This article proposes that we should think differently about predicting and interpreting measured field electron emission (FE) current–voltage [Im(Vm)] characteristics. It is commonly assumed that Im(Vm) data interpretation is a problem in emission physics and related electrostatics. Many experimentalists then apply the Fowler–Nordheim plot methodology, developed in 1929. However, with modern emitting materials, this 90-year-old interpretation methodology often fails (maybe in nearly 50% of cases) and yields spurious values for characterization parameters, particularly field enhancement factors. This has generated an unreliable literature. Hence, validity checks on experimental Im(Vm) data are nearly always needed before use. A new check, supplementing existing checks, is described. Twelve different “system complications” that, acting singly or in combinations, can cause validity-check failure are identified. A top-level path forward from this unsatisfactory situation is proposed. The term “field electron emission system (FE system)” is defined to include all aspects of an experimental system that affect the measured Im(Vm) characteristics. The analysis of FE systems should now be regarded as a specialized form of electronic/electrical engineering, provisionally called “FE Systems Engineering.” In this approach, the Im(Vm) relationship is split as follows: (a) the current is expressed as a function Im(FC) of the local surface-field magnitude FC at some defined emitter surface location “C,” and (b) the relationship between FC and measured voltage Vm is expressed and determined separately. Determining Im(FC) is mostly a problem in emission physics. Determining the relationship FC(Vm) depends on system electrostatics and (for systems failing a validity check) on the other aspects of FE Systems Engineering, in particular, electrical-circuit modeling. The scope of FE Systems Engineering and some related research implications and problems are outlined.

Large-area electron emission sources have many actual and potential technological applications. One available source-technology is field electron emission (FE). In consequence, the last 20-plus years have seen extensive amounts of related emitter-materials’ research. This has mostly aimed at developing large-area field electron emitters (LAFEs) that have high macroscopic (i.e., “area-average”) electron-current density JM. (This article uses the customary field emission convention that electron currents and current densities are treated as positive, although negative in classical electromagnetism.)

Very many papers relating to FE technology make the assumption that the interpretation of measured current–voltage [Im(Vm)] characteristics is a problem in emission physics and related (zero-current) electrostatics. Such papers often then analyze their data using the electrostatics of 150 years ago1 and a data-analysis methodology—the Fowler–Nordheim (FN) plot—introduced2 in 1929, nearly 100 years ago.

The main objective of most FN-plot users has been the extraction of emitter electrostatic characterization data from the FN-plot slope. For this objective, data analysis based on FN plots worked adequately in the period 1929 to around 1950 (or slightly later), because in this period (and earlier in the 1920s), (a) field emitters were nearly always metal; (b) mounting arrangements nearly always provided a low-electrical-resistance path to the high-voltage source; (c) emitters were usually operated at fields where space-charge effects were not a major influence; and (d) system vacuum levels were good enough that vacuum breakdown was not a significant factor. Thus, in this period, FE systems were nearly always what is described below as electronically ideal.

With modern emitting materials (semiconductors, carbon-based materials, etc.), which began to be seriously developed from around the 1950s, the FE-system characteristics just stated are no longer necessarily all applicable. As a result, in many modern cases (maybe in nearly 50% of cases), the 90-year-old data-analysis methodology based on FN plots fails: it can yield spurious values for emitter characterization parameters, particularly field enhancement factors (FEFs).3 Briefly, the argument is that if the slope extracted from a FN (or related) data-analysis plot causes the failure of the orthodoxy test,3 then it will also generate a spurious FEF value (for some detailed discussions of this effect, see Refs. 3–5).

Improved modern FE data-analysis techniques, such as the Murphy–Good plot6 and numerical multivariable regression techniques7 based on the Kyritsakis–Xanthakis (“earthed sphere”) FE equation,8 can also fail if they are applied to emitters and FE systems that are not electronically ideal.

In the author’s perception, this situation has led to the massive breakdown of the peer-review system in this technological area and has generated a FE-technology literature where sensible users of published FE characterization data (but particularly industrialists interested in medical applications and national defense scientists) should treat ALL published FEF-values as UNVERIFIED, unless or until the results of interest have been or can be proved valid—e.g., by some form of validity check (see below).

