Editing Work function (section)

=== Doping and electric field effect (semiconductors) ===
[[File:Semiconductor vacuum junction.svg|thumb|[[Band diagram]] of semiconductor-vacuum interface showing [[electron affinity]] ''E''<sub>EA</sub>, defined as the difference between near-surface vacuum energy ''E''<sub>vac</sub>, and near-surface [[conduction band]] edge ''E''<sub>C</sub>. Also shown: [[Fermi level]] ''E''<sub>F</sub>, [[valence band]] edge ''E''<sub>V</sub>, work function ''W''.]]

In a [[semiconductor]], the work function is sensitive to the [[doping (semiconductor)|doping level]] at the surface of the semiconductor. Since the doping near the surface can also be [[field effect (semiconductor)|controlled by electric fields]], the work function of a semiconductor is also sensitive to the electric field in the vacuum.

The reason for the dependence is that, typically, the vacuum level and the conduction band edge retain a fixed spacing independent of doping. This spacing is called the [[electron affinity]] (note that this has a different meaning than the electron affinity of chemistry); in silicon for example the electron affinity is 4.05 eV.<ref>{{cite web|url=http://www.virginiasemi.com/pdf/generalpropertiessi62002.pdf|title=The General Properties of Si, Ge, SiGe, SiO2 and Si3N4 |author=Virginia Semiconductor|date=June 2002|access-date=6 Jan 2019}}</ref> If the electron affinity ''E''<sub>EA</sub> and the surface's band-referenced Fermi level ''E''<sub>F</sub>-''E''<sub>C</sub> are known, then the work function is given by
:<math> W = E_{\rm EA} + E_{\rm C} - E_{\rm F}</math>
where ''E''<sub>C</sub> is taken at the surface.

From this one might expect that by doping the bulk of the semiconductor, the work function can be tuned. In reality, however, the energies of the bands near the surface are often pinned to the Fermi level, due to the influence of [[surface state]]s.<ref>{{cite web|url=http://academic.brooklyn.cuny.edu/physics/tung/Schottky/surface.htm|title=Semiconductor Free Surfaces|website=academic.brooklyn.cuny.edu|access-date=11 April 2018}}</ref> If there is a large density of surface states, then the work function of the semiconductor will show a very weak dependence on doping or electric field.<ref>{{Cite journal | last1 = Bardeen | first1 = J. | title = Surface States and Rectification at a Metal Semi-Conductor Contact | doi = 10.1103/PhysRev.71.717 | journal = Physical Review | volume = 71 | issue = 10 | pages = 717–727 | year = 1947 |bibcode = 1947PhRv...71..717B }}</ref>