JanSpintronics
I have a Question to the Independence of the probe distance for a four-probe-measurement technique. In a paper the author is argument that the resistance of a 2D shape is NOT dependent of the distance between the probe which measure the voltage drop, cause he says that the current spreading, which is injected form the outer 2 probes, is lower the resistance.

So the Point doesn't make sense to me, cause if i have a current which is spreading, i will have a bigger resistance, just because the current will take a larger way cause of this spreading. Am i right what point i don't see?

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I have a Question to the Independence of the probe distance for a four-probe-measurement technique. In a paper the author is argument that the resistance of a 2D shape is NOT dependent of the distance between the probe which measure the voltage drop, cause he says that the current spreading, which is injected form the outer 2 probes, is lower the resistance.

So the Point doesn't make sense to me, cause if i have a current which is spreading, i will have a bigger resistance, just because the current will take a larger way cause of this spreading. Am i right what point i don't see?
Do you understand the fundamental concept of parallel components and how parallel resistance act together?

JanSpintronics
ehm i think so... but i don't see the relation to my Problem. Maybe not if you know it and i don't see it.

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2022 Award
ehm i think so... but i don't see the relation to my Problem. Maybe not if you know it and i don't see it.
Well, perhaps I've misunderstood your question. I'm not familiar w/ four-probe-measurement technique but it sounded to me from your description like it's one probe on the voltage in question and 3 more probes on various places on the ground wire. If that were the case, it would be a clear case of parallel resitive paths (of low resistance). Guess I mis-understand the probe placement.

JanSpintronics
ohhh god! i think i have it thank you sooo much. Because the totally resistance is smaller than the lowest, you will have smaller resistance if you have an additional spreading current, Right?

but just to make sure of that the author really meant this i just want to take a look in this paper:
Surface-sensitive conductance measurements from Hoffmann 2009, where he argues on page 8 that the Formular : $$R_{2D}^{4pp} = \frac{ln(2)}{\sigma \pi}$$ is cause of that Independent of this.
But if so why it is inverse Independent of the 3D resistance?:

$$R_{3D}^{4pp} = \frac{1}{\sigma 2\pi s}$$
where s is that probe distance.

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2022 Award
ohhh god! i think i have it thank you sooo much. Because the totally resistance is smaller than the lowest, you will have smaller resistance if you have an additional spreading current, Right?
Exactly.

JanSpintronics
Well, perhaps I've misunderstood your question. I'm not familiar w/ four-probe-measurement technique but it sounded to me from your description like it's one probe on the voltage in question and 3 more probes on various places on the ground wire. If that were the case, it would be a clear case of parallel resitive paths (of low resistance). Guess I mis-understand the probe placement.
mhmmm but it still not that what i meant...close but not the same...is it still the Right Explanation? And can you argue for the same with the 3D resistance, but here we have the Argumentation that you have an additional circuit in the bulk (because in the paper the author says in the 3D case, if you making the distance greater, you cannot compensate it with the current spread )?

It will kinda make sense cause in the 3D case you have more circuits as in the 2D case.

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JanSpintronics
The expressions for the resistances in case of four-point probe measurements can be exactly derived for homogeneous 3-dimensional semi-infinite bulk and infinite 2-dimensional systems. Maybe, the following might be of help:
(PDF) The 100th anniversary of the four-point probe technique ...
Yes that's the paper i read first and than i come to the one which i quote here :D the Problem is it doesn't help because it refers to the one i quote :( . Ist just the same just a bit shorter. i totally understand the Maths behind it (i think so), but not the Physics which he is complaining :(

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You have to think in terms of the electric potential distribution around a point-like or dipole-like current source in an infinite conducting sheet. The potential distribution is uniquely related to the injected current and the material's resistivity. Maybe, the following article in the "THE BELL SYSTEM TECHNICAL JOURNAL" might be of help: "Measurement of Sheet Resistivities with the Four-Point Probe" by F. M. SMITS
[PDF]THE BELL SYSTEM TECHNICAL JOURNAL volume xxxvxx ...

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