This paper proposes that we should think differently about how to predict and interpret measured FE current–voltage characteristics. In principle, we should treat the analysis of measured FE current–voltage characteristics as a specialized form of electrical and electronic engineering. Perhaps, this could be called FE Systems Engineering.

FE Systems Engineering would not be ordinary electrical/electronic engineering, because it would involve currents, voltages, and fields (and more besides), but this is also true for some other forms of electrical engineering, for example, high-voltage engineering. A field electron emitter is, in effect, a new form of electronic circuit element, and appropriate field-emitter-specific forms of electrical-circuit theory and circuit modeling will probably need to be developed.

For example, Fig. 1 illustrates a simple application of FE Systems Engineering. The circuit model shown, presented some years ago,9 is a basic attempt to represent the effects due to the emitter, series resistances, and a parallel resistance that gives rise to leakage currents. It would be useful to develop much more comprehensive forms of circuit model.

FIG. 1.

Basic circuit model that represents an FE system containing an emitter “e,” series resistances Rs1 and Rs2, and a parallel resistance Rp that gives rise to leakage current. (Electron currents are treated as positive.)

FIG. 1.

Basic circuit model that represents an FE system containing an emitter “e,” series resistances Rs1 and Rs2, and a parallel resistance Rp that gives rise to leakage current. (Electron currents are treated as positive.)

Close modal

This paper aims at presenting a top-level overview of the main issues that seem to arise when attempting to establish FE Systems Engineering. This overview includes a brief discussion of some specific issues that have already been discussed in more detail elsewhere. The paper itself is based on a presentation made at the 2022 35th International Vacuum Nanoelectronics Conference10 (see https://doi.org/10.13140/RG.2.2.10294.57927), but aspects of the argument have been developed further since the original presentation.

The structure of the rest of the paper is as follows. After a brief description in Sec. I B of how FN plots are currently used, Sec. II identifies 12 “system complications” that can cause the FN-plot-based data-analysis methodology to fail. Section III then outlines the top-level components of a new, more general approach. Section IV discusses the existing validity checks and a new form of check. Section V discusses the need to develop methods for diagnosing the cause or causes of validity-check failure and makes some initial suggestions about how this might be done. Section VI makes some other suggestions related to the development of FE Systems Engineering. Section VII provides a summary. An  Appendix makes suggestions for the possible content of a multiday short course related to FE Systems Engineering.

To provide a starting point, this section describes 1929-style FE data-analysis methodology2 as currently commonly used. As is well known, the commonest (but not the only possible) experimental FE data-analysis methodology is the Fowler–Nordheim (FN) plot, which—when natural logarithms are used—is a data plot of the form ln{Y/X2} vs 1/X, where X is the input variable (normally a field or a voltage) and Y is the output variable (normally a current or a current density). The “curly bracket notation” {Q} means “take the numerical value of Q when Q is expressed in the designated units.”

Nowadays, FN and related data-analysis plots are most commonly made using natural logarithms. Although common logarithms have been used in older work and are sometimes still used, it is usually better practice to convert all common logarithms to natural logarithms. Thus, only plots using natural logarithms will be discussed here.

Obviously, when raw measured current–voltage Im(Vm) data are used, then X becomes Vm, and Y becomes Im. The author’s view is that using raw measured Im(Vm) data is the best practice, because the resulting FN or related plot is then clearly an experimental result. The local-field magnitude FC at some characteristic location “C” on the emitter surface at or near its apex can then be related to Vm by the following equation:
(1)
where ζmC is the characteristic local voltage conversion length (LVCL), defined by this equation.

An electronically ideal FE system is, by definition, one where the parameter ζmC is a constant, independent of the values of Vm and Im, and the measured current–voltage characteristics are determined by the emission physics and the zero-current system electrostatics alone. For an electronically ideal FE system, an experimental FN plot of type ln{Im/Vm2} vs 1/Vm is “nearly straight” and ζmC is a constant that can be extracted from the slope of the plot. (Or, alternatively, the reciprocal of ζmC can be used in the theory.)

