Evidence of anomalous hopping and tunneling effects on the conductivity of a fractal Pt-film system

The temperature dependence of the conductance and the nonlinear electrical response of a Pt-film percolation system, deposited on fracture surfaces of α-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ 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 β=(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 ${\mathit{S}}_{\mathit{R}}$∝(p-${\mathit{p}}_{\mathit{c}}$ ${)}^{\mathrm{-}\mathrm{\kappa }}$, R∝(p-${\mathit{p}}_{\mathit{c}}$ ${)}^{\mathrm{-}\mathit{t}}$, and then ${\mathit{S}}_{\mathit{R}}$∝${\mathit{R}}^{\mathit{w}}$ with w=κ/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±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.