Van der Pauw method for sheet resistance measurement

[Dario56]

In the Van der Pauw method, two resistances are measured in orthogonal directions to each other. These are used to calculate sheet resistance from the Van der Pauw equation. Why is it that resistances are measured specifically in mutually orthogonal directions? I tried finding an answer in different papers, online sources and by looking at the derivation of the van der Pauw equation. I didn't really find the answer.

 

[Baluncore]

Why is it that resistances are measured specifically in mutually orthogonal directions?

Because a magnitude, in any direction, can be expressed as the sum of two orthogonal magnitude components, aligned with the sides of the four electrode square.

In effect, it is doing a polar to rectangular conversion.

 

[Dario56]

Because a magnitude, in any direction, can be expressed as the sum of two orthogonal magnitude components, aligned with the sides of the four electrode square.

In effect, it is doing a polar to rectangular conversion.

Hmm, well resistivity isn't a vector, so that the values of resistivity in both directions are equal to the vector components in both directions

 

[Baluncore]

How do you select the alignment of the electrode square on the sample?

 

[Dullard]

If I understand your question:

Describing the method as '2 resistances' is accurate, but (maybe) misleadingly over-simple. 4 'contact' points are used for each 'measurement;' the arrangement of the sense and excitation pairs is what is actually 'orthogonal' for the '2 resistances.' The measured values are influenced by all of the material between all 4 of the probes for any measurement.

 

[Baluncore]

If I understand your question:

My question is much simpler than you imagine.
I understand the field pattern and the two orthogonal measurements on the sample. If the sample was anisotropic, the orthogonal measurements might give different numbers.

A sample is placed on the stage and some orthogonal measurements are taken. What strategy was used by the experimenter, to decide the orientation of the four electrode square on the sample? Is the electrode square randomly oriented, or is some rational strategy employed to orient the square?

Imagine the worst anisotropic case, where a resistive material was covered by many thin parallel lines of excellent conductor.

If the sample-electrode-square edge was parallel to the conductive lines, one resistivity measured would be zero, while the other would be closer to the underlying resistive material. The experimenter would know that the material was anisotropic.

If the sample-electrode square diagonal was parallel to the lines, the two orthogonal measurements would be the same, so the experimenter might believe that the sample was isotropic.

 

[Dullard]

Sorry - was replying to OP.

 

[Dullard]

@Baluncore:

This technique is valid only for thin, isotropic materials (for the reasons that you note).