Cluster-size distribution in Al-Al2O3 films near the metal-insulator transition

We have measured the cluster-size distribution in thin Al-Al2O3 films near the metal-insulator transition for sheet resistances of about 1000 Ω and metal area fraction of the order of 0.5. Our results show for the first time that this distribution follows a power-law dependence and that the perimeter-to-area ratio is approximately constant for large clusters. We find good quantitative agreement between our obseryations and the predictions of percolation theory.