Editing Thermionic emission (section)

== Schottky emission ==
{{Main|Schottky effect}}
[[File:Schottky-Emitter 01.jpg|thumb|Schottky-emitter electron source of an [[electron microscope]]]]

In electron emission devices, especially [[electron gun]]s, the thermionic electron emitter will be biased negative relative to its surroundings. This creates an electric field of magnitude ''E'' at the emitter surface. Without the field, the surface barrier seen by an escaping Fermi-level electron has height ''W'' equal to the local work-function. The electric field lowers the surface barrier by an amount Δ''W'', and increases the emission current. This is known as the ''Schottky effect'' (named for [[Walter H. Schottky]]) or field enhanced thermionic emission. It can be modeled by a simple modification of the Richardson equation, by replacing ''W'' by (''W''&nbsp;−&nbsp;Δ''W''). This gives the equation<ref>{{ cite journal | last1 = Kiziroglou |first1 = M. E. | last2 = Li |first2 = X. | last3 = Zhukov |first3 = A. A. | last4 = De Groot |first4 = P. A. J. | last5 = De Groot |first5 = C. H. | year = 2008 | title = Thermionic field emission at electrodeposited Ni-Si Schottky barriers | journal = [[Solid-State Electronics]] | volume = 52 |issue = 7 |pages = 1032–1038 | bibcode = 2008SSEle..52.1032K | doi = 10.1016/j.sse.2008.03.002
|url = https://eprints.soton.ac.uk/143941/1/Thermionic_field_emission_at_electrodeposited_Ni%25E2%2580%2593Si_Schottky_barriers.pdf }}</ref><ref name=Orloff>{{ cite book | last1 = Orloff | first1 = J. | year = 2008 | chapter = Schottky emission | chapter-url = https://books.google.com/books?id=y0FF19lud5YC&pg=PA6 | title = Handbook of Charged Particle Optics | pages = 5–6 | edition = 2nd | publisher = [[CRC Press]] | isbn = 978-1-4200-4554-3 | url-status = live | archive-url = https://web.archive.org/web/20170117111100/https://books.google.it/books?id=y0FF19lud5YC&pg=PA6&lpg=PA6&dq= | archive-date = 2017-01-17 }}</ref>
: <math>J (E,T,W) = A_{\mathrm{G}} T^2 e^{ - (W - \Delta W) \over k T}</math>
: <math>\Delta W = \sqrt{{q_\text{e}}^3 E \over 4\pi \epsilon_0},</math>
where ''ε''<sub>0</sub> is the electric constant (also called the [[vacuum permittivity]]).

Electron emission that takes place in the field-and-temperature-regime where this modified equation applies is often called [[Schottky emission]]. This equation is relatively accurate for electric field strengths lower than about {{val|e=8|u=V⋅m<sup>−1</sup>}}. For electric field strengths higher than {{val|e=8|u=V⋅m<sup>−1</sup>}}, so-called [[field electron emission|Fowler–Nordheim (FN) tunneling]] begins to contribute significant emission current. In this regime, the combined effects of field-enhanced thermionic and field emission can be modeled by the Murphy-Good equation for thermo-field (T-F) emission.<ref>{{ cite journal | last1 = Murphy |first1 = E. L. | last2 = Good |first2 = G. H. | year = 1956 | title = Thermionic Emission, Field Emission, and the Transition Region | journal = [[Physical Review]] | volume = 102 |issue = 6 |pages = 1464–1473 | bibcode = 1956PhRv..102.1464M | doi = 10.1103/PhysRev.102.1464 }}</ref> At even higher fields, FN tunneling becomes the dominant electron emission mechanism, and the emitter operates in the so-called [[field electron emission|"cold field electron emission (CFE)"]] regime.

Thermionic emission can also be enhanced by interaction with other forms of excitation such as light.<ref>{{ cite journal | last1 = Mal'Shukov |first1 = A. G. | last2 = Chao |first2 = K. A. | year = 2001 | title = Opto-Thermionic Refrigeration in Semiconductor Heterostructures | journal = [[Physical Review Letters]] | volume = 86 |issue = 24|pages = 5570–5573 | bibcode = 2001PhRvL..86.5570M | doi = 10.1103/PhysRevLett.86.5570 |pmid = 11415303 }}</ref> For example, excited [[Cesium]] (Cs) vapors in thermionic converters form clusters of Cs-[[Rydberg matter]] which yield a decrease of collector emitting work function from 1.5&nbsp;eV to 1.0–0.7&nbsp;eV. Due to long-lived nature of [[Rydberg matter]] this low work function remains low which essentially increases the low-temperature converter's efficiency.<ref>{{ cite journal | last1 = Svensson |first1 = R. | last2 = Holmlid |first2 = L. | year = 1992 | title = Very low work function surfaces from condensed excited states: Rydber matter of cesium | journal = [[Surface Science (journal)|Surface Science]] | volume = 269/270 |pages = 695–699 | bibcode = 1992SurSc.269..695S | doi = 10.1016/0039-6028(92)91335-9 }}</ref>