Talk:Van der Pauw method

Removal Of Cleanup Tag
Cleanup tag removed as I believe I have sufficiently cleaned this page up. It still requires some additions (which I plan to do in the next few days) but it is now in a 'clean' state. Blair - Speak to me 05:32, 25 June 2006 (UTC)

Hall measurements complete
The Hall measurements section is at least complete now, though I have plans for further improvement. Blair - Speak to me 04:44, 7 October 2006 (UTC)

I don't think that this "overall Hall voltage" thing makes sense. You average over incompatible quantities. The only thing that can be averaged is the change of the van der Pauw resistance due to the switch of $$B$$, usually abbreviated $$\Delta R_{13,24}$$ etc. – Torsten Bronger 12:45, 18 January 2007 (UTC)

Iterative solver
I don't think that this iterative solver works. At least for my values of R it didn't. Apparently, it uses the Banach fixed point theorem and its preconditions are not fulfilled. I recommend to recommend nested intervals for solving the equation. – Torsten Bronger 11:49, 26 January 2007 (UTC)

Some comments
"The Van der Pauw Method is a commonly used technique, based around the Hall effect" should be changed to "The Van der Pauw Method is a commonly used technique, used to measure resistivity and Hall coefficient".,,,

Van der Pauw's original paper says "sheet resistivity and Hall Effect" throughout the paper, so clearly, Van der Pauw thought that the two things were separable. Moreover, the second part of the sentence states "be successfully completed with a current source and a voltmeter," but the Hall coefficient measurement requires an external magnetic field to induce the Hall Effect in the sample.

The second paragraph seems to be missing a bullet which therefore states "Hall coefficient of the material," since that's the second part of Van der Pauw's paper as well as the second part of the Wikipedia article.

I would suggest "presented" instead of "propounded" since Van der Pauw uses "presented" in his summary. —Preceding unsigned comment added by IRStuff (talk • contribs) 17:50, 23 November 2007 (UTC)

Iterative solution
It's unclear that an iterative solution is required. Van der Pauw gives an equation for which f is a solution based on Rab,cd and Rbc,da. This would seem to be an easy target for an Excel-based or Mathcad solver.

I would suggest just putting equations 11 and 12 from Van der Pauw's article into the Wikipedia article and let the reader deal with finding a numerical solution for f. —Preceding unsigned comment added by IRStuff (talk • contribs) 18:33, 23 November 2007 (UTC)

Arbitrary shape - Contradiction?
The introduction says the method allows one to "accurately measure the properties of a sample of any arbitrary shape" (emphasis mine), but then in the article itself it turns out there are actually a lot of restrictions on the shape of the sample: it must "have a flat shape of uniform thickness", must not "have any isolated holes" and should ideally have the cloverleaf form shown in the picture. How can this be reconciled with the claim that it is good for arbitrary shapes? --188.99.236.164 (talk) 20:41, 3 April 2016 (UTC)

Conditions & Sample preparation
Is there not substantial overlap between these two sections? Could they not be usefully combined? Moletrouser (talk) 09:14, 5 December 2019 (UTC)

modification of the "Van der Pauw Method"
I propose, that in the article "Van der Pauw method", after the title there should be precise description of the concept of method formulated originally by Leo J. van der Pauw in 1958. His papers should appear as the first references. The van der Pauw method was formulated precisely for two dimensional, homogeneous, isotropic samples having no isolated holes (topologically equivalent to disk) and four point contacts located at four different arbitrary located points at sample perimeter. Mathematical proof of the method was given in:

van der Pauw, L.J. (1958). "A method of measuring specific resistivity and Hall effect of discs of arbitrary shape" (PDF). Philips Research Reports. 13: 1–9. van der Pauw, L.J. (1958). "A method of measuring the resistivity and Hall coefficient on lamellae of arbitrary shape" (PDF). Philips Technical Review. 20: 220–224.

The original idea is not described in the article "Van der Pauw method" and I propose the description based on the original van der Pauw paper:

Consider a two dimensional, singly connected (the sample does not have isolated holes), homogeneous, isotropic sample of arbitrary shape with successive contacts a, b, c, and d fixed on arbitrary places along the circumference (see Fig). We define the resistance Rabcd as the ratio of the potential difference Vd-Vc between the contacts d and c,  and the current through the contacts a and b. The current enters the sample through the contact a and leave it through the contact b. Similarly we define the resistance Rbcda. The relation holds:

exp(-Pi*Rabcd*rho)+exp(-Pi*Rbcda*rho)=1,

where rho is so called sheet resistance, i.e ratio of the specific resistance to sample thickness.

It is important to stress that the cited equation is the essence of the idea of the Van der Pauw method. As usually in science, experimental realisation require some careful procedures, as desribed in the article starting from "Contents".

I Propose to shift "This difference becomes important for anisotropic materials, which can be properly measured using the Montgomery Method, an extension of the van der Pauw Method." to the new section "Extensions of the van der Pauw method" citation: H. C. Montgomery, Method for Measuring Electrical Resistivity of Anisotropic Materials, Journal of Applied Physics 42, 2971 (1971); doi: 10.1063/1.1660656

Other extentions or analogous methods are given below

application to heat transfer phenomena:

O. Paul; P. Ruther; L. Plattner; H. Baltes, A thermal van der Pauw test structure, IEEE Transactions on Semiconductor Manufacturing ( Volume: 13, Issue: 2, May 2000), DOI: 10.1109/66.843631

Johannes de Boor, Volker Schmidt, Complete Characterization of Thermoelectric Materials by a Combined van der Pauw Approach (2010) Adv. Mater. 22, 4303, doi.org/10.1002/adma.201001654

application to samples with holes:

K. Szymański, J.L. Cieśliński and K. Łapiński, Van der Pauw method on a sample with an isolated hole (2013) Phys. Lett. A 377, 651, 	10.1016/j.physleta.2013.01.008

K Szymański, K Łapiński and J L Cieśliński, Determination of the Riemann modulus and sheet resistance of a sample with a hole by the van der Pauw method, Measurement Science and Technology, (2015) Volume 26, Number 5

Quite recently extension of van der Pauw method, a method of measuring sheet resistance of infinite sample or sample with topology of sphere, with five point contacts located at arbitrary positions was presented:

Krzysztof R. Szymański, Piotr A. Zaleski, Determination of the sheet resistance of an infinite thin plate with five point contacts located at arbitrary positions, Measurement 169 (2021) 108360, 9 pp

Krzysztof R. Szymański, Mirosław Kondratiuk, Extensions of four-point methods with arbitrarily located contacts for determination of physical quantities and sheet resistance imaging, Measurement, 178 (2021) 109426

212.33.71.158 (talk) 12:50, 24 January 2022 (UTC)
 * Hi I see no concerns with the edits above presented (suggest the spelling of "extentions" be corrected however) and you are approved to make those changes. For references, please use cite journal for your citations. Best,  Spencer T• C 22:47, 27 January 2022 (UTC)
 * Hi, I am ready edit the changes, however I am affraid, that some mistakes may appear during my editing. Is it a way to edit it not for publicity, and after checking make it public? I have no experience with the Wikiedia.
 * Regards 109.231.50.111 (talk) 22:00, 15 March 2022 (UTC)