Theory and experimental measurements of contact resistance

Summary form only given. Electrical contact is an important issue for high power microwave sources, wire-array Z pinches, field emitters, and metal-insulator-vacuum junctions. Because of the surface roughness on a microscopic scale, true contact between two pieces of metal occurs only on the asperities of the two contacting surfaces. Current flows only through these asperities, which occupy a small fraction of the area of the nominal contacting surfaces. This gives rise to contact resistance. We have developed a novel analytic theory of contact resistance of an asperity of transverse dimension (a) and finite axial length (h) connecting two metal blocks. For asperity of rectangular, cylindrical or funnel shape, we find that the contact resistance is of the form R[1+p(h/a)] where R is the corresponding h = 0 "a-spot" theory limit of Holm and Timsit, p has a simple form which we have verified against electrostatic code results. This higher-dimensional treatment links the contact resistance to the geometrical deformations in response to an applied pressure, and to the hardness of the material. Experimental measurements of the contact resistance of a single Z-pinch wire were performed at the Plasma, Pulsed Power and Microwave Laboratory at the University of Michigan. The measurements were taken for several wire types and contact methods. Traditionally strung wires (with a wire weight hanging from each end) had contact resistance values that were on the order of, or much greater than, the resistance of the wire itself. The contact resistance was significantly lower for all wires when metal gaskets were clamped over the wire at both contact points. In all cases, as the applied force normal to the contact point was increased, the contact resistance decreased. This agrees qualitatively with the theoretical predictions. Potential applications and extensions of the theory, such as the RF contact resistance, will be presented.