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

TL;DR

This paper extends the van der Pauw method to samples with holes, enabling determination of resistivity and the Riemann modulus, which characterizes the hole's geometry, through resistance measurements and conformal invariance.

Contribution

It introduces a novel approach to measure the Riemann modulus and sheet resistance in samples with holes using resistance correlations, validated experimentally.

Findings

Successful determination of the Riemann modulus and sheet resistance

Experimental verification confirms the method's accuracy

The Riemann modulus remains invariant under conformal mappings

Abstract

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.