### Dr Richard Forbes

## Academic and research departments

Department of Electrical and Electronic Engineering, Advanced Technology Institute.### My publications

### Publications

) for this array is also derived. Since ±

j1, it follows that a macroscopic pre-exponential correction factor (»

) must be included in the formula for the macroscopic ("LAFE-average") emission current density (J

) for a large-area field emitter (LAFE). Omission of »

may cause great theoretical over-prediction of the value of J

. © 2012 IEEE.

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.

Simmons' equation for the local current density in

metal-vacuum-metal junctions, Jordan Journal of Physics Yarmouk University, Irbid, Jordan

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.

*³*

_{C}. 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

*³*

_{C}. 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.

*F*

_{M}. 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

*F*

_{M}. 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.

(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.

asopis The Faculty of Electrical Engineering and Information Technology of the Slovak University of Technology in Bratislava

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.

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.

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.

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).

Carbon Nanotubes using the Induced Electron Density, JOURNAL OF CHEMICAL INFORMATION AND MODELING American Chemical Society

(SWCNTs), the SWCNT stands on one of two well-separated parallel plane plates,

with a macroscopic ýeld FM applied between them. For any given location "L" on

the SWCNT surface, a ýeld enhancement factor (FEF) is deýned as FL/FM, where

FL is a local ýeld deýned 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 op-

posed to classical electrostatic) calculations. Density functional theory (DFT) is used

to analyze the properties of two short,

oating SWCNTS, capped at both ends, namely

a (6,6) and a (10,0) structure. Both have eýectively the same height (ý 5:46 nm) and

radius (ý 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 relate to the

SWCNT longitudinal system polarizabilities, which are presumed similar. The DFT

calculations also generate \real", as opposed to \induced", potential-energy (PE) bar-

riers for the two SWCNTs, for FM-values from 3 V/ým to 2 V/nm. PE proýles along

the SWCNT axis and along a parallel \observation line" through one of the topmost

atoms are similar. At low macroscopic ýelds the details of barrier shape diýer for the

two SWCNT types. Even for FM = 0, there are distinct PE structures present at the

emitter apex (diýerent for the two SWCNTs); this suggests the presence of structure-

speciýc chemically induced charge transfers and related patch-ýeld distributions.