Finite element and analytical solutions for van der Pauw and four-point probe correction factors when multiple non-ideal measurement conditions coexist

Abstract

This paper presents an extensive collection of calculated correction factors that account for the combined effects of a wide range of non-ideal conditions often encountered in realistic four-point probe and van der Pauw experiments. In this context, "non-ideal conditions" refer to conditions that deviate from the assumptions on sample and probe characteristics made in the development of these two techniques. We examine the combined effects of contact size and sample thickness on van der Pauw measurements. In the four-point probe configuration, we examine the combined effects of varying the sample's lateral dimensions, probe placement, and sample thickness. We derive an analytical expression to calculate correction factors that account, simultaneously, for finite sample size and asymmetric probe placement in four-point probe experiments. We provide experimental validation of the analytical solution via four-point probe measurements on a thin film rectangular sample with arbitrary probe placement. The finite sample size effect is very significant in four-point probe measurements (especially for a narrow sample) and asymmetric probe placement only worsens such effects. The contribution of conduction in multilayer samples is also studied and found to be substantial; hence, we provide a map of the necessary correction factors. This library of correction factors will enable the design of resistivity measurements with improved accuracy and reproducibility over a wide range of experimental conditions.