Effective constriction resistance for isotropic and anisotropic film conductors

Abstract

When two electrical conductors with rough surfaces are in contact, the apparent contact area can be regarded as an ensemble of small real contact spots, as noted by Holm. The currents flowing through a real contact spot are influenced by the electrical current spread from the adjacent real contact spots. Greenwood considered the interference between a pair of real contact spots. The effective constriction resistance thus obtained can be evaluated once the positions of the real contact spots have been determined. For decades, the expressions for the constriction resistance obtained by Holm and Greenwood have been widely used to interpret and characterize experimental data. Here, we take a completely different approach. Instead of explicitly considering the interference between the real contact spots using their specific positions, we regard the apparent contact area composed of an ensemble of real contact spots as a homogeneous effective conductor. The effective medium theory is not rigorous but its simplicity allows us to study the effective constriction resistance of film and bulk conductors, including the effect of conductivity anisotropy, approximately. We show that the obtained effective resistance is consistent with that obtained by Greenwood for bulk isotropic conductors. We also propose a phenomenological equation to describe the relation between the Holm radius and the number of real contact spots.