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

Abstract

A short review is presented of a recently developed computational approach which allows the study of the resistance noise over the full range of bias values, from the linear regime up to electrical breakdown. Resistance noise is described in terms of two competing processes in a random resistor network. The two processes are thermally activated and driven by an electrical bias. In the linear regime, a scaling relation has been found between the relative variance of resistance fluctuations and the average resistance. The value of the critical exponent is significantly higher than that associated with 1/f noise. In the nonlinear regime, occurring when the bias overcomes the threshold value, the relative variance of resistance fluctuations scales with the bias. Two regions can be identified in this regime: a moderate bias region and a pre-breakdown one. In the first region, the scaling exponent has been found independent of the values of the model parameters and of the bias conditions. A strong nonlinearity emerges in the pre-breakdown region which is also characterized by non-Gaussian noise. The results compare well with measurements of electrical breakdown in composites and with electromigration experiments in metallic lines.

Distribution of Return Periods of Rare Events in Correlated Time Series

“…At small λ values (high level of intrinsic disorder), we have found that the auto-correlation function displays a non-exponential (but non-power-law) decay. This behavior is different from that displayed at high λ values (low level of intrinsic disorder), where C x exhibits an exponential decay (consistent with the Lorentzian power spectrum reported in previous works [16,17,19]). Here we will focus on the case of non-exponential and non-power-law decay of correlations, a situation typical of systems which are approaching criticality, and we will show the results obtained by taking λ = 0.33 for a network of size 125 × 125, biased by a current I = 0.011 A.…”

“…When I > I B the resistor undergoes an electrical breakdown, associated with an irreversible divergence of its resistance [16,17,18,20]. For a generic value of λ this breakdown corresponds to a first order transition [17,18,19]. However, for decreasing λ values, when λ → λ min , the system becomes more and more close to its critical point [17,18,19].…”

“…Precisely, we have analyzed the auto-correlation function and the distribution of the return intervals of extreme values of the resistance fluctuations displayed by a resistor with granular structure in nonequilibrium stationary states. The resistance fluctuations were calculated by Monte Carlo simulations using the SBRN model [16,17,18,19,20]. We have found that for highly disordered networks, when the auto-correlation function displays a non-exponential (precisely, a stretched exponential) decay and the resistance fluctuations are characterized by a finite correlation time, the distribution of return intervals of the extreme values is well described by a stretched exponential with exponent γ largely independent of the threshold q.…”

Modelling and detection of failure in medical electrodes

“…7 (a) simulation results for the probability density function (PDF) of resistance fluctuations are given and qualitatively compared with theoretical distributions; Gaussian and Bramwell-Holdsworth-Pinton (BHP) distribution [18]. It is evident that for higher activation energy E D , PDF shows Gaussian-like behavior.…”

Statistics of extreme values in time series with intermediate-term correlations

“…As a result, the power spectral density of the resistance fluctuations shows a 1/f α dependence of frequency, with α ≈ 1 for T ≤ T * . It should be also noted that the MSN model represents an extension to systems characterized by 1/f noise of a previous model existing in the literature, the stationary and biased resistor network (SBRN) model [31,32,33]. In any case, it must be underlined that, apart from the specific system described by the MSN model, the method used here for generating the time series can be also viewed as a pure numerical algorithm for generating numerical series with different and tunable correlation properties.…”