Location of electrons (not excess charge) in a conductor [static case]

[Kostik]

In a conductor, excess charge resides on the surface. That seems odd, because one would think that the overall energy of the system could be lowered by allowing some of the excess charge to move inward and away from all the charge on the surface, but obviously that can't be true, because charge inside the conductor would create a field that causes other charges to move. (I suppose a single excess point charge could disengage from the surface and take up residence inside the conductor, but only one!)

My question concerns the free electrons that belong to the atoms in the conducting material. Suppose there is no excess charge in the conductor: just a solid block of copper. Are the free electrons distributed uniformly throughout the material? Every copper atom looks neutral to an electron located far away from it, so I suppose there are no forces present that would act on the free electrons, other than the coloumb force of the nucleus to which it is nominally attached.

 

[anuttarasammyak]

Hi.

Summary:: Suppose there is no excess charge in a conductor, i.e., consider a solid block of copper. Are the free electrons distributed uniformly throughout the material?

In bulk yes but on surface band structure changes and it would cause surface states of free electrons in general.

ref. WIKI surface states https://en.wikipedia.org/wiki/Surface_states

 

[Lord Jestocost]

Summary:: Suppose there is no excess charge in a conductor, i.e., consider a solid block of copper. Are the free electrons distributed uniformly throughout the material?

Theories of metal surfaces have to consider the rapid decrease of the electron density near the surface and the loss of translational symmetry. In the framework of the jellium model of metal surfaces, the electron distribution does not follow the sharp edge of the positive background but rather exhibits a damped oscillatory structure inside the jellium, the so-called Friedel oscillations. Have a look at Fig. 4 in the paper "Theory of Metal Surfaces: Charge Density and Surface Energy" by N. D. Lang and W. Kohn, Phys. Rev. B 1, 4555, 1970:

Theory of Metal Surfaces: Charge Density and Surface Energy