Field electron emission theory (October 2016)

Forbes, Richard G.

doi:10.1109/vmneyr.2016.7880403

Cited by 12 publications

(6 citation statements)

References 23 publications

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“…The electric field lowers the surface barrier by an amount ∆(|𝑒|𝜑) = ½|𝑒| I 𝑊 and increases the emission current in correspondence to the Schottky effect [12] (see also [20, p. 588]). When the field emission from the surface of a metal takes place (nanotubes are absent), the transparency coefficient 𝐷 by contrast with (19) includes Nordheim function θ(y) [12].…”

Section: The Influence Of Nanotube Length At Field Emission On the No...mentioning

confidence: 99%

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Field emission in an array of homogeneous identical nanometer-long nanotubes

2023

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We consider the problem of field emission based on carbon nanotubes. The length of these nanotubes differ from several nanometers to several hundreds of nanometers. We obtain the particle transmission function, considering the difference of potentials on the ends of nanotubes to be 𝑈 = 2 ÷ 3.5 V. Basing on the transmission function we calculate emission current. We establish the dependence of the Nordheim function on the length of nanoparticles. The limiting transition is considered for the transmission coefficient for field emission from the cathode surface in the absence of nanoparticles on it. We establish the linear dependence of current I on the field strength W and the linear dependence of function 𝐼/𝑊on the inverse value of field strength 1/W.

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Section: The Influence Of Nanotube Length At Field Emission On the No...mentioning

confidence: 99%

“…In papers [12,19] (see also [20]) the core equation for local emission current density (ECD) j, in terms of local work-function 𝜑 and a characteristic local electrostatic field (magnitude 𝑊) at the emitter surface (usually the field is at the emitter apex), is given by 𝑗 = 𝜆 ? @ 𝑎𝜑 B2 𝑊 -expF−𝜈 ?…”

Section: Introductionmentioning

confidence: 99%

Field emission in an array of homogeneous identical nanometer-long nanotubes

2023

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“…For an appropriate and thorough theoretical discussion, the author would like to refer to the tutorial papers on the electron sources by Jensen [21] and Forbes [24]. For field emission, usually, the Fowler-Nordheim (F-N) equation is commonly applied [19,20].…”

Section: Basics Of the Fe Cathodesmentioning

confidence: 99%

Field Emission Cathodes to Form an Electron Beam Prepared from Carbon Nanotube Suspensions

Laszczyk

2020

Micromachines

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In the first decade of our century, carbon nanotubes (CNTs) became a wonderful emitting material for field-emission (FE) of electrons. The carbon nanotube field-emission (CNT-FE) cathodes showed the possibility of low threshold voltage, therefore low power operation, together with a long lifetime, high brightness, and coherent beams of electrons. Thanks to this, CNT-FE cathodes have come ahead of increasing demand for novel self-sustaining and miniaturized devices performing as X-ray tubes, X-ray spectrometers, and electron microscopes, which possess low weight and might work without the need of the specialized equipped room, e.g., in a harsh environment and inaccessible-so-far areas. In this review, the author discusses the current state of CNT-FE cathode research using CNT suspensions. Included in this review are the basics of cathode operation, an evaluation, and fabrication techniques. The cathodes are compared based on performance and correlated issues. The author includes the advancement in field-emission enhancement by postprocess treatments, incorporation of fillers, and the use of film coatings with lower work functions than that of CNTs. Each approach is discussed in the context of the CNT-FE cathode operating factors. Finally, we discuss the issues and perspectives of the CNT-FE cathode research and development.

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“…We use the Sommerfeld model of quasi-free electrons with a Fermi distribution of energies, confined by a step potential U = E F + W, where E F is the Fermi energy and W is the work function of the metal. This setup was first used by Fowler and Nordheim [27] in 1928 for a time-independent field, and is commonly used as a model for the process of emission, both for a constant and an oscillating field [1,4,22,24,[27][28][29][30][31][32][33][34][35]. In both cases one imagines the metal occupies the half space x < 0, and focuses attention on electrons, part of the Fermi sea, moving from the left towards the metal surface at x = 0.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of the 1D time-dependent Schrödinger equation for the emission of quasi-free electrons from a flat metal surface by a laser

Costin¹,

Costin²,

Jauslin³

et al. 2020

J. Phys. A: Math. Theor.

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We solve exactly the one-dimensional Schrödinger equation for ψ(x, t) describing the emission of electrons from a flat metal surface, located at x = 0, by a periodic electric field E cos(ωt) at x > 0, turned on at t = 0. We prove that for all physical initial conditions ψ(x, 0), the solution ψ(x, t) exists, and converges for long times, at a rate t − 3 2 , to a periodic solution considered by Faisal et al (2005 Phys. Rev. A 72 023412). Using the exact solution, we compute ψ(x, t), for t > 0, via an exponentially convergent algorithm, taking as an initial condition a generalized eigenfunction representing a stationary state for E = 0. We find, among other things, that: (i) the time it takes the current to reach its asymptotic state may be large compared to the period of the laser; (ii) the current averaged over a period increases dramatically as ω becomes larger than the work function of the metal plus the ponderomotive energy in the field. For weak fields, the latter is negligible, and the transition is at the same frequency as in the Einstein photoelectric effect; (iii) the current at the interface exhibits a complex oscillatory behavior, with the number of oscillations in one period increasing with the laser intensity and period. These oscillations get damped strongly as x increases.

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Field electron emission theory (October 2016)

Cited by 12 publications

References 23 publications

Field emission in an array of homogeneous identical nanometer-long nanotubes

Field emission in an array of homogeneous identical nanometer-long nanotubes

Field Emission Cathodes to Form an Electron Beam Prepared from Carbon Nanotube Suspensions

Exact solution of the 1D time-dependent Schrödinger equation for the emission of quasi-free electrons from a flat metal surface by a laser

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