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I’ve a got a question; and I am hopeful that you can provide any information or direct me to a better resource. I'm not a physicist; so please correct me if I'm wrong.

Scanning Probe Microscopy (SPM) can be used to probe and map the surface of electrical potential distribution. For example, let’s say that a Scanning Kelvin probe microscopy (SKPM) was used in some experiment to provide quantitative values of surface potential by determining the potential difference between the conductive probe tip and the sample surface (say NW assemblies).

I was wondering whether there is any physical formula to model/describe the behavior of the electrical potential distribution at nano/atomic scale.

Also, do you think Maxwell's equations holds?

I appreciate any input.

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I came across this paper… Do you guys think it's related to my question? – user9292 Jul 19 '13 at 19:36

I am by no means an expert on this subject, but the following might be helpful.

The properties sampled and imaged using the various forms of scanning probe microscopy (SPM) are related to electronic structure. Electronic structure calculations rely on a quantummechanical treatment of the electronic degrees of freedom (the dynamics of the electrons in materials) and are computationally extremely demanding. These calculations are often done using the various forms of density functional theory (DFT).

The combination of SPM (Binnig and Rohrer, 1986 Nobel Prize in Physics) and DFT (Kohn, 1998 Nobel Prize in Chemistry) constitutes an active area of research.

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