However, particularly when analyzing the data from LAFEs, where the individual emitters are “protrusions” that stand on an underlying substrate, it has become customary to preconvert the experimental data, in one or both of the following ways, before making a data-analysis plot.

First, a macroscopic (or LAFE-average) current density JM can be defined by
(2)
where AM is the macroscopic area (or “footprint”) of the emitter. The explicit inclusion of the subscript “M” on JM and use of the description “macroscopic” (or equivalent) are important because massive confusion exists in the FE technological literature between JM and characteristic local emission current density JC. Both JM and JC are commonly denoted by the same symbol J, but JC is very much larger than JM.
Second, a so-called macroscopic field FM (also called an “applied field”) is defined within the context of the relevant system geometry. This field FM is the electrostatic field magnitude at the position (on the substrate) of the base of the protrusion, in the absence of the protrusion. It can be written in terms of Vm by the following equation:
(3)
where d is a parameter with the units of distance. Many LAFEs use so-called “PPP” geometry where the protruding emitters are on one of a pair of parallel planar plates of lateral extent that is large in comparison with the plate separation. If a system with this geometry is electronically ideal, then d is a constant equal to the plate separation dsep. If the system is not electronically ideal, then d will likely be a variable parameter not equal to the plate separation.

With experiments in PPP geometry, it is important to ensure that (a) the plates really are parallel (so that the interplate field is uniform or very nearly uniform across the plate except near the plate edges); (b) dsep is measured accurately; and (c) the height h of emitting protrusions is always very much less than dsep. Ideally, we should perhaps have h < dsep/10, unless it is intended that the emitter apex should be near the counter-electrode (in which case special electrostatic theory is needed).

With LAFEs, it is customary to define a characteristic macroscopic field enhancement factor (MFEF), denoted here by γMC (but often by β in the FE literature). This is done via the following relation:
(4)
where the second part of the relation follows from Eqs. (1) and (3). For electronically ideal emitters, γMC is a constant. When the protrusion height h is very much less than d, then γMC is a useful parameter that characterizes the sharpness of the most strongly emitting protrusions. (However, difficulties of interpretation can arise if the LAFE layer is not reasonably uniform.)

When the measured voltage has been preconverted to a macroscopic field, (for electronically ideal emitters, and when the local work function is known or can be adequately estimated) the value of γMC can be obtained from the slope of a FN or related plot made by taking X as FM, and Y as either JM or Im. Alternatively (and better in the author’s view5), again for electronically ideal emitters, ζmC can be obtained from the slope of a FN or related plot made using the raw measured Im(Vm) data and γMC then obtained as d/ζmC.

In summary, an electronically ideal FE system is one for which the parameters ζmC, d, and γMC are constant and independent of the measured voltage and measured current. For such systems, the values of these parameters can be obtained from the slope of a FN or related data-analysis plot. For such systems, the values of area-like quantities can be obtained from the intercept that the experimental plot makes on the vertical (1/X = 0) axis (see Refs. 4 and 6), but procedures are not discussed in detail here. The underlying point is that 1929-style FE data-analysis works reliably only for electronically ideal systems. It fails in many modern cases, because the FE system is not ideal.

Even for electronically ideal emitters and FE systems, the 1929 FN plot is not the most modern or the most useful form of FE experimental data-analysis now available. However, a much bigger data-analysis issue is that many reasons are now known that cause FE systems not to be electronically ideal, and more reasons continue to be realized. These causes have been termed system complications. As of the time of submission (January 2023), the following are the known possible system complications.

  1. Significant series resistance in the current path between the emitter and the high-voltage generator. This cause includes safety resistors and current-measurement resistors whose circuit effects have not been correctly taken into account, and series transistors used as current-limiting devices.

  2. Voltage-loss effects along the emitter (which can lead to current-dependence in characterization parameters such as ζmC and γMC).

