Electronic Transport in Granular Metal Films

Abstract

Granular metals are composites consisting of a random mixture of nanometer-sized metal and insulator grains. As a function of metal volume fraction, the structure and electrical properties of the granular metals can be divided into two regimes, separated by the percolation threshold. In the metal-rich regime, metal grains form a connected network, and electrical conduction is by electron percolation through the metallic channels. The physical basis and formulation of an effective-medium theory are described for the calculation of this percolative aspect of the electrical transport. The role of microstructure in the effective medium property is particularly emphasized. In the insulator-rich regimes, metal grains are dispersed in the matrix of the insulator. Electrical conduction in this dielectric regime is via the hopping mechanism, which is a term coined to denote the combination of thermal activation and tunneling. A critical-path method is presented to show that activation and tunneling, nominally independent, can actually couple to give a -ln σ ∝ T-α type of temperature dependence for the conductivity σ. For granular metals, the widely observed -ln σ ∝ 1 / √T behavior is ascribed to be an interpolation between the high-temperature activated behavior and the low-temperature α = 1/4 behavior. The alternative mechanism of the correlation gap is also discussed.