Dr Richard G. Forbes


Visiting Associate Professor (formerly Reader in High Electric Field Nanoscience)
MA, PhD, DSc, EurIng, CEng, CPhys, FIET, FInstP, SMIEEE
By prior appointment only (contact via e-mail)
+44 (0)7480 116 792

Academic and research departments

School of Mathematics and Physics.

About

Areas of specialism

High electric field nanoscience, including charged surfaces theory; Field electron (FE) and field ion (FI) emission theory, including the electronic engineering of FE systems, and the theory of their technological applications; Quantum tunnelling theory & related statistical mechanics; Use of density functional theory in field emission theory, particularly electron emission from carbon nanotubes; Zero-current and finite-current Electrostatics, and related aspects of Chemical Thermodynamics; Electroformation and relevant aspects of electrohydrodynamics; Field-emission-related aspects of electrical breakdown, both in air and in vacuum; Standardization issues, and issues relating to the integrity of FE literature.

University roles and responsibilities

  • Retired Reader who continues to be active in research, now as a Visiting Associate Professor

    My qualifications

    MA, PhD, DSc, EurIng, CEng, CPhys, FInstP, FIET

    Affiliations and memberships

    Institute of Physics
    Fellow (FInstP)
    Institution of Engineering and Technology
    Fellow (FIET)
    Institution of Electrical and Electronic Engineers
    Senior Member
    American Vacuum Society
    Member
    Russian Academy of Natural Sciences
    Foreign Member
    International Field Emission Society
    Member and Inaugural Fellow
    Royal Society of Arts
    Fellow

    Research

    Research interests

    Supervision

    Postgraduate research supervision

    Teaching

    Publications

    Richard bes, Richard G. Forbes (1972)A theory of field-ion imaging: I. A quasi-classical site-current formula, In: Journal of microscopy (Oxford)96(1)57pp. 57-61

    A quasi-classical formulation of field-ion imaging theory is defined and discussed. Concepts and terminology are defined, and a formula is established for the ion current generated above a single surface site.

    Richard bes, Richard G. Forbes (1972)A theory of field-ion imaging: II. On the origin of site-current variations, In: Journal of microscopy (Oxford)96(1)63pp. 63-75

    Experimental evidence demonstrates the incompleteness of the usual rate constant explanation of field-ion image appearance, and suggests that gas distribution effects may be the dominant influence on image contrast, certainly in some circumstances. Further evidence shows that gas concentration variations across the surface would not be given by any simple formal rule. However, significant features of image behaviour in the helium-on-tungsten system can be rationalized by closer examination of gas behaviour during and after accommodation. For the normal imaging range a provisional working rule is suggested, that regional contrast may be primarily determined by supply-and-capture effects, but local contrast by a tendency for local gas equilibria to be established.

    R. G. Forbes (1996)The Liquid Metal Ion Source as an Electrically Driven Vena Contracta, andsome Comments on LMIS Stability, In: Le Journal de Physique IV6(C5)pp. C5-43-C5-47 EDP Sciences

    This paper discusses recent items of progress in understanding liquid-metal ion source (LMIS) behaviour, in the more general context of electrohydrodynamics. (1) Like the Taylor-Gilbert cone, the phenomenon of the vena contracta has been known for several hundred years. It is argued that the cusp-on-a-cone shape of an operating LMIS is a similar phenomenon, except that the forces acting are electrical rather than gravitational, and the pressure in the jet is negative rather than positive. (2) In discussing LMIS stability in engineering terms, mechanisms affecting the jet shape can be classified as giving negative feedback (stabilising), or positive feedback (destabilising). Effects associated with field evaporation andlor space charges give negative feedback, effects associated with pressure changes positive feedback. Attention is drawn to the arguments of Ganan-Calvo about the role of 'supercritical' flow as a stabilising factor against hydrodynamic disturbances. (3) Electrohydrodynamic spraying is superficially very similar to LMIS operation, and both sprayers and ion sources adopt a cusp-on-a-cone (or 'cone-jet') shape. But the accepted theoretical explanations of the driving mechanisms are different. Confirmation is offered that the LMIS story is the correct one for very highly conducting liquids, and that a difference in driving mechanism is plausible.

    Richard Forbes (2007)The International Field Emission Society, In: Surface and interface analysis39(2-3)pp. 91-91 John Wiley & Sons, Ltd
    Richard G. Forbes (1979)The influence of depolarisation on surface-atom polarisation energy, In: Surface science82(2)L620pp. L620-L624 Elsevier B.V
    Richard G Forbes (1977)Atomic polarisability values in the SI system, In: Surface science64(1)pp. 367-371 Elsevier B.V
    E. O. Popov, S. V. Filippov, A. G. Kolosko, P. A. Romanov, R. G. Forbes (2016)Extracting formal emission area by on-line processing of current-voltage data, using FN-type equations for the Schottky-Nordheim barrier, In: 2016 29TH INTERNATIONAL VACUUM NANOELECTRONICS CONFERENCE (IVNC)7551514pp. 1-2 IEEE

    We have implemented experimental methods for determining emission area parameters by using online processing of current-voltage characteristics (IVC). We calculated the formal emission area for each experimental IVC: for a single tungsten emitter and for several multi-tip emitters based on CNT and graphene. Voltage dependence in emission area is observed.

    Two conducting nanostructures on a conducting base-plate, and with a common applied electrostatic field, interact because their electrons are a common electron-thermodynamic system. Except at small separations, the interaction reduces the apex field enhancement factor (FEF) of each nanostructure, by means of "charge blunting". A parameter of interest is the fractional reduction (-d) of the apex FEF, as compared with the apex FEF for the same emitter when standing alone on the base-plate. For systems of two or a few identical post-like emitters, or regular arrays of such emitters, details have been investigated by methods based on numerical solution of Laplace's equation, and by using line-charge models. For post separations c comparable with post height h, several authors have shown that the variation of (-d) with c is well described by formulae having exponential or quasi-exponential form. By contrast, explorations of the two-emitter situation using the "floating-sphere-at-emitter-plane potential" (FSEPP) model have predicted that, for large c-values, (-d) falls off as 1/c*c*c. Numerical Laplace-type simulations carried out by de Assis and Dall'Agnol (arXiv:1711.00601v2) have confirmed this limiting dependence for six different situations involving pairs of protruding nanostructures; hence they suggest it as an universal law. By using the FSEPP model for the central structure, and by adopting a "first moments" representation for the distant structure, this letter shows that a clear physical reason can be given for this numerically discovered general limiting (1/c*c*c) dependence. An implication is that the quasi-exponential formula found useful for c comparable with h is simply a good fitting formula. A second implication is that the FSEPP model, which currently is used mainly in nanoscience, may have much wider applicability to electrostatic phenomena.

    Richard G. Forbes, Jonathan H. B. Deane (2017)Simplified re-derivation of the Murphy-Goodpre-exponential correction factors, In: 2017 30th International Vacuum Nanoelectronics Conference (IVNC)8051626pp. 236-237 IEEE

    This Poster outlines simple general derivations of the correction factors λ T =πp/sin(πp) and λ F =πq/sin(πq) that first appeared in this form in the 1973 re-formulation by Swanson and Bell of equations originally derived by Murphy and Good in 1956. The original proofs and results apply only to the Schottky-Nordheim barrier. For planar smooth-surface conceptual models, analyzed via the Kemble approach, the proofs outlined here apply to any barrier, provided that appropriate detailed (barrier-dependent) expressions can be found for the parameters p and q. An assessment of mathematical validity is reported on the Poster.

    Vasily G Suvorov, Richard G Forbes (2004)Theory of minimum emission current for a non-turbulent liquid-metal ion source, In: Microelectronic engineering73-74126pp. 126-131 Elsevier Science
    Mahendra A More, Dilip S Joag, Richard G Forbes (2015)Field Electron Emission from Nanomaterials Springer
    Richard G. Forbes (1997)On the Problem of Establishing the Location of the Electrical Surface (Image Plane) for a Tungsten Field Emitter, In: Zeitschrift für physikalische Chemie (Neue Folge)202(1-2)139pp. 139-161
    Mark Schulz, Vesselin Shanov, Zhangzhang Yin, Marc Cahay, Richard G. Forbes (2019)Nanotube superfiber materials: science, manufacturing, commercialization William Andrew

    Nanotube superfiber materials refers to different forms of macroscale materials with unique properties constructed from carbon nanotubes. These materials include nanotube arrays, ribbons, scrolls, yarn, braid, and sheets. Nanotube materials are in the early stage of development and this is the first dedicated book on the subject.

    E. O. Popov, A. G. Kolosko, S. V. Filippov, P. A. Romanov, R. G. Forbes (2015)Real-time verification of current-voltage characteristics conformity to the classical field emission theory by 'orthodoxy' test, In: 2015 28th International Vacuum Nanoelectronics Conference (IVNC)7225524pp. 44-45 IEEE

    An experimental apparatus and a LabView-based software suite for real-time research on field emission were developed. The current-voltage characteristics of field emitters based on carbon nanotube/polymer nanocomposite were observed and analyzed using a simple quantitative test for lack of conformity with classical field emission theory.

    Richard G. Forbes (2017)Field electron emission theory for technology, In: 2017 EIGHTEENTH INTERNATIONAL VACUUM ELECTRONICS CONFERENCE (IVEC)2018-pp. 1-2 IEEE

    The process of field electron emission (FE) is relevant to several technological applications of interest to vacuum electronics. In such contexts, it is helpful to be able to accurately simulate the electron emission process itself and (where relevant) the behavior of technological devices and processes based on FE. It is also necessary to be able to correctly interpret the results of experimental investigations into the behavior of specific field emitters. A fully realistic theory of FE would be intensely difficult in its fine details, and full understanding seems well beyond the existing frontiers of theoretical physics. Nevertheless, over the last ten years there has been significant progress in physical and mathematical understanding. This paper aims to give a high-level overview of these developments and how they improve our ability to understand and simulate field emitter behavior in technological contexts.

    Richard G. Forbes (2014)Development of an integrated theory of field emitter optics, In: 2014 20th International Workshop on Beam Dynamics and Optimization (BDO)6890017pp. 1-2 IEEE

    This paper reports progress in developing an integrated theory of field emitter optics that covers both electron and ion emission (including liquid metal ion sources and atom probe tomography). Issues covered include resolution theory, Hawkes-Kasper angular magnification, discrepancies in brightness theory, and whether reduced brightness really is a conserved quantity.

    Richard Forbes, Fred Danoix, John Xanthakis (2007)49th International Field Emission Symposium, In: Surface and interface analysis39(2-3)pp. 92-92 John Wiley & Sons, Ltd
    Jie Peng, Zhibing Li, Chunshan He, Guihua Chen, Weiliang Wang, Shaozhi Deng, Ningsheng Xu, Xiao Zheng, GuanHua Chen, Chris Edgcombe, Richard Forbes (2008)The roles of apex dipoles and field penetration in the physics of charged, field emitting, single-walled carbon nanotubes, In: Journal of applied physics104(1)014310pp. 014310-014310-12 American Institute of Physics

    A 1   μ m long, field emitting, (5, 5) single-walled carbon nanotube (SWCNT) closed with a fullerene cap, and a similar open nanotube with hydrogen-atom termination, have been simulated using the modified neglect of diatomic overlap quantum-mechanical method. Both contain about 80 000 atoms. It is found that field penetration and band bending, and various forms of chemically and electrically induced apex dipole play roles. Field penetration may help explain electroluminescence associated with field emitting CNTs. Charge-density oscillations, induced by the hydrogen adsorption, are also found. Many of the effects can be related to known effects that occur with metallic or semiconductor field emitters; this helps both to explain the effects and to unify our knowledge about FE emitters. However, it is currently unclear how best to treat correlation-and-exchange effects when defining the CNT emission barrier. A new form of definition for the field enhancement factor (FEF) is used. Predicted FEF values for these SWCNTs are significantly less than values predicted by simple classical formulae. The FEF for the closed SWCNT decreases with applied field; the FEF for the H-terminated open SWCNT is less than the FEF for the closed SWCNT but increases with applied field. Physical explanations for this behavior are proposed but the concept of FEF is clearly problematical for CNTs. Curved Fowler-Nordheim plots are predicted. Overall, the predicted field emission performance of the H-terminated open SWCNT is slightly better than that of the closed SWCNT, essentially because a C-H dipole is formed that reduces the height of the tunneling barrier. In general, the physics of a charged SWCNT seems much more complex than hitherto realized.

    This conference talk serves two purposes. By considering a thought experiment involving two connected wires with different work functions, it shows that the "practical voltage" measured by a galvanometer-type voltmeter (or modern equivalents) does NOT coincide with the quantity "IEC voltage" defined in the International Standard for Electromagnetism and related documents. The probable cause of this discrepancy and some other related issues will be discussed. Further study of the thought experiment leads to a more complete explanation of patch fields, and insights into the theory of electron emission, and into the behavior of charged entities near metal surfaces that exhibit areas of different local work function.

    Richard G. Forbes (2000)Theory and Modelling of Field-Induced Electron Emission, In: MRS proceedings621R3.1.1pp. R311-R315 Cambridge University Press

    This paper addresses issues in the theory of field-induced electron emission. First, it summarises our present understanding of the theory of Fowler-Nordheim (FN) plots, and shows the relationship between a recent precise (in standard FN theory) approach to the interpretation of the FN-plot intercept and older approximate approaches. Second, it comments on the interpretation of FN plots taken from semiconductor field emitters. Third, it summarises the main points of a recent hypothesis about the mechanism of field-induced emission from carbonbased films and other electrically nanostructured heterogeneous (ENH) materials. Weaknesses in previous hypotheses are noted. It is hypothesised that thin films of all ENH materials, when deposited on a conducting substrate, will emit electrons in appropriate circumstances. Such films emit electrons at low macroscopic fields because they contain conducting nanostructure inside them: this structure generates sufficient geometrical field enhancement near the film/vacuum interface that more-or-less normal Fowler-Nordheim emission can occur. In connection with experiments on amorphous carbon films carried out by a group in Fribourg, it is shown that nanostructure of the size measured by scanning probe techniques should be able to generate field enhancement of the size measured in field electron spectroscopy experiments. This result provides a quantitative corroboration of other work suggesting that emission from amorphous carbon films is primarily due to geometrical field enhancement by nanostructures inside the film. Some counter-arguments to the internal-field-enhancement hypothesis are considered and disposed of. Some advantages of ENH materials as broad-area field emission electron sources are noted; these include control of material design.

