Electrical contact resistance theory for conductive rough surfaces

TLDR

The theory employs fractal geometry to model surface topography, elastic‑plastic deformation of asperities, and size‑dependent constriction resistance, and it also describes simple measurement methods for surface roughness, material properties, and real contact area. From first principles, the authors derived a general ECR theory for conductive rough surfaces, producing load‑ and area‑dependent relations for isotropic, homogeneous materials, a dimensionless link between real contact area and ECR based solely on electron mean free path, and practical design guidelines.

Abstract

A general electrical contact resistance (ECR) theory for conductive rough surfaces was derived from first principles. The analysis is based on fractal geometry for the surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent constriction resistance of microcontacts. Relations for the ECR in terms of contact load and apparent contact area are obtained for isotropic, homogeneous, conductive surfaces with known material properties and surface topography. Useful design guidelines for electrical contacts are extracted from the numerical results. A general relation between the dimensionless real contact area and the dimensionless ECR is introduced for lightly loaded contacts that depends only on the electron mean free path. Approaches for determining the surface roughness, material properties, and real contact area are discussed in the context of relatively simple ECR measurements.