# Work function

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In solid state physics, the work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi level into vacuum). Here "immediately" means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale. The work function is a characteristic property for any solid face[1] of a substance with a conduction band (whether empty or partly filled). For a metal, the Fermi level is inside the conduction band, indicating that the band is partly filled. For an insulator, the Fermi level lies within the band gap, indicating an empty conduction band; in this case, the minimum energy to remove an electron is about the sum of half the band gap and the work function.

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### Photoelectric work function

The work function is the minimum energy that must be given to an electron to liberate it from the surface of a particular substance. In the photoelectric effect, electron excitation is achieved by absorption of a photon. If the photon's energy is greater than the substance's work function, photoelectric emission occurs and the electron is liberated from the surface. (Excess photon energy results in a liberated electron with non-zero kinetic energy.)

The photoelectric work function is

where $h\,$ is Planck's constant and $f_0\,$ is the minimum (threshold) frequency of the photon required to produce photoelectric emission.