Fractal Electrode Formation in Metal–Insulator Composites Near the Percolation Threshold

Abstract

Over the past 20 years, there have been a variety of experiments that have revealed a large increase in the low-frequency capacitance of devices constructed from metal-insulator nanocomposite materials. These capacitive increases are typically reported as dramatic increases in the effective relative dielectric constants of the nanocomposite materials. A class of these materials that operate at room temperature and have metal particle concentrations near the percolation threshold have been shown to have dramatic increases in the effective dielectric constant on the order of 104-1010. The simulations in this paper reveal that electrical contact to large metal clusters inside the composite material near the percolation threshold form fractal-like electrodes that deeply penetrate into the host dielectric material, which result in an effective dielectric constant that is 104-105 times greater than the host dielectric. Furthermore, insulating the planar electrodes so that no electrical contact is made to the metallic clusters inside a near-percolation-threshold composite material reveals a much smaller increase (40×) in the effective dielectric constant. Finally, a new physical scaling model and a simple geometric model for capacitance estimation in metal-insulator composites are developed and used to enhance understanding of the physical effects behind the results of these numerical simulations.