Question about electrostatic potential

Question

The work function W for a given surface is defined by the difference, where −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and EF is the Fermi level (electrochemical potential of electrons) inside the material.

Could you please explain what is the electrostatic potential in the vacuum nearby the surface. I don't understand this concept.

Answer 1

What you may be missing is the fact that an electron that is barely liberated from a solid surface and finds itself just immediately outside the surface will not be completely out of the influence of the surface forces.

The electrostatic potential in vacuum nearby the surface represents the amount of energy needed to bring a unit charge from an infinite distance in vacuum to a point barely outside the metal surface

It will still feel electrical influence of the surface. This electrical environment the electron finds itself in is, however, very different from that it finds itself inside a solid surface, where it is bound by several forces due to ions/atoms/electrons within the solid surface. Therefore, it has a different electrostatic potential inside a solid. It is represented by the Fermi Level, since the electron most likely to leave the metal has to be at the top of the energy levels within the solid.

The difference between the electrostatic potential of the electron just inside and outside the surface is called work-function.

Let me know if this is still not clear.