  3. Effects due to field emitted vacuum space charge (FEVSC).

  4. Field-dependent changes in FE-system geometry (reversible or permanent) due to Maxwell stress, and permanent changes due to various forms of emitter erosion.

  5. Changes in local work function due to current-related heating effects (Joule and/or Nottingham heating) and related desorption of surface adsorbates.

  6. Various effects related to field penetration into semiconductor emitters, and/or to the condition of the semiconductor surface, and/or to the mechanism of electron supply for semiconductors.

  7. Charge-trapping on nonmetallic surfaces adjacent to the emitting surface.

  8. Use, in data analysis, of a seriously incorrect value of the effective emitter local work function.

  9. The actual operating regime of the emitter is not the Murphy–Good FE regime.

  10. The emitter is so sharp that Murphy–Good FE theory does not apply.

  11. With so-called nanoscale vacuum channel transistors (NVCTs), the use of diode-type theory that does not accurately model the behavior of a three-terminal electronic device.

  12. With LAFEs, plot nonlinearity (upward bending at the left-hand-side of a FN plot) can occur because the emission comes from the distribution of many individual emitters, all with different field enhancement factors. In this case, despite (usually slight) nonlinearity, the behavior of individual emitters may be orthodox.

The situation is made even more complicated if (as is sometimes, or maybe often, the case) several different system complications are operating simultaneously.

At present, we do not know the relative significances of these various factors (and, in any case, relativities may vary as between different experimental situations). However, the author’s guess is that cause (2) may be more common than is currently realized (see Ref. 11 for detailed discussion).

Subsections III AIII C outline the top-level components of a proposed new, more general, approach.

The term field electron emission system (FE system) is defined to include all aspects of an experimental or technological system that affect the measured current–voltage characteristics. This includes

  • the emitter configuration (composition, geometry, and surface condition);

  • geometrical, mechanical, and electrical arrangements in the vacuum system;

  • all aspects of the electronic circuitry and all electronic measurement instruments;

  • the emission physics; and

  • all other relevant physical processes that might be happening (as exemplified by some items in the list in Sec. II).

As already indicated, the proposal is that the science and engineering of FE systems should be regarded as a specialized form of electronic/electrical engineering, called here FE Systems Engineering.

The theory of FE Systems Engineering has two main components: (a) emission physics and (b) circuit and field-voltage (CFV) behavior. Field emitter electrostatics can be seen as an auxiliary topic that contributes to both but more to CFV behavior.

The emission physics yields an expression for the predicted emission current Ie as a function of the local electrostatic field magnitude FC at some characteristic location “C” near or at the emitter apex “a.” Thus, the emission physics yields Ie(FC). If there is no significant leakage current, then this can usually be treated as a predicted measured current Im(FC). (If there is significant leakage current, then a correction factor needs to be included.12)

Modern accounts of basic FE emission physics can be found, for example, in Refs. 13–15.

Note that due to uncertainties in (a) current understandings of emission physics and (b) the accuracy of models for the emitter configuration, the predictions of measured current for real emitters are subject to massive uncertainty,12 perhaps sometimes as much as a factor of 1000 or more.

At least in principle, analyzing the circuit and field-voltage (CFV) aspects of FE-system behavior provides a link between the characteristic local-field magnitude FC and the measured voltage Vm. As already indicated, this link can be written in form (1) above.

Alternatively, it can be written in the following equivalent form:
(5)
where KmC [≡1/ζmC] is the (characteristic) voltage-to-local-field conversion factor. In both cases, the “voltage” in question is the measured voltage, but (for simplicity) this is not explicitly indicated in the terminology, in this paper. Typically, ζmC is measured in “nm” but KmC in “m–1.”

[Note that the conversion factor KmC is usually denoted by β (or βV) in the FE literature, but I avoid this notation, in order to prevent confusion with the dimensionless field enhancement factor commonly denoted by β in the FE literature.]

In reality, in nearly all cases, each of the individual “FE-system complications” has its own “theory of ζmC (or KmC).” No integrated general theory of CFV behavior (i.e., no general theory of ζmC or KmC) currently exists.

