Editing Work function (section)

== Definition ==

The work function {{math|''W''}} for a given surface is defined by the difference<ref name="Kittel">{{cite book |title=[[Introduction to Solid State Physics]] |edition=7th |last1=Kittel |first1=Charles |author-link1=Charles Kittel |date= 1996 |publisher=Wiley }}</ref>
:<math>W = -e\phi - E_{\rm F}, </math>
where {{math|−''e''}} is the charge of an [[electron]], {{math|''ϕ''}} is the [[electrostatic potential]] in the vacuum nearby the surface, and {{math|''E''<sub>F</sub>}} is the [[Fermi level]] ([[electrochemical potential]] of electrons) inside the material. The term {{math|−''eϕ''}} is the energy of an electron at rest in the vacuum nearby the surface.

[[File:Work function mismatch gold aluminum.svg|thumb|300 px|Plot of electron energy levels against position, in a gold-vacuum-aluminium system. The two metals depicted here are in complete thermodynamic equilibrium. However, the vacuum [[electrostatic potential]] {{math|''ϕ''}} is not flat due to a difference in work function.]]

In practice, one directly controls {{math|''E''<sub>F</sub>}} 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 {{math|''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
:<math>\phi = V - \frac{W}{e}</math>
where {{math|''V'' {{=}} −''E''<sub>F</sub> / ''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 {{math|''ϕ''}} depends on the 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).

The work function refers to removal of an electron to a position that is far enough from the surface (many nm) that the force between the electron and its [[Method of image charges|image charge]] in the surface can be neglected.<ref name="Kittel" /> The electron must also be close to the surface compared to the nearest edge of a crystal facet, or to any other change in the surface structure, such as a change in the material composition, surface coating or reconstruction. The built-in electric field that results from these structures, and any other ambient electric field present in the vacuum are excluded in defining the work function.<ref name="Gersten 2001">{{cite book | last=Gersten | first=Joel | title=The physics and chemistry of materials | publisher=Wiley | publication-place=New York | year=2001 | isbn=978-0-471-05794-9 | oclc=46538642}}</ref>