Measurement of the fourth moment of the current distribution in two-dimensional random resistor networks

Ma, Dejian; Yc, Hui; Mb, Weissman; Jc, Garland

doi:10.1103/physrevb.39.6807

Cited by 63 publications

(57 citation statements)

References 24 publications

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“…For a random resistor network, the change in resistance due to Joule heating, in the first approximation, DR R 2 R o is given by abhR 2 o SI 2 [12]. Hence,…”

Section: Predictable Electrical Breakdown In Compositesmentioning

confidence: 99%

Predictable Electrical Breakdown in Composites

Mukherjee

Bardhan

Heaney³

1999

Phys. Rev. Lett.

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The Joule regime at large electric fields in composites is presented in the context of a conduction phase diagram in the field-concentration plane. A sample suffers breakdown when the field is too large. The resistance up to breakdown is described by a universal curve as a function of field. It is found that the ratio of the breakdown resistance to the zero-field resistance assumes a fixed value Y at breakdown. Y is found to be 1.37 in carbon high-density polyethylene composites and is independent of carbon fraction and external conditions but depends on the nature of the conductor. A quantity which is independent of conducting material is defined. Results are compared with previous data.PACS numbers: 72.80.Ng, 05.70.Jk, 72.20.Ht Application of finite force (F, mechanical or electrical) in disordered systems usually results in a nonlinear response leading to some sort of catastrophic behavior in the extreme limit (e.g., fracture in mechanical systems and dielectric breakdown or burning in electrical systems). In recent years there has been a renewed interest in the problem of catastrophic phenomena [1] although the problem of non-Ohmic electrical conductivity in the precatastrophic regime in various disordered systems has been studied for a long time [2,3]. However, there have been very few attempts so far to describe the behavior of a system over the full range of the applied force. Such a study holds the promise of unraveling many important aspects such as precursor effects, predictability, and the effect of disorder on the nature of breakdown. Yagil et al.[4] carried out somewhat limited measurements of I-V curves in thin semicontinuous metallic films of Ag and Au. Focusing on breakdown events, it was concluded that breakdown currents I b in the films scale as I b ϳ B 2x , where B is the normalized third harmonic component (see below) generated as a result of Joule heating. Breakdown was assumed to occur when the sample resistance R exhibited the first irreversible discontinuity as a function of applied current I. The exponent x was measured to be 0.48 and 0.41 in films of Ag and Au, respectively. The authors also derived theoretical bounds for x, 0.5 $ x $ 0.5͓1 2 1͞t͑2 1 w J ͔͒ so that breakdown currents were expected to lie between two bounds. Here, t is the electrical conductivity exponent and w J k͞t, k being the noise exponent [5].In this Letter, we present systematic measurements of electrical resistance, particularly in the Joule regime of a composite system of carbon high-density polyethylene (HDPE) up to breakdown. The breakdown in a sample has the nature of a first-order transition: as soon as the current from a constant current source exceeds a certain value I b , the sample resistance R starts increasing uncontrollably and becomes unsteady. Let R o R͑0͒ be the linear or zero-field resistance, R b R͑I b ͒ be the breakdown resistance and Y R b ͞R o . It is found that for p . p J , where p is the (volume) fraction of conducting component (carbon) and p J is a fraction characteristic of the system ...

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“…For a random resistor network, the change in resistance due to Joule heating, in the first approximation, DR R 2 R o is given by abhR 2 o SI 2 [12]. Hence,…”

Section: Predictable Electrical Breakdown In Compositesmentioning

confidence: 99%

Predictable Electrical Breakdown in Composites

Mukherjee

Bardhan

Heaney³

1999

Phys. Rev. Lett.

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“…We think, however, that the potential distribution across the whole structure ͑especially at the dead ends͒ might take place in such a way that it leads to nearly the same resistance values in the LRS for different Ge 0.3 Se 0.7 layer thicknesses. 21 We cannot exclude, however, that the resistances in the LRS will show some scaling behavior with further increase in thickness.…”

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Reliability analysis of the low resistance state stability of Ge0.3Se0.7 based solid electrolyte nonvolatile memory cells

Soni

Meuffels

Kohlstedt

et al. 2009

Applied Physics Letters

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We report on the low resistance state (LRS) stability analysis of Ge0.3Se0.7 based solid electrolyte nonvolatile memory cells under elevated temperature and bias current stress conditions. The activation energy was found to be about 1.02 eV, which is comparable to that of an electromigration-induced failure process. Experimental results also show that there is trade-off between the LRS stability and the thickness of Ge0.3Se0.7 layer.

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“…The cubic nonlinearity can be accessed in ac transport measurements by detecting a third-harmonic voltage signal V 3ω , see e.g. [20,22,23]. In general, noise spectroscopy and nonlinear transport are a measure of the fourth moment of the current distribution [22] and therefore probe the microgeometry of the electronic system, which is not accessible by the linear (Ohmic) resistance, being related to the second moment of the current distribution [24].…”

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confidence: 99%

Magnetically driven electronic phase separation in the semimetallic ferromagnet EuB6

et al. 2012

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From measurements of fluctuation spectroscopy and weak nonlinear transport on the semimetallic ferromagnet EuB6 we find direct evidence for magnetically-driven electronic phase separation consistent with the picture of percolation of magnetic polarons (MP), which form highly conducting magnetically-ordered clusters in a paramagnetic and 'poorly conducting' background. These different parts of the conducting network are probed separately by the noise spectroscopy/nonlinear transport and the conventional linear resistivity. We suggest a comprehensive and 'universal' scenario for the MP percolation, which occurs at a critical magnetization either induced by ferromagnetic order at zero field or externally applied magnetic fields in the paramagentic region.

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Measurement of the fourth moment of the current distribution in two-dimensional random resistor networks

Cited by 63 publications

References 24 publications

Predictable Electrical Breakdown in Composites

Predictable Electrical Breakdown in Composites

Reliability analysis of the low resistance state stability of Ge0.3Se0.7 based solid electrolyte nonvolatile memory cells

Magnetically driven electronic phase separation in the semimetallic ferromagnet EuB6

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