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

  • Thread starter Martin Pecha
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In summary: I was wondering if there is a conversion factor between resistance values in cm and ohm?There is no conversion factor - resistance values are in ohm.In summary, Van der Pauw method depends on the size of the sample.
  • #1
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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  • #2
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.
 
  • #3
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
 
  • #4
The shape of the material matters - a different shape will lead to a different result.
 
  • #5
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
 
  • #6
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.
 
  • #7
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.
 
  • #8
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
 
  • #9
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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1. How does the size of the sample affect van der Pauw measurements?

The size of the sample can have a significant impact on van der Pauw measurements. This is because the van der Pauw method relies on the homogeneity of the sample, meaning that the sample needs to have uniform thickness and composition throughout. If the sample is too large, there may be variations in thickness or composition that can affect the accuracy of the measurement. Additionally, larger samples may have more edge effects, which can also influence the measurement.

2. Is there an optimal size for the sample in van der Pauw measurements?

While there is no fixed optimal size for the sample in van der Pauw measurements, it is generally recommended to use a sample with a diameter of at least 2-3 times the distance between the measurement points. This allows for a more accurate measurement and reduces the potential for edge effects. However, the size of the sample should also be chosen based on the capabilities of the measurement equipment and the desired level of precision.

3. Can the size of the sample affect the measured resistivity?

Yes, the size of the sample can affect the measured resistivity in van der Pauw measurements. This is because the resistivity is calculated based on the measured voltage and current, which are influenced by the size and geometry of the sample. In larger samples, the current may be more evenly distributed, leading to more accurate measurements of resistivity.

4. How does the shape of the sample influence van der Pauw measurements?

The shape of the sample can also affect van der Pauw measurements. The method assumes that the sample is circular, so any deviation from this shape can introduce errors in the measurement. Additionally, non-uniform shapes may have different current paths, leading to inaccuracies in the measured resistivity. It is important to carefully choose the shape and size of the sample to ensure accurate van der Pauw measurements.

5. Are there any limitations to using van der Pauw measurements with small samples?

Yes, there are limitations to using van der Pauw measurements with small samples. As the sample size decreases, the accuracy of the measurement also decreases. This is because smaller samples are more susceptible to edge effects and variations in thickness or composition. Additionally, the measurement equipment may not be able to detect small changes in voltage or current, reducing the precision of the measurement.

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