Third-harmonic generation in semicontinuous metal films.

Abstract

The weak nonlinear electrical response of two-dimensional semicontinuous Ag and Au films was measured over three decades of sheet resistance. The third-harmonic component generated by the films, due to local Joule heating, is interpreted as a measure of the fourth moment of the current distribution. Higher harmonics corresponding to higher moments of the current distribution were also observed. Under certain conditions, measurement of the third harmonic lends the same critical exponent as that of 1/f noise, which obeys a power-law dependence ${\mathit{S}}_{\mathit{R}}$\ensuremath{\propto}(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\kappa}}}$, where ${\mathit{S}}_{\mathit{R}}$ is the mean square of resistance fluctuations, p the surface coverage fraction, and ${\mathit{p}}_{\mathit{c}}$ its critical value where the metal-insulator transition occurs. The film resistance obeys another power law R\ensuremath{\propto}(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{-}}\mathit{t}}$, hence ${\mathit{S}}_{\mathit{R}}$\ensuremath{\propto}${\mathit{R}}^{\mathit{w}}$ with w=\ensuremath{\kappa}/t. We have found that w=1.2\ifmmode\pm\else\textpm\fi{}0.1 for Ag samples, which is somewhat higher, but close to the lattice percolation value (random resistor network: 0.82w1.05). For the Au samples, w=1.65\ifmmode\pm\else\textpm\fi{}0.15, which is higher than the lattice percolation exponent and lower than the Swiss-cheese-model continuum percolation estimate (w>4.5). Comparison of our data on gold films with 1/f noise measurements on similar samples suggests the equivalence of these two techniques in probing the microgeometry details.