Constriction Resistance of Thin Film Contacts

The electrical constriction resistance of a circular a-spot in a bulk interface stems from convergence of electrical current flow lines from a distance far from the constriction, and the subsequent spreading out of the current from the constriction. The spreading resistance of an a-spot located in a thin film cannot be identical to that generated in a bulk component of the same material since current spreading is constrained by the thin film boundaries. This paper addresses the effect of film thickness on spreading resistance, and hence on constriction resistance, in a thin conducting layer. If a and L are, respectively, the constriction radius and the film thickness, the spreading resistance is found to deviate significantly from that in a bulk solid only for relatively thin film and for values of a/L greater than 0.02. This paper also compares the dc spreading resistance in a thin film to the spreading resistance for high-frequency current in a bulk solid where current flow is limited to the electromagnetic skin depth. It turns out that spreading resistance at high-signal frequencies is comparable with the dc spreading resistance in a thin film if the thickness of the equivalent thin film is identified as the skin depth at the relevant frequency.