A.C. conductivity and dielectric constant in a two-dimensional Swiss cheese percolation system

Abstract

To find a.c. conductivity (σ) and dielectric constant (ε) of a continuum percolation system, we prepared 2-D Swiss cheese percolation samples by punching holes in a highly resistive thin film. An impedance analyzer was used for the frequency range between 10 Hz and 10 Mhz. As predicted by theory based on anomalous diffusion or intercluster polarization, σ and ε show a power law dependence such as σ− w x , ε− w −y on frequency near the percolation threshold. Our result of x = 0.95 ± 0.10 and y = 0.16 ± 0.05 satisfies the general scaling law, x + y = 1. However, the detailed values of x and y do not follow the predictions of the anomalous diffusion theory ( x = 0.34, y = 0.66) or the intercluster polarization theory ( x = 0.5, y = 0.5). Our measured values of x and y are consistent with all the published results of the experiments for various two-dimensional systems (discontinuous gold thin film, lattice system on Al or Cr thin film). The implications of this will be discussed.