Editing Electron affinity (section)

== "Electron affinity" as defined in solid state physics ==

[[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 the field of [[solid state physics]], the electron affinity is defined differently than in chemistry and atomic physics. For a semiconductor-vacuum interface (that is, the surface of a semiconductor), electron affinity, typically denoted by ''E''<sub>EA</sub> or ''χ'', is defined as the energy obtained by moving an electron from the vacuum just outside the semiconductor to the bottom of the [[conduction band]] just inside the semiconductor:<ref>{{cite web|first = Raymond T. |last =  Tung | url=http://academic.brooklyn.cuny.edu/physics/tung/Schottky/surface.htm|title=Free Surfaces of Semiconductors|work= Brooklyn College}}</ref>
:<math>E_{\rm ea} \equiv E_{\rm vac} - E_{\rm C}</math>
In an intrinsic semiconductor at [[absolute zero]], this concept is functionally analogous to the chemistry definition of electron affinity, since an added electron will spontaneously go to the bottom of the conduction band. At nonzero temperature, and for other materials (metals, semimetals, heavily doped semiconductors), the analogy does not hold since an added electron will instead go to the Fermi level on average. In any case, the value of the electron affinity of a solid substance is very different from the chemistry and atomic physics electron affinity value for an atom of the same substance in gas phase. For example, a silicon crystal surface has electron affinity 4.05&nbsp;eV, whereas an isolated silicon atom has electron affinity 1.39&nbsp;eV.

The electron affinity of a surface is closely related to, but distinct from, its [[work function]]. The work function is the [[thermodynamic work]] that can be obtained by reversibly and isothermally removing an electron from the material to vacuum; this thermodynamic electron goes to the ''[[Fermi level]]'' on average, not the conduction band edge: <math> W = E_{\rm vac} - E_{\rm F}</math>. While the work function of a semiconductor can be changed by [[doping (semiconductor)|doping]], the electron affinity ideally does not change with doping and so it is closer to being a material constant. However, like work function the electron affinity does depend on the surface termination (crystal face, surface chemistry, etc.) and is strictly a surface property.

In semiconductor physics, the primary use of the electron affinity is not actually in the analysis of semiconductor–vacuum surfaces, but rather in heuristic [[electron affinity rule]]s for estimating the [[band bending]] that occurs at the interface of two materials, in particular [[metal–semiconductor junction]]s and semiconductor [[heterojunction]]s.

In certain circumstances, the electron affinity may become negative.<ref>{{Cite journal | last1 = Himpsel | first1 = F. | last2 = Knapp | first2 = J. | last3 = Vanvechten | first3 = J. | last4 = Eastman | first4 = D. | title = Quantum photoyield of diamond(111)—A stable negative-affinity emitter | doi = 10.1103/PhysRevB.20.624 | journal = Physical Review B | volume = 20 | issue = 2 | pages = 624 | year = 1979 |bibcode = 1979PhRvB..20..624H }}</ref> Often negative electron affinity is desired to obtain efficient [[cathode]]s that can supply electrons to the vacuum with little energy loss. The observed electron yield as a function of various parameters such as bias voltage or illumination conditions can be used to describe these structures with [[band diagram]]s in which the electron affinity is one parameter. For one illustration of the apparent effect of surface termination on electron emission, see Figure 3 in [[Marchywka Effect]].