Four-Probe Methods for Measuring the Resistivity of Samples in the Form of Rectangular Parallelepipeds

TL;DR

This paper develops and analyzes four-probe measurement techniques for determining the resistivity of rectangular parallelepiped samples, including solutions for different contact arrangements and extensions to anisotropic materials like highly oriented pyrolytic graphite.

Contribution

It introduces new solutions for electric potential distribution in four-probe resistivity measurements and extends the method to anisotropic samples, including practical application to pyrolytic graphite.

Findings

Solutions for potential distribution in different contact configurations.

Extension of the method to anisotropic resistivity tensors.

Successful measurement of resistivity in highly oriented pyrolytic graphite.

Abstract

The problem of measuring the resistivity of isotropic samples of finite dimensions in the form of rectangular parallelepipeds using the four-probe technique was considered. Two variants of contact arrangements were studied: (1) four collinear probes are positioned on one side of a sample symmetrically with respect to the other sides, and (2) two probes on one side of a sample and two on the opposite side are placed precisely in opposite positions and symmetrically with respect to the other sides of the sample (the Schnabel method). Solutions of the problem of the electric field potential distribution in a sample for different positions of the current contacts were found. The solutions were obtained in the form of double series and methods of their summation are presented. The obtained results are extended to the case of measuring the resistivity of anisotropic samples when the resistivity tensor has two independent components. The results of using the developed technique for measuring the resistivity of such a highly anisotropic material as highly oriented pyrolitic graphite using the Schnabel method are presented.