    Caio P. de Castro, Thiago A. de Assis, Roberto Rivelino, Fernando de B. Mota, Caio M.C. de Castilho, Richard G. Forbes (2020)First-principles evidence of a constant effective field enhancement factor for carbon nanotube field emitters, In: 2020 33rd International Vacuum Nanoelectronics Conference (IVNC)9203565pp. 1-2 IEEE

    In recent density-functional-theory (DFT) calculations on small single-walled carbon nanotubes, it has been found that subtracting-off the zero-field components to form induced charge, potential, field and field-enhancement-factor distributions leads to useful theoretical insights and better consistency with the best experiments. This Poster represents an interim report that summarizes the current state of our thinking, and indicates the issues that we consider need to be explored further.

    R.G. Forbes (1976)On the need for new measurements of the field-ion appearance potential for helium, In: International journal of mass spectrometry and ion physics21(3)417pp. 417-420 Elsevier B.V
    Richard G. Forbes (2021)A Tutorial Commentary on the Schottky Constant, In: 2021 34th International Vacuum Nanoelectronics Conference (IVNC)pp. 1-2 IEEE

    The Schottky constant plays a central role in modern theories of field electron emission, thermal electron emission, and ionic field evaporation, particularly since the 1970s reforms in the international system of measurement. However, it is not widely recognised as a useful universal constant. This Poster provides a brief "tutorial" introduction to the Schottky constant, primarily for those not familiar with it. It provides a definition, and proof of relevant equations. It indicates the main contexts in which the Schottky constant is used, and demonstrates that the Schottky constant is a "property of the world" that is represented by technically different physical quantities in different equation systems.

    Richard G. Forbes (1976)A generalised theory of standard field ion appearance energies, In: Surface science61(1)pp. 221-240 Elsevier B.V

    By means of arguments based on a thermodynamic cycle, general formulae are derived which express standard field ion appearance energies in terms of atomic parameters and molecular term values, and in terms of thermodynamic parameters. These formulae may be applied to field ionization, field evaporation, or to the field desorption of well-behaved molecules, and apply to a very wide range of desorption mechanisms. Previous theories of energy deficits are reviewed in the light of the general result. The extent of agreement between theory and experiment is assessed, and the need for continued theoretical development is noted. Formulae are provided for converting the variety of energy-deficit parameters encountered in the literature into appearance energies; and the various terminologies are correlated.

    Richard G. Forbes (2018)Comparison of the Lepetit Field emission currentdensity calculations with the Modinos-Forbes uncertainty limits, In: 2018 31st International Vacuum Nanoelectronics Conference (IVNC)8520077pp. 1-2 IEEE

    This poster makes some preliminary comparisons between (a) the results of atomic-level theories of metal field electron emission (FE) recently reported by Lepetit, and (b) the Modinos-Forbes uncertainty limits relating to the accuracy of zero-temperature Murphy-Good theory (which is based, like most existing FE theory, on an unrealistic smooth-surface conceptual model). It is found that there is broad consistency between the new results and the old uncertainty limits. The poster briefly indicates some further steps that would now be useful, on the long and winding path towards developing accurate and reliable field emission theory.

    Richard G. Forbes (2014)Comments on the voltage scaling of field electron emission current-voltage characteristics, In: 2014 27th International Vacuum Nanoelectronics Conference (IVNC)6894781pp. 116-117 IEEE

    This conference presentation comments on the recent report of nearly-exact voltage scaling, in field electron emission measurements made when a single-tip emitter faces an extended planar surface. An alternative, "intuitive", explanation is offered for this effect, and supplements the more quantitative explanations presented in the literature.

    Richard G. Forbes (2014)Progress in establishing field electron emission science, In: 2014 Tenth International Vacuum Electron Sources Conference (IVESC)6891979pp. 1-2 IEEE

    This paper has three related aims. First, it argues that there is a need for a carefully formulated and properly established body of field electron emission science. Second, it outlines what this body of science should include. Third, it reports on progress on putting this science into place.

    J. J VAN ES, J Gierak, R. G Forties, V. G Suvorov, T VAN DEN BERGHE, Ph Dubuisson, I Monnet, A Septier, Richard G. Forbes (2004)An improved gallium liquid metal ion source geometry for nanotechnology, In: Microelectronic engineering73-74132pp. 132-138 Elsevier Science
    J. Ludwick, M. Cahay, N. Hernandez, H. Hall, J. O'Mara, K. L. Jensen, J. H. B. Deane, R. G. Forbes, T. C. Back (2021)A new multiscale approach to rapidly determine the local emission current density of nanoscale metallic field emitters, In: Journal of applied physics130(14)144302 AIP Publishing

    We advocate the use of lookup tables in the development of extremely fast and accurate multiscale models based on the coupling of a quantum-mechanical wave impedance approach and finite-element simulations to determine the local emission current density (LECD) from a metallic emitter of arbitrary shape. The lookup tables are prepopulated with numerical solutions of LECD that can be adjusted to accommodate any form of higher order physics, which is critical for current state-of-the-art emitters. Results show that the use of lookup tables can speed up numerical simulations of the field emission current from metallic cathodes by a factor of about 1000 x while retaining high precision, with a maximum error of less than 1% when compared to direct numerical solutions. Implementation of nanoscale emitter physics into lookup tables is discussed and used to assess the validity of the Kemble approximation for nanoscale metallic cathodes. The use of lookup tables is illustrated through a calculation of the LECDs of a metallic field emitter with a rugged surface and from an array of ellipsoid-on-a-post emitters. Section V contains our conclusions and suggestions for future work.

    R G Forbes (1976)INTRINSIC ENERGY-LOSSES OF FIELD-EVAPORATED IONS - REPLY, In: Journal of physics. D, Applied physics9(15)pp. L191-L193 Iop Publishing Ltd
    X-Z Qin, W-L Wang, N-S Xu, Z-B Li, RG Forbes (2011)Analytical treatment of cold field electron emission from a nanowall emitter, including quantum confinement effects, In: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES467(2128)pp. 1029-1051 ROYAL SOC
    J Peng, Z Li, C He, G Chen, W Wang, S Deng, N Xu, X Zheng, G Chen, CJ Edgcombe, RG Forbes (2008)The roles of apex dipoles and field penetration in the physics of charged, field emitting, single-walled carbon nanotubes, In: Journal of Applied Physics104(1)
    M. Cahay, W. Zhu, J. Ludwick, K.L. Jensen, R.G. Forbes, S.B. Fairchild, T.C. Back, P.T. Murray, J.R. Harris, D.A. Shiffler (2019)Multiscale Modeling of Field Emission Properties of Carbon-Nanotube-Based Fibers, In: Mark Schulz, Vesselin Shanov, Zhangzhang Yin, Marc Cahay (eds.), Nanotube Superfiber Materials: Science, Manufacturing, Commercializationpp. 541-568 Elsevier Inc

    In the previous chapter, building on recent efforts to characterize carbon nanotube fibers (CNFs) as efficient electron emission sources suitable for compact, high power, high frequency vacuum electronic devices, an exhaustive approach towards optimizing CNF field electron emission (FE) properties was proposed. It consists of a platform of scientific enquiry geared towards a meaningful comparison between different CNF-based emitters. The platform envisages an iterative procedure involving (a) the growth, processing, and functionalization of CNFs, (b) full investigation of the CNF material properties before and after FE diagnosis, and (c) multi-scale modeling of FE properties, including self-heating, shielding effects and beam characteristics for both CNFs and the emitting carbon nanotubes (CNTs) at the fiber apexes. The modeling would be applicable to a wide variety of CNFs and wire-like sources, and would provide essential feedback to the growth, processing, and functionalization of CNFs, in order to optimize their FE properties, especially long-term stability, low noise and maximum emission current, current density, emittance and brightness. In this chapter, we first report simulations of the influence of self-heating effects on the field emission (FE) properties of CNFs and their dependence on the product of the electrical and thermal conductivities of the fibers. We study the sensitivity of the FE of CNFs as the dimensions and numbers of CNTs at the apex of the fiber are varied. The influence of the field enhancement factors of both the shank of the fiber and the CNTs at its apex on the FE properties of CNFs is also analyzed. We conclude the chapter with a study of the influence of the electrostatic shielding on the FE characteristics of two CNFs as a function of the distance between the axes of the two fibers.

    M. Cahay, W. Zhu, J. Ludwick, K.L. Jensen, R.G. Forbes, S.B. Fairchild, T.C. Back, P.T. Murray, J.R. Harris, D.A. Shiffler (2019)Optimising the field emission properties of carbon-nanotube-based fibers, In: Mark Schulz, Vesselin Shanov, Zhangzhang Yin, Marc Cahay (eds.), Nanotube Superfiber Materials: Science, Manufacturing, Commercializationpp. 511-532 Elsevier Inc

    Building on recent efforts to characterize carbon nanotube fibers (CNFs) as efficient electron emission sources suitable for compact, high power, high frequency vacuum electronic devices, this chapter proposes an exhaustive approach towards optimizing CNF field emission (FE) properties. It outlines how a platform of scientific enquiry geared towards a meaningful comparison between different CNF-based emitters can be developed. The platform envisages an iterative procedure involving (a) the growth, processing, and functionalization of CNFs, (b) full investigation of the CNF material properties before and after FE diagnosis, and (c) multi-scale modeling of FE properties, including self-heating, shielding effects and beam characteristics in the CNFs and in the emitting carbon nanotubes (CNTs) at the fiber apexes. The modeling would be applicable to a wide variety of CNFs and wire-like sources, and would provide essential feedback to the growth, processing, and functionalization of CNFs, in order to optimize their FE properties, especially long-term stability, low noise, maximum emission current, current density, emittance, and brightness.

    U588: These Notes support a spreadsheet called <Spreadsheet for high-precision evaluation of the field emission special mathematical functions, November 2023 (v2311)>. They explain the structure of the spreadsheet and the background to the parameters and formulae used in the spreadsheet.

    —For explaining electrical breakdown, field electron emission (FE) is a mechanism of interest. In the period 2006 to 2010 there were significant developments in basic FE theory, but these have not yet fully entered general thinking in technological FE areas, which are often still based on 1960s thinking or (in some contexts 1920s thinking) about FE theory. This paper outlines the history of FE theory and provides an overview of modern developments and of some related topics, in so far as these affect the interpretation of experiments and the explanation of physical phenomena. The paper concentrates on principles, with references given where details can be found. Some suggestions are made about moving to the use of "21st-Century" FE theory. In addition, an error in Feynman's treatment of the electrostatics of pointed conductors is displayed, and it is found that Zener tunneling is implausible as a primary cause of vacuum breakdown from a CuO overlayer.

    This paper focuses on one small but significant part of a long-term project that aims to improve the interpretation of measured field electron emission (FE) current-voltage [I_m(V_m)] data, and (later) the formulation of FE theory. A new form of FE I_m(V_m) data-analysis plot - the so-called "Murphy-Good (MG) plot" - has recently been introduced, within the general framework of the prevailing "smooth planar metal-like emitter" methodology. This new plot form, and the reasons for its introduction, are discussed. It is shown that the MG plot can perform all the functions that the traditional (90-year old) Fowler-Nordheim plot does, but in addition yields relatively precise results for the characterization parameter formal emission area. It can be argued that, certainly in scientific contexts, the use of MG plots could usefully replace the use of FN plots.

    Richard G. Forbes, Sergey V. Filippov, Anatoly G. Kolosko, Eugeni O. Popov (2023)Progress on the Journey to Put Field Electron Emission Onto a Better Scientific Basis, In: Proceedings of the 2023 IEEE 36th International Vacuum Nanoelectronics Conference (IVNC 2023)pp. 152-154 Institute of Electrical and Electronics Engineers (IEEE)

    This presentation is part of a long-term project to put field electron emission (FE) onto a better scientific basis, by seeking reliable quantitative agreement between theory and experiment, especially as regards emission-current values. The main paper aims are: (1) to respond to remarks made in recent papers [1], [2]; (2) to restate the thinking behind our 2022 methodology [3] for choosing between different FE models using experiments; (3) to assess progress; and (4) to make further suggestions about improved approaches.

    Caio P. de Castro, Thiago A. de Assis, Roberto Rivelino, Fernando B. Mota, Caio M. C. de Castilho, Richard G. Forbes (2023)Evidence for a Field-Independent Enhancement Factor in the Real Tunneling Potential Barrier of Nanotube Emitters, In: Proceedings of the 2023 IEEE 36th International Vacuum Nanoelectronics Conference (IVNC)pp. 25-27 Institute of Electrical and Electronics Engineers (IEEE)

    We have demonstrated evidence that: (a) a constant characteristic induced field enhancement factor (FEF) can be determined from ab initio density functional theory (DFT) calculations on carbon nanotubes; and (b) this FEF adequately describes the real tunneling barrier. We have confirmed this finding in capped (6,6) armchair, (10,0) zigzag and (10,5) single walled carbon nanotubes (SWCNTs). In all these cases, we have verified that the characteristic local induced field enhancement factor (LIFEF) does not significantly depend on the macroscopic applied field. This establishes the LIFEF as a field-independent characterization parameter for nano-emitters.

