Spreading Resistance of a Contact Spot on a Thin Film

Thin film contacts are becoming increasingly important in the miniaturization of electronic devices. This paper considers the spreading resistance of a microscopic contact of size a ("a- spot") on a thin film. The effect of the film thickness h on the spreading resistance is evaluated over a large range of the aspect ratio a/h, for both Cartesian and cylindrical geometries. In the limit h → 0, the normalized spreading resistance converges to finite values. An interpretation of these limits is given, along with the implication of intense local heating at the rim of the a-spot. The analytic theory is extended to a-spots of arbitrary shape; and is applicable to AC bulk contact resistance calculations at sufficiently high excitation frequencies. Results of the analytic theory are compared with recent measurements and simulations of contact resistance in cylindrically symmetric contacts. Because existing models are generally valid over different ranges of contact radius and film thickness, even for an idealized geometry, this paper emphasizes the importance of comparing measured spreading resistance with values calculated from the model that is applicable to the experimental situation.