Van der Pauw method on a sample with an isolated hole

TL;DR

This paper extends the van der Pauw method to samples with an isolated hole, presenting explicit results, experimental validation, and proposing an inequality for resistivity measurements that can assess sample quality.

Contribution

It introduces a new inequality related to the van der Pauw method for samples with holes, supported by experimental and numerical analysis.

Findings

The inequality holds for samples with an isolated hole and contacts on the same edge.

Experimental results confirm the validity of the inequality.

Numerical analysis supports the proposed inequality's applicability.

Abstract

Explicit results of the van der Pauw method for a sample containing an isolated hole are presented together with experimental confirmation. Results of measurements and numerical analysis strongly suggest that four probe resistivities obey inequality similar in the form to the famous van der Pauw equation. The inequality seems to be valid for any sample with an isolated hole and contacts located on the same edge, however rigorous proof is not given. The inequality can be used for experimental detection of the sample quality.