Critical behaviors in a Pt-film percolation system deposited on fracture surfaces of α-Al2O3ceramics

The dc resistance R, critical current ${\mathit{I}}_{\mathit{c}}$, ac dielectric constant ε(ω), and ac conductivity σ(ω) have been studied in a Pt-film percolation system deposited on α-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ fracture surfaces by dc- and rf-magnetron sputtering methods. The fractal dimension of the surfaces is found to be 2.20±0.06. Although the percolation system is entirely different from both the lattice-percolation system and the continuum-percolation system, the power-law behaviors, ${\mathit{I}}_{\mathit{c}}$∝${\mathit{R}}^{\mathrm{-}\mathrm{\alpha }}$, σ(ω)∝${\mathrm{\omega }}^{\mathit{x}}$, and ε(ω)∝${\mathrm{\omega }}^{\mathrm{-}\mathit{y}}$, are observed near the percolation threshold. The exponent α is determined to be 1.12±0.05, which is significantly different from both predictions of two-dimensional (2D) percolation theories and the recent experimental results on Au-film and Ag-film continuum-percolation systems. The exponents x and y are found to be 0.89±0.06 and 0.05±0.02, respectively, in agreement with the general scaling relation x+y=1. These results suggest that the power-law behaviors as well as the general scaling relation in percolation systems could not be affected by the statistical fractal structure of the substrates. The experimental results also support the prediction that the exponents x and y are universal.