Richard Forbes

Dr Richard Forbes


Visiting Reader (formerly Reader) in High Electric Field Nanoscience
MA, PhD, DSc, EurIng, CEng, CPhys, FIET, FInstP, SMIEEE
+44 (0)1483 689140
AB 04
After 11 am, most days.

My publications

Publications

—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.

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
RG Forbes (1995)A new magnetic vocabulary, In: Physics World8pp. 21-22
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 (1991)The physicists' Amount too, In: School Science Review73pp. 133-133
RG Forbes (2005)How the world first saw atoms: an outline of how field ion imaging works, In: Microscopy and Microanalysis11 (Supp. 860-861
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
BM Cook, RG Forbes (1989)ISIS in the educational environment, In: Design & test techniques for VLSI & WSI circuits(7)pp. 109-118 Peter Peregrinus
RG Forbes (1985)The concept: Amount of Substance, In: School Science Review66pp. 787-788
RG Forbes (1990)What do we mean by work-function ?pp. 163-173
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, 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
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 (2014)Use of a Spreadsheet to Test for Lack of Field Emission Orthodoxy, In: 2014 TENTH INTERNATIONAL VACUUM ELECTRON SOURCES CONFERENCE (IVESC) IEEE
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.

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
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
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).

JHB Deane, Richard Forbes, A Fischer, MS Mousa (2014)The effect of barrier form on the analysis of Fowler-Nordheim plots
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, 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 (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.

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, 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 (1979)THE INFLUENCE OF DEPOLARIZATION ON SURFACE-ATOM POLARIZATION ENERGY, In: SURF SCI82(2)pp. L620-L624 ELSEVIER SCIENCE BV
RG Forbes (1972)PROBLEMS IN THE THEORY OF FIELD-ION IMAGING, In: VACUUM22(11)pp. 517-520 PERGAMON-ELSEVIER SCIENCE LTD
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 (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 (1980)DERIVATION OF SURFACE-ATOM POLARIZABILITY FROM FIELD-ION ENERGY DEFICITS, In: APPLIED PHYSICS LETTERS36(9)pp. 739-740 AMER INST PHYSICS
RG Forbes, GLR Mair (2008)Liquid metal ion sources, In: HANDBOOK OF CHARGED PARTICLE OPTICS, 2nd Edition CRC Press
RG Forbes (2008)Gas Field Ionization Sources, In: HANDBOOK OF CHARGED PARTICLE OPTICS(3) CRC Press

2

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
RG FORBES, MK WAFI (1980)THE FIELD ADSORPTION OF HELIUM IN ARRAY-TYPE MODELS, In: ULTRAMICROSCOPY5(2)pp. 265-265
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 (1976)A fundamental proposal concerning the "mole", In: Education in Chemistry13pp. 92-?
RG Forbes (1978)Amount of substance: An alternative proposal, In: Physics Education13(5)pp. 269-272
Richard G. Forbes (2020)Use of amount-of-substance terminology and equations in field desorption theory, In: Topics in Catalysis 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.

RG FORBES (1980)ANOTHER LOOK AT FIELD PENETRATION AND SURFACE-ATOM POLARIZABILITY, In: ULTRAMICROSCOPY5(2)pp. 264-264
RG Forbes (1972)A theory of field ion imaging: I - A quasi-classical site-current formula, In: Journal of Microscopy96pp. 57-61
RG FORBES, RA MUNOZ (1980)A PRELIMINARY EXPLORATION OF ION-DIPOLE CORRELATION ENERGIES, In: ULTRAMICROSCOPY5(2)pp. 265-265
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.

GLR Mair, RG Forbes, RV Latham, T Mulvey (1983)ENERGY SPREAD MEASUREMENTS ON A LIQUID METAL ION SOURCE.pp. 171-178
R.G. Forbes (2018)Field electron and ion emission: basic formulae and constants, In: 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

Richard G. Forbes (2020)Use of amount-of-substance terminology and equations in field desorption theory, In: Topics in Catalysis Springer

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.

