Cluster-size distribution in Al-Al2O3films near the metal-insulator transition

Abstract

We have measured the cluster-size distribution in thin Al-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ films near the metal-insulator transition for sheet resistances of about 1000 $\frac{\Omega }{\square }$ 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.