An Efficient Integration Technique for Use in the Multilayer Analysis of Spreading Resistance Profiles

Abstract

The efficiency of multilayer analysis in calculating resistivity profiles from spreading resistance measurements depends on the rapid numerical evaluation of the well‐known correction factor integral first introduced by Schumann and Gardner. We present a new approximate form for the correction factor which allows its numerical evaluation with only 22 integrand values for each evaluation of the integral. When this technique is used in our multilayer analysis program, we unfold spreading resistance profiles at the real time rate of less than 3 sec/point on a desktop computer. Its results match those of analytic evaluations of special two layer cases or with more elaborate numerical evaluations of graded structures to within 1%.