value of σ and depends on $p_{{\mathrm{O}}_{\mathrm{2}}}$ by power law for $p_{{\mathrm{O}}_{\mathrm{2}}}\text{<1–10\hspace{0.05em}}\mathrm{mbar}.$ The electrical properties of reduced nanoporous ${\mathrm{TiO}}_{\mathrm{2}}$ are determined by surface chemical reactions which lead to the formation of shallow donor and deep trap states.