Effect of film thickness on the width of percolation threshold in metal-dielectric composites

The effect of thickness on the width of the percolation threshold in metal-dielectric composite films was examined. The distribution of current intensities through cubic networks of metal and dielectric components was determined using Kirchhoff's equations. From the tail of current distribution, the width of the percolation threshold was defined using L\'evy statistics, and determined as a function of the film thickness for a system size 100. In the 2D-3D crossover region, the percolation width decreases as a power-law with a power exponent of $ 0.36\pm 0.01$.