Correction factors for 4-probe electrical measurements with finite size electrodes and material anisotropy: a finite element study

Abstract

In four-probe (4-probe) electrical measurements, especially on highly resistive materials, it is not always possible to configure the electrodes such that the current density is uniform throughout the sample. Under such circumstances, simply considering the material's electrical resistivity to be proportional to the measured resistance with the proportionality constant given by the sample geometry can give an incorrect result. In this paper, a numerical finite element model is presented which can extract a material's true resistivity from co-linear 4-probe electrical measurements on highly resistive samples with large electrodes that extend across the sample width. The finite element model is used to investigate the influence of material anisotropy, the resistance of the sample-electrode interfaces and the relative electrode-to-sample size on the potential and current density distributions in the sample. A correction factor is introduced to account for the impact of these effects on the measured resistivity. In the limit of large interface resistance, excellent agreement is found with an analytical expression derived elsewhere (Esposito et al 2000 J. Appl. Phys. 88 2724. The approach presented here can be used to evaluate a variety of effects on co-linear 4-probe electrical measurements, can be extended to complex specimen geometries with arbitrary electrode arrangements and, additionally, could find use in the evaluation of data from 4-probe thermal conductivity measurements.

The electrode factor on the accuracy of electrical resistivity measurement in diamond anvil cell

“…Using Smits's method [10], we can get very similar result. But using Zimney's [11], the result would be quite different, because the latter was only put forward for the case that the specimen should be rectangular and the electrodes must span the width of the specimen.…”

An international Comparison Measurement of Silicon Wafer Sheet Resistance using the Four-point Probe Method

“…However, measurement accuracy using a FPP method is generally more than five times superior to that using an eddy current method. The FPP method is divided into two techniques: a single configuration technique [1][2][3][4][5][6] and a dual configuration technique [7][8][9]. With the single configuration technique, the sample thickness and sample size correction factor against the probe spacing should always be applied in order to determine the sheet resistance [5,6].…”

“…The FPP method is divided into two techniques: a single configuration technique [1][2][3][4][5][6] and a dual configuration technique [7][8][9]. With the single configuration technique, the sample thickness and sample size correction factor against the probe spacing should always be applied in order to determine the sheet resistance [5,6]. However, with the dual configuration technique, correction factors of the sample thickness and size effects are not applied and the edge effect is also very slight compared with the single configuration technique.…”

Electrical conductivity measurements on disk-shaped samples

“…For this reason finite element (FE) modeling has become an efficient approach to determine geometrical correction factors for arbitrary measurement configurations. [20][21][22][23] We have adapted this approach to determine the GCFs for the measurement geometry depicted in Figure 1(c) for a range of experimentally relevant sample dimensions and probe spacings. From the result, a simple analytical fit function is derived that allows for the calculation of GCFs(D, s, t) for an arbitrary configuration in a typical geometry range.…”