The spreading resistance of a homogeneous slab on a high-resistivity substrate: Mixed boundary value solutions

Abstract

The range of applicability of the mixed boundary value method for calculating spreading resistance is extended to a homogeneous slab with a disc contact source and backed by a substrate of arbitrary, but finite resistivity. Solutions are presented in terms of the spreading resistance correction factors and the source current density distributions for a slab of varying thickness and with various high resistivity substrates. In particular, the results for a thin slab indicate that, as the substrate resistivity increases, more and more of the source current is concentrated near the edge of the disc electrode. A comparison is made of the source current density and potential corresponding to the mixed boundary value method with those given by the uniform flux and the variable flux (power-loss) method. It is found that, except for large slab thicknesses, the source potential distributions for a slab with a high resistivity substrate are not strongly influenced by the particular form of the source current density distribution assumed in either the uniform flux or the variable flux method. In consequence, both these two methods yield correction factors which agree quite closely with those derived from the mixed boundary value method.