Determination of the Riemann modulus and sheet resistivity by a six-point generalization of the van der Pauw method

A six-point generalization of the van der Pauw method is presented. The method is applicable for 2D homogeneous systems with an isolated hole. A single measurement performed on the contacts located arbitrarily on the sample edge allows us to determine the specific resistivity and a dimensionless parameter related to the hole, known as the Riemann modulus. The parameter is invariant under conformal mappings of the sample shape. The hole can be regarded as a high resistivity defect. Therefore, the method can be applied for the experimental determination of the sample inhomogeneity.