Theory of percolation and tunneling regimes in nanogranular metal films

Nanogranular metal composites, consisting of immiscible metallic and insulating phases deposited on a substrate, are characterized by two distinct electronic transport regimes depending on the relative amount of the metallic phase. At sufficiently large metallic loadings, granular metals behave as percolating systems with a well-defined critical concentration above which macroscopic clusters of physically connected conductive particles span the entire sample. Below the critical loading, granular metal films are in the dielectric regime, where current can flow throughout the composite only via hopping or tunneling processes between isolated nanosized particles or clusters. In this case transport is intrinsically nonpercolative in the sense that no critical concentration can be identified for the onset of transport. It is shown here that, although being very different in nature, these two regimes can be described by treating percolation and hopping on equal footing. By considering general features of the microstructure and of the electrical connectedness, the concentration dependence of the dc conductivity of several nanogranular metal films is reproduced to high accuracy within an effective-medium approach. In particular, fits to published experimental data enable us to extract the values of microscopic parameters that govern the percolation and tunneling regimes, explaining thus the transport properties observed in nanogranular metal films.