    Sergey V. Filippov, Richard G. Forbes, Eugeni O. Popov, Anatoly G. Kolosko, Fernando F. Dall'Agnol (2023)Further Studies on Using the AHFP Exponent to Choose Between Alternative Field Emission Theories, In: Proceedings of the 2023 IEEE 36th International Vacuum Nanoelectronics Conference (IVNC 2023)pp. 177-179 Institute of Electrical and Electronics Engineers (IEEE)

    The general background to this research is set out in [1], [2]. It is based on the idea that an experimentally measured value of the so-called "AHFP exponent" kmight be used to choose between alternative theories of field electron emission (FE), in the first instance between 1928/29 Fowler-Nordheim (FN) FE theory and 1956 Murphy-Good (MG) FE theory. Amongst several factors that influence predicted theoretical ranges for x-values are the shape and local work function of a point-like or post-like field emitter. Our earlier work [1] explored a limited range of these parameters, but the overall conclusion was that the only x-value (1.63) considered adequately reliable did not yield a decisive result. As discussed in detail in this presentation, we have now explored a wider range of these parameters, but the outcome is still not a decisive result. Implications are discussed in a separate presentation [2].

    Richard G. Forbes (2020)Use of Amount-of-Substance Terminology and Equations in Field Desorption Theory, In: Topics in Catalysis63(15-18)pp. 1502-1508 Springer Verlag

    This note proposes that the theories of field evaporation and field desorption, as used in atom-probe microscopy and related atomic-level contexts, should be consistently formulated in terms of a set of "seven-dimensional (7-D)" formulae and equations that involve the physical quantity "amount of substance", but make use of an atomiclevel constant effectively equal to "one atom" (or, more generally, "one entity"). It is argued that the term "count" should be introduced as an alternative name (more suited to atomic-level contexts) for the quantity "amount of substance". For field evaporation/desorption theories, relevant definitions and formulae are proposed, and compared with the "six-dimensional" system (based on the dimensionless quantity "number of atoms/entities") sometimes used in the literature. Advantages of using a 7-D system are noted. It is argued that there is also an increasing need for a comprehensive system of official nomenclature for atomic-level constants and units, for all three of the extensive quantities "mass", "electric charge" and "amount of substance". It is also argued that, in the longer term, considerations of the kind being proposed here for field evaporation/desorption theories might usefully be applied more generally in atomic-level rate theory.

    U589: This Technical Report provides background theory and guidelines relating to the practical analysis of experimental field (electron) emission (FE) current-voltage data, using Murphy-Good FE theory. Uploaded version is the March 2024 version.

    JJ Van Es, J Gierak, RG Forbes, VG Suvorov, T Van den Berghe, P Dubuisson, I Monnet, A Septier (2004)An improved gallium liquid metal ion source geometry for nanotechnology, In: MICROELECTRONIC ENGINEERING73-4pp. 132-138 ELSEVIER SCIENCE BV
    VG Suvorov, RG Forbes (2004)Theory of minimum emission current for a non-turbulent liquid-metal ion source, In: MICROELECTRONIC ENGINEERING73-4pp. 126-131 ELSEVIER SCIENCE BV

    These comments aim to correct some apparent weaknesses in the theory of field electron emission given in a recent paper about nanoscale vacuum channel transistors, and to improve the presentation of this theory. In particular, it is argued that a “simplified” formula stated in the paper should not be used, because this formula is known to under-predict emission current densities by a large factor (typically around 300 for an emitting surface with local work function 4.5 eV). Thus, the “simplified” formula may significantly under-predict the practical performance of a nanoscale vacuum channel transistor.

    R.G. Forbes (2017)Introduction to field electron and ion emission and customary units, In: G. Chiarotti, P. Chiaradia (eds.), Landolt-Börnstein: Numerical data and Functional Relationships in Science and Technology - New Series - Physics of Solid SurfacesIII/45pp. pp 657-723 Springer-Verlag
    A Fischer, MS Mousa, JHB Deane, RG Forbes (2013)The effect of barrier form on slope and intercept correction factors for curved emitters: Development of some enabling theory, In: 2013 26th International Vacuum Nanoelectronics Conference, IVNC 2013

    The work described in this conference poster follows up recent work on the interpretation of Fowler-Nordheim (FN) plots. It puts in place some enabling theory that should allow further development of plot interpretation theory, in the context of the sphere-on-othogonal-cone (SOC) emitter model. This model is expected to be more suitable, for small-apex-radius emitters, than the spherical-emitter (SPH) model. First, this report shows (as expected) that use of the spherical image-potential-energy formula, rather than the planar formula, appears to make little difference to the values of calculated parameters. Second, values of the exponent n (in the SOC model) are tabulated as a function of internal cone half-angle. Third, an expression is derived for the electrostatic component of electron motive energy, in the SOC model. Finally, the results of a sample calculation are presented. This compares values of the slope correction factor σ for the SPH and SOC models, for emitter-radius values 20 nm and 5 nm. As expected, the results for the two models are similar for 20 nm, but diverge as apex radius decreases. © 2013 IEEE.

    RG Forbes, JHB Deane, RW Shail (2007)Exact mathematical solution for the principal field emission correction function v used in Standard Fowler-Nordheim theory, In: Technical Digest of the 20th International Vacuum Nanoelectronics Conference, IVNC 07pp. 149-150
    Alexandre Mayer, Marwan S. Mousa, Mark J. Hagmann, Richard Forbes (2019)Numerical testing by a transfer-matrix technique of Simmons' equation for the local current density in metal-vacuum-metal junctions, In: Jordan Journal of Physics Yarmouk University, Irbid, Jordan

    We test the consistency with which Simmons' model can predict the local current density obtained for at metal-vacuum-metal junctions. The image potential energy used in Simmons' original papers had a missing factor of 1=2. Besides this technical issue, Simmons' model relies on a mean-barrier approximation for electron transmission through the potential-energy barrier between the metals. In order to test Simmons' expression for the local current density when the correct image potential energy is included, we compare the results of this expression with those provided by a transfer-matrix technique. This technique is known to provide numerically exact solutions of Schrodinger's equation for this barrier model. We also consider the current densities provided by a numerical integration of the transmission probability obtained with the WKB approximation and Simmons' mean-barrier approximation. The comparison between these different models shows that Simmons' expression for the local current density actually provides results that are in good agreement with those provided by the transfer-matrix technique, for a range of conditions of practical interest. We show that Simmons' model provides good results in the linear and weld-emission regimes of current density versus voltage plots. It loses its applicability when the top of the potential-energy barrier drops below the Fermi level of the emitting metal.

    Richard Forbes (2017)Field electron emission theory, In: Young Researchers in Vacuum Micro/Nano Electronics (VMNE-YR) ISBN: 78-1-5090-4605-8 IEEE

    This conference paper provides an overview of the material presented in two field electron emission tutorial lectures given at the 2016 Young Researchers' School in Vacuum Microand NanoElectronics, held in Saint-Petersburg on October 5-6 2016. This paper aims to indicate the scope and structure of the tutorials, and also where some of the related published material can be found.

    Mahendra A. More, Dilip S. Joag, Richard G. Forbes (2015)Field Electron Emission from Nanomaterials, In: Bharat Bhushan (eds.), Encyclopedia of Nanotechnologypp. 1-23 Springer
    Michael K. Miller, Richard G. Forbes (2014)Atom-Probe Tomography - The Local Electrode Atom Probe, In: Atom-Probe Tomography Springer US
    Mohammad M. Allaham, Richard Forbes, Marwan S. Mousa (2020)Applying the Field Emission Orthodoxy Test to Murphy-Good Plots, In: Jordan Journal of Physics Yarmouk University

    In field electron emission (FE) studies, it is important to check and analyse the quality and validity of results experimentally obtained from samples, using suitably plotted current-voltage [Im(Vm)] measurements. For the traditional plotting method, the Fowler-Nordheim (FN) plot, there exists a so-called "orthodoxy test" that can be applied to the FN plot, in order to check whether the FE device/system generating the results is "ideal". If it is not ideal, then emitter characterization parameters deduced from the FN plot are likely to be spurious. A new form of FE Im(Vm) data plot, the so-called "Murphy-Good (MG) plot" has recently been introduced (R.G. Forbes, Roy. Soc. open sci. 6 (2019) 190912. This aims to improve the precision with which characterization-parameter values (particularly values of formal emission area) can be extracted from FE Im(Vm) data. The present paper compares this new plotting form with the older FN and Millikan-Lauritsen (ML) forms, and makes an independent assessment of the consistency with which slope (and hence scaled-field) estimates can be extracted from a MG plot. It is shown that, by using a revised formula for the extraction of scaled-field values, the existing orthodoxy test can be applied to Murphy-Good plots. The development is reported of a prototype web tool that can apply the orthodoxy test to all three forms of FE data plot (ML, MG and FN).

    Thiago A. de Assis, Fernando F. Dall'Agnol, Richard G. Forbes (2022)Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling, In: Journal of Physics: Condensed Matter34(49)493001 IOP Publishing

    This review of the quantitative electrostatics of field emitters, covering analytical, numerical and "fitted formula" approaches, is thought to be the first of its kind in the 100 years of the subject. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is "polarity independent", so the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors—which exhibit the "electrostatic lightning-rod effect", but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than fields) becomes apparent. Space and time limitations have meant the review cannot be comprehensive in both detail and scope. Rather, it focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called "screening" or "shielding"). Core to the review are discussions of the "minimum domain dimensions" method for implementing effective finite-element-method electrostatic simulations, and of the variant that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001 % in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many "related considerations" relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

    RICHARD G. FORBES (2023)Field emission: Applying the "magic emitter" validity test to a recent paper, and related research-literature integrity issues, In: Journal of vacuum science and technology. B, Nanotechnology & microelectronics41(4)042807 A V S Amer Inst Physics

    This work concerns field electron emission (FE) from large-area emitters. It corrects literature weaknesses in analyzing experimental current-voltage data and related emitter characterization. A recent paper in Applied Surface Science exemplifies these difficulties: (1) for many modern emitters, traditional data-analysis methodologies, such as the Fowler-Nordheim plot developed in 1929, yield spurious results; (2) confusion occurs between the concepts of local and macroscopic (or "emitter average") current density; (3) data analysis uses 1920s-style emission equations that were proved seriously incorrect (by a factor typically of order 100) in the 1950s. These weaknesses can combine to yield large undetected discrepancies between theory and experiment in published papers (a factor of 10(16) in the example under discussion). The present work shows how a recently introduced validity test-the "magic emitter" test-can sometimes be used, at the immediate-presubmission or review stage, to help uncover scientific problems. In literature concerning large-area FE over the last 15 years or so, there seem many papers (perhaps hundreds) with some or all of the weaknesses discussed: very many authors and reviewers in this community, and many editors, seem to have been "hoaxed" by what sociologists of science call a "pathological literature." The scientific integrity of this research area, and the related peer review processes, appear significantly damaged, and attempts to correct this by normal procedures have had limited effect. There seems a growing case for independent "official" wider investigation into research integrity issues of this general kind, and maybe, for a later regulatory action.

    RG Forbes, JHB Deane, N Hamid, HS Sim (2004)Extraction of emission area from Fowler-Nordheim plots, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B22(3)pp. 1222-1226 A V S AMER INST PHYSICS
    RG FORBES (1989)ON CHARGED-SURFACE MODELS AND THE ORIGIN OF FIELD ADSORPTION, In: SURFACE SCIENCE223(1-2)pp. 326-352 ELSEVIER SCIENCE BV
    RG FORBES, NN LJEPOJEVIC (1989)MODELING OF LIQUID-METAL ION SOURCES, In: VACUUM39(11-12)pp. 1153-1155 PERGAMON-ELSEVIER SCIENCE LTD
    RK BISWAS, RG FORBES (1988)A CLASSIFICATION OF TESTS AGAINST THE MULLER ESCAPE MECHANISM, In: JOURNAL DE PHYSIQUE49(C-6)pp. 11-16 EDITIONS PHYSIQUE
    RG FORBES (1991)FURTHER COMMENTS ON FIELD ADSORPTION, In: SURFACE SCIENCE246(1-3)pp. 386-389 ELSEVIER SCIENCE BV
    RG FORBES, RK BISWAS, K CHIBANE (1982)FIELD EVAPORATION THEORY - A REANALYSIS OF PUBLISHED FIELD SENSITIVITY DATA, In: SURFACE SCIENCE114(2-3)pp. 498-514 ELSEVIER SCIENCE BV
    RG FORBES (1981)PROGRESS WITH THE THEORY OF NOBLE-GAS FIELD ADSORPTION, In: VACUUM31(10-1)pp. 567-570 PERGAMON-ELSEVIER SCIENCE LTD
    RG FORBES (1982)A NEW FORMULA FOR PREDICTING LOW-TEMPERATURE EVAPORATION FIELD, In: APPLIED PHYSICS LETTERS40(3)pp. 277-279 AMER INST PHYSICS
    RG FORBES (1980)WAVE-MECHANICAL THEORY OF FIELD-IONIZATION AND FIELD-ION ENERGY-DISTRIBUTIONS, In: PROGRESS IN SURFACE SCIENCE10(2)pp. 249-285 PERGAMON-ELSEVIER SCIENCE LTD
    RG FORBES (1981)CHARGE HOPPING AND CHARGE DRAINING - 2 MECHANISMS OF FIELD DESORPTION, In: SURFACE SCIENCE102(1)pp. 255-263 ELSEVIER SCIENCE BV
    RG FORBES (1980)APPEARANCE ENERGIES FOR TUNGSTEN IONS FIELD-EVAPORATED FROM IONIC BONDING STATES, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS13(7)pp. 1357-1363 IOP PUBLISHING LTD
    Fernando F Dall'Agnol, Thiago A de Assis, Richard Forbes (2018)Physics-based derivation of a formula for the mutual depolarisation of two post-like field emitters, In: Journal of Physics: Condensed Matter30(37)375703 IOP Publishing

    Recent analyses of the apex field enhancement factor (FEF) for many forms of field emitter have revealed that the depolarization effect is more persistent with respect to the separation between the emitters than originally assumed. It has been shown that, at sufficiently large separations, the fractional reduction of the FEF decays with the inverse cube power of separation, rather than exponentially. The behavior of the fractional reduction of the FEF encompassing both the range of technological interest (c being the separation and h is the height of the emitters) and large separations () has not been predicted by the existing formulas in field emission literature, for post-like emitters of any shape. In this work, we use first principles to derive a simple two-parameter formula for fractional reduction that can be useful for experimentalists for modeling and interpreting the FEFs for small clusters of emitters or arrays at separations of interest. For the structures tested, the agreement between numerical and analytical data is  ~1%.

