Measurements of the ac conductivity and dielectric constant in a two-dimensional lattice percolation system

We have fabricated a well-defined two-dimensional lattice percolation system on an aluminum film by using a computer-controlled x-y plotter. The ac conductivity σ and dielectric constant ε of these samples were measured for a frequency range of 10 Hz to 1 MHz. Our data for σ and ε near ${\mathit{p}}_{\mathit{c}}$ show that the power-law dependences on the stimulating frequency are of the form σ∼${\mathit{w}}^{\mathit{x}}$ and ε∼${\mathit{w}}^{\mathrm{-}\mathit{y}}$. Our results (x=0.996±0.050, y=0.024±0.005) are in good agreement with previous measurements of a discontinuous gold film prepared by Laibowitz et al. However, both results show large discrepancies with the theoretical predictions based on the anomalous diffusion or intercluster polarization effect. Despite these discrepancies, the general scaling law (x+y=1) still holds. We also observed that the intercluster polarization effect plays a more important role than anomalous diffusion in our system.