Simulation of the enhancement factor from an individual 3D hemisphere-on-post field emitter by using finite elements method

Roveri, Davi Sabbag; Sant'Anna, Guilherme Mauad; Bertan, Hilton Henrique; Mologni, Juliano Fujioka; Alves, Marco Túlio Santana; Braga, Edmundo S.

doi:10.1016/j.ultramic.2015.10.018

Cited by 30 publications

(22 citation statements)

References 13 publications

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“…This leads to challenges that remain to be overcome. For instance, the field enhancement factor, b, plays a critical role in predicting experimental results for microscale gaps due to the dominance of field emission; however, accurately determining b a priori can be difficult as it depends upon both the geometry and space-charge, [53][54][55] which will often depend upon the surface roughness of the electrodes. Experimental, theoretical, and simulation studies assessing the impact of surface roughness on these parameters may provide bounds that guide experimentalists in predicting the breakdown voltage, which becomes even more critical at smaller gap distances.…”

Section: Discussionmentioning

confidence: 99%

A universal theory for gas breakdown from microscale to the classical Paschen law

Loveless

Garner

2017

Physics of Plasmas

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While well established for larger gaps, Paschen's law (PL) fails to accurately predict breakdown for microscale gaps, where field emission becomes important. This deviation from PL is characterized by the absence of a minimum breakdown voltage as a function of the product of pressure and gap distance, which has been demonstrated analytically for microscale and smaller gaps with no secondary emission at atmospheric pressure [A. M. Loveless and A. L. Garner, IEEE Trans. Plasma Sci. 45, 574-583 (2017)]. We extend these previous results by deriving analytic expressions that incorporate the nonzero secondary emission coefficient, c SE , that are valid for gap distances larger than those at which quantum effects become important ($100 nm) while remaining below those at which streamers arise. We demonstrate the validity of this model by benchmarking to particle-in-cell simulations with c SE ¼ 0 and comparing numerical results to an experiment with argon, while additionally predicting a minimum voltage that was masked by fixing the gap pressure in previous analyses. Incorporating c SE demonstrates the smooth transition from field emission dominated breakdown to the classical PL once the combination of electric field, pressure, and gap distance satisfies the conventional criterion for the Townsend avalanche; however, such a condition generally requires supra-atmospheric pressures for breakdown at the microscale. Therefore, this study provides a single universal breakdown theory for any gas at any pressure dominated by field emission or Townsend avalanche to guide engineers in avoiding breakdown when designing microscale and larger devices, or inducing breakdown for generating microplasmas.

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Section: Discussionmentioning

confidence: 99%

A universal theory for gas breakdown from microscale to the classical Paschen law

Loveless

Garner

2017

Physics of Plasmas

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“…A common practice to model a CNT or CNF is take the emitter as a cylindrical classical conductor capped with a conducting hemisphere, both of radius r. The total emitter's height is h. This model is known as the "hemisphere-on-cylindrical post" (HCP), have been extensively studied theoretically [6][7][8][9][10][11][12] and is known to have an analytical counterpart of great complexity as compared with computational solution [7]. In some studies, the hemi-ellipsoid model is preferred to represent the emitter for a couple of reasons: in this case, the the electrostatic potential distribution in the system has analytical solution and is a better representation of the emitter when the radius at the apex is much smaller than the radius at the base [7].…”

Section: Introductionmentioning

confidence: 99%

Minimal domain size necessary to simulate the field enhancement factor numerically with specified precision

Assis

Dall’Agnol

2019

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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In the literature about field emission, finite elements and finite differences techniques are being increasingly employed to understand the local field enhancement factor (FEF) via numerical simulations. In theoretical analyses, it is usual to consider the emitter as isolated, i.e, a single tip field emitter infinitely far from any physical boundary, except the substrate. However, simulation domains must be finite and the simulation boundaries influences the electrostatic potential distribution. In either finite elements or finite differences techniques, there is a systematic error ( ) in the FEF caused by the finite size of the simulation domain. It is attempting to oversize the domain to avoid any influence from the boundaries, however, the computation might become memory and time consuming, especially in full three dimensional analyses. In this work, we provide the minimum width and height of the simulation domain necessary to evaluate the FEF with at the desired tolerance. The minimum width (A) and height (B) are given relative to the height of the emitter (h), that is, (A/h)min × (B/h)min necessary to simulate isolated emitters on a substrate. We also provide the (B/h)min to simulate arrays and the (A/h)min to simulate an emitter between an anode-cathode planar capacitor. At last, we present the formulae to obtain the minimal domain size to simulate clusters of emitters with precision tol . Our formulae account for ellipsoidal emitters and hemisphere on cylindrical posts. In the latter case, where an analytical solution is not known at present, our results are expected to produce an unprecedented numerical accuracy in the corresponding local FEF.

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“…где X F = 1/U и Y F = ln(I/U 2 ), а индекс Elns обозначает приближение Элинсона. Экспериментальная ВАХ строится в тех же координатах и аппроксимируется рямолинейной зависимостью, что позволяет найти наклон S fit и отсечку ln(R fit ) для уравнения (10). По найденным величинам R fit и S fit вычисляются значения эффективных параметров S eff-Elns и β eff-Elns :…”

Section: варианты определения площади эмитирующей поверхностиunclassified

“…равна E 0 = 5.89 • 10 7 V/cm. Этот результат согласуется с литературными данными по моделированию аналогичных систем в других программных средах [10,26]. Для получения общей ВАХ модельного эмиттера его вершина была виртуально разделена на сегменты равной площади: пятьдесят сегментов в полусфере и еще пятьдесят на цилиндре под ней (рис.…”

Section: моделирование расчет и сравнение видов эмиссионных площадейunclassified

“…Одним из ключевых факторов при переходе от математических зависимостей полевой эмиссии к реальным источникам электронов является площадь полевой эмиссии. Существуют различные методы экспериментального получения ее значений (по картинам свечения полевого эмиссионного проектора [5,6], по изображениям сканирующего эмиссионного микроскопа SAFEM [7]), а также несколько способов ее определения в теоре-тических расчетах с применением как аналитических вычислений, так и компьютерного моделирования [8][9][10].…”

Section: Introductionunclassified

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Десять Способов Определения Площади Полевой Эмиссии

Попов¹,

Колосько²,

Чумак³

et al. 2019

Журнал Технической Физики

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A variety of types for formal determination of one of the main parameters of field emission systems - the emission area was investigated. Using hemisphere on a cylindrical post model built using the COMSOL Multiphysics software package the relationship between known types of emission area estimation was shown. The corresponding values of emission currents were calculated. It was shown that the formal emission area (the ratio of the total current to the current density at the top) provides only ~ 75% of the emission current value. The effect of the anomalous behavior of the effective emission area (intercept of the trend line of current-voltage characteristics) is obtained when the voltage level changes in standard Fowler-Nordheim coordinates. A method for an experimental estimate of the field emission area using the modified Fowler-Nordheim coordinates ln (I/U^(2-η/6)) vs 1/U is proposed. The method is applied to the analysis of field emission data of a multi-tip nanocomposite emitter with carbon nanotubes.

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Simulation of the enhancement factor from an individual 3D hemisphere-on-post field emitter by using finite elements method

Cited by 30 publications

References 13 publications

A universal theory for gas breakdown from microscale to the classical Paschen law

A universal theory for gas breakdown from microscale to the classical Paschen law

Minimal domain size necessary to simulate the field enhancement factor numerically with specified precision

Десять Способов Определения Площади Полевой Эмиссии

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