    RG FORBES, K CHIBANE (1986)DERIVATION OF AN ACTIVATION-ENERGY FORMULA IN THE CONTEXT OF CHARGE DRAINING, In: JOURNAL DE PHYSIQUE47(C-7)pp. 65-70 EDITIONS PHYSIQUE
    RG Forbes (2004)On the use of energy-space diagrams in free-electron models of field electron emission, In: SURFACE AND INTERFACE ANALYSIS36(5-6)pp. 395-401 JOHN WILEY & SONS LTD

    An improved method is reported for deriving the equations for cold field electron emission from a free-electron metal. It is shown that the derivation of these equations can be presented as a straightforward double integral in a space where the vertical axis represents the total electron energy, and the horizontal axis represents the component of electron kinetic energy parallel to the emitter surface. A general approach is developed that applies to a tunnelling barrier of any shape. It is shown that the temperature-correction factor derived by Murphy and Good for emission through an image-rounded barrier also applies to a more general barrier. For the standard image-rounded barrier the results coincide with those of Murphy and Good, but the derivation is more straightforward mathematically and the physics involved can be visualized more easily. The method developed here should be a good foundation for developing an improved theory of cold field electron emission from semiconductors: the main object of the paper is to lay this foundation. Copyright (C) 2004 John Wiley Sons, Ltd.

    RG FORBES (1986)TOWARDS A UNIFIED THEORY OF HELIUM FIELD-IONIZATION PHENOMENA, In: JOURNAL DE PHYSIQUE47(C-2)pp. 3-10 EDITIONS PHYSIQUE
    RG Forbes, JHB Deane (2007)Reformulation of the standard theory of Fowler-Nordheim tunnelling and cold field electron emission, In: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES463(2087)pp. 2907-2927 ROYAL SOC
    RG Forbes (2013)Development of a simple quantitative test for lack of field emission orthodoxy, In: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES469(2158)ARTN 20130 ROYAL SOC
    RG Forbes (2016)Physical electrostatics of small field emitter arrays/clusters, In: Journal of Applied Physics120

    This paper aims to improve qualitative understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays/clusters. Using the “floating sphere at emitter-plate potential” (FSEPP) model, it re-examines the electrostatics and mathematics of three simple systems of identical post-like emitters. For the isolated emitter, various approaches are noted. An adequate approximation is to consider only the effects of sphere charges and (for significantly separated emitters) image charges. For the 2-emitter system, formulas are found for charge-transfer (“charge-blunting”) effects and neighbor-field effects, for widely spaced and for “sufficiently closely spaced” emitters. Mutual charge-blunting is always the dominant effect, with a related (negative) fractional AFEF-change δ two. For sufficiently small emitter spacing c, |δ two| varies approximately as 1/c; for large spacing, |δ two| decreases as 1/c 3. In a 3-emitter equispaced linear array, differential charge-blunting and differential neighbor-field effects occur, but differential charge-blunting effects are dominant, and cause the “exposed” outer emitters to have higher AFEF (γ 0) than the central emitter (γ 1). Formulas are found for the exposure ratio Ξ = γ 0/γ 1, for large and for sufficiently small separations. The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge models (LCMs) are an alternative, but an apparent difficulty with recent LCM implementations is identified. Better descriptions of array electrostatics may involve developing good fitting equations for AFEFs derived from accurate numerical solution of Laplace's equation, perhaps with equation form(s) guided qualitatively by FSEPP-model results. In existing fitting formulas, the AFEF-reduction decreases exponentially as c increases, which is different from the FSEPP-model formulas. This discrepancy needs to be investigated, using systematic Laplace-based simulations and appropriate results analysis. FSEPP models might provide a useful provisional guide to the qualitative behaviour of small field emitter clusters larger than those investigated here.

    RG FORBES, MK WAFI (1980)AN ARRAY MODEL FOR THE FIELD ADSORPTION OF HELIUM ON TUNGSTEN (111), In: SURFACE SCIENCE93(1)pp. 192-212 ELSEVIER SCIENCE BV
    Richard Forbes (2017)The theoretical link between voltage loss, reduction in field enhancement factor, and Fowler-Nordheim-plot saturation, In: Applied Physics Letters110(13)133109pp. 133109-1 AIP Publishing

    With a large-area field electron emitter, when an individual post-like emitter is sufficiently resistive, and current through it is sufficiently large, then voltage loss occurs along it. This letter provides a simple analytical and conceptual demonstration that this voltage loss is directly and inextricably linked to a reduction in the field enhancement factor (FEF) at the post apex. A formula relating apex-FEF reduction to this voltage loss was obtained in the paper by Minoux et al. [Nano Lett. 5, 2135 (2005)] by fitting to numerical results from a Laplace solver. This letter derives the same formula analytically, by using a “floating sphere” model. The analytical proof brings out the underlying physics more clearly and shows that the effect is a general phenomenon, related to reduction in the magnitude of the surface charge in the most protruding parts of an emitter. Voltage-dependent FEF-reduction is one cause of “saturation” in Fowler-Nordheim (FN) plots. Another is a voltage-divider effect, due to measurement-circuit resistance. An integrated theory of both effects is presented. Both together, or either by itself, can cause saturation. Experimentally, if saturation occurs but voltage loss is small (

    RG FORBES (1978)FIELD ADSORPTION - MONOPOLE-DIPOLE INTERACTION, In: SURFACE SCIENCE78(2)pp. L504-L507 ELSEVIER SCIENCE BV
    RG Forbes, JHB Deane (2010)Comparison of approximations for the principal Schottky-Nordheim barrier function v(f), and comments on Fowler-Nordheim plots, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B28(2)pp. C2A33-C2A42 A V S AMER INST PHYSICS
    RG Forbes (2008)Physics of generalized Fowler-Nordheim-type equations, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B26(2)pp. 788-793 A V S AMER INST PHYSICS
    RG Forbes (1996)Charged surfaces, field adsorption, and appearance-energies: An unsolved challenge, In: JOURNAL DE PHYSIQUE IV6(C5)pp. 25-30 EDITIONS PHYSIQUE
    RG FORBES, GLR MAIR (1982)ARGUMENTS ABOUT EMITTER SHAPE FOR A LIQUID-METAL FIELD-ION EMISSION SOURCE, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS15(11)pp. L153-L158 IOP PUBLISHING LTD
    L Bischoff, W Pilz, T Ganetsos, RG Forbes, C Akhmadaliev (2007)GaBi alloy liquid metal ion source for microelectronics research, In: ULTRAMICROSCOPY107(9)pp. 865-868 ELSEVIER SCIENCE BV
    A Fischer, MS Mousa, RG Forbes (2013)Influence of barrier form on Fowler-Nordheim plot analysis, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B31(3)ARTN 03220 A V S AMER INST PHYSICS
    RG Forbes (2009)Use of the concept "area efficiency of emission" in equations describing field emission from large-area electron sources, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B27(3)pp. 1200-1203 A V S AMER INST PHYSICS
    RG FORBES (1980)DERIVATION OF SURFACE-ATOM POLARIZABILITY FROM FIELD-ION ENERGY DEFICITS, In: APPLIED PHYSICS LETTERS36(9)pp. 739-740 AMER INST PHYSICS
    RK BISWAS, RG FORBES (1982)THEORETICAL ARGUMENTS AGAINST THE MULLER-SCHOTTKY MECHANISM OF FIELD EVAPORATION, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS15(7)pp. 1323-1338 IOP PUBLISHING LTD
    RG FORBES (1979)CONCEPTUAL ERRORS IN THE THEORY OF FIELD ADSORPTION, In: SURFACE SCIENCE87(1)pp. L278-L284 ELSEVIER SCIENCE BV
    MK Miller, RG Forbes (2009)Atom probe tomography, In: MATERIALS CHARACTERIZATION60(6)pp. 461-469 ELSEVIER SCIENCE INC
    RG FORBES (1982)ELECTRO-THERMODYNAMIC CYCLES APPLIED TO IONIC POTENTIALS AND TO FIELD EVAPORATION, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS15(7)pp. 1301-1322 IOP PUBLISHING LTD
    RG Forbes (2010)Thin-slab model for field electron emission, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B28(2)pp. C2A43-C2A49 A V S AMER INST PHYSICS
    Richard G. Forbes (2019)The Murphy-Good plot: a better method of analysing field emission data, In: Royal Society Open Science The Royal Society

    Measured field electron emission (FE) current-voltage Im(Vm) data are traditionally analysed via Fowler-Nordheim (FN) plots, as ln{Im/(Vm)**2} vs 1/Vm. These have been used since 1929, because in 1928 FN predicted they would be linear. In the 1950s, a mistake in FN's thinking was found. Corrected theory by Murphy and Good (MG) made theoretical FN plots slightly curved. This causes difficulties when attempting to extract precise values of emission characterization parameters from straight lines fitted to experimental FN plots. Improved mathematical understanding, from 2006 onwards, has now enabled a new FE data-plot form, the "Murphy-Good plot". This plots ln{Im/(Vm)**(2-({____eta}/6)} vs 1/Vm, where {____eta} depends only on local work function. Modern ("21st century") MG theory predicts that a theoretical MG plot should be "almost exactly" straight. This makes precise extraction of well-defined characterization parameters from ideal I_m(V_m) data much easier. This article gives the theory needed to extract characterization parameters from MG plots, setting it within the framework of wider difficulties in interpreting FE Im(Vm) data (among them, use of the "planar emission approximation"). Careful use of MG plots could also help remedy other problems in FE technological literature. It is argued MG plots should now supersede FN plots.

    RG Forbes (1998)Calculation of the electrical-surface (image-plane) position for aluminium, In: ULTRAMICROSCOPY73(1-4)pp. 31-35 ELSEVIER SCIENCE BV
    RG Forbes (1996)Field-ion imaging old and new, In: APPLIED SURFACE SCIENCE94-5pp. 1-16 ELSEVIER SCIENCE BV
    RG FORBES (1982)TOWARDS A CRITERION FOR THE A-PRIORI PREDICTION OF FIELD-EVAPORATION MECHANISM, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS15(8)pp. L99-L104 IOP PUBLISHING LTD
    Richard G. Forbes (2019)Comments on the continuing widespread and unnecessary use of a defective emission equation in field emission related literature, In: Journal of Applied Physics126(21)210901pp. 210901-1 AIP Publishing

    Field electron emission (FE) has relevance in many technological contexts. However, many technological papers use a physically defective elementary FE equation for local emission current density (LECD). This equation takes the tunneling barrier as exactly triangular, as in the original FE theory of 90 years ago. More than 60 years ago, it was shown that the Schottky-Nordheim (SN) barrier, which includes an image-potential-energy term (that models exchange-and-correlation effects) is better physics. For a metal-like emitter with work-function 4.5 eV, the SN-barrier-related Murphy-Good FE equation predicts LECD values that are higher than the elementary equation values by a large factor, often between 250 and 500. By failing to mention/apply this 60-year-old established science, or to inform readers of the large errors associated with the elementary equation, many papers (aided by inadequate reviewing) spread a new kind of "pathological science", and create a modern research-integrity problem. The present paper aims to enhance author and reviewer awareness by summarizing relevant aspects of FE theory, by explicitly identifying the misjudgment in the original 1928 Fowler-Nordheim paper, by explicitly calculating the size of the resulting error, and by showing in detail why most FE theoreticians regard the 1950s modifications as better physics. Suggestions are made, about nomenclature and about citation practice, that may help diminish misunderstandings. It is emphasized that the correction recommended here is one of several needed to improve the presentation of theory in FE literature, and only a first step towards higher-quality emission theory and improved methodology for current-voltage data interpretation.

    Caio P. de Castro, Thiago A. de Assis, Roberto Rivelino, Fernando de B. Mota, Caio M. C. de Castilho, Richard. G. Forbes (2019)Restoring Observed Classical Behavior of the Carbon Nanotube Field Emission Enhancement Factor from the Electronic Structure, In: The Journal of Physical Chemistry C123(8)pp. 5144-5149 American Chemical Society

    Experimental Fowler–Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields FM. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF values that vary with FM. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use first-principles electronic structure calculations to derive real-charge distributions and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analyzed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the first-principles local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field and behave in the same qualitative manner as the classical FEF values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via first-principles approaches. This is a significant step forward in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.

