Editing Field electron emission (section)

== Early history of field electron emission ==
In retrospect, it seems likely that the electrical discharges reported by J.H. Winkler<ref name="Winkler1744">{{Cite book|title = Gedanken von den Eigenschaften, Wirkungen und Ursachen der Electricität nebst Beschreibung zweiner electrischer Maschinen|year = 1744|author = Winkler, J.H.|publisher = Book Chapter Breitkopf|location = Leipzig}}</ref> in 1744 were started by CFE from his wire electrode. However, meaningful investigations had to wait until after [[J.J. Thomson]]'s<ref name="Thomson1897">{{cite journal|title=Cathode Rays|date = October 1897|last = Thomson|first = J.J.|author-link=J. J. Thomson|journal = Phil. Mag.|pages = 293–316|volume = 44|issue = 269|series = 5th series|doi = 10.1080/14786449708621070|url = https://zenodo.org/records/1431235/files/article.pdf}}</ref> identification of the electron in 1897, and until after it was understood – from [[thermionic emission|thermal emission]]<ref name="Richardson1916">{{Cite book|title = The Emission of Electricity from Hot Bodies|year = 1916|last = Richardson|first = O.W.|publisher =Longmans|location = London}}</ref> and [[photoemission|photo-emission]]<ref name="Einstein1905">{{cite journal|title = On a heuristic point of view about the creation and conversion of light|year = 1905|last = Einstein|first = A.|journal = Ann. Phys. Chem.|pages = 132–148|volume = 17|issue = 6|bibcode = 1905AnP...322..132E |doi = 10.1002/andp.19053220607 |doi-access = free}}</ref> work – that electrons could be emitted from inside metals (rather than from [[adsorption|surface-adsorbed gas molecules]]), and that – in the absence of applied fields – electrons escaping from metals had to overcome a [[work function]] barrier.

It was suspected at least as early as 1913 that field-induced emission was a separate physical effect.<ref name="Richardson">{{cite journal |title=Thermionic phenomena and the laws which govern them |url=https://www.nobelprize.org/physics/laureates/1928/richardson-lecture.pdf |last1=Richardson |first1=O.W. |journal=Nobel Lectures, Physics 1922-1941 |year=1929 |access-date=2009-10-25}}</ref> However, only after vacuum and specimen cleaning techniques had significantly improved, did this become well established. [[Julius Edgar Lilienfeld|Lilienfeld]] (who was primarily interested in electron sources for medical [[X-ray]] applications) published in 1922<ref name="Lilienfeld1922">{{cite journal|year = 1922|last = Lilienfeld|first = J. E.|journal = Am. J. Roentgenol.|page = 192|volume = 9
}}</ref> the first clear account in English of the experimental phenomenology of the effect he had called "autoelectronic emission". He had worked on this topic, in Leipzig, since about 1910.<ref name="Kleint1993">{{cite journal|title = On the early history of field emission including attempts of tunneling spectroscopy|year = 1993|author = Kleint, C.|journal = Progress in Surface Science|pages = 101–115|volume = 42|issue = 1–4|doi=10.1016/0079-6816(93)90064-3|bibcode = 1993PrSS...42..101K }}</ref><ref name="Kleint2004">{{cite journal|title = Comments and references relating to early work in field electron emission|year = 2004|author = Kleint, C.|journal = Surface and Interface Analysis|pages = 387–390|volume = 36|issue = 56|doi=10.1002/sia.1894| s2cid=95452585 }}</ref>

