Noise scaling in continuum percolating films

Abstract

Measurements of the scaling of \/f noise magnitude versus resistance were made in metal films as the metal was removed by sandblasting. This procedure gives an approximate experimental realization of a Swiss-cheese continuum-percolation model, for which theory indicates some scaling properties very different from lattice percolation. The ratio of the resistance and noise exponents was in strong disagreement with lattice-percolation predictions and agreed approximately with simple continuum predictions. PACS numbers: 72.70. + m, 05.40. +j, 05.70.Jk, 71.30. + h The critical scaling of various transport properties on percolating clusters provides a probe of the structure of those clusters. Recently, attention has been drawn to the possibility that the scaling of the mean square fluctuations S R in electrical resistance may provide information not obtainable from the scaling of R, the resistance itself. 1,2 In particular, since S R is sensitive to a higher moment of the current density distribution than is R it may be among those transport properties 3 " 5 for which the universality of scaling found in lattice models and many continuum models breaks down, according to theory. In this Letter we report measurements of the scaling of S R vs R in a simple experimental system which show unambiguously that the lattice models are inapplicable to continuum systems and which approximately confirm theoretical expectations for a simple continuum model.Monte Carlo simulations 1,6 of percolating clusters on a lattice (consisting of identical resistors with independent fluctuations) yield resistance and noise critical exponents K=1.12 and /3 L = -0.973, where the exponents are defined by R ~ £ L --A v L and S R /R 2 -A _K , with £ the percolation coherence length and p = p c + A the filling fraction. Halperin et al? have recently suggested that the permeability and elasticity exponents for the Swiss-cheese model, in which round holes with a fixed radius and randomly placed centers are removed from a material, are larger than those for the standard lattice model, while the resistance exponent vf3 L should not differ significantly. These Swiss-cheese calculations were made with a nodeslinks-blobs (NLB) model. 7 The agreement of the resistance exponent with the lattice value is also consistent with previous works, 4,5 which predict deviations only for singular distributions of single-link conductivities.Whether a quantity scales the same in a continuum model as in lattice models depends on how sensitive it is to the behavior of the weakest or narrowest links in the network. In other words, it depends on what moment of the current density, strain, etc., is probed by that quantity. Although the NLB model is not especially accurate for f3 L , which probes the second mo-ment of the current density and thus depends on blobs as well as links, it is expected to become increasingly accurate for higher moments, since the scaling of the number of links is known exactly. Recent experiments have shown that the conclusion that /3 L is unchang...

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