A unified compact model of electrical and thermal 3-D spreading resistance between eccentric rectangular and circular contacts

The spreading resistance between two parallel contacts, the smaller of which is located arbitrarily over the area of the larger, is of wide interest in electrical/thermal design of devices and ICs. We propose a simple, continuous, and asymptotically correct closed-form expression to predict the accurate but involved calculations of this resistance for all contact conditions. The contacts may be rectangular or circular, and the boundary condition on these may either be equipotential/isothermal or uniform current density/uniform heat flux. The validity of the model is established by comparisons with accurate numerical calculations of spreading resistances having aspect ratios in the range zero to 1000 and with experimental observations.