    RG Forbes, JP Xanthakis (2007)Field penetration into amorphous-carbon films: consequences for field-induced electron emission, In: SURFACE AND INTERFACE ANALYSIS39(2-3)pp. 139-145 JOHN WILEY & SONS LTD
    RG Forbes (1999)Refining the application of Fowler-Nordheim theory, In: ULTRAMICROSCOPY79(1-4)pp. 11-23 ELSEVIER SCIENCE BV
    Thiago Albuquerque de Assis, Richard Forbes, Roberto Moreno, Caio Mário Castro de Castilho, Caio Castro, Fernando Brito Mota (2019)On the quantum mechanics of how an ideal carbon nanotube field emitter can exhibit a constant field enhancement factor, In: Journal of Applied Physics AIP Publishing
    RG Forbes (1997)Understanding how the liquid-metal ion source works, In: VACUUM48(1)pp. 85-97 PERGAMON-ELSEVIER SCIENCE LTD
    RG FORBES, K CHIBANE, N ERNST (1984)DERIVATION OF BONDING DISTANCE AND VIBRATION FREQUENCY FROM FIELD EVAPORATION EXPERIMENTS, In: SURFACE SCIENCE141(1)pp. 319-340 ELSEVIER SCIENCE BV
    GLR MAIR, T MULVEY, RG FORBES (1984)ENERGY SPREADS IN FIELD EVAPORATION AND LIQUID-METAL ION SOURCES, In: JOURNAL DE PHYSIQUE45(NC9)pp. 179-182 EDITIONS PHYSIQUE
    RG Forbes (2008)Description of field emission current/voltage characteristics in terms of scaled barrier field values (f-values), In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B26(1)pp. 209-213 A V S AMER INST PHYSICS
    RG Forbes (1999)The electrical surface as centroid of the surface-induced charge, In: ULTRAMICROSCOPY79(1-4)pp. 25-34 ELSEVIER SCIENCE BV
    Mohammad M. Allaham, Richard G. Forbes, Alexandr Knápek, Marwan S. Mousa (2019)Implementation of the Orthodoxy Test as a Validity Check on Experimental Field Emission Data, In: Journal of Electrical Engineering ─ Elektrotechnický časopis The Faculty of Electrical Engineering and Information Technology of the Slovak University of Technology in Bratislava

    In field electron emission (FE) studies, it is important to check and analyse the quality and validity of experimental current-voltage data, which is usually plotted in one of a small number of standard forms. These include the so-called Fowler-Nordheim (FN), Millikan- Lauritsen (ML) and Murphy-Good (MG) plots. The Field Emission Orthodoxy Test is a simple quantitative test that aims to check for the reasonableness of the values of the parameter "scaled field" that can be extracted from these plots. This is done in order to establish whether characterization parameters extracted from the plot will be reliable or, alternative, likely to be spurious. This paper summarises the theory behind the orthodoxy test, for each of the plot forms, and confirms that it is easy to apply it to the newly developed MG plot. A simple, new, accessible web application has been developed that extracts scaled-field values from any of these three plot forms, and tests for lack of field emission orthodoxy.

    RG Forbes, JHB Deane, A Fischer, MS Mousa (2013)Illustrating field emission theory by using Lauritsen plots of transmission probability and barrier strength, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B31(2)ARTN 02B10 A V S AMER INST PHYSICS
    SRP Silva, RG Forbes (1998)Controlling mechanisms for field-induced electron emission from diamond-like carbon films, In: ULTRAMICROSCOPY73(1-4)pp. 51-57 ELSEVIER SCIENCE BV
    RG FORBES (1982)AN EVAPORATION-FIELD FORMULA INCLUDING THE REPULSIVE ION-SURFACE INTERACTION, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS15(7)pp. L75-L77 IOP PUBLISHING LTD
    RG Forbes, A Fischer, MS Mousa (2013)Improved approach to Fowler-Nordheim plot analysis, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B31(2)ARTN 02B10 A V S AMER INST PHYSICS
    RG Forbes (1999)Field emission: New theory for the derivation of emission area from a Fowler-Nordheim plot, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B17(2)pp. 526-533 AMER INST PHYSICS
    RG Forbes, HJ Kreuzer, RLC Wang (1996)On the theory of helium field adsorption, In: APPLIED SURFACE SCIENCE94-5pp. 60-67 ELSEVIER SCIENCE BV
    RG Forbes (2008)Appendix to "Coulomb interactions in Ga LMIS" by Radlicka and Lencova, In: ULTRAMICROSCOPY108(5)pp. 455-457 ELSEVIER SCIENCE BV
    K CHIBANE, RG FORBES (1982)THE TEMPERATURE-DEPENDENCE OF EVAPORATION FIELD FOR GOMER-TYPE FIELD-EVAPORATION MECHANISMS, In: SURFACE SCIENCE122(2)pp. 191-215 ELSEVIER SCIENCE BV
    RG FORBES, K CHIBANE (1982)A FRESH LOOK AT THE ELECTRIC-FIELD DEPENDENCE OF SURFACE-ATOM BINDING-ENERGY, In: SURFACE SCIENCE121(2)pp. 275-289 ELSEVIER SCIENCE BV
    RG Forbes (1999)Use of a spreadsheet for Fowler-Nordheim equation calculations, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B17(2)pp. 534-541 AMER INST PHYSICS
    RLC Wang, HJ Kreuzer, RG Forbes (1996)Field adsorption of helium and neon on metals: An integrated theory, In: SURFACE SCIENCE350(1-3)pp. 183-205 ELSEVIER SCIENCE BV
    RG FORBES (1982)EXPERIMENTAL SUPPORT FOR A GOMER-TYPE ESCAPE MECHANISM AND HEAVY-ION TUNNELLING IN FIELD EVAPORATION, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS15(11)pp. L149-L152 IOP PUBLISHING LTD
    RG Forbes (1996)Some comments on the simultaneous desorption of He-3 and He-4, In: APPLIED SURFACE SCIENCE94-5pp. 73-78 ELSEVIER SCIENCE BV
    RG FORBES (1978)NEGATIVE WORK-FUNCTION CORRECTION AT A POSITIVELY-CHARGED SURFACE, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS11(14)pp. L161-L164 IOP PUBLISHING LTD
    RG FORBES (1978)FIELD EVAPORATION THEORY - ATOMIC-JUG FORMALISM, In: SURFACE SCIENCE70(1)pp. 239-254 ELSEVIER SCIENCE BV
    RG Forbes (2008)On the need for a tunneling pre-factor in Fowler-Nordheim tunneling theory, In: JOURNAL OF APPLIED PHYSICS103(11)ARTN 1pp. ?-? AMER INST PHYSICS
    AG Kolosko, SV Filippov, PA Romanov, EO Popov, Richard Forbes (2016)Real-time implementation of the "orthodoxy test" for conformity of current-voltage characteristics with classical field electron emission theory, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B34(4)ARTN 04180 A V S AMER INST PHYSICS

    An experimental apparatus and a LabView-based software suite were developed to conduct realtime research on field electron emission. The authors observed and analyzed the current–voltage characteristics of emitters based on carbon nanotube/polystyrene nanocomposites. A simple quantitative test was used to compare such characteristics with the classical field electron emission theory. Copyright 2016 American Vacuum Society

    RG Forbes (2010)Simple derivation of the formula for Sommerfeld supply density used in electron-emission physics and limitations on its use, In: Journal of Vacuum Science and Technology B: Microelectronics and Nanometer Structures28(6)pp. 1326-1329
    K CHIBANE, RG FORBES (1984)ON THE USE OF CURVE INTERSECTION FORMALISMS IN FIELD EVAPORATION THEORY, In: JOURNAL DE PHYSIQUE45(NC9)pp. 99-104 EDITIONS PHYSIQUE
    RG Forbes, CJ Edgcombe, U Valdre (2003)Some comments on models for field enhancement, In: ULTRAMICROSCOPY95(1-4)PII S0304-pp. 57-65 ELSEVIER SCIENCE BV
    NN LJEPOJEVIC, RG FORBES (1992)A COMPARISON OF THE NUMERICAL AND ANALYTICAL TREATMENTS OF A LIQUID-METAL ION-SOURCE, In: SURFACE SCIENCE266(1-3)pp. 176-179 ELSEVIER SCIENCE BV
    WB LIU, RG FORBES (1995)MODELING THE LINK BETWEEN EMISSION CURRENT AND LMIS CUSP LENGTH, In: APPLIED SURFACE SCIENCE87-8(1-4)pp. 122-126 ELSEVIER SCIENCE BV
    RG FORBES (1984)ON THE SHAPE OF A LIQUID-METAL FIELD-ION EMITTER, In: JOURNAL DE PHYSIQUE45(NC9)pp. 161-166 EDITIONS PHYSIQUE
    RG FORBES, GLR MAIR, NN LJEPOJEVIC, WB LIU (1995)NEW UNDERSTANDINGS IN THE THEORY OF LIQUID-METAL ION SOURCES, In: APPLIED SURFACE SCIENCE87-8(1-4)pp. 99-105 ELSEVIER SCIENCE BV
    GLR MAIR, RG FORBES (1991)ANALYTICAL DETERMINATION OF THE DIMENSIONS AND EVOLUTION WITH CURRENT OF THE ION-EMITTING JET IN LIQUID-METAL ION SOURCES, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS24(12)pp. 2217-2221 IOP PUBLISHING LTD
    GLR MAIR, RG FORBES (1992)AN ANALYTICAL CALCULATION OF LMIS CUSP LENGTH, In: SURFACE SCIENCE266(1-3)pp. 180-184 ELSEVIER SCIENCE BV
    RG FORBES (1986)FIELD-ION ENERGY DEFICITS IN THE ATOM PROBE FIM, In: JOURNAL DE PHYSIQUE47(C-2)pp. 31-36 EDITIONS PHYSIQUE
    RG FORBES (1995)FIELD EVAPORATION THEORY - A REVIEW OF BASIC IDEAS, In: APPLIED SURFACE SCIENCE87-8(1-4)pp. 1-11 ELSEVIER SCIENCE BV
    DN Zurlev, RG Forbes (2003)Field ion emission: the effect of electrostatic field energy on the prediction of evaporation field and charge state, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS36(17)PII S0022-pp. L74-L78 IOP PUBLISHING LTD
    RG FORBES (1985)SEEING ATOMS - THE ORIGINS OF LOCAL CONTRAST IN FIELD-ION IMAGES, In: JOURNAL OF PHYSICS D-APPLIED PHYSICS18(6)pp. 973-1018 IOP PUBLISHING LTD
    Caio P. de Castro, Thiago A. de Assis, Roberto Rivelino, Fernando de B. Mota, Caio M.C de Casthilo, Richard Forbes (2019)Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes using the Induced Electron Density, In: Journal of Chemical Information and Modeling60(2)pp. 714-721 American Chemical Society

    In many field electron emission experiments on single-walled carbon nanotubes (SWCNTs), the SWCNT stands on one of two well-separated parallel plane plates, with a macroscopic field FM applied between them. For any given location “L” on the SWCNT surface, a field enhancement factor (FEF) is defined as FL/FM, where FL is a local field defined at “L”. The best emission measurements from small-radii capped SWCNTs exhibit characteristic FEFs that are constant (i.e., independent of FM). This paper discusses how to retrieve this result in quantum-mechanical (as opposed to classical electrostatic) calculations. Density functional theory (DFT) is used to analyze the properties of two short, floating SWCNTs, capped at both ends, namely, a (6,6) and a (10,0) structure. Both have effectively the same height (∼5.46 nm) and radius (∼0.42 nm). It is found that apex values of local induced FEF are similar for the two SWCNTs, are independent of FM, and are similar to FEF values found from classical conductor models. It is suggested that these induced-FEF values are related to the SWCNT longitudinal system polarizabilities, which are presumed similar. The DFT calculations also generate “real”, as opposed to “induced”, potential-energy (PE) barriers for the two SWCNTs, for FM values from 3 V/μm to 2 V/nm. PE profiles along the SWCNT axis and along a parallel “observation line” through one of the topmost atoms are similar. At low macroscopic fields, the details of barrier shape differ for the two SWCNT types. Even for FM = 0, there are distinct PE structures present at the emitter apex (different for the two SWCNTs); this suggests the presence of structure-specific chemically induced charge transfers and related patch-field distributions.

    Richard G. Forbes (2019)Why converting field emission voltages to macroscopic fields before making a Fowler-Nordheim plot has often led to spurious characterization results, In: Journal of Vacuum Science & Technology B37(5)051802pp. 1-6 AIP Publishing

    An important parameter used to characterize large-area field electron emitters (LAFEs) is the characteristic apex field enhancement factor γC. This parameter is normally extracted from the slope of a Fowler-Nordheim (FN) plot. Several years ago, the development of an “orthodoxy test” allowed a sample of 19 published FN plots relating to LAFEs to be tested, and it was found that about 40% of the related papers were reporting spuriously high values for γC. In technological papers relating to LAFE characterization, the common practice is to preconvert the measured voltage into an (apparent) value of the macroscopic field before making and analyzing an FN plot. This paper suggests that the cause of the “spurious field enhancement factor value” problem is the widespread use of a preconversion equation that is defective (for example, not compatible with ordinary electrical circuit theory) when it is applied to so-called “nonideal” field emission devices/systems. Many real devices/systems are nonideal. The author argues that FN plots should be made using raw experimental current-voltage data, that an orthodoxy test should be applied to the resulting FN plot before any more-detailed analysis, and that (in view of growing concerns over the reliability of published “scientific” results) reviewers should scrutinize field emission materials characterization papers with enhanced care.

    Johannes Bieker, Richard G. Forbes, Stefan Wilfert, Helmut F. Schlaak (2019)Simulation-Based Model of Randomly Distributed Large-Area Field Electron Emitters, In: IEEE Journal of the Electron Devices Society7pp. 997-1006 Institute of Electrical and Electronics Engineers (IEEE)

    With a large-area field electron emitter (LAFE), it is desirable to choose the spacings of individual emitters in such a way that the LAFE-average emission current density and total current are maximised, when the effects of electrostatic depolarization (mutual screening) are taken into account. This paper uses simulations based on a finite element method to investigate how to do this for a LAFE with randomly distributed emitters. The approach is based on finding the apex field enhancement factor and the specific emission current for an emitter, as a function of the average nearest neighbor spacing between emitters. Using electrostatic simulations based on the finite element method, the influence of neighboring emitters on a reference emitter being placed at the LAFE centre is investigated. Arrays with 25 ideal (identical) conical emitters with rounded tops are studied for different emitter densities and applied macroscopic fields. A theoretical average spacing is derived from the Poisson Point Process Theory. An optimum average spacing, and hence optimum emitter density, can be predicted for each macroscopic field.

