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

TL;DR

This paper introduces a six-point generalization of the van der Pauw method to determine the sheet resistivity and Riemann modulus of 2D systems with a hole, enabling inhomogeneity assessment.

Contribution

It presents a novel measurement technique that allows for the determination of resistivity and hole-related parameters from a single arbitrary contact measurement.

Findings

Accurately determines sheet resistivity and Riemann modulus.

Applicable to samples with isolated holes and inhomogeneities.

Invariant under conformal mappings.

Abstract

Six point generalization of the van der Pauw method is presented. The method is applicable for two dimensional homogeneous systems with an isolated hole. A single measurement performed on the contacts located arbitrarily on the sample edge allows 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 experimental determination of the sample inhomogeneity.