Editing Field electron emission (section)

=== Field electron microscopy and related basics ===
As already indicated, the early experimental work on field electron emission (1910–1920)<ref name="Lilienfeld1922"/> was driven by [[Julius Edgar Lilienfeld|Lilienfeld's]] desire to develop miniaturized [[X-ray]] tubes for medical applications. However, it was too early for this technology to succeed.{{Why|date=March 2025}}

After Fowler–Nordheim theoretical work in 1928, a major advance came with the development in 1937 by [[Erwin Wilhelm Mueller|Erwin W. Mueller]] of the spherical-geometry [[field emission microscope|field electron microscope]] (FEM)<ref name=Mueller1937>{{cite journal|year = 1937|author = Mueller, E.W.|journal = Z. Phys.|pages = 541–550|volume = 106|doi = 10.1007/BF01339895|title = Elektronenmikroskopische Beobachtungen von Feldkathoden|bibcode = 1937ZPhy..106..541M|issue = 9–10 |s2cid = 120836411}}</ref> (also called the "field emission microscope"). In this instrument, the electron emitter is a sharply pointed wire, of apex radius ''r''. This is placed, in a vacuum enclosure, opposite an image detector (originally a phosphor screen), at a distance ''R'' from it. The microscope screen shows a projection image of the distribution of current-density ''J'' across the emitter apex, with magnification approximately (''R''/''r''), typically 10<sup>5</sup> to 10<sup>6</sup>. In FEM studies the apex radius is typically 100&nbsp;nm to 1 μm. The tip of the pointed wire, when referred to as a physical object, has been called a "field emitter", a "tip", or (recently) a "Mueller emitter".

When the emitter surface is clean, this FEM image is characteristic of: (a) the material from which the emitter is made: (b) the orientation of the material relative to the needle/wire axis; and (c) to some extent, the shape of the emitter endform. In the FEM image, dark areas correspond to regions where the local work function ''φ'' is relatively high and/or the local barrier field ''F'' is relatively low, so ''J'' is relatively low; the light areas correspond to regions where ''φ'' is relatively low and/or ''F'' is relatively high, so ''J'' is relatively high. This is as predicted by the exponent of Fowler–Nordheim-type equations [see eq. (30) below].

The [[adsorption]] of layers of gas atoms (such as oxygen) onto the emitter surface, or part of it, can create surface [[electric dipole]]s that change the local work function of this part of the surface. This affects the FEM image; also, the change of work-function can be measured using a Fowler–Nordheim plot (see below). Thus, the FEM became an early observational tool of [[surface science]].<ref name=Gomer1961>{{Cite book|title = Field emission and field ionization|year = 1961|author = Gomer, R.|publisher = Harvard Univ. Press|location = Cambridge, Massachusetts|isbn = 1-56396-124-5}}</ref><ref>{{cite journal|title = Recent advances in field electron microscopy of metals|year = 1975|journal =Advances in Electronics and Electron Physics|pages = 193–309|volume = 32|last1 = Swanson|first1 = L.W.|last2 = Bell|first2 = A.E.|doi = 10.1016/S0065-2539(08)60236-X|isbn = 9780120145324}}</ref> For example, in the 1960s, FEM results contributed significantly to discussions on [[heterogeneous catalysis]].<ref>"The role of the adsorbed state in heterogeneous catalysis", Discuss. Faraday Soc., Vol. 41 (1966)</ref> FEM has also been used for studies of [[surface diffusion|surface-atom diffusion]]. However, FEM has now been almost completely superseded by newer surface-science techniques.

A consequence of FEM development, and subsequent experimentation, was that it became possible to identify (from FEM image inspection) when an emitter was "clean", and hence exhibiting its clean-surface work-function as established by other techniques. This was important in experiments designed to test the validity of the standard Fowler–Nordheim-type equation.<ref name=Dyke1953>{{Cite journal|title = Field emission: Large current densities, space charge, and the vacuum arc
|year = 1953|journal = Physical Review|pages = 799–808
|volume = 89|issue = 4|last1 = Dyke |first1 = W.P.
|last2 = Trolan|first2 = J.K.|doi=10.1103/PhysRev.89.799|bibcode = 1953PhRv...89..799D }}</ref><ref>{{cite journal|title = Field emission
|year = 1956|journal = Advances in Electronics and Electron Physics
|pages = 89–185|volume = 8|last1 = Dyke|first1 = W.P.
|last2 = Dolan|first2 = W.W.|doi=10.1016/S0065-2539(08)61226-3| bibcode=1956AEEP....8...89D |isbn = 9780120145089}}</ref> These experiments deduced a value of voltage-to-barrier-field conversion factor ''β'' from a Fowler–Nordheim plot (see below), assuming the clean-surface ''φ''–value for tungsten, and compared this with values derived from [[transmission electron microscope|electron-microscope]] observations of emitter shape and electrostatic modeling. Agreement to within about 10% was achieved. Only very recently<ref>{{cite journal|title = Field emission from crystalline niobium|year = 2009|journal = Physical Review Special Topics - Accelerators and Beams
|page = 023501|volume = 12|issue = 2|doi=10.1103/PhysRevSTAB.12.023501|last1 = Pandey|first1 = A D|last2 = Muller|first2 = Gunter|last3 = Reschke|first3 = Detlef|last4 = Singer|first4 = Xenia|bibcode = 2009PhRvS..12b3501D |doi-access = free}}</ref> has it been possible to do the comparison the other way round, by bringing a well-prepared probe so close to a well-prepared surface that approximate parallel-plate geometry can be assumed and the conversion factor can be taken as 1/''W'', where ''W'' is the measured probe-to emitter separation. Analysis of the resulting Fowler–Nordheim plot yields a work-function value close to the independently known work-function of the emitter.