Energy band diagram of a polar material

Question

For a single piece of a polar material (ex. GaN, AlN, etc), there exists a constant electric field inside the material due to the bound charges at the surface.

Above figure shows the resulting band diagram with a flat fermi level since there will be no current flow assuming the material is floating.

According to the fermi-Dirac distribution, the closer the fermi level is to the conduction band, the electron concentration is higher. So my question is, the band diagram above seems to suggest that the electron concentration increases as we go from left to right, but how could this be true if there is no current flow? Wouldn't a gradient in electron concentration leads to a diffusion current? But there can't be any current flow since the gradient in electron concentration came from the assumption that there is no current flow (flat fermi level)...

Answer 1

Assuming that diagram is true.

It may happen the very same phenomenon that happens at the PN junction after doping Silicon with donors and acceptors.

That is, a built-in static electric field does exist, but as soon as you close the loop with a wire that electric field vanishes and the system enters a new equilibrium state where no net conduction current density Ĵ(x,y,z,t) exists.