    RG FORBES, NN LJEPOJEVIC (1992)LIQUID-METAL ION-SOURCE THEORY - ELECTROHYDRODYNAMICS AND EMITTER SHAPE, In: SURFACE SCIENCE266(1-3)pp. 170-175 ELSEVIER SCIENCE BV
    RG Forbes, JHB Deane (2011)Transmission coefficients for the exact triangular barrier: an exact general analytical theory that can replace Fowler & Nordheim's 1928 theory, In: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES467(2134)pp. 2927-2947 ROYAL SOC
    RG FORBES, NN LJEPOJEVIC (1991)CALCULATION OF THE SHAPE OF THE LIQUID CONE IN A LIQUID-METAL ION-SOURCE, In: SURFACE SCIENCE246(1-3)pp. 113-117 ELSEVIER SCIENCE BV
    Richard G. Forbes (2023)Proposal that interpretation of field emission current-voltage characteristics should be treated as a specialized form of electrical engineering, In: Journal of Vacuum Science & Technology B41(2)028501 American Institute of Physics

    This article proposes that we should think differently about predicting and interpreting measured field electron emission (FE) current-voltage [I_m(V_m)] characteristics. It is commonly assumed that I_m(V_m) 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 I_m(V_m) 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 I_m(V_m) 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 I_m(V_m) relationship is split as follows: (a) the current is expressed as a function I_m(F_C) of the local surface-field magnitude F_C at some defined emitter surface location "C", and (b) the relationship between F_C and measured voltage V_m is expressed and determined separately. Determining I_m(F_C) is mostly a problem in emission physics. Determining the relationship F_C(V_m) 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.

    Fernando F. Dall'Agnol, Thiago A. de Assis, Richard G. Forbes (2023)Field emitter electrostatics: Efficient improved simulation technique for highly precise calculation of field enhancement factors, In: Journal of Vacuum Science & Technology B4122803 American Institute of Physics

    When solving the Laplace equation numerically via computer simulation, in order to determine the field values at the surface of a shape model that represents a field emitter, it is necessary to define a simulation box and, within this, a simulation domain. This domain must not be so small that the box boundaries have an undesirable influence on the predicted field values. A recent paper discussed the situation of cylindrically symmetric emitter models that stand on one of a pair of well-separated parallel plates. This geometry can be simulated by using two-dimensional domains. For a cylindrical simulation box, formulas have previously been presented that define the minimum domain dimensions (MDD) (height and radius) needed to evaluate the apex value of the field enhancement factor for this type of model, with an error-magnitude never larger than a " tolerance " ε tol. This MDD criterion helps to avoid inadvertent errors and oversized domains. The present article discusses (in greater depth than previously) a significant improvement in the MDD method; this improvement has been called the MDD extrapolation technique (MDDET). By carrying out two simulations with relatively small MDD values, it is possible to achieve a level of precision comparable with the results of carrying out a single simulation using a much larger simulation domain. For some simulations, this could result in significant savings of memory requirements and computing time. Following a brief restatement of the original MDD method, the MDDET method is illustrated by applying it to the hemiellipsoid-on-plane and hemisphere-on-cylindrical-post emitter shape models.

    Georg Gaertner, Wolfram Knapp, RICHARD GORDON FORBES (2020)Modern Developments in Vacuum Electron Sources

    This book gives an overview of modern cathodes and electron emitters for vacuum tubes and vacuum electron devices in general. It covers the latest developments in field emission theory as well as new methods towards improving thermionic and cold cathodes. It addresses thermionic cathodes, such as oxide cathodes, impregnated and scandate cathodes, as well as photocathodes and field emitters – the latter comprising carbon nanotubes, graphene and Spindt-type emitter arrays. Despite the rise and fall of the once dominant types of vacuum tubes, such as radio valves and cathode ray tubes, cathodes are continually being improved upon as new applications with increased demands arise, for example in electron beam lithography, high-power and high-frequency microwave tubes, terahertz imaging and electron sources for accelerators. Written by 17 experts in the field, the book presents the latest developments in cathodes needed for these applications, discussing the state of the art and addressing future trends.

    R. G Forbes, E. O Popov, A. G Kolosko, S. V Filippov (2021)The pre-exponential voltage-exponent as a sensitive test parameter for field emission theories, In: Royal Society Open Science8(3)201986 Royal Society Publishing

    For field electron emission (FE), an empirical equation for measured current I m as a function of measured voltage V m has the form I m = CV m k exp[– B / V m ], where B is a constant and C and k are constants or vary weakly with V m . Values for k can be extracted (i) from simulations based on some specific FE theory, and in principle (ii) from current–voltage measurements of sufficiently high quality. This paper shows that a comparison of theoretically derived and experimentally derived k- values could provide a sensitive and useful tool for comparing FE theory and experiment, and for choosing between alternative theories. Existing methods of extracting k -values from experimental or simulated current–voltage data are discussed, including a modernized ‘least residual’ method, and existing knowledge concerning k -values is summarized. Exploratory simulations are reported. Where an analytical result for k is independently known, this value is reliably extracted. More generally, extracted k -values are sensitive to details of the emission theory used, but also depend on assumed emitter shape; these two influences will need to be disentangled by future research, and a range of emitter shapes will need examination. Other procedural conclusions are reported. Some scientific issues that this new tool may eventually be able to help investigate are indicated.

    Ramya Cuduvally, Richard J.H. Morris, Giel Oosterbos, Piero Ferrari, Claudia Fleischmann, RICHARD G. FORBES, Wilfried Vandervorst (2022)Post-field ionization of Si clusters in atom probe tomography: A joint theoretical and experimental study, In: Journal of Applied Physics132(7)074901 AIP

    A major challenge for Atom Probe Tomography (APT) quantification is the inability to decouple ions which possess the same mass-charge (m/n) ratio but a different mass. For example, 75 As + and 75 As2 2+ at ~75 Da or 14 N + and 28 Si 2+ at ~14 Da, cannot be differentiated without the additional knowledge of their kinetic energy or a significant improvement of the mass resolving power. Such mass peak overlaps lead to ambiguities in peak assignment, resulting in compositional uncertainty and an incorrect labelling of the atoms in a reconstructed volume. In the absence of a practical technology for measuring the kinetic energy of the field-evaporated ions, we propose and then explore the applicability of a post-experimental analytical approach to resolve this problem based on the fundamental process that governs the production of multiply charged molecular ions/clusters in APT, i.e., Post-Field Ionization (PFI). The ability to predict the PFI behaviour of molecular ions as a function of operating conditions could offer the first step towards resolving peak overlap and minimizing compositional uncertainty. We explore this possibility by comparing the field dependence of the charge-state-ratio for Si clusters (Si2, Si3 and Si4) with theoretical predictions using the widely accepted Kingham PFI theory. We then discuss the model parameters that may affect the quality of the fit and the possible ways in which the PFI of molecular ions in APT can be better understood. Finally, we test the transferability of the proposed approach to different material systems and outline ways forward for achieving more reliable results.

    This Comment suggests that technological field electron emission (FE) papers, such as the paper under discussion [P. Serbun et al., Rev. Sci. Instrum. 91, 083906 (2020)], should use FE theory based on the 1956 work of Murphy and Good (MG), rather than a simplified version of FE theory based on the original 1928 work of Fowler and Nordheim (FN). The use of the 1928 theory is common practice in the technological FE literature, but the MG treatment is known to be better physics than the FN treatment, which contains identifiable errors. The MG treatment predicts significantly higher emission current densities and currents for emitters than does the FN treatment. From the viewpoint of the research and development of electron sources, it is counterproductive (and unhelpful for non-experts) for the technological FE literature to use theory that undervalues the performance of field electron emitters.

    Mohammad M. Allaham, Richard G. Forbes, Alexandr Knápek, Dinara Sobola, Daniel Burda, Petr Sedlák, Marwan S. Mousa (2022)Interpretation of field emission current–voltage data: Background theory and detailed simulation testing of a user-friendly webtool, In: Materials today communications31103654 Elsevier Ltd

    In field electron emission (FE) studies, interpretation of measured current–voltage characteristics and extraction of emitter characterization parameters are usually carried out within the framework of “smooth planar metal-like emitter (SPME) methodology”, using a data-analysis plot. This methodology was originally introduced in the 1920s. Three main data-plot types now exist: Millikan–Lauritsen (ML) plots, Fowler–Nordheim (FN) plots, and Murphy–Good (MG) plots. ML plots were commonly used in early FE studies, but most modern analysis uses FN plots. MG plots are a recent introduction. Theoretically, it is now known that ML and FN plots are predicted to be slightly curved in SPME methodology, but a Murphy–Good plot will be very nearly straight. Hence (because 1956 Murphy–Good emission theory is “better physics” than 1928 Fowler–Nordheim emission theory as corrected in 1929), expectation is that parameter extraction using a MG plot will be more precise than extraction using either ML plots or FN plots. In technological FE studies, current–voltage characteristics are often converted into other forms. Thus, measured voltage may be converted to (apparent) macroscopic field, and/or current values may be converted to macroscopic current densities. Thus, four data-input forms can be found in the context of analysing FE current–voltage results. It is also the case that over-simplified models of measurement-system behaviour are very widely assumed, and the question of whether simple use of a data-analysis plot is a valid data-interpretation procedure for the particular system under investigation has often been neglected. Past published studies on field emitter materials development appear to contain a high incidence of spurious values for the emitter characterization parameter “characteristic field enhancement factor”. A procedure (the so-called “Orthodoxy Test”) was described in 2013 that allows a validity check on measurement-system behaviour, and found that around 40% of a small sample of results tested were spuriously high, but has had limited uptake so far. To assist with FE current–voltage data interpretation and validity checks, a simple user-friendly webtool has been under design by the lead author. The webtool needs as user input some system specification data and some “range-limits” data from any of the three forms of data-analysis plot, using any of the four data-input variations. The webtool then applies the Orthodoxy Test, and—if the Test is passed—calculates values of relevant emitter characterization parameters. The present study reports the following: (1) systematic tests of the webtool functionality, using simulated input data prepared using Extended Murphy–Good field electron emission theory; and (2) systematic comparisons of the three different data-plot types, again using simulated input data, in respect of the accuracy with which extracted characterization parameter values match the simulation input values. The paper is introduced by a thorough summary review of the theory on which modern SPME-based current–voltage data-analysis procedures are based. The need in principle to move on (in due course) to data-analysis procedures based on curved-emitter emission theory is noted. An important result is to confirm (by simulations) that, particularly in respect of the extraction of formal emission areas, the performance of the Murphy–Good plot is noticeably better than the performances of Fowler–Nordheim and Millikan–Lauritsen plots. This result is important for field electron emission science because it is now known that differences as between different theories of field electron emission often affect the formal emission area.

    Sergey V. Filippov, Anatoly G. Kolosko, Eugeni O. Popov, Richard G. Forbes (2022)Field emission: calculations supporting a new methodology of comparing theory with experiment, In: Royal Society Open Science9(11)220748 The Royal Society

    This paper provides a demonstration-of-concept of a new methodology for comparing field electron emission (FE) theory and experiment. It uses the parameter κ in the mathematical equation Im = CVmκ exp[–B/Vm] (where B and C are weakly varying or constants) that is taken to describe how measured current Im depends on measured voltage Vm for electronically ideal FE systems (i.e. systems that (i) have constant configuration during voltage application and (ii) have Im(Vm) given by the emission physics alone). Experimental parameter values (κm) are used to compare two alternative FE theories, for which allowable (but different) κ ranges have been established. At present, contributions to the ‘total theoretical κ’ made by voltage dependence of notional emission area are not well known: simulations reported here provide data about four commonly investigated emitter shapes. The methodology is then applied to compare 1928/1929 Fowler–Nordheim (FN) FE theory and 1956 Murphy–Good (MG) FE theory. It is theoretically certain that the 1956 theory is ‘better physics’ than the 1928/1929 theory. As in previous attempts to reach known correct theoretical conclusions by experimentally based argument, the new methodology tends to favour MG FE theory, but is formally indecisive at this stage. Further progress needs better methods of establishing error limits and of measuring κm.

    Richard Forbes, Jonathan Deane, Andreas Fischer, Marwan S. Mousa (2015)Fowler-Nordheim Plot Analysis: a Progress Report, In: Jordan Journal of Physics8(3)pp. 125-147 Deanship of Research & Graduate Studies, Yarmouk University, Irbid, Jordan.

    The commonest method of characterizing a cold field electron emitter is to measure its current-voltage characteristics, and the commonest method of analysing these characteristics is by means of a Fowler-Nordheim (FN) plot. This tutorial/review-type paper outlines a more systematic method of setting out the Fowler-Nordheim-type theory of cold field electron emission, and brings together and summarises the current state of work by the authors on developing the theory and methodology of FN plot analysis. This has turned out to be far more complicated than originally expected. Emphasis is placed in this paper on: (a) the interpretation of FN-plot slopes, which is currently both easier and of more experimental interest than the analysis of FN-plot intercepts; and (b) preliminary explorations into developing methodology for interpreting current-voltage characteristics when there is series resistance in the conduction path from the high-voltage generator to the emitter's emitting regions. This work reinforces our view that FN-plot analysis is best carried out on the raw measured current-voltage data, without pre-conversion into another data format, particularly if series resistance is present in the measuring circuit. Relevant formulae are given for extracting field-enhancement-factor values from such an analysis.

