Van-der-Pauw measurement on devices with four contacts and two orthogonal mirror symmetries

Resistive thin film devices with four contacts of arbitrary size are discussed analytically by conformal mapping and equivalent resistor circuit. The device symmetry is assumed to be mirror symmetric to two lines, which are perpendicular. These lines go either through the contacts or midway between the contacts. This limits the degrees of freedom (DoF) to three. It is shown how to derive the sheet resistance and the other two DoF by Van-der-Pauw measurement without knowledge of the specific device geometry. It is also elucidated why conventional Van-der-Pauw method fails for devices with large contacts - an alternative procedure is proposed. The results are applicable to Van-der-Pauw devices, Hall plates, Vertical Hall effect devices, and mechanical stress sensors.