Free Electron Gas Model
In the free electron model the valence electrons roam freely (zero force) inside the metal but find a confining potential step at the boundary of the metal. In the system's ground state, states with energy less than the Fermi Level are occupied, and states above the Fermi Level are not occupied. The energy required to liberate an electron in the Fermi Level is the work function. If, as in the diagram right, we define the Fermi Energy from the bottom of the well, the results reported in the Wiki page Fermi energy are applicable. However, usually the Fermi energy is referenced to energy zero: that of the lowest energy electron free of the metal. In that case the Fermi energy would have a negative value (i.e., the Fermi Level lies below those of escaped electrons) (but see below).
Read more about this topic: Work Function
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