In a few cases, the integrated theory of two system complications has been developed—e.g., “series resistance” and “voltage loss” have been jointly discussed.11 However, in many cases, it can be that, due to the lack of appropriate theory, experimental current–voltage characteristics cannot be reliably interpreted.

In practice, this implies an engineering need to first sort measured current–voltage [Im(Vm)] characteristics into two groups: those that can be reliably interpreted (if up-to-date emission theory is used) and those that—at present—cannot. This initial sorting process can be formalized as described next.

As indicated earlier, an FE system is termed electronically ideal (in a range of Vm—values of interest) if no “system complications” are operating in the voltage-range of interest, and hence the parameters ζmC and KmC are constant, independent of the values of Vm and Im. With LAFEs, the parameters d and γMC will also be constant for electronically ideal systems. The behavior of an electronically ideal system can be described by emission physics and zero-current system electrostatics alone.

An electronically ideal FE system is further described as orthodox (or as orthodoxly behaving) if the emission process can be adequately described by Murphy–Good FE theory16 (for a modern derivation, see Ref. 17) and if the value of the relevant emitter local work function (assumed unchanging during the relevant experimental run) is adequately known. An FE system may be “orthodoxly behaving” over part of its Vm operating range (usually the low-voltage part) but may be “nonorthodox” in other parts of the range.

For FE systems behaving orthodoxly, traditional data-analysis methodology works “more-or-less adequately” (if up-to-date emission theory is used). However, as discussed elsewhere,6,7,18,19 improved modern versions of data-analysis theory (e.g., the Murphy–Good plot6) may often work slightly better.

The term validity check refers to a check that FE-system behavior is orthodox and, hence, that characterization parameters extracted using traditional methodology are adequately valid (if up-to-date emission theory is used). Three forms of validity check are now recognized:

  1. Near-linearity of a Fowler–Nordheim (FN) plot (or similar data-analysis plot). The theory and analysis of FN and related data plots has been discussed elsewhere4,6,15,18,19 (also see: https://doi.org/10.13140/RG.2.2.32112.81927/3). Nonlinearity implies test failure. However, linearity does not guarantee that emitter behavior is orthodox, and in this case, it is necessary also to apply the orthodoxy test.

  2. The orthodoxy test. This is well described in the literature.3 Essentially, the procedure tests, for the given emitter, whether the apparent operating range of characteristic local fields FC, as derived from a FN or similar data plot, is physically reasonable, as compared to well-established operating ranges for metal emitters. The test is, in fact, carried out with the quantity characteristic scaled-field fC, which is related to FC by fC = FC/FR, where the reference field FR is the field necessary to pull down to the Fermi level the top of a Schottky–Nordheim barrier of zero-field height equal to the local work function ϕ. For an early user application of the test, see Ref. 20.

  3. The “magic emitter” test. This is a new test, described in Sec. IV B.

As indicated above, in the FE material-technology community, it is common practice, before making a data-analysis plot, to “preconvert” experimental Im(Vm) data into an alternative form involving macroscopic fields. This is done by using a conversion equation that—in fact5—is often of questionable validity and hence may yield “apparent macroscopic fields” rather than “true macroscopic fields.” Tests (1) and (2) above will normally work with “preconverted” data sets, but it is strongly advised that it is better practice to use the raw measured Im(Vm) data to make the data-analysis plot and carry out the validity checks of the first two types.

The magic emitter test is a validity check that can be carried out on published experimentally derived data, when this is plotted in a preconverted form that shows the range of apparent macroscopic fields FMapp over which significant FE current is emitted, when the relevant local work function value ϕ is stated (or can be estimated from the stated nature of the emitting material), and when the extracted (apparent) field enhancement factor is stated.

Essentially, this is a simpler and quicker variant of the orthodoxy test that can be used to identify emitters/systems that are in the “fail” range of the orthodoxy test.

