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 limited in a thin film. This paper addresses the effect of film thickness on spreading resistance, and hence on constriction resistance, in a thin conducting layer. It is shown that the spreading resistance of a circular constriction of radius a located in a cylindrical film of outer radius b and thickness L may be written as R-N (rho / 4a), where R-N is a factor that depends on the ratio L/b and a/b. Calculations indicate that RN deviates from 1 i.e. spreading resistance deviates significantly from that in a bulk solid, only for relatively thin film where L/b is small and for relatively large values of a/b.