After 1922, experimental interest increased, particularly in the groups led by [[Robert Andrews Millikan|Millikan]] at the California Institute of Technology (Caltech) in [[Pasadena, California]],<ref name="Millikan1926">{{cite journal |title=Laws governing the pulling of electrons out of metals under intense electrical fields |year=1926 |journal=Phys. Rev. |pages=51–67 |volume=27 |issue=1 |last1=Millikan |first1=R.A. |author-link1=Robert Andrews Millikan |last2=Eyring |first2=C.F. |author-link2=Carl F. Eyring |doi=10.1103/PhysRev.27.51 |bibcode=1926PhRv...27...51M |url=http://resolver.caltech.edu/CaltechAUTHORS:MILpr26d|url-access=subscription }}</ref> and by Gossling at the [[General Electric Company]] in London.<ref>{{cite journal|first=B. S. |last=Gossling |title=The emission of electrons under the influence of intense electric fields |journal=[[Phil. Mag.]] |issue=3 |volume=1 |series=7th series |year=1926 |pages=609–635 |doi=10.1080/14786442608633662}}</ref> Attempts to understand autoelectronic emission included plotting experimental current–voltage (''i''–''V'') data in different ways, to look for a straight-line relationship. Current increased superlinearly with voltage, but plots of type log(''i'') vs. ''V'' were not straight.{{r|Millikan1926}} [[Walter H. Schottky]]<ref>{{cite journal |title = Über kalte und warme Elektronenentladungen|date = December 1923|journal = Zeitschrift für Physik A|pages = 63–106|volume = 14|issue = 63|last1 = Schottky |first1 = W.|author-link1 = Walter H. Schottky |doi=10.1007/bf01340034|bibcode = 1923ZPhy...14...63S |s2cid = 119879862}}</ref> suggested in 1923 that the effect might be due to thermally induced emission over a field-reduced barrier. If so, then plots of log(''i'') vs. {{sqrt|''V''}} should be straight, but they were not.{{r|Millikan1926}} Nor is Schottky's explanation compatible with the experimental observation of only very weak temperature dependence in CFE{{r|Lilienfeld1922}} – a point initially overlooked.{{r|Richardson}}

A breakthrough came when [[Charles Christian Lauritsen|C.C. Lauritsen]]<ref name="Millikan">{{cite journal |title=Relations of field-currents to thermionic-currents |year=1928 |journal=[[PNAS]] |pages=45–49 |volume=14 |issue=1 |last1=Millikan |first1=R.A. |author-link1=Robert Andrews Millikan |last2=Lauritsen |first2=C.C. |author-link2=Charles Christian Lauritsen |doi=10.1073/pnas.14.1.45 |pmid=16587302 |pmc=1085345 |bibcode=1928PNAS...14...45M |doi-access=free}}</ref> (and [[J. Robert Oppenheimer]] independently<ref name="Oppenheimer1928">{{cite journal |title=Three notes on the quantum theory of aperiodic effects |year=1928 |author=Oppenheimer, J.R. |journal=Physical Review |pages=66–81 |volume=31 |issue=1 |doi=10.1103/PhysRev.31.66 |bibcode=1928PhRv...31...66O}}</ref>) found that plots of log(''i'') vs. 1/''V'' yielded good straight lines. This result was published by Millikan and Lauritsen in early 1928.{{r|Millikan}}  Theoretical explanation and the original Fowler–Nordheim-type equation came shortly thereafter.  

Oppenheimer had predicted{{r|Oppenheimer1928}} that the field-induced tunneling of electrons from atoms (the effect now called field ionization) would have this ''i''(''V'') dependence, had found this dependence in the published experimental field emission results of Millikan and Eyring,{{r|Millikan1926}} and proposed that CFE was due to field-induced [[quantum tunnelling|tunneling]] of electrons [[atomic orbital|from atomic-like orbitals]] in surface metal atoms. An alternative [[Ralph H. Fowler|Fowler]]–[[Lothar Wolfgang Nordheim|Nordheim]] theory{{r|Fowler1928}} proposed field-induced tunneling from [[free electron model|free-electron-type states]] in what we would now call a metal [[electronic band structure|conduction band]], with the electron states occupied in accordance with [[Fermi–Dirac statistics]].  The Fowler-Nordheim theory explained both the Millikan–Lauritsen finding and the very weak dependence of current on temperature.{{cn|date=March 2025}} 

