Effects of macroscopic inhomogeneities on resistive and Hall measurements on crosses, cloverleafs, and bars

The effect of macroscopic inhomogeneities on resistivity and Hall angle measurements is studied by calculating weighting functions (the relative effect of perturbations in a local transport property on the measured global average for the object) for cross, cloverleaf, and bar‐shaped geometries. The ‘‘sweet spot,’’ the region in the center of the object that the measurement effectively samples, is smaller for crosses and cloverleafs than for the circles and squares already studied, and smaller for the cloverleaf than for the corresponding cross. Resistivity measurements for crosses and cloverleafs suffer from singularities and negative weighting, which can be eliminated by averaging two independent resistance measurements, as done in the van der Pauw technique. Resistivity and Hall measurements made on sufficiently narrow bars are shown to effectively sample only the region directly between the voltage probes.