Editing Field electron emission (section)

{{short description|Emission of electrons induced by an electrostatic field}}
{{split|Fowler–Nordheim theory|date=November 2024}}
'''Field electron emission''', also known as '''field-induced electron emission, field emission''' ('''FE''') and '''electron field emission''', is the emission of [[electron]]s from a material placed in an [[electrostatic field]]. The most common context is field emission from a [[solid]] surface into a [[vacuum]]. However, field emission can take place from solid or [[liquid]] surfaces, into a vacuum, a [[fluid]] (e.g. [[air]]), or any [[non-conducting]] or weakly conducting [[dielectric]]. The field-induced promotion of electrons from the [[valence (chemistry)|valence]] to [[conduction band]] of [[semiconductors]] (the [[Zener effect]]) can also be regarded as a form of field emission. 

Field emission in pure metals occurs in high [[electric field]]s: the gradients are typically higher than 1 gigavolt per metre and strongly dependent upon the [[work function]]. While electron sources based on field emission have a number of applications, field emission is most commonly an undesirable primary source of [[electrical breakdown|vacuum breakdown and electrical discharge]] phenomena, which engineers work to prevent. Examples of applications for surface field emission include the construction of bright electron sources for high-resolution [[electron microscope]]s or the discharge of induced charges from [[spacecraft]]. Devices that eliminate induced charges are termed [[charge-neutralizer]]s.

Historically, the phenomenon of field electron emission has been known by a variety of names, including "the aeona effect", "autoelectronic emission", "cold emission", "cold cathode emission", "field emission", "field electron emission" and "electron field emission".  In some contexts (e.g. spacecraft engineering), the name "field emission" is applied to the field-induced emission of ions (field ion emission), rather than electrons, and because in some theoretical contexts "field emission" is used as a general name covering both field electron emission and field ion emission.

Field emission was explained by [[quantum tunneling]] of electrons in the late 1920s. This was one of the triumphs of the nascent [[quantum mechanics]]. The theory of field emission from bulk metals was proposed by [[Ralph H. Fowler]] and [[Lothar Wolfgang Nordheim]].<ref name="Fowler1928">{{cite journal |last=Fowler |first=R.H. |author2=Dr. L. Nordheim |date=1928-05-01 |title=Electron Emission in Intense Electric Fields |url=http://www-project.slac.stanford.edu/lc/wkshp/RFBreakdwn/references/fowler.pdf |journal=[[Proceedings of the Royal Society A]] |volume=119 |issue=781 |pages=173–181 |bibcode=1928RSPSA.119..173F |doi=10.1098/rspa.1928.0091 |access-date=2009-10-26 |doi-access=free}}</ref>  A family of approximate equations, [[#Fowler–Nordheim-type equations|Fowler–Nordheim equations]], is named after them. Strictly, Fowler–Nordheim equations apply only to field emission from bulk metals and (with suitable modification) to other bulk [[crystalline solid]]s, but they are often used – as a rough approximation – to describe field emission from other materials.{{cn|date=March 2025}}

The related phenomena of surface photoeffect, [[thermionic emission]] (or [[Richardson–Dushman effect]]) and "cold electronic emission", i.e. the emission of electrons in strong static (or quasi-static) electric fields, were discovered and studied independently from the 1880s to 1930s. In the modern context, '''cold field electron emission''' (CFE) is the name given to a particular statistical emission regime, in which the electrons in the emitter are initially in internal [[thermodynamic equilibrium]], and in which most emitted electrons escape by Fowler–Nordheim tunneling from electron states close to the emitter [[Fermi level]]. (By contrast, in the [[Thermionic emission|Schottky emission]] regime, most electrons escape over the top of a field-reduced barrier, from states well above the Fermi level.) Many solid and liquid materials can emit electrons in a CFE regime if an electric field of an appropriate size is applied.  When the term ''field emission'' is used without qualifiers, it typically means "cold emission".{{cn|date=March 2025}}  

For metals, the CFE regime extends to well above room temperature. There are other electron emission regimes (such as "[[Thermionic emission|thermal electron emission]]" and "[[Thermionic emission|Schottky emission]]") that require significant external heating of the emitter. There are also emission regimes where the internal electrons are not in thermodynamic equilibrium and the emission current is, partly or completely, determined by the supply of electrons to the emitting region. A non-equilibrium emission process of this kind may be called field (electron) emission if most of the electrons escape by tunneling, but strictly it is not CFE, and is not accurately described by a Fowler–Nordheim-type equation.