RG Forbes (1977)Confusion over the avogadro constant, In: Physics Education12(5)pp. 273-274
RG FORBES (1979)CONCEPTUAL ERRORS IN THE THEORY OF FIELD ADSORPTION, In: SURFACE SCIENCE87(1)pp. L278-L284 ELSEVIER SCIENCE BV
RG Forbes (1972)Reply to "Comments on field ion image formation", In: Nature Physical Science239pp. 15-16
RG FORBES (1978)FIELD ADSORPTION - MONOPOLE-DIPOLE INTERACTION, In: SURFACE SCIENCE78(2)pp. L504-L507 ELSEVIER SCIENCE BV
RG Forbes (1972)A theory of field ion imaging: II - On the origin of site-current variations, In: Journal of Microscopy96pp. 63-75
RG Forbes (1978)More confusion over the Avogadro constant, In: Physics Education13(1)pp. 5-6
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 (1979)In defence of seven dimensions, In: International Journal of Mechanical Engineering Education7pp. 203-204
RG Forbes (2008)Appendix to "Coulomb interactions in Ga LMIS" by Radlicka and Lencova, In: ULTRAMICROSCOPY108(5)pp. 455-457 ELSEVIER SCIENCE BV
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
R.G. Forbes (2017)Introduction to field electron and ion emission and customary units, In: Landolt-Börnstein: Numerical data and Functional Relationships in Science and Technology - New Series - Physics of Solid SurfacesIII/45pp. pp 657-723 Springer-Verlag
Michael K. Miller, Richard G. Forbes (2014)Atom-Probe Tomography - The Local Electrode Atom Probe, In: Atom-Probe Tomography Springer US
MK Miller, RG Forbes (2009)Atom probe tomography, In: MATERIALS CHARACTERIZATION60(6)pp. 461-469 ELSEVIER SCIENCE INC
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
Mahendra A. More, Dilip S. Joag, Richard G. Forbes (2015)Field Electron Emission from Nanomaterials, In: Encyclopedia of Nanotechnologypp. 1-23 Springer
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 (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 (1977)Some new ideas in field-ion theorypp. 387-390
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
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 (1996)The electron energy distribution from very sharp field emitters, In: IVMC '96 - 9TH INTERNATIONAL VACUUM MICROELECTRONICS CONFERENCE, TECHNICAL DIGESTpp. 58-61
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 (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 (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 (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 (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
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 (1998)The field emitter and its applications, In: ELECTRONpp. 334-340
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.

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 (1996)Charged surfaces, field adsorption, and appearance-energies: An unsolved challenge, In: JOURNAL DE PHYSIQUE IV6(C5)pp. 25-30 EDITIONS PHYSIQUE
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
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 (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 (1998)Calculation of the electrical-surface (image-plane) position for aluminium, In: ULTRAMICROSCOPY73(1-4)pp. 31-35 ELSEVIER SCIENCE BV
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.

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.

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 (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
RG Forbes (1999)Refining the application of Fowler-Nordheim theory, In: ULTRAMICROSCOPY79(1-4)pp. 11-23 ELSEVIER SCIENCE BV
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 (1999)The electrical surface as centroid of the surface-induced charge, In: ULTRAMICROSCOPY79(1-4)pp. 25-34 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
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 (1999)Use of a spreadsheet for Fowler-Nordheim equation calculations, In: JOURNAL OF VACUUM SCIENCE & TECHNOLOGY B17(2)pp. 534-541 AMER INST PHYSICS
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 (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 (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 (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, 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
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.

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
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, 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
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 (1996)Field-ion imaging old and new, In: APPLIED SURFACE SCIENCE94-5pp. 1-16 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 (1997)Understanding how the liquid-metal ion source works, In: VACUUM48(1)pp. 85-97 PERGAMON-ELSEVIER SCIENCE LTD
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 (1982)A NEW FORMULA FOR PREDICTING LOW-TEMPERATURE EVAPORATION FIELD, In: APPLIED PHYSICS LETTERS40(3)pp. 277-279 AMER INST PHYSICS
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, 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
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.

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.

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

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.

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.

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.

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.

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.

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)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
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)PROGRESS WITH THE THEORY OF NOBLE-GAS FIELD ADSORPTION, In: VACUUM31(10-1)pp. 567-570 PERGAMON-ELSEVIER SCIENCE LTD
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.

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, 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, 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 (1988)ON THE POSITION OF THE ELECTRICAL REFERENCE SURFACE, In: VACUUM38(4-5)pp. 429-429
RG Forbes (2011)Comments on discrepancies in the Fowler and Nordheim 1928 paper, In: 2011 24TH INTERNATIONAL VACUUM NANOELECTRONICS CONFERENCE (IVNC)pp. 113-114
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 (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 (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 (1986)THE PHYSICS OF LIQUID-METAL FIELD-ION SOURCE, In: VACUUM36(11-12)pp. 1020-1020
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.

RG FORBES (1986)TOWARDS A UNIFIED THEORY OF HELIUM FIELD-IONIZATION PHENOMENA, In: JOURNAL DE PHYSIQUE47(C-2)pp. 3-10 EDITIONS PHYSIQUE
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
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.