    Richard G Forbes (2020)Renewing the Mainstream Theory of Field and Thermal Electron Emission, In: Modern Developments in Vacuum Electron Sourcespp. 387-447 Springer International Publishing

    Mainstream field electron emission (FE) theory—the theory normally used by FE experimentalists—employs a Sommerfeld-type free-electron model to describe FE from a metal emitter with a smooth planar surface of very large extent. This chapter reviews the present state of mainstream FE theory, noting aspects of the history of FE and thermal electron emission theory. It sets out ways of improving the theory’s presentation, with the ultimate aim of making it easier to reliably compare theory and experiment. This includes distinguishing between (a) emission theory and (b) device/system theory (which deals with field emitter behaviour in electrical circuits), and between ideal and non-ideal device behaviours. The main focus is the emission theory. Transmission regimes and emission current density regimes are discussed. With FE, a method of classifying different FE equations is outlined. With theories that assume tunnelling through a Schottky-Nordheim (SN) (“planar-image-rounded”) barrier, a careful distinction is needed between the barrier form correction factor ν (“nu”) and the special mathematical function v (“vee”). This function v is presented as dependent on the Gauss variable x. The pure mathematics of v(x) is summarised, and reasons are given for preferring the use of x over the older convention of using the Nordheim parameter y [=+√x]. It is shown how the mathematics of v(x) is applied to wave-mechanical transmission theory for basic Laurent-form barriers (which include the SN barrier). A brief overview of FE device/system theory defines and discusses different auxiliary parameters currently in use, outlines a preferred method for characterising ideal devices when using FN plots and notes difficulties in characterising non-ideal devices. The chapter concludes by listing some of the future tasks involved in upgrading FE science.

    RG Forbes (1985)The concept: Amount of Substance, In: School Science Review66pp. 787-788
    RG Forbes (2007)Tutorial lecture on the theory of cold field electron emission, In: 2007 IEEE 20TH INTERNATIONAL VACUUM NANOELECTRONICS CONFERENCEpp. 34-35
    RG Forbes, Z Djuric (1996)Progress in understanding liquid-metal ion source operation, In: IVMC '96 - 9TH INTERNATIONAL VACUUM MICROELECTRONICS CONFERENCE, TECHNICAL DIGESTpp. 468-472
    GL LAWDAY, RG FORBES (1989)ASIC DESIGN, THE SOLO 1000 TOOL SET, AND BTEC COURSES, In: INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING EDUCATION26(1-2)pp. 30-37 MANCHESTER UNIV PRESS
    RG Forbes (2009)Proposal to replace Fowler-Nordheim plots by Millikan-Lauritsen plots as the basic method of analysing experimental field emission data, In: Technical Digest - 2009 22nd International Vacuum Nanoelectronics Conference, IVNC 2009pp. 13-14
    RG Forbes, JHB Deane (2006)Analytical approximations for the special elliptic functions of standard Fowler-Nordheim theory, In: IVNC and IFES 2006 - Technical Digest - l9th International Vacuum Nanoelectronics Conference and 50th International Field Emission Symposiumpp. 265-?
    RG Forbes (1998)The field emitter and its applications, In: A Kirkland, PD Brown (eds.), ELECTRONpp. 334-340
    RG Forbes (2012)Field enhancement factor for a tall closely-spaced array of identical conducting posts, and implications for fowler-nordheim theory, In: Technical Digest - 25th International Vacuum Nanoelectronics Conference, IVNC 2012pp. 284-285

    This paper derives an approximate formula for the field enhancement factor for a tall closely-packed array of identical conducting posts. It confirms a formula derived from the work of Zhbanov et al. [J. Appl. Phys. 110, 114311 (2011)], but displays the principles underlying collective screening more clearly. A formula for the area efficiency of emission (α ) for this array is also derived. Since α ≪1, it follows that a macroscopic pre-exponential correction factor (λ ) must be included in the formula for the macroscopic ("LAFE-average") emission current density (J ) for a large-area field emitter (LAFE). Omission of λ may cause great theoretical over-prediction of the value of J . © 2012 IEEE.

    JHB Deane, Richard Forbes, A Fischer, MS Mousa (2014)The effect of barrier form on the analysis of Fowler-Nordheim plots
    RG Forbes (1978)Field ionization and surface plasmons: an alternative theoretical formulation, In: Nederlands Tidjschrift voor Vacuumtechniek16pp. 268-268
    RG Forbes (2012)Resolving power of the field electron and field ion imaging processes, In: Technical Digest - 25th International Vacuum Nanoelectronics Conference, IVNC 2012pp. 286-287

    This conference paper reports the interim conclusions of a re-examination of the theory of the resolving power of the field electron and field ion microscopes. It argues that existing theory contains multiple errors and needs to be completely replaced. Progress made is reported. The nature of problems remaining to be solved is briefly discussed. © 2012 IEEE.

    R.G. Forbes (2018)Field electron and ion emission: basic formulae and constants, In: G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces (Subvolume B)3pp. 661-723 Springer

    These chapters define and explain numerous formulae that appear in the theory of field electron and ion emission and closely related topics, and give and (where relevant) discuss the best current values for numerous constants that appear in these formulae

    RG Forbes (2011)Comments on discrepancies in the Fowler and Nordheim 1928 paper, In: A Klumper (eds.), 2011 24TH INTERNATIONAL VACUUM NANOELECTRONICS CONFERENCE (IVNC)pp. 113-114
    RG FORBES (1986)THE PHYSICS OF LIQUID-METAL FIELD-ION SOURCE, In: VACUUM36(11-12)pp. 1020-1020
    A Fischer, JHB Deane, MS Mousa, RG Forbes (2012)Illustrating field emission theory by using plots of transmission probability and barrier strength, In: Technical Digest - 25th International Vacuum Nanoelectronics Conference, IVNC 2012pp. 290-291

    This poster is part of a continuing attempt to make field emission theory more transparent. When interpreting current-voltage characteristics related to cold field electron emission (CFE), it is widely assumed that these are controlled and dominated by the behaviour of the tunneling barrier at the emitter/vacuum interface. The transmission probability D for this barrier can be written D ≈ P exp[-G], where P is a transmission pre-factor and G is the JWKB exponent or "barrier strength". The influence of theoretical effects on the barrier form and on D can be illustrated by plotting (-G) and/or lnD as functions of reciprocal field or voltage. This is a specialized form of Fowler-Nordheim (FN) plot. Its usefulness as a pedagogical tool has perhaps been under-appreciated; it may also prove useful for discussing the issue of what causes curvature in FN plots. © 2012 IEEE.

    RG Forbes (1996)The electron energy distribution from very sharp field emitters, In: IVMC '96 - 9TH INTERNATIONAL VACUUM MICROELECTRONICS CONFERENCE, TECHNICAL DIGESTpp. 58-61
    RG FORBES (1980)ANOTHER LOOK AT FIELD PENETRATION AND SURFACE-ATOM POLARIZABILITY, In: ULTRAMICROSCOPY5(2)pp. 264-264
    RG Forbes (1977)Confusion over the avogadro constant, In: Physics Education12(5)pp. 273-274
    RG Forbes (1990)What do we mean by work-function ?pp. 163-173
    RG Forbes (1980)Reply to comments on: "In defence of seven dimensions", In: International Journal of Mechanical Engineering Education8pp. 99-100
    RG Forbes (2005)A look at the basic physics of cold field electron emission, In: Technical Digest of the 18th International Vacuum Nanoelectronics Conference, IVNC 20052005pp. 1-2
    RG Forbes (2012)Recent progress in reshaping the theory of orthodox field electron emission, In: Technical Digest - 25th International Vacuum Nanoelectronics Conference, IVNC 2012pp. 22-23

    As part of a continuing attempt to build a more coherent scientific structure for the theory of field-assisted electron emission, and in particular for the interpretation of measured current-voltage data, this paper provides an overview of recent progress in what is proving to be a very messy and complicated task. © 2012 IEEE.

    RG Forbes (1978)More confusion over the Avogadro constant, In: Physics Education13(1)pp. 5-6
    RG Forbes (1976)Comments on "intrinsic energy losses of field evaporated ions", In: J PHYS D APPL PHYS9(15)pp. L191-L193 IOP PUBLISHING LTD
    RG Forbes (1976)A GENERALIZED THEORY OF STANDARD FIELD-ION APPEARANCE ENERGIES, In: SURF SCI61(1)pp. 221-240 ELSEVIER SCIENCE BV
    RG Forbes (1996)The liquid metal ion source as an electrically driven vena contracta, and some comments on LMIS stability, In: JOURNAL DE PHYSIQUE IV6(C5)pp. 43-47 EDITIONS PHYSIQUE
    BM Cook, RG Forbes (1989)ISIS in the educational environment, In: RE Massara, IOE Engineers (eds.), Design & test techniques for VLSI & WSI circuits(7)pp. 109-118 Peter Peregrinus
    J Duffell, RG Forbes (1978)FIELD-ION IMAGE-CONTRAST - THE GAS-DISTRIBUTION HYPOTHESIS REEXAMINED, In: J PHYS D APPL PHYS11(9)pp. L123-L125 IOP PUBLISHING LTD
    RG Forbes (2000)Theory and modelling of field-induced electron emission, In: Materials Research Society Symposium - Proceedings621

    This paper addresses issues in the theory of field-induced electron emission. First, it summarises our present understanding of the theory of Fowler-Nordheim (FN) plots, and shows the relationship between a recent precise (in standard FN theory) approach to the interpretation of the FN-plot intercept and older approximate approaches. Second, it comments on the interpretation of FN plots taken from semiconductor field emitters. Third, it summarises the main points of a recent hypothesis about the mechanism of field-induced emission from carbon- based films and other electrically nanostructured heterogeneous (ENH) materials. Weaknesses in previous hypotheses are noted. It is hypothesised that thin films of all ENH materials, when deposited on a conducting substrate, will emit electrons in appropriate circumstances. Such films emit electrons at low macroscopic fields because they contain conducting nanostructure inside them: This structure generates sufficient geometrical field enhancement near the film/vacuum interface that more-or-less normal Fowler-Nordheim emission can occur. In connection with experiments on amorphous carbon films carried out by a group in Fribourg, it is shown that nanostructure of the size measured by scanning probe techniques should be able to generate field enhancement of the size measured in field electron spectroscopy experiments. This result provides a quantitative corroboration of other work suggesting that emission from amorphous carbon films is primarily clue to geometrical field enhancement by nanostructures inside the film. Some counter-arguments to the internal-field-enhancement hypothesis are considered and disposed of. Some advantages of ENH materials as broad-area field emission electron sources are noted; these include control of material design.

    RG FORBES, RA MUNOZ (1980)A PRELIMINARY EXPLORATION OF ION-DIPOLE CORRELATION ENERGIES, In: ULTRAMICROSCOPY5(2)pp. 265-265
    RG Forbes (1971)Field ion image formation, In: Nature Physical Science230pp. 165-166
    RG Forbes (2009)Theories of field emission from graphene based on thin-slab and atomic-array models, In: Technical Digest - 2009 22nd International Vacuum Nanoelectronics Conference, IVNC 2009pp. 99-100
    RG Forbes (2008)Gas Field Ionization Sources, In: J ORLOFF (eds.), HANDBOOK OF CHARGED PARTICLE OPTICS(3) CRC Press

    2

    RG Forbes (1974)AN ALTERNATIVE THEORETICAL APPROACH TO FIELD EVAPORATION RATE SENSITIVITIES, In: SURF SCI46(2)pp. 577-601 ELSEVIER SCIENCE BV
    RG FORBES, MK WAFI (1980)THE FIELD ADSORPTION OF HELIUM IN ARRAY-TYPE MODELS, In: ULTRAMICROSCOPY5(2)pp. 265-265
    RG Forbes (1976)A fundamental proposal concerning the "mole", In: Education in Chemistry13pp. 92-?
    GLR Mair, RG Forbes, RV Latham, T Mulvey (1983)ENERGY SPREAD MEASUREMENTS ON A LIQUID METAL ION SOURCE.pp. 171-178
    RG Forbes (2010)5.4: Analysis of experimental field emission current-voltage characteristics (especially those from carbon nanotubes), In: Proceedings of 23rd International Vacuum Nanoelectronics Conferencepp. 92-93

    This paper discusses alternative physical explanations of experimental field emission current-voltage characteristics (particularly those from carbon-nanotube arrays), and re-examines the existing theory of Fowler-Nordheim plots.

    RG Forbes, JHB Deane (2013)Progress with developing theory for Fowler-Nordheim plot interpretation, In: 2013 26TH INTERNATIONAL VACUUM NANOELECTRONICS CONFERENCE (IVNC) IEEE COMPUTER SOC
    RG Forbes, A Fischer, MS Mousa, A Fischer (2012)New type of intercept correction factor for Fowler-Nordheim plots, In: Technical Digest - 25th International Vacuum Nanoelectronics Conference, IVNC 2012pp. 288-289

    This paper defines a new type of intercept correction factor for use in connection with the tangent method of analyzing Fowler-Nordheim plots. Unlike the factor previously used, the new factor is well defined and can be evaluated precisely for simple barrier models. Theory using the new factor is intended to replace existing theory. Applications will be presented elsewhere. © 2012 IEEE.

    RG Forbes (1995)A new magnetic vocabulary, In: Physics World8pp. 21-22
    DN Zurlev, JHB Deane, RG Forbes (2006)Forbidden ions in field evaporation, In: IVNC and IFES 2006 - Technical Digest - l9th International Vacuum Nanoelectronics Conference and 50th International Field Emission Symposiumpp. 87-88
    RG Forbes (1972)Reply to "Comments on field ion image formation", In: Nature Physical Science239pp. 15-16
    RG Forbes (2012)Scaled form for kernel Fowler-Nordheim-type expression based on the Schottky-Nordheim barrier, and test for orthodoxy of field electron emission, In: Technical Digest - 25th International Vacuum Nanoelectronics Conference, IVNC 2012pp. 282-283

    This conference paper supports an overview presented elsewhere in this conference, by setting out detailed theory about the concept of "kernel current density", and about the development of a simple numerical test for (lack of) emission orthodoxy. The test can be applied to any form of linear (or nearly linear) Fowler-Nordheim plot. © 2012 IEEE.

