Work function

In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e. energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" means that the final electron position is far from the surface on the atomic scale, but still too close to the solid to be influenced by ambient electric fields in the vacuum. The work function is not a characteristic of a bulk material, but rather a property of the surface of the material (depending on crystal face and contamination).

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 E_F is the Fermi level (electrochemical potential of electrons) inside the material. The term −eϕ is the energy of an electron at rest in the vacuum nearby the surface. In words, the work function is thus defined as the thermodynamic work required to remove an electron from the material to a state at rest in the vacuum nearby the surface.

In practice, one directly controls E_F by the voltage applied to the material through electrodes, and the work function is generally a fixed characteristic of the surface material. Consequently, this means that when a voltage is applied to a material, the electrostatic potential ϕ produced in the vacuum will be somewhat lower than the applied voltage, the difference depending on the work function of the material surface. Rearranging the above equation, one has

where V = −E_F/e is the voltage of the material (as measured by a voltmeter, through an attached electrode), relative to an electrical ground that is defined as having zero Fermi level. The fact that ϕ depends on material surface means that the space between two dissimilar conductors will have a built-in electric field, when those conductors are in total equilibrium with each other (electrically shorted to each other, and with equal temperatures). An example of this situation is depicted in the adjacent figure. As described in the next section, these built-in vacuum electric fields can have important consequences in some cases.

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