2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L-2 x h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L-2-plane parallel to the film. For thicknesses ranging from h/L = 0.01 to h/L = 0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L approximate to 0.1. In the finite-size regime (h/L >= 0.01), the percolation threshold scales as p(c)(h) - p(c3) proportional to h(-1/x), the exponent x being compatible with that of the critical exponent of the 3D correlation length, nu(3). The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope nu(D) compatible with 2 + nu(2). where nu(2) is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1 + 1/nu(3). In this regime we also observed a logarithmic dependence of the conductivity exponent on hIL. (C) 2010 Elsevier B.V. All rights reserved.