A derivation of the van der Pauw formula from electrostatics

The van der Pauw formula for determining the electrical resistivity of an irregularly-shaped material was derived by him with the help of conformal mapping and is inherently two-dimensional. Thus, it is valid in the limiting case of a sample of infinitesimal thickness. In this paper, we demonstrate how the same formula can be derived from classical electrostatics for a rectangular sample of non-zero thickness which is allowed to approach zero. The calculation is carried out with the current probes at two adjacent corners and the voltage probes at the other two. In addition, the effects of non-ideality, particularly non-zero thickness and non-point contact voltage and current probes, are examined using the analytic formulation derived here and a semiconductor device code.