The resistance of an infinite slab with a disc electrode as a mixed boundary value problem

We consider the resistance of an infinite slab of material with a disc contact source on one side and with current collected over the entire back plane. By imposing the boundary condition of a constant potential over the source region, the problem becomes one of mixed boundary conditions, requiring the solution of a pair of dual integral equations. These equations are solved in terms of a Fredholm integral equation of the second kind.Calculations of the resistance are performed for values of slab thicknesses ranging from 0·05 to 4 times the disc contact radius, and the solutions obtained agree closely with Foxhall and Lewis' electrolytic tank measurements. The results are used to establish the range of validity of two approximate methods previously proposed for correction factor calculations in spreading resistance measurements on semiconductor device structures.