Spreading Resistance Between Constant Potential Surfaces

The resistance associated with the nonparallel current flow between a spacially separated source and sink is referred to as spreading resistance. Calculation of spreading resistance is often required in the analytical treatment of semiconductor devices. In particular, electrical current flow in a slice of silicon between a surface contact and a back-plane contact involves the calculation of the ohmic spreading resistance. The heat flow between an active transistor or integrated circuit and an external heat sink involves a calculation of the thermal spreading resistance in the device carrier. Also, for a given structure, the capacitance including fringing is directly related to the conductance including spreading. Two cases are considered in this paper. The spreading resistance is determined for an infinite sheet of homogeneous material of uniform thickness with a disk contact source on one side and with current collected (i) at a completely metallized back plane, and (u) at a corresponding disk on the back plane. D. P. Kennedy analyzed these cases for finite cylindrical volumes but with nonmixed boundary conditions. 1 He assumed a constant flux over the source region and 775