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An electrical contact resistance (ECR) theory is presented for conductive and rough (fractal) surfaces separated by a thin insulating film, which is treated as an energy barrier that impedes current flow due to the electric-tunnel effect. The analysis yields insight into the effects of film properties, current flow, surface topography, mechanical properties, and contact load on the ECR. It is shown that the variation of ECR with the contact load is less pronounced than that observed in the absence of an insulating layer due to the intrinsic voltage dependence of the tunnel resistance and the associated voltage compensation mechanism. The effect of nonohmic behavior on the relationships of the ECR with the contact load and the real contact area is discussed and results are compared with approximate analytical relationships developed herein. The relationship between the real contact area and the ECR depends on the current intensity and film properties and is independent of the surface topography and mechanical properties. Approaches for determining the surface roughness, mechanical properties, insulating film properties, and real contact area from ECR measurements are interpreted in light of the theory developed. © 2004 American Institute of Physics.