An exact formulation of thin film contact resistance with dissimilar materials

Summary form only given. Thin film contact is a very important issue in many areas, such as integrated circuits, thin film devices, carbon nanotube and carbon nanofiber based cathodes and interconnects, field emitters, etc. In high energy density physics, the electrical contacts between the electrode plates and in Z-pinch wire arrays are crucial for high current delivery. This paper presents results of thin film contact resistance with dissimilar materials, based on an exact analytic formulation of a model for both cylindrical and Cartesian geometry. In the cylindrical geometry, the model consists of a long cylindrical rod of radius a standing on the center of large thin-film circular disk of thickness h, and radius b (>; a). The rod´s electrical resistivity and the thin film´s electrical resistivity may have an arbitrary ratio. We found that, over a large range of parameters, the contact resistance does not depend on b as long as either b >;>; a or b >;>; h. We also found that the contact resistance is insensitive to the resistivity ratio for a/h <; 1, but becomes rather sensitive to the resistivity ratio for a/h >; 1. Our calculations are verified in various known limits. We obtained the condition under which the thin film contact resistance is minimized, for arbitrary resistivity ratio. Electric field patterns will also be presented that show crowding of the field lines in the contact region for h >;>; a and for a >;>; h. The contact resistance for the Cartesian thin-film geometry will be presented. Our theory was validated against MAXWELL 3D simulation, and against conformal mapping results for unity resistivity ratio. Optimal conditions to minimize the thin film contact resistance are identified.