Determination of the fractal dimension of equipotential surfaces in a region confined by rough conductors

Abstract

We consider a region bounded by two conductors held to a constant voltage bias, one of them with an irregular rough shape andthe other being a 6at one. The irregular pro$le can be either a curve with a formation rule or the result of a deposition process. The rough shape of the pro$le in6uences the equipotential lines, which we have characterizedby numerically evaluating their roughness exponent andfractal dimension Df. For a $xed$nite size system, the less corrugatedlines, far away from the rough pro$le, have higher . For a line corresponding to a $xedvalue of the potential, the roughness exponent decreases with the size of the pro$le, suggesting that a single constant value characterizes all lines for an in$nite system. c 2004 Elsevier B.V. All rights reserved.