Scaling Law of Resistance Fluctuations in Stationary Random Resistor Networks

Abstract

In a random resistor network we consider the simultaneous evolution of two competing random processes consisting in breaking and recovering the elementary resistors with probabilities W(D) and W(R). The condition W(R)>W(D)/(1+W(D)) leads to a stationary state, while in the opposite case, the broken resistor fraction reaches the percolation threshold p(c). We study the resistance noise of this system under stationary conditions by Monte Carlo simulations. The variance of resistance fluctuations <deltaR2> is found to follow a scaling law |p-p(c)|(-kappa(0)) with kappa(0) = 5.5. The proposed model relates quantitatively the defectiveness of a disordered media with its electrical and excess-noise characteristics.

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

“…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 .…”

“…By focusing on the steady-state, the behavior of the average network resistance and the properties of the resistance fluctuations are analyzed as a function of the bias. At low bias, an effective defect generation probability can be defined controlling the network behavior 49 . In this Ohmic regime, a scaling relation has been found between the relative variance of resistance fluctuations and the average network resistance 49 .…”

“…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.…”

A percolative model of soft breakdown in ultrathin oxides

“…Figure 4 reports the normalized variance of resistance fluctuations as a function of the applied voltage. Starting from the intrinsic value of the network [6], the variance is found to increase significantly as a net effect of the stressing voltage which is ultimately responsible of the breakdown at about 0.9 V . Recent observations of SILC measurements reported non-Gaussian current fluctuations in the soft breakdown region of ultra-thin dielectrics [1].…”