    RG Forbes (2006)Tutorial lecture on field electron emission theory, In: IVNC and IFES 2006 - Technical Digest - l9th International Vacuum Nanoelectronics Conference and 50th International Field Emission Symposiumpp. 559-560
    RG Forbes, JHB Deane (2011)Progress in securing the foundations of field-assisted electron emission theory, In: Proceedings of 24th International Vacuum Nanoelectronics Conferencepp. 1-2

    This paper presents the results of a re-examination of the wave-mechanical theory of electron emission across an exact triangular barrier. This is a fourth-generation treatment of a problem first addressed by Fowler and Nordheim in 1928, subsequently by other researchers. The outcome is a transparent derivation of an exact general analytical formula (previously found by Jensen) and the identification of numerous special cases in which specific approximations to the general formula apply.

    E Morton, D Taylor, DC Patel, RG Forbes (1996)Mixed signal ASIC for amorphous silicon pixellated array X-ray imaging systempp. 161-166
    RG Forbes (1976)Comment on "surface plasmon excitation in field ion emission" by R. Brako and M. Šunjić, In: SURF SCI60(1)pp. 260-261 ELSEVIER SCIENCE BV
    E Braun, RG Forbes, J Pearson, JM Pelmore, RV Latham (1978)AN ADVANCED FIELD ELECTRON-EMISSION SPECTROMETER, In: J PHYS E SCI INSTRUM11(3)pp. 222-228 IOP PUBLISHING LTD
    RG Forbes (1978)Amount of substance: An alternative proposal, In: Physics Education13(5)pp. 269-272
    RG FORBES (1982)NEW ACTIVATION-ENERGY FORMULAS FOR CHARGE-EXCHANGE TYPE MECHANISMS OF FIELD EVAPORATION, In: SURFACE SCIENCE116(2)pp. L195-L201 ELSEVIER SCIENCE BV
    RG Forbes (2007)Analysis of planar field-stimulated vacuum space-charge using a dimensionless equation, In: 2007 IEEE 20TH INTERNATIONAL VACUUM NANOELECTRONICS CONFERENCEpp. 133-134
    RG Forbes (1972)PROBLEMS IN THE THEORY OF FIELD-ION IMAGING, In: VACUUM22(11)pp. 517-520 PERGAMON-ELSEVIER SCIENCE LTD
    RG Forbes (1978)Reply to comments on "Opinion on SI", In: Physics Bulletin29pp. 247-?
    RG Forbes (1977)Some new ideas in field-ion theorypp. 387-390
    RG FORBES, NN LJEPOJEVIC (1989)RECENT PROGRESS IN LMIS THEORY, In: JOURNAL DE PHYSIQUE50(C8)pp. C83-C88 EDITIONS PHYSIQUE
    RG Forbes (2001)Is uniform electron emission possible at low macroscopic fields?, In: CE Hunt, AG Chakhovskoi, NN Chubun, M Hajra (eds.), IVMC 2000: PROCEEDINGS OF THE 14TH INTERNATIONAL VACUUM MICROELECTRONICES CONFERENCEpp. 79-79
    RG Forbes, JHB Deane (2009)Comparison of approximations for the principal Schottky-Nordheim barrier function v(f), In: Technical Digest - 2009 22nd International Vacuum Nanoelectronics Conference, IVNC 2009pp. 97-98
    RG Forbes (2005)How the world first saw atoms: an outline of how field ion imaging works, In: Microscopy and Microanalysis11 (Supp. 860-861
    RG Forbes (1991)The physicists' Amount too, In: School Science Review73pp. 133-133
    RG Forbes, GLR Mair (2008)Liquid metal ion sources, In: J ORLOFF (eds.), HANDBOOK OF CHARGED PARTICLE OPTICS, 2nd Edition CRC Press
    RG Forbes, JHB Deane (2005)Fowler-nordheim parameters for sharply-curved emitters, In: Technical Digest of the 18th International Vacuum Nanoelectronics Conference, IVNC 20052005pp. 109-110
    RG Forbes, JHB Deane, RW Shail (2007)Exact mathematical solution for the principal field emission correction function nu used in Standard Fowler-Nordheim theory, In: 2007 IEEE 20TH INTERNATIONAL VACUUM NANOELECTRONICS CONFERENCEpp. 135-136
    A Fischer, MS Mousa, RG Forbes (2010)P1-27: Influence of improved surface potential-energy model on CFE characteristics and related slope and intercept correction factors, In: Proceedings of 23rd International Vacuum Nanoelectronics Conference, IVNC 2010pp. 79-79

    This poster explores the influence of an improved surface potential energy model on the predicted characteristics of cold field electron emission. We explore effects on the shape of Fowler-Nordheim plots, and on the values of slope and intercept correction functions.

    A Mayer, JHB Deane, RG Forbes (2010)P1-28: Use, in Fowler-Nordheim-type equations, of accurate solution of the schrödinger equation for the schottky-nordheim barrier, In: Proceedings of 23rd International Vacuum Nanoelectronics Conferencepp. 80-81

    The Schottky-Nordheim (SN) barrier is used in the "standard" theory of cold field electron emission (CFE) developed by Murphy and Good in 1956. For the SN barrier, it is mathematically impossible to derive analytical solutions of the Schrödinger equation in terms of the common functions of mathematical physics. Existing simple analytical CFE theories are based on so-called "quasi-classical" quantum-mechanical methods, typically a JWKB-type approximation. Recently, numerical methods have been applied to the SN barrier that should generate accurate solutions for the transmission coefficient DT. This poster is a "tidy-up" exercise that explores quantitatively how these accurate solutions put correction factors into Fowler-Nordheim-type equations.

    RG Forbes (1977)Atomic polarizability values in the SI system, In: SURF SCI64(1)pp. 367-371 ELSEVIER SCIENCE BV
    RG Forbes (2006)Another look at the classical calculation of evaporation fields, In: IVNC and IFES 2006 - Technical Digest - l9th International Vacuum Nanoelectronics Conference and 50th International Field Emission Symposiumpp. 85-86
    RG Forbes (2003)Theories of low-macroscopic-field electron emission, In: MM Takai, Y Gotoh, J Ishikawa (eds.), TECHNICAL DIGEST OF THE 16TH INTERNATIONAL VACUUM MICROELECTRONICS CONFERENCEpp. 3-3
    RG Forbes (1997)On the problem of establishing the location of the electrical surface (image plane) for a tungsten field emitter, In: ZEITSCHRIFT FUR PHYSIKALISCHE CHEMIE-INTERNATIONAL JOURNAL OF RESEARCH IN PHYSICAL CHEMISTRY & CHEMICAL PHYSICS202pp. 139-161 R OLDENBOURG VERLAG
    RG Forbes (2014)Use of a Spreadsheet to Test for Lack of Field Emission Orthodoxy, In: NV Egorov (eds.), 2014 TENTH INTERNATIONAL VACUUM ELECTRON SOURCES CONFERENCE (IVESC) IEEE
    RG Forbes (1979)In defence of seven dimensions, In: International Journal of Mechanical Engineering Education7pp. 203-204
    RG Forbes (2007)The physics of generalized Fowler-Nordheim-type equations, In: Technical Digest of the 20th International Vacuum Nanoelectronics Conference, IVNC 07pp. 44-45
    RG FORBES (1989)ON DIFFERENT TYPES OF DIPOLE-DIPOLE INTERACTION, In: JOURNAL DE PHYSIQUE50(C8)pp. C815-C820 EDITIONS PHYSIQUE
    RG Forbes (2001)Models for low-macroscopic-field electron emission, In: CE Hunt, AG Chakhovskoi, NN Chubun, M Hajra (eds.), IVMC 2000: PROCEEDINGS OF THE 14TH INTERNATIONAL VACUUM MICROELECTRONICES CONFERENCEpp. 71-71
    RG Forbes (2010)P2-32: Accurate calculation of the Schottky-Nordheim barrier functions, In: Proceedings of 23rd International Vacuum Nanoelectronics Conferencepp. 183-184

    This poster records the various methods historically used to accurately calculate the Schottky-Nordheim barrier functions used in tunnelling theory. This can now be done via a spreadsheet. Electronic copies of a suitable spreadsheet can be made available. This extended abstract also contains some underlying basic theory.

    RG Forbes (1978)Opinion on SI, In: Physics Bulletin29pp. 103-?
    RG Forbes (2001)Update on analysis of Fowler-Nordheim plots from nonmetallic emitters, In: CE Hunt, AG Chakhovskoi, NN Chubun, M Hajra (eds.), IVMC 2000: PROCEEDINGS OF THE 14TH INTERNATIONAL VACUUM MICROELECTRONICES CONFERENCEpp. 95-95
    RG Forbes (1972)A theory of field ion imaging: I - A quasi-classical site-current formula, In: Journal of Microscopy96pp. 57-61
    JP Xanthakis, RG Forbes (2005)Field screening by amorphous carbon thin films, In: Technical Digest of the 18th International Vacuum Nanoelectronics Conference, IVNC 20052005pp. 107-108
    RG Forbes (2003)More about the extraction of emission area from Fowler-Nordheim plots, In: MM Takai, Y Gotoh, J Ishikawa (eds.), TECHNICAL DIGEST OF THE 16TH INTERNATIONAL VACUUM MICROELECTRONICS CONFERENCEpp. 89-89
    RG Forbes, WB Liu (1995)Electrohydrodynamic theory of liquid metal ion sources, In: S Cunningham (eds.), ELECTROSTATICS 1995143pp. 193-200
    RG Forbes (1976)ON THE NEED FOR NEW MEASUREMENTS OF FIELD-ION APPEARANCE POTENTIAL FOR HELIUM, In: INT J MASS SPECTROM21(3-4)pp. 417-420 ELSEVIER SCIENCE BV
    RG Forbes (2006)Comments on the JWKB approximation, In: IVNC and IFES 2006 - Technical Digest - l9th International Vacuum Nanoelectronics Conference and 50th International Field Emission Symposiumpp. 11-12
    RG Forbes, AG Bailey, AA Berezin, I Harpur, W Kleber, BC ONeill, C Vossen, D Hu, S Cunningham, G Touchard (1995)Analytical techniques - Discussion, In: S Cunningham (eds.), ELECTROSTATICS 1995143pp. 219-221
    A Fischer, MS Mousa, AN Al-Rabadi, RG Forbes (2010)P1-26: Influence of tip curvature on field electron emission characteristics, In: Proccedings of 23rd International Vacuum Nanoelectronics Conference, IVNC 2010pp. 78-78

    This poster explores the influence of tip curvature on field electron emission characteristics. We look at predicted changes in: Fowler-Nordheim plots (which tend to become curved); the dependence of notional emission area on voltage; and the slope and intercept correction functions.

    RG Forbes (2009)Use of the concept "area efficiency of emission" in equations describing field emission from large-area electron sources, In: Technical Digest - 2009 22nd International Vacuum Nanoelectronics Conference, IVNC 2009pp. 131-132 IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

    Cold field electron emission (CFE) is a statistical electron emission regime where the emitted current is generated by the escape of electrons by Fowler-Nordheim (FN) tunnelling from states close in energy to the emitter's Fermi level. Particularly over the last ten years or so, there has been much interest in developing electron sources based on CFE from relatively large substrate areas that support many individual emitters or emission sites. In this paper, the use of the concept of "area efficiency of emission" when dealing with equations describing field emission from large-area electron sources is presented.

    RG Forbes (1977)The mole––interpreting it, In: Education in Chemistry14pp. 124-?
    RG Forbes, T Ganetsos, GLR Mair, VG Suvorov (2004)Liquid metal ion sources at Aston in the 1980s and what followed, In: Proceedings of the Royal Microscopical Society39pp. 218-226
    RG Forbes (2010)P2-31: Simple derivation of formula for sommerfeld supply density, In: Proceedings of 23rd International Vacuum Nanoelectronics Conferencepp. 181-182

    This poster presents a simple derivation of the result that (for a large free-electron conductor) the electron supply density is constant in energy-space and is given by the Sommerfeld supply density zS, and also proves the formula for zS. This result is the best starting point for deriving Richardson-Schottky-type and Fowler-Nordheim-type equations. For small emitters the supply density is not constant in energy-space; consequently, emission from small emitters is not well described by these equations.

    RG Forbes, Z Li (2011)Emission reference level: A missing concept in emission theory, In: Proceedings of 24th International Vacuum Nanoelectronics Conferencepp. 121-122

    This paper introduces the physical concept of Emission Reference Level (ERL) and relates it to the already-used concept of reference barrier height HR. The ERL is a concept particularly helpful for small emitters, where quantum confinement effects occur, but can also be used to clarify energy diagrams drawn to explain field electron emission from bulk emitters.

    RG Forbes (1979)THE INFLUENCE OF DEPOLARIZATION ON SURFACE-ATOM POLARIZATION ENERGY, In: SURF SCI82(2)pp. L620-L624 ELSEVIER SCIENCE BV
    RG Forbes (1982)The seventh SI quantity, In: Education in Chemistry19pp. 102-?
    RG FORBES (1988)ON THE POSITION OF THE ELECTRICAL REFERENCE SURFACE, In: VACUUM38(4-5)pp. 429-429
    RG Forbes (2011)Comments on inconsistencies in a recent handbook theory chapter, In: Proceedings of 24th International Vacuum Nanoelectronics Conferencepp. 117-118

    This note records theoretical inconsistencies found in the theory chapter of a recent handbook relating to carbon nanotube field electron emitters, suggests corrections and makes some general comments.

    RG FORBES, BM COOK (1989)THE ROLE OF THE FULL-CUSTOM DESIGN EXERCISE IN TEACHING, In: INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING EDUCATION26(1-2)pp. 100-102 MANCHESTER UNIV PRESS
    RG Forbes (1972)A theory of field ion imaging: II - On the origin of site-current variations, In: Journal of Microscopy96pp. 63-75
    JWW CHONG, RG FORBES (1992)DESIGN OF BASIC CMOS CELL LIBRARY, In: IEE PROCEEDINGS-G CIRCUITS DEVICES AND SYSTEMS139(2)pp. 256-260 IEE-INST ELEC ENG