A higher dimensional theory of contact resistance

Electrical contact is an important issue for wafer evaluation of manufactured integrated circuits. It has also repeatedly surfaced in our ongoing studies of 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 recently developed an analytic theory of the contact resistance of an asperity that has a finite axial length (h) connecting two metal blocks. We construct a scaling law for arbitrary aspect ratios of the asperity, with the h = 0 limit reducing to the classical "a-spot theory" of Holm and Timsit. While asperities of finite length may be a small step closer to reality, this higher-dimensional treatment could link the contact resistance to the geometrical deformations in response to an applied pressure, and eventually to the hardness of the material. Potential applications and extensions of the theory, such as the RF contact resistance, will be presented.