Four-point probe geometric correction factor for isotropic cylindrical samples with non-equal probe distances

Abstract

Resistivity of ceramics is usually measured by the DC-four-point-probe setup, which requires a geometric correction factor (GCF). We calculated a GCF for the general case of unequally spaced, in-line probes on isotropic, cylindrical specimens of variable size, radius and thickness. An analytical expression was obtained for the potential difference between the voltage probes by solving Laplace's equation. We show how the relative error of GCF varies with the number of Bessel functions and the number of extrema in them. GCF’s sensitivity vis-à-vis probe distances, sample radius r0 and thickness d was studied to provide an error estimate dependent on measurement errors in those parameters. Contour plots of r0-d provide GCF values without additional calculations, if the instrument’s specifications are the same. Our GCF reproduced the final results from a commercial instrument very well. The deviation between the two results was 1.5% in our temperature range of 25°–300 °C.