Relationship Between Work Function, Vacuum Electric Potential, and Fermi Level (voltage)
If we remove an electron from a solid, to a state of zero total energy, then the thermodynamic work required is given by -EF, where EF is the Fermi level (electrochemical potential) in that system. The work function is however defined by placing the electron into the vacuum nearby the surface, where there is an electrostatic potential ϕ; at this point, the electron's total energy is not zero but instead Evac=-eϕ. Thus, the work function W is defined by
In other words, it is the sum of the work required to completely remove the electron (-EF), and the work required to place it back just outside the surface (-eϕ).
The work function is in fact a property of the surface material, and EF is fixed by the electrode that is attached to the material. Practically, this means that the material's work function acts to determine the value of ϕ (rather than the other way around). We can define the electrode's internal voltage V as V = -EF/e, giving
In other words, if we use a battery to apply a voltage V to an electrode, then the actual ϕ produced in the vacuum will vary depending on the work function. W depends on what material the electrode is made from. The reason for this dependence of W on material can be attributed to a variety of effects (binding energy, surface dipoles, etc.), discussed below.
Read more about this topic: Critical Absorption Energy
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