ac conduction and 1/f noise in a Cr-film lattice-percolation system

The ac conductivity \ensuremath{\sigma}(\ensuremath{\omega}), ac dielectric constant \ensuremath{\epsilon}(\ensuremath{\omega}), and (1/f)-noise spectral density ${\mathit{S}}_{\mathit{v}}$(f) have been studied in a Cr-film lattice-percolation system generated by electron-beam lithography. A power-law behavior, \ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\propto}${\mathrm{\ensuremath{\omega}}}^{\mathit{x}}$ and \ensuremath{\epsilon}(\ensuremath{\omega})\ensuremath{\propto}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}\mathit{y}}$, is observed near the percolation threshold. The ac-conductivity and ac-dielectric-constant exponents x and y are found to be 0.98\ifmmode\pm\else\textpm\fi{}0.09 and 0.08\ifmmode\pm\else\textpm\fi{}0.04, respectively. While these results satisfy the general scaling law x+y=1 and are consistent with those previously obtained on Au-film continuum-percolation systems, they cannot be explained by present percolation theories applied to two-dimensional (2D) systems. The normalized (1/f)-noise spectral density ${\mathit{S}}_{\mathit{v}}$(f)/${\mathit{V}}^{2}$ is found to scale as ${\mathit{R}}^{\mathit{w}}$ (where R is the sample resistance) with critical exponent w=1.18\ifmmode\pm\else\textpm\fi{}0.19. Once again, the numerical value of w is appreciably different from the predictions of present percolation theories applied to 2D systems. We discuss the discrepancy between the experimental results and percolation theories.

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