Quantifying the spreading currents over the circular contact region in a good conducting cover layer on a substrate

Abstract

If a poorly conducting slab is covered with a good conducting cover layer, the resistance of the substrate with the cover layer might be considered to still be high. However, if the contact resistance is measured through a small circular region, the spreading currents conducting parallel to the cover layer surface could lower the resistance. We investigate theoretically the contact resistance of a circular spot and the electric field lines when a conducting substrate is covered with a good conducting thin film. Though an approximate expression of the contact resistance is derived when a metal slab is covered with a thin surface layer, which is easily able to be generalized for the semiconductor substrate, the validity of the approximate expressions of the contact resistance has not been fully understood. We present an accurate theoretical method for finding the correction terms to the approximate expressions and assess the validity of the approximation. We show that the approximate expressions give qualitatively correct results but a quantitatively large error is found for a thin cover layer on a poorly conducting substrate. The accurate theoretical results are useful to understand the dependence of the electrical spreading resistance on the conductivity of the layer and/or that of the substrate as well as the layer thickness. The results could also be used to detect the presence of the surface layer with a different electrical conductivity from that of the substrate through the measurement of the contact resistance with varying the contact area.