Theory of Four-Point Alternating Current Potential Drop Measurements on a Layered Conductive Half-Space

摘要

An analytic expression describing the complex voltage measured between the pickup points of a four-point probe, in contact with the surface of a layered metal half-space, is derived. The driving current is assumed to be time-harmonic. A Green's function formulation leads to a result in which the voltage is expressed as a sum of two terms. One represents the potential drop due to a homogeneous half-space conductor with properties the same as those of the surface layer. The other represents the effect of the substrate and is expressed as a Hankel transform. A scheme for numerical evaluation of this term, by truncating the range of integration, is presented. An example calculation is given.