Papers of interest will almost always report the value of the apparent field enhancement factor (γMCapp here, but usually “β” in the FE literature). From Eq. (3), using this value γMCapp, the highest reported value of FMapp (derived from the lowest reported value of 1/FMapp on the FN or related data-analysis plot) can be converted to a corresponding (apparent) characteristic local-field FCapp(highest).

For a material of local work function ϕ, the corresponding reference field FR(ϕ) as defined above is given by (see: https://doi.org/10.13140/RG.2.2.34321.35681/1)
(6)
This value can be used to convert FCapp(highest) to a corresponding “highest” value fCapp(highest) of characteristic scaled-field fCapp, using the following equation:
(7)
Here, universal constants are stated to seven significant figures but should be rounded as appropriate. For a ϕ = 4.50 eV emitter, FR is about 14.1 V/nm.

For a given ϕ-value, a scaled-field value fub(ϕ) that represents the lower limit of the “definitely fail” range is given in Table II of Ref. 3. (For a ϕ = 4.50 eV emitter, fub = 0.75.) The “magic emitter” test is to compare fCapp(highest) with fub(ϕ). If fCapp(highest) > fub(ϕ), then the test is failed: in this case, the authors apparently have a “magic emitter” operating in a field range where a normal emitter would have exploded or otherwise failed. The reality is that their emitter/system is nonideal and that the reported value of the field enhancement factor is spurious.

A current best guess, based on a small survey,3 is that up to 40% of the many hundreds of published values of apparent field enhancement factors may be spurious, in the sense that the reported experimental data would fail a validity check.

Significant questions are how to interpret this “failed” experimental data, or (in some cases) how to “adjust” a spurious derived LVCL or MFEF value, in order to derive at least a rough estimate of what the “true” value would be if the FE system were electronically ideal.

There exists a method of the latter kind, called phenomenological adjustment. This has been described elsewhere4 and will not be discussed in detail here.

To interpret experimental data that have failed a validity check, it would usually be necessary to know the cause of failure. However, as noted earlier, there can, in principle, be many different causes of failure, and more than one cause could be operating.

In general, making an accurate diagnosis of the cause(s) of validity-check failure is an unsolved problem in the theory of how to interpret measured current–voltage data and an unsolved problem more generally in FE Systems Engineering. In general, the problem is complicated and difficult and deserves much more research attention than it has so far received. Some initial suggestions follow about what might be possible ways forward:

  1. Measure the total energy deficit (TED) of an electron emerging from the emitter apex, either by retarding potential analysis (e.g., Refs. 21 and 22) or by a direct contact method (e.g., Ref. 23). Measurement of a TED value of a few eV (or slightly more) may be an indicator that voltage-loss effects along the emitter are reducing the MFEF value.11 

  2. As suggested by Bachmann et al.,24 model the system as a resistance Z in series with a field emitter and establish the functional dependence of Z on measured current and on any other relevant parameters.

  3. Try to establish if physically different causes lead to qualitatively different shapes for [Im(Vm)] data plots or related FN (etc.) plots.

  4. In cases where the low-voltage part of a FN or related data plot exhibits orthodox behavior, but the high-voltage part “saturates,” investigate if it might be possible to obtain useful information from study of how the “observed” slope correction factor varies with Vm, for high Vm.

Eventually, it may be useful to develop a short course on FE Systems Engineering and the interpretation of measured FE current–voltage characteristics. Some suggestions for the content are made in the  Appendix.

It also seems that it might be useful to modify the formal scope of the International Vacuum Nanoelectronics Conference (and of related special issues of JVSTB). Thus, the “ Science and Technology” section of the IVNC “Call for Topics” could perhaps be modified in the following way (additions in italics):

Science, Engineering and Technology

  • Emission physics—Electron emission theory, including ab initio and classic tunneling approaches.

  • Emission modeling—Modeling and simulation of electron emission physics from surfaces and devices, including microtips, nanogaps, and photoemission.

  • Field Emission Systems Engineering—Theory and electrical-engineering analysis of complete field electron emission systems, including methods for interpreting measured current–voltage characteristics.

  • Fundamental—Fundamental studies.

