Van der Pauw method for sheet resistance measurement

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Discussion Overview

The discussion centers on the Van der Pauw method for measuring sheet resistance, specifically exploring the rationale behind measuring resistances in mutually orthogonal directions. Participants delve into the implications of this measurement strategy, particularly in relation to isotropic and anisotropic materials.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why resistances are measured in orthogonal directions, indicating a lack of clarity in existing literature.
  • Another participant suggests that measuring in orthogonal directions allows for a conversion from polar to rectangular coordinates, implying a mathematical basis for this approach.
  • A different viewpoint is raised regarding the nature of resistivity, noting that it is not a vector and questioning the equivalence of resistivity values in both directions.
  • Concerns are expressed about the selection of electrode square alignment on the sample, particularly in relation to anisotropic materials.
  • One participant emphasizes that the method involves four contact points for each measurement, suggesting that the arrangement of sense and excitation pairs is critical to understanding the measurements.
  • Another participant elaborates on the implications of anisotropic materials, discussing how the orientation of the electrode square could affect the interpretation of measurements.
  • A later reply asserts that the technique is valid only for thin, isotropic materials, aligning with earlier concerns about the method's limitations.

Areas of Agreement / Disagreement

Participants express differing views on the implications of orthogonal measurements, particularly regarding isotropy and anisotropy of materials. There is no consensus on the best practices for electrode square orientation or the interpretation of results in anisotropic cases.

Contextual Notes

Participants highlight limitations related to the assumptions of isotropy in the Van der Pauw method, as well as the potential influence of sample geometry on measurement outcomes.

Dario56
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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.
 
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Dario56 said:
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.
 
Baluncore said:
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
 
How do you select the alignment of the electrode square on the sample?
 
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.
 
Dullard said:
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.
 
Sorry - was replying to OP.
 
@Baluncore:

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

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