van der Pauw’s Theorem on Sheet Resistance

摘要

The sheet resistance of a conducting material of uniform thickness is analogous to the resistivity of a solid material and provides a measure of electrical resistance. In 1958, L. J. van der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from four points on the edge of a simply connected sample of material. In this article we give a statement and proof of the van der Pauw theorem using ideas from complex variables. We also include details of a demonstration of the method for finding the sheet resistance of a stainless steel shim using typical equipment in a physics laboratory.