Conductance regimes of W-based granular metals prepared by electron beam induced deposition

We prepared a series of W-based granular metals by means of electron beam induced deposition from the carbonyl percursor W(CO)(6). For samples with W-contents of 31.8(+/- 1.4), 34.0(+/- 1.7) and 36.9(+/- 1.8) at%, we observed a modified power law dependence sigma = sigma(0) + bT(beta) of the electrical conductivity with beta = 0.47-0.58, which we found to be approximately fulfilled over the temperature range from about 2 to 265 K. Deviations from this modified power law are discussed. Existing theoretical approaches that can, in principle, account for power-law dependencies in sigma(T) for homogeneously disordered or granular metals are reviewed and their relevance for explaining our data is critically examined. Firstly, if a percolating path is formed by touching metallic particles, the formation of a pseudo-gap at the Fermi level that follows a T-1/2 temperature dependence according to Altshuler and Aronov may explain our data. However, the Altshuler-Aronov result is valid for weak Coulomb coupling and represents a small, low-temperature correction. Its applicability close to a metal-insulator transition is questionable. Secondly, we analyze whether an alternative transport mechanism may be at work that is based on the onset of large-scale coherent electron motion along a tunnel-percolation path in the limit of large inter-grain tunneling. Again, this approach cannot be unambiguously applied to explain our experimental findings.