Determination of the Riemann modulus and sheet resistance of a sample with a hole by the van der Pauw method

The van der Pauw method for two-dimensional samples of arbitrary shape with an isolated hole is considered. Correlations between extreme values of the resistances allow one to determine the specific resistivity of the sample and the dimensionless parameter related to the geometry of the isolated hole, known as the Riemann modulus. The parameter is invariant under conformal mappings. Experimental verification of the method is presented.