Nonlinear electrical response and breakdown of semicontinuous metal films

The weakly nonlinear electrical response, determined by 3rd harmonic generation, and the breakdown current I_b of percolating systems are measured in real materials: semicontinuous Ag and Au films. The 3rd harmonic is interpreted as a direct measure of the 4th moment of the current distribution, and thus provides the critical exponent κ (normally determined by 1/f{hook} noise measurements). Observations of higher harmonics (5th and 7th), corresponding to higher moments of the current distribution, provide an estimation of higher critical indices. The breakdown current I_b was measured over three decades of film resistance. A new criterion for I_b is suggested, defined as the current at which a hot spot reaches the melting temperature of the metallic grains T_m. This criterion remains valid in the presence of nonlinear effects. The hot spot model yields a power law I_b ∞B^-x, B=V_3f{hook}/I³ where the upper and lower bounds of x are found to be 0.5 (extreme case of continuum percolation) and 0.36 (lattice percolation lower bound), respectively, in excellent agreement with the measured data.