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
RG FORBES (1991)FURTHER COMMENTS ON FIELD ADSORPTION, In: SURFACE SCIENCE246(1-3)pp. 386-389 ELSEVIER SCIENCE BV
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, 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, NN LJEPOJEVIC (1989)MODELING OF LIQUID-METAL ION SOURCES, In: VACUUM39(11-12)pp. 1153-1155 PERGAMON-ELSEVIER SCIENCE LTD
RG FORBES, NN LJEPOJEVIC (1989)RECENT PROGRESS IN LMIS THEORY, In: JOURNAL DE PHYSIQUE50(C8)pp. C83-C88 EDITIONS PHYSIQUE
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 (1989)ON DIFFERENT TYPES OF DIPOLE-DIPOLE INTERACTION, In: JOURNAL DE PHYSIQUE50(C8)pp. C815-C820 EDITIONS PHYSIQUE
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 (1989)ON CHARGED-SURFACE MODELS AND THE ORIGIN OF FIELD ADSORPTION, In: SURFACE SCIENCE223(1-2)pp. 326-352 ELSEVIER SCIENCE BV
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 (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.

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 (1974)AN ALTERNATIVE THEORETICAL APPROACH TO FIELD EVAPORATION RATE SENSITIVITIES, In: SURF SCI46(2)pp. 577-601 ELSEVIER SCIENCE BV
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
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.

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)
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
RG Forbes (1976)A GENERALIZED THEORY OF STANDARD FIELD-ION APPEARANCE ENERGIES, In: SURF SCI61(1)pp. 221-240 ELSEVIER SCIENCE BV
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, 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 (1971)Field ion image formation, In: Nature Physical Science230pp. 165-166
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.

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
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, 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
RG Forbes (1977)Atomic polarizability values in the SI system, In: SURF SCI64(1)pp. 367-371 ELSEVIER SCIENCE BV
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
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 (1978)FIELD EVAPORATION THEORY - ATOMIC-JUG FORMALISM, In: SURFACE SCIENCE70(1)pp. 239-254 ELSEVIER SCIENCE BV
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.

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 (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)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 (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 (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
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 (1980)Reply to comments on: "In defence of seven dimensions", In: International Journal of Mechanical Engineering Education8pp. 99-100
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 (1982)The seventh SI quantity, In: Education in Chemistry19pp. 102-?
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 (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 (1995)FIELD EVAPORATION THEORY - A REVIEW OF BASIC IDEAS, In: APPLIED SURFACE SCIENCE87-8(1-4)pp. 1-11 ELSEVIER SCIENCE BV
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: 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.

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: 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.

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 (2003)Theories of low-macroscopic-field electron emission, In: TECHNICAL DIGEST OF THE 16TH INTERNATIONAL VACUUM MICROELECTRONICS CONFERENCEpp. 3-3
RG Forbes (2003)More about the extraction of emission area from Fowler-Nordheim plots, In: TECHNICAL DIGEST OF THE 16TH INTERNATIONAL VACUUM MICROELECTRONICS CONFERENCEpp. 89-89
RG Forbes (1978)Reply to comments on "Opinion on SI", In: Physics Bulletin29pp. 247-?
RG Forbes (1978)Opinion on SI, In: Physics Bulletin29pp. 103-?
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, 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
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.

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
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
RG FORBES (1986)FIELD-ION ENERGY DEFICITS IN THE ATOM PROBE FIM, In: JOURNAL DE PHYSIQUE47(C-2)pp. 31-36 EDITIONS PHYSIQUE
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 (2001)Update on analysis of Fowler-Nordheim plots from nonmetallic emitters, In: IVMC 2000: PROCEEDINGS OF THE 14TH INTERNATIONAL VACUUM MICROELECTRONICES CONFERENCEpp. 95-95
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 (1978)Field ionization and surface plasmons: an alternative theoretical formulation, In: Nederlands Tidjschrift voor Vacuumtechniek16pp. 268-268
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
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: ELECTROSTATICS 1995143pp. 219-221
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
RG Forbes, WB Liu (1995)Electrohydrodynamic theory of liquid metal ion sources, In: ELECTROSTATICS 1995143pp. 193-200
RG Forbes (2001)Models for low-macroscopic-field electron emission, In: IVMC 2000: PROCEEDINGS OF THE 14TH INTERNATIONAL VACUUM MICROELECTRONICES CONFERENCEpp. 71-71
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
RG Forbes (1977)The mole––interpreting it, In: Education in Chemistry14pp. 124-?
RG Forbes (2001)Is uniform electron emission possible at low macroscopic fields?, In: IVMC 2000: PROCEEDINGS OF THE 14TH INTERNATIONAL VACUUM MICROELECTRONICES CONFERENCEpp. 79-79
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
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 (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.