Electrical breakdown measurements of semicontinuous metal films.

Abstract

The breakdown current ${\mathit{I}}_{\mathit{c}}$ of a percolating system is measured on real materials. We find that ${\mathit{I}}_{\mathit{c}}$\ensuremath{\propto}${\mathit{B}}^{\mathrm{\ensuremath{-}}\mathit{x}}$, B is the weakly nonlinear response determined by third-harmonic generation. A new criterion for ${\mathit{I}}_{\mathit{c}}$ is suggested, defined as the current at which a hot spot reaches the melting temperature of the metallic grains, ${\mathit{T}}_{\mathit{m}}$. This criterion remains valid in the presence of nonlinear effects. It is also consistent with the experimental observations: At ${\mathit{I}}_{\mathit{c}}$ the resistance either increases to infinity or decreases, i.e., the local geometry is changed at ${\mathit{T}}_{\mathit{m}}$. Modeling the breakdown by hot spots yields the above power law with 0.5\ensuremath{\ge}x\ensuremath{\ge}0.36, in excellent agreement with the measured data: x=0.48 and 0.41 for Ag and Au films.