As already indicated, it seems to the author that if we wish to put the subject area of field electron emission onto a better and more respectable scientific basis, then a key requirement is for the subject area to carry out much more research into methodologies for interpreting measured current–voltage characteristics, particularly those taken from FE systems that are not electronically ideal. Hence, this suggestion that we should explicitly make this a topic of stated interest to IVNC.

It has been argued that the interpretation of FE measured current–voltage characteristics should be regarded as part of a specialized branch of electrical/electronic engineering, called here “Field Electron Emission Systems Engineering.” Its two major components would be (a) emission physics and (b) “integrating theory” (including electrical-circuit theory) that builds relationships between voltages, fields, and currents. Field emitter electrostatics can be seen as an auxiliary topic that contributes to both components, though more to the integrating theory than to the emission physics.

FE Systems Engineering needs to include validity checks that can determine whether a FE system is “electronically ideal” (i.e., current–voltage characteristics are determined by emission physics and zero-current system electrostatics alone and, hence, can be validly interpreted by the modern versions of traditional methodology, such as Fowler–Nordheim plots). Twelve different effects/situations that can cause an FE system to be electronically nonideal have been identified in this article.

There is a need to establish methodologies that can diagnose the cause or causes of non-ideality. Some suggestions about possible methodologies have been made, but there is a great need for systematic research into this issue and into the wider general issue of how to set about interpreting nonideal current–voltage characteristics. It has been argued that the importance of these issues should be recognized by modifying the “calls for topics” for IVNC and for the related special issue of JVSTB.

It has also been proposed that it might be useful to develop a short course on FE Systems Engineering. Suggestions have been made about the possible content.

It can be argued that, in order to be regarded as scientifically respectable, a research topic needs to have reliable procedures for making comparisons between theory and experiment. Currently, this aspect of field electron emission is undesirably weak, both for reasons discussed above and for more basic reasons.25 Introducing the idea of FE Systems Engineering could be a useful part of the process of putting field electron emission onto a better and more respectable scientific basis.

The author has no conflicts to disclose.

Richard G. Forbes: Conceptualization (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (lead); Validation (lead); Writing – original draft (lead); Writing – review & editing (lead).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Basic knowledge needs for FE Systems Engineering include the following topics. Ideally, most of these could be included in a multiday short course, at least at the introductory level. The length of the list shows the large extent of the underlying scientific knowledge needed in order to have a good understanding of FE Systems Engineering.

  • - Relevant basic aspects of statistical thermodynamics and of the theory of electricity.

  • - Relevant aspects of the theory of charged surfaces and of work-functions and related concepts.

  • - Planar emission physics, at least at the level of so-called “21st Century smooth-surface planar FE theory” (see https://arxiv.org/ftp/arxiv/papers/2107/2107.08801.pdf).

  • - As relevant, theory relating to the effect of temperature on FE.

  • - Field emitter electrostatics in the zero-current approximation.

  • - Introduction to finite-current FE-system electrostatics and related practical implications.

  • - Introduction to the physics of field emitted vacuum space charge (FEVSC).

  • - Theory and phenomenology of field-induced stress (Maxwell stress).

  • - Introduction to the dynamics of adsorption, migration, and desorption of surface adsorbates and to the role of adsorbates in emission physics.

  • - Electronic/electrical-circuit modeling for FE systems, including (where appropriate and available) relevant forms of the equivalent circuit.

  • - Standard “planar emission theory” methodologies for interpreting measured current–voltage data taken from electronically ideal systems.

  • - Methodology for applying “earthed-sphere-model” data-analysis techniques, using the Kryritsakis–Xanthakis FE equation8 and/or a related procedure.7 

  • - As relevant, introductions to the special problems of FE from (a) semiconductors, (b) carbon nanotubes, (c) graphene edges and blade-type emitters, and (d) rough and/or inhomogeneous surfaces.

  • - Introduction to relevant atomic level and bond-level emission physics, as these things may affect FE theory.

  • - Introduction to the “deep problems” of FE that relate to the issue to how to apply quantum mechanics to FE in a manner that is “exactly correct.”

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