Current crowding and spreading resistance of electrical contacts with irregular contact edges

Practical electrical contact edges are irregular either macroscopically due to fabrication errors or microscopically due to the nature of edge or surface roughness. However, electrical contact models typically assume ideal and regular contact geometries, where geometrical effects of the irregular electrode edges are not well characterized. This paper studies current crowding and spreading resistance of electrical contacts with irregular contact edges. Using finite element method based numerical simulations, we investigate the scaling of total resistance, spreading resistance, potential drop and current distribution for electrical contacts of tilted contact edges, with various electrode lengths a and edge angles θ. It is found that as the contact edge angle θ increases, the spreading resistance and therefore the total resistance decreases. This is attributed to the increased current crowding towards the corner of the longer electrode side edge when the edge tilt increases, leading to shorter current conduction paths. For a given edge tilt angle θ, the scaling of spreading resistance with a follows closely that of zero edge angle θ: the spreading resistance decreases with a when and a/h < 1 then converges to a constant when a/h > 1, where h is the thickness of the conductor. The current density distribution near the electrical contacts are shown for different edge angles θ.