Electrical transport properties of thick and thin Ta-doped SnO$_2$ films

Ta-doped SnO$_2$ films with high conductivity and high optical transparency have been successfully fabricated using rf-sputtering method and their electrical transport properties have been investigated. All films reveal degenerate semiconductor (metal) characteristics in electrical transport properties. For the thick films ($t\sim 1\,\mu \rm{m}$ with $t$ being the thickness) deposited in pure argon, the electron-phonon scattering alone cannot explain the temperature dependent behaviors of resistivity, the interference effect between electron-phonon and electron-impurity scattering should be considered. For the $t\lesssim 36$ nm films, both conductivity and the Hall coefficient show linear relation with the logarithm of temperature ($\ln T$) from $\sim$100 K down to liquid helium temperature. The $\ln T$ behaviors of conductivity and Hall coefficient cannot be explained by the Altshuler-Aronov type electron-electron interaction effect, but can be quantitatively interpreted by the electron-electron interaction effects in the presence of granularity. Our results not only provide strong supports for the theoretical results on the electron-phonon-impurity interference effect, but also confirm the validity of the theoretical predictions of charge transport in granular metals in strong coupling regime.