Resistance and resistance fluctuations in random resistor networks under biased percolation

Abstract

We consider a two-dimensional random resistor network (RRN) in the presence of two competing biased processes consisting of the breaking and recovering of elementary resistors. These two processes are driven by the joint effects of an electrical bias and of the heat exchange with a thermal bath. The electrical bias is set up by applying a constant voltage or, alternatively, a constant current. Monte Carlo simulations are performed to analyze the network evolution in the full range of bias values. Depending on the bias strength, electrical failure or steady state are achieved. Here we investigate the steady state of the RRN focusing on the properties of the non-Ohmic regime. In constant-voltage conditions, a scaling relation is found between <R>/<R>(0) and V/V(0), where <R> is the average network resistance, <R>(0) the linear regime resistance, and V0 the threshold value for the onset of nonlinearity. A similar relation is found in constant-current conditions. The relative variance of resistance fluctuations also exhibits a strong nonlinearity whose properties are investigated. The power spectral density of resistance fluctuations presents a Lorentzian spectrum and the amplitude of fluctuations shows a significant non-Gaussian behavior in the prebreakdown region. These results compare well with electrical breakdown measurements in thin films of composites and of other conducting materials.

Resistance Noise Near to Electrical Breakdown: Steady State of Random Networks as a Function of the Bias

“…Further details can be found in Ref. 51 . The different curves correspond to different values of r 0 , as specified in the figure, and to a common value of E R = 0.026 (eV).…”

“…This defect generation process is taken to occur in competition with an opposite process, named defect recovery, which mimics the healing mechanisms. Electromigration of metallic lines 4,26 instability of the electrical properties of composites or semicontinuous metal films 2,3 , 13-19 , 22,23 or soft dielectric breakdown of ultra-thin oxides 4,29 , are examples of phenomena that can be successfully described by this approach 25,31,[49][50][51] . In the case of electromigration phenomena, for example, the defect generation corresponds to the formation of voids induced by the electronic wind, while the defect recovery is related to the void healing due to mechanical stress and thermal gradients inside a metallic film 4,26 .…”

“…In this Ohmic regime, a scaling relation has been found between the relative variance of resistance fluctuations and the average network resistance 49 . The properties of the nonlinear regime, occurring when the bias overcomes a threshold value, are studied for different values of the model parameters and for different bias conditions (constant voltage or constant current) 50,51 . Scaling relations are found relating the average resistance and the resistance noise with the external bias.…”

“…Recently, a new approach has been proposed to investigate the resistance noise in thin films over the full range of bias values, from the linear regime up to electrical breakdown [49][50][51] . In this paper, I will present a brief review of this approach.…”

“…In this paper, I will present a brief review of this approach. The model consists of describing the resistance noise in a conducting film in terms of two competing processes taking place in a random resistor network (RRN) [49][50][51] . The two processes are driven by the joint effect of the electrical bias and of the heat exchange with a thermal bath.…”