Modified van der Pauw method based on formulas solvable by the Banach fixed point method

TL;DR

This paper introduces a modified van der Pauw method that employs a new formula, solvable via the Banach fixed point method, enabling efficient and accurate resistivity measurements for arbitrarily shaped thin samples.

Contribution

It presents a novel formula for the van der Pauw method that can be quickly solved using the Banach fixed point method, improving computational efficiency.

Findings

Fast convergence for symmetric configurations

Applicable to arbitrary sample shapes

Enhanced numerical stability

Abstract

We propose a modification of the standard van der Pauw method for determining the resistivity and Hall coefficient of flat thin samples of arbitrary shape. Considering a different choice of resistance measurements we derive a new formula which can be numerically solved (with respect to sheet resistance) by the Banach fixed point method for any values of experimental data. The convergence is especially fast in the case of almost symmetric van der Pauw configurations (e.g., clover shaped samples).