Crossover of electron-electron interaction effect in Sn-doped indium oxide films

We systematically study the structures and electrical transport properties of a series of Sn-doped indium oxide (ITO) films with thickness $t$ ranging from $\sim$5 to $\sim$53\,nm. Scanning electron microscopy and x-ray diffraction results indicate that the $t\lesssim 16.8$\,nm films are polycrystalline, while those $t\gtrsim 26.7$\,nm films are epitaxially grown along [100] direction. For the epitaxial films, the Altshuler and Aronov electron-electron interaction (EEI) effect governs the temperature behaviors of the sheet conductance $\sigma_\square$ at low temperatures, and the ratios of relative change of Hall coefficient $\Delta R_H/R_H$ to relative change of sheet resistance $\Delta R_\square/R_\square$ are $\approx$2, which is quantitatively consistent with Altshuler and Aronov EEI theory and seldom observed in other systems. For those polycrystalline films, both the sheet conductance and Hall coefficient vary linearly with logarithm of temperature below several tens Kelvin, which can be well described by the current EEI theories in granular metals. We extract the intergranular tunneling conductance of each film by comparing the $\sigma_\square(T)$ data with the predication of EEI theories in granular metals. It is found that when the tunneling conductance is less than the conductance of a single indium tin oxide (ITO) grain, the ITO film reveals granular metal characteristics in transport properties, conversely, the film shows transport properties of homogeneous disordered conductors. Our results indicate that electrical transport measurement can not only reveal the underlying charge transport properties of the film but also be a powerful tool to detect the subtle homogeneity of the film.