The role of source boundary condition in spreading resistance calculations

Abstract

Solutions are presented for the current density distribution at an equipotential disc electrode in contact with a slab backed by a perfect conductor. These exact solutions provide a basis for testing the validity of the two forms of source current density distribution assumed in approximate calculations of spreading resistance correction factors, viz. a uniform distribution and the distribution given by the classical solution for the infinitely thick slab. By using the latter distribution and the power loss definition for spreading resistance, a new correction factor integral has been obtained. Correction factors have been calculated by using this integral and those given by Schumann and Gardner, by Lee and by assuming a uniform current distribution. Except for Schumann and Gardner's method, all the methods yield results consistent with those obtained for the current density distributions. In the case of Schumann and Gardner's method, the correction factors obtained for thin slabs agree closely with those given by the exact method, despite the fact that the assumed source current distribution is in gross disagreement with the exact distribution. The close agreement in correction factors is fortuitous and is a consequence of the definition that Schumann and Gardner used for the spreading resistance. For a slab with a perfectly insulating substrate, exact solutions are not available. A comparative study has therefore been made in this case between the correction factors obtained by the four approximate methods themselves. The overall conclusion is that of the approximate methods, the uniform current density method is the most satisfactory from the point of view of self-consistency and overall accuracy.