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The third-harmonic coefficient ${\mathit{B}}_{0}$ in a Au-film percolation system deposited on \ensuremath{\alpha}-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ fracture surfaces by dc magnetron sputtering method is studied. The critical current ${\mathit{I}}_{\mathit{c}}$, coefficient ${\mathit{B}}_{0}$, and the relation between ${\mathit{I}}_{\mathit{c}}$ and ${\mathit{B}}_{0}$ are measured as functions of the zero-power sheet resistance ${\mathit{R}}_{0}$. The power-law behaviors ${\mathit{I}}_{\mathit{c}}$\ensuremath{\propto}${\mathit{R}}_{0}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ and ${\mathit{I}}_{\mathit{c}}$\ensuremath{\propto}${\mathit{B}}_{0}^{\mathrm{\ensuremath{-}}\mathit{x}}$ are observed in the system and the exponents \ensuremath{\alpha} and x are found to be 0.51\ifmmode\pm\else\textpm\fi{}0.05 and 0.24\ifmmode\pm\else\textpm\fi{}0.08, respectively, which are different from those of other percolation systems and predictions of present theories applied to two-dimensional systems. The physical interpretation of the results and the universality discussion are also presented.

The temperature dependence of the conductance and the nonlinear electrical response of a Pt-film percolation system, deposited on fracture surfaces of \ensuremath{\alpha}-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ ceramics, have been measured over three decades of sheet resistance. We find that in the temperature interval of T=77--300 K, the resistance temperature coefficient \ensuremath{\beta}=(1/R)dR/dT is not a constant, which is different from that for flat films. A dc I-V characteristic which strongly depends on the thickness of the film is found and it can be interpreted as a competition among the local Joule heating, hopping, and tunneling effects. The third-harmonic measurement suggests that the critical exponent comes from 1/f noise, which obeys the power-law dependences ${\mathit{S}}_{\mathit{R}}$\ensuremath{\propto}(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\kappa}}}$, R\ensuremath{\propto}(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{-}}\mathit{t}}$, and then ${\mathit{S}}_{\mathit{R}}$\ensuremath{\propto}${\mathit{R}}^{\mathit{w}}$ with w=\ensuremath{\kappa}/t, where ${\mathit{S}}_{\mathit{R}}$ is the mean square of resistance fluctuations, p the surface coverage fraction, and ${\mathit{p}}_{\mathit{c}}$ its percolation critical value. We find that w=0.45\ifmmode\pm\else\textpm\fi{}0.06, which is lower than the flat-film exponent. This result indicates that the tunneling and hopping effects in the fractal samples are much stronger than that of flat films.