How van der Pauw measurement is influenced by the size of the sample

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The Van der Pauw method allows for resistance measurement in uniform two-dimensional materials, where scaling the sample size should not affect resistance values if the ratio of distances between voltage and current probes is maintained. However, the shape of the specimen does influence results, particularly if the specimen is thin and probes are near the edges. For rectangular samples, a conversion factor is necessary, which can be calculated through simulations if the sample is not homogeneous. Recommendations for measuring low-resistance rectangular samples include using simulations to account for inhomogeneities. Relevant literature and resources for further reading on the Van der Pauw method are also provided.
Martin Pecha
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Dear all,

I am trying to use Van der Pauw method to measure some samples, however I cannot get where in calculations van der Pauw method includes size of the sample. F.e. if I have circle with diameter of 2 cm or 5 cm there must be a difference right? Can anyone explain to me why or why not depends van der Pauw on the size of sample?
Thank you so much.
 
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For a completely uniform two-dimensional material, scaling everything to a different size should not change the resistance values. You double the length (doubling the resistance) but also the width (halving the resistance), both effects cancel.
 
So basicaly I should keep the ratio of distances between voltage probes and current ones when I scale up samples? Or it does not depend on it either
 
The shape of the material matters - a different shape will lead to a different result.
 
If the specimen is thin and the probes are close to the edge of the specimen then the size and shape of the specimen are not important.
The technique is common for determining properties of thin semiconductor specimens
 
can I characterize a rectangular shape sample by Van der Pauw method? Is there any equation for that?

Could you please recommend me any technique to measure lowresistance (100 mohm) rectangular sample which cannot be homogenous and has 2 mm thickness?

Or any literature for that. I woul appreciate that a lot.
 
Martin Pecha said:
can I characterize a rectangular shape sample by Van der Pauw method? Is there any equation for that?
If the rectangle is not a square, you'll need some conversion factor which can be calculated, probably via simulations.

If your sample is not homogeneous but you know the deviations, you can simulate that as well. If you don't know how inhomogeneous the sample is, there is nothing you can do.
 
there are some great references (in pdf) at www.utdallas.edu>LabManuals>3

and detailed analysis of Van der Pauw derivation at www.calvin.udu>MichMAA-2015
 
lychette said:
there are some great references (in pdf) at www.utdallas.edu>LabManuals>3

and detailed analysis of Van der Pauw derivation at http://www.calvin.udu >MichMAA-2015

Thanks, the second one I know and it is great.
 
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