Contact resistance is important to integrated circuits and thin film devices, carbon nanotube based cathodes and interconnects, field emitters, wire-array z-pinches, metal-insulator-vacuum junctions, and high power microwave sources, etc. In other applications, the electrical contacts are formed by thin film structures of a few microns thickness, such as in micro-electromechanical system (MEMS) relays and microconnector systems. This paper summarizes the recent modeling efforts at the University of Michigan, addressing the effect of dissimilar materials and of finite dimensions on the contact resistance of both bulk contacts and thin film contacts. The Cartesian and cylindrical geometries are analyzed. Accurate analytical scaling laws are constructed for the contact resistance of both bulk contacts and thin film contacts over a large range of aspect ratios and resistivity ratios. These were validated against known limiting cases and spot-checks with numerical simulations.
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