Theory of Four-Point Direct-Current Potential Drop Measurements on a Metal Plate

ABSTRACT Four-point direct-current potential drop techniques are well-suited for accurate, nondestructive measurement of material conductivity (or resistivity). From measurements of potential drop on a large metal plate, the electrical conductivity of the plate can be inferred if the thickness of the plate and the dimensions of the probe are known. In this work, an expression for the voltage measured by a four-point probe in contact with a large metal plate of arbitrary thickness is derived from an analytic series representation of the electric field in the plate. The position of the voltage pickup points is permitted to be offset with respect to the current injection points, allowing analysis of colinear, rectangular, and square-head probes. Analytical asymptotic expressions are derived in the limiting cases of plates that are thin or thick with respect to the dimensions of the probe. The range of plate thicknesses for which the asymptotic expressions are valid is determined as a function of relevant probe dimensions. The results of this study provide a useful guide in selecting the most appropriate arrangement of probe points for measurement of the electrical conductivity of large metal plates, depending on the level of accuracy required. Theory is compared with experimental data for measurements made with colinear probes on a variety of metal plates and very good agreement is obtained.