Field electron emission
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.
Lilienfeld (who was primarily interested in electron sources for medical X-ray applications) published in 1922[7] the first clear account in English of the experimental phenomenology of the effect he had called "autoelectronic emission".
Oppenheimer had predicted[14] 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,[10] and proposed that CFE was due to field-induced tunneling of electrons from atomic-like orbitals in surface metal atoms.
[15] There was also a small numerical error in the final equation given by Fowler–Nordheim theory for CFE current density: this was corrected in the 1929 paper of (Stern, Gossling & Fowler 1929).
The ideas of Oppenheimer, Fowler and Nordheim were also an important stimulus to the development, by George Gamow,[19] and Ronald W. Gurney and Edward Condon,[20][21] later in 1928, of the theory of the radioactive decay of nuclei (by alpha particle tunneling).
[22] As already indicated, the early experimental work on field electron emission (1910–1920)[7] was driven by Lilienfeld's desire to develop miniaturized X-ray tubes for medical applications.
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.
[44][45][46] Nowadays, the facility to simulate field emission from Mueller emitters is often incorporated into the commercial electron-optics programmes used to design electron beam instruments.
[58] Common problems with all field-emission devices, particularly those that operate in "industrial vacuum conditions" is that the emission performance can be degraded by the adsorption of gas atoms arriving from elsewhere in the system, and the emitter shape can be in principle be modified deleteriously by a variety of unwanted subsidiary processes, such as bombardment by ions created by the impact of emitted electrons onto gas-phase atoms and/or onto the surface of counter-electrodes.
The development of large-area field emission sources was originally driven by the wish to create new, more efficient, forms of electronic information display.
And only recently has it been possible to complete the definition of ν(ℓ′) by developing and proving the validity of an exact series expansion for this function (by starting from known special-case solutions of the Gauss hypergeometric differential equation).
For tunneling well below the top of a well-behaved barrier of reasonable height, the escape probability D(h, F) is given formally by: where ν(h, F) is a correction factor that in general has to be found by numerical integration.
As noted at the beginning, the effects of the atomic structure of materials are disregarded in the relatively simple treatments of field electron emission discussed here.
The approach may be adapted to apply (approximately) to situations where the electrons are initially in localized states at or very close inside the emitting surface, but this is beyond the scope of this article.
[34] To see how the total energy distribution can be calculated within the framework of a Sommerfeld free-electron-type model, look at the P-T energy-space diagram (P-T="parallel-total").
Normal thinking has been that, in the CFE regime, λT is always small in comparison with other uncertainties, and that it is usually unnecessary to explicitly include it in formulae for the current density at room temperature.
The so-called elementary Fowler–Nordheim-type equation, that appears in undergraduate textbook discussions of field emission, is obtained by putting λZ → 1, PF → 1,
The so-called standard Fowler–Nordheim-type equation, originally developed by Murphy and Good,[72] and much used in past literature, is obtained by putting λZ → tF−2, PF → 1,
Probably, in the present state of knowledge, the best approximation for simple Fowler–Nordheim-type equation based modeling of CFE from metals is obtained by putting λZ → 1, PF → 1,
For a metal emitter, the β−value for a given position will be constant (independent of voltage) under the following conditions: (1) the apparatus is a "diode" arrangement, where the only electrodes present are the emitter and a set of "surroundings", all parts of which are at the same voltage; (2) no significant field-emitted vacuum space-charge (FEVSC) is present (this will be true except at very high emission current densities, around 109 A/m2 or higher[27][80]); (3) no significant "patch fields" exist,[63] as a result of non-uniformities in local work-function (this is normally assumed to be true, but may not be in some circumstances).
The latter depends on the work function and the field, but in cases of practical interest, the SN barrier approximation can be considered valid for emitters with radii R > 20 nm, as explained in the next paragraph.
[1] However, it should now be possible to make reasonably accurate measurements of dlni/d(1/V) (if necessary by using lock-in amplifier/phase-sensitive detection techniques and computer-controlled equipment), and to derive κ from the slope of an appropriate data plot.
[90] A first experimental test of this proposal has been carried out by Kirk, who used a slightly more complex form of data analysis to find a value 1.36 for his parameter κ.
The original theoretical equation derived by Fowler and Nordheim[1] has, for the last 80 years, influenced the way that experimental CFE data has been plotted and analyzed.
It subsequently became clear that the original thinking above is strictly correct only for the physically unrealistic situation of a flat emitter and an exact triangular barrier.
In practice, due to the extra complexity involved in taking the slope correction factor into detailed account, many authors (in effect) put σFN = 1 in eq.
In general, it may be assumed that the parameter B in the empirical equation is related to the unreduced height H of some characteristic barrier seen by tunneling electrons by (In most cases, but not necessarily all, H would be equal to the local work-function; certainly this is true for metals.)
[citation needed] This correction procedure for Millikan–Lauritsen plots will become easier to apply when a sufficient number of measurements of κ have been made, and a better idea is available of what typical values actually are.
However, notwithstanding such differences, one expects (for thermodynamic equilibrium situations) that all CFE equations will have exponents that behave in a generally similar manner.
If interest is only in parameters (such as field enhancement factor) that relate to the slope of Fowler–Nordheim or Millikan–Lauritsen plots and to the exponent of the CFE equation, then Fowler–Nordheim-type theory will often give sensible estimates.
