A quantitative approach to the effects of surface topography on tunnelling current between two large rough metal bodies

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Abstract
A convenient method is proposed to deal with the effects of some large-scale surface roughness when calculating the tunnelling current between two macroscopic rough metal bodies-for instance the two members of an electrical 'quasi-contact'. Surface topography is introduced through the distribution of local distances between electrodes, which describes both their nominal shape and their local roughness. Even for surfaces as simple as a plane, cylinder or sphere, this distribution is quite intricate and exhibits a highly tortuous shape. A few periodic roughness models, and a more realistic approach by means of fractals, are successively considered. In any case, the authors prove that only the beginning of the distance distribution is essential from the viewpoint of the tunneling current. A computed example allows one to assess quantitatively how the local topography may change drastically any prediction concerning the value of the current. Comparison between some reliable sphere/plane experimental results and the corresponding theoretical predictions proves to be very good and attests to the relevance of the proposed method.