Van-der-Pauw measurement

The Van der Pauw measurement technique, named after its creator Leo J. van der Pauw, is a widely employed 4-point method for evaluating the sheet resistance and Hall coefficient of materials.

In 1958, van der Pauw addressed the general challenge of potential distribution in a thin, conductive layer of any shape, enabling Hall and resistance measurements. However, specific conditions must be met for accurate results. The sample thickness (t) must be uniform and significantly smaller than the distance between contacts. The sample should be mathematically continuous without holes or islands of highly conductive material, and the four contacts must be situated at the sample’s edge and be small relative to its area.

Fig. 1) Experimental setup for Van-der-Pauw measurement
Fig. 2 a) Contacting of a sample for the Van-der-Pauw measurement. b) Contacting the sample on the TFA measurement chip, including its dimensions.

By cyclically changing contacts, the vertical resistance can be determined. With both horizontal and vertical resistances obtained, surface resistance or resistivity can be calculated by numerically solving the Van der Pauw formula:

To determine the Hall coefficient, an external magnetic field (\( B_Z \)) is applied perpendicular to the sample surface, and changes in the diagonal Van der Pauw resistance are measured. The Hall coefficient (\( A_H \)) is then calculated using:

Sample configuration for the Hall coefficient measurement using Van der Pauw measurement technology, with an applied magnetic field perpendicular to the sample surface.

In the case, the following is valid:

such as

Offset effects are mitigated by measuring the diagonal voltage (\( V_{\text{Hall}} \)) at different magnetic field strengths, and the Hall coefficient is derived from the slope of the Hall voltage over magnetic field strength.

For AC measurement, an alternating magnetic field is applied, and the resulting Hall voltage is read out using a lock-in amplifier. This method accommodates materials with low mobilities, as small Hall voltages are not overshadowed by misalignment offsets.

What properties are determined?

The Van der Pauw method is employed to determine various electrical transport properties, including electrical conductivity, resistivity, Hall constant, charge carrier concentration, and charge carrier mobility in materials, both bulk and thin films.

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