Oppenheimer had mathematical details of his theory seriously incorrect.<ref>{{cite journal|title = Theory of the ionization of the hydrogen atom by an external electrostatic field|year = 1977|journal = Physical Review A|pages = 877–890|volume = 16|issue = 3|last1 = Yamabe|first1 = T.|last2 = Tachibana|first2 = A.|last3 = Silverstone|first3 = H.J.|doi=10.1103/PhysRevA.16.877|bibcode = 1977PhRvA..16..877Y }}</ref> There was also a small numerical error in the final equation given by Fowler–Nordheim theory for CFE [[current density]], corrected in a 1929 paper.<ref name="sgf29">{{cite journal|title = Further studies in the emission of electrons from cold metals|jstor = 95240|year = 1929|journal = [[Proceedings of the Royal Society A]]|pages = 699–723|last1 = Stern|first1 = T.E.|last2 = Gossling|first2 = B.S. |last3 = Fowler|first3 = R.H.|volume = 124|issue = 795|doi=10.1098/rspa.1929.0147|bibcode = 1929RSPSA.124..699S |doi-access = free}}</ref>  If the barrier field in Fowler–Nordheim 1928 theory is exactly proportional to the applied voltage, and if the emission area is independent of voltage, then the Fowler–Nordheim 1928 theory predicts that plots of log(''i''/''V''<sup>2</sup>) vs. 1/''V'' should be exact straight lines. However, contemporary experimental techniques could not distinguish between the Fowler–Nordheim theoretical result and the Millikan–Lauritsen experimental result.

The physics literature often presents Fowler and Nordheim's work as a proof of [[quantum tunnelling|electron tunneling]], as predicted by wave-mechanics. Whilst this is correct, wave-mechanics was largely accepted by 1928. Instead, the Fowler–Nordheim paper was more revolutionary in establishing modern [[Electronic band structure|electron band theory]].  Prior to 1928 it had been hypothesized that two types of electrons, "thermions" and "conduction electrons", existed in metals, and that thermally emitted electron currents were due to the emission of thermions, but that field-emitted currents were due to the emission of conduction electrons, only in 1927 did [[Arnold Sommerfeld|Sommerfeld]] argue that [[Fermi–Dirac statistics]] applied to the behavior of electrons in metals.<ref name="Sommerfeld1927">{{cite journal |author=Sommerfeld, A. |year=1927 |title=Zur Elektronentheorie der Metalle |journal=Naturwissenschaften |volume=15 |issue=41 |page=825 |bibcode=1927NW.....15..825S |doi=10.1007/BF01505083 |s2cid=39403393}}</ref>  The Fowler–Nordheim 1928 work suggested that thermions did not need to exist as a separate class of internal electrons: electrons could come from a single [[Electronic band structure|band]] occupied in accordance with Fermi–Dirac statistics, but would be emitted in statistically different ways under different conditions of temperature and applied field.  The success of Fowler–Nordheim theory did much to support the correctness of Sommerfeld's ideas.<ref name="som1963">{{cite journal|title = Handbuch der Physik|year = 1963|journal = Julius Springer-Verlag|volume = 24|last1 = Sommerfeld|first1 = A.|last2= Beth|first2 = H.}}</ref> 

In particular, the original Fowler–Nordheim-type equation was one of the first to incorporate the [[Statistical mechanics|statistical-mechanical]] consequences of the existence of [[electron spin]] into the theory of an experimental condensed-matter effect. The Fowler–Nordheim paper also established the physical basis for a unified treatment of field-induced and [[Thermionic emission|thermally induced electron emission]].{{r|som1963}} 

The ideas of [[J. Robert Oppenheimer|Oppenheimer]], Fowler and Nordheim were also an important stimulus to the development, by [[George Gamow]],<ref>''Z. Physik'' '''5'''1, 204 (1928) G. Gamow, "Zur Quantentheorie des Atomkernes".</ref> and [[Ronald W. Gurney]] and [[Edward Condon]],<ref>{{cite journal|title = Wave mechanics and radioactive disintegration|year = 1928|journal = Nature|page = 439|volume = 122|issue = 3073|last1 = Gurney|first1 = R.W.|last2 = Condon|first2 = E.U.|doi = 10.1038/122439a0|bibcode = 1928Natur.122..439G |doi-access = free}}</ref><ref>{{cite journal|title = Quantum mechanics and radioactive disintegration|year = 1929|journal = Physical Review|pages = 127–140|volume = 33|issue = 2|last1 = Gurney|first1 = R.W.|last2 = Condon|first2 = E.U.|doi=10.1103/PhysRev.33.127|bibcode = 1929PhRv...33..127G }}</ref> later in 1928, of the theory of the [[radioactive decay]] of nuclei (by [[alpha particle]] tunneling).<ref name=Condon1978>{{cite journal|title = Tunneling – How It All Started|year = 1978|author = Condon, E.U.|journal = American Journal of Physics|pages = 319–323|volume = 46|issue = 4|doi=10.1119/1.11306|bibcode = 1978AmJPh..46..319C }}</ref>