Granular-composite-like electrical transport properties of polycrystalline cubic TaN$_{x}$ thin films prepared by rf sputtering method

We have systematically investigated the electrical transport properties of polycrystalline TaN$_x$ ($0.83$$\lesssim$$x$$\lesssim$1.32) films with rocksalt structure from 300 down to 2 K. It is found that the conductivity varies linearly with $\ln T$ from $\sim$6 K to $\sim$30 K, which does not originate from the conventional two dimensional weak-localization or electron-electron interaction effects, but can be well explained by the intergrain Coulomb effect which was theoretically proposed in the granular metals. While the fluctuation-induced tunneling conduction process dominates the temperature behaviors of the conductivities (resistivities) above $\sim$60 K. Normal state to superconductive state transition is observed in the $x$$\gtrsim$1.04 films in low temperature regime. The superconductivity can still be retained at a field of 9 T. The upper critical field increases linearly with decreasing temperature in the vicinity of the superconductive transition temperature, which is the typical feature of granular superconductors or dirty type-II superconductors. The granular-composite-like electrical transport properties of the polycrystalline TaN$_x$ films are related to their microstructure, in which the TaN$_x$ grains with high conductivity are separated by the poorly conductive amorphous transition layers (grain boundaries).