Restoring Observed Classical Behavior of the Carbon Nanotube Field Emission Enhancement Factor from the Electronic Structure

Castro, Caio P. de; Assis, Thiago A. de; Rivelino, Roberto; Mota, F.; Castilho, C.M.C. de; Forbes, Richard G.

doi:10.1021/acs.jpcc.9b00959

Cited by 11 publications

(5 citation statements)

References 29 publications

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“…The Kohn–Sham equations were solved using the PBE exchange-correlation potential scheme, which has been demonstrated to work well for these types of systems. ,, Core electrons were described in terms of the Troullier–Martins norm-conserving pseudopotentials and valence electrons with double-ζ basis sets, including polarization functions, using an energy cutoff of 300 Ry and sampling in the Γ point of the Brillouin zone.…”

Section: Computational Methods and Systemsmentioning

confidence: 99%

“…However, some earlier theoretical treatments of CNT behavior, for example, Ref., 18 have used a different definition of characteristic FEF. These treatments use electronic structure theory to calculate the total polarized charge distribution, and then use this to define (what we have called 16 ) real local-field and local-FEF distributions. With this approach, their characteristic FEF is a value of real-FEF taken at some chosen location in space above the CNT apex.…”

Section: Introductionmentioning

confidence: 99%

“…One way of representing the field-enhancing properties of a nanostructure is to calculate the so-called “local induced FEF” by considering the emitter’s induced-charge distribution. − Provided that it is reasonable to make the assumption that there are no significant changes in the positions of the atomic nuclei, this induced-charge distribution is given by the induced electron density. It follows that one way of calculating a characteristic FEF is to use the distribution of induced charge to calculate related induced-field and induced-FEF distributions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes Using the Induced Electron Density

Castro

Assis

Rivelino

et al. 2019

J. Chem. Inf. Model.

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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 F L /F M , where F L 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 F M ). 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 F M , 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) 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 F M = 0, there are distinct PE structures present at the emitter apex (different for the two SWCNTs); this suggests the presence of structurespecific chemically induced charge transfers and related patch-field distributions.

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Section: Computational Methods and Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes Using the Induced Electron Density

Castro

Assis

Rivelino

et al. 2019

J. Chem. Inf. Model.

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“…Our previous paper [18], called here "C19", showed the following. After a density-functional-theory (DFT) calculation [6] of the real-charge-density distribution, we evaluated the related induced-charge-density distributions.…”

mentioning

confidence: 90%

On the quantum mechanics of how an ideal carbon nanotube field emitter can exhibit a constant field enhancement factor

Castro

Assis

Rivelino

et al. 2019

Journal of Applied Physics

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Measurements of current-voltage characteristics from ideal carbon nanotube (CNT) field electron emitters of small apex radius have shown that these emitters can exhibit a linear Fowler-Nordheim (FN) plot [e.g., Dean and Chalamala, Appl. Phys. Lett., 76, 375, 2000]. From such a plot, a constant (voltage-independent) characteristic field enhancement factor (FEF) can be deduced. Over fifteen years later, this experimental result has not yet been convincingly retrieved from firstprinciples electronic structure calculations, or more generally from quantum mechanics (QM). On the contrary, several QM calculations have deduced that the characteristic FEF should be a function of the macroscopic field applied to the CNT. This apparent contradiction between experiment and QM theory has been an unexplained feature of CNT emission science, and has raised doubts about the ability of existing QM models to satisfactorily describe experimental CNT emission behavior. In this work we demonstrate, by means of a density functional theory analysis of single-walled CNTs "floating" in an applied macroscopic field, the following significant result. This is that agreement between experiment, classical-conductor CNT models and QM calculations can be achieved if the latter are used to calculate (from the "real" total-charge-density distributions initially obtained) the distributions of induced charge-density, induced local fields and induced local FEFs. The present work confirms, more reliably and in significantly greater detail than in earlier work on a different system, that this finding applies to the common "post-on-a-conducing plane" situation of CNT field electron emission. This finding also brings out various further theoretical questions that need to be explored. PACS numbers: 73.61.At, 74.55.+v, 79.70.+q Carbon nanotubes (CNTs) are effective in field electron emission (FE) applications [1-5] because, in the presence of an applied macroscopic field F M , a sharp nanostructure develops high local fields F (r ) at points in space near its apex. At any point r , a local field enhancement factor (FEF) can be defined by γ(r ) = F (r )/F M . In what follows, we consider the common situation where the field F M is parallel to the axis of a quasi-cylindrical CNT. The CNT itself is a "floating CNT" capped at both ends, or (what is electrostatically equivalent) a "half-CNT" standing upright on one of a pair of well-separated parallel plates and capped at the top end.Applying the macroscopic field F M to a CNT changes its "real" charge-density distribution ρ r (r , F M ) from that existing in the case F M = 0. The change is mainly in the electron density distribution, although there may also be small movements in the positions of the carbon-atom nuclei. The related "real-local-field" distribution can be

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“…We also need to make the point that this is an article about the electrostatics of classical conductors with smooth surfaces, and about how to implement this type of electrostatics effectively. There are also important issues, particularly with carbon nanotubes (e.g., [24]), about how to relate classical-conductor electrostatics to electrostatic treatments where atomic structure is taken into account. There have been important recent developments in this area, e.g.…”

Section: Introductionmentioning

confidence: 99%

Field emitter electrostatics: efficient improved simulation technique for highly precise calculation of field enhancement factors

Dall’Agnol¹,

Assis²,

Forbes³

2023

Preprint

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

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Restoring Observed Classical Behavior of the Carbon Nanotube Field Emission Enhancement Factor from the Electronic Structure

Cited by 11 publications

References 29 publications

Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes Using the Induced Electron Density

Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes Using the Induced Electron Density

On the quantum mechanics of how an ideal carbon nanotube field emitter can exhibit a constant field enhancement factor

Field emitter electrostatics: efficient improved simulation technique for highly precise calculation of field enhancement factors

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