Cluster statistics in dielectric breakdown

We present the results of a numerical study of the growth and development of breakdown with the applied voltage in a two dimensional random metal-dielectric composite. The cluster size distribution and its moments are determined for the clusters formed by the conducting sites in the system and the evolution of the distribution with applied voltage is obtained. For sufficiently large starting concentration of the conducting sites, various quantities, like the average cluster size, dispersion in cluster size or the total number of conducting sites, are found to change more rapidly as the breakdown field Vb is approached. The rate of change of all these quantities with the field diverges at Vb.