Electrostatics analysis of two Hall measurement configurations

Along with a resistivity measurement, the measurement of the Hall voltage can provide a useful characterization of the electrical properties of a bulk semiconductor. Typically, both use a Van der Pauw-type configuration on a thin, planar material. Ideally, this involves infinitesimal current and voltage contacts on the periphery of a sample of infinitesimal thickness. When deviations from ideality occur, geometric errors are introduced, which can have an important impact on the accuracy of the measurement. These are in addition to errors such as those caused by offsets in the measurement system and any non-uniformity in the applied magnetic field. Assuming an ideally-thin, rectangular sample, analyses of two different measurement configurations of the Hall voltage are presented, illustrating the consequences of some of these geometric errors. They are the result of a solution to an electrostatics boundary-value problem.

► Two Van der Pauw type Hall voltage measurement configurations are presented.
► Positional errors in the voltage and current contacts are introduced.
► Non-point-like current pads are also introduced.
► The resulting measurement errors are analyzed using an electrostatics technique.
► One of the two configurations produces noticeably smaller measurement errors.