A closed-form solution for the computation of geometric correction factors for four-point resistivity measurements on cylindrical specimens

Abstract

The present work deals with the evaluation of geometric correction factors for dc four-point probe measurements on finite cylindrical specimens for a random placement of the four probes on a circular face of the specimen. A closed-form (CF) analytical expression is obtained for the potential difference between the voltage probes via the solution of Laplace's equation using the variable-separation technique. The potential difference thus obtained is subsequently used to compute the geometric correction factor. The applicability of the solution is illustrated for two specific cases using a collinear probe-array, namely probes arranged along a radius and normal to a radius. Correction factors obtained from the CF solution are validated in each case by a finite-element simulation solution obtained using COMSOL Multiphysics 3.2. Additionally, the correction factors from the two methods are compared to analytical approximation factors, evaluated using expressions that exist in the literature. A range defined by a lower and an upper analytical approximation factor is computed for each specific case. Correction factors from the CF and COMSOL solutions show an excellent match with each other and lie within the analytical approximation bounds. The application of the CF solution is demonstrated for experimental measurements on copper specimens of different cylindrical geometries.