Seminarium Fizyki Materii Skondensowanej

A method of measuring specific resistivity of flat samples ofarbitrary shape based upon a theorem which holds for the contactslocated at the circumference of the sample was discovered by van derPauw at the end of fifties. The sample must be singly connected, i.e.it should not have isolated holes. Recently explicit results of the van der Pauw method for a samplecontaining an isolated hole were obtained. Correlations betweenextreme values of the resistances allow one to determine the specificresistivity of the sample and the dimensionless parameter related tothe size of the isolated hole, known as the Riemann modulus. Theparameter is invariant under the conformal mapping. Experimentalverification of the method will be presented. An isolated hole may be considered as a sample inhomogeneity,therefore the method may have potential applications in materialtesting. We have also proposed a six-point method of measurement ofthe geometrical parameter related to the isolated hole. The advantageof the method is that single six-point measurement of theresistivities allows one determination of the van der Pauw resistivityand the dimensionless geometrical parameter. Samples with the theMobius strip topologies will be also considered.