A comparison of two van-der-Pauw measurement configurations of resistivity

Based on the solution of an electrostatics boundary-value problem, this paper compares two van-der-Pauw-type measurement configurations of resistivity, with respect to the movement of the point-like voltage and current contacts away from the periphery of a thin, square sample. The movement involves both a reduction in the size of the contact array, without any change in its shape or orientation, and a displacement of its center. The formulas derived are applicable to any rigid displacement such that all contacts remain within the boundary of the sample, but only displacements parallel to the edges of the sample or along its diagonal are examined. Both arrays are square, with the first initially coinciding with the corners of the sample and the second initially having its corners centered on the edges of the sample. The solution indicates that the deviation from the ideal van der Pauw resistivity measurement is less sensitive to a reduction in the size of the undisplaced contact array when the first configuration is used. However, under displacements, the situation is complicated markedly by boundary effects, with the results depending on the direction of displacement and the size of the array.