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

1. Mar 27, 2017

### Martin Pecha

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.

2. Mar 27, 2017

### Staff: Mentor

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. Mar 27, 2017

### Martin Pecha

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. Mar 27, 2017

### Staff: Mentor

The shape of the material matters - a different shape will lead to a different result.

5. Mar 27, 2017

### lychette

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. Mar 30, 2017

### Martin Pecha

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. Mar 30, 2017

### Staff: Mentor

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. Mar 30, 2017

### lychette

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. Mar 31, 2017

### Martin Pecha

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

Last edited by a moderator: May 8, 2017