Close proximity electrostatic effect from small clusters of emitters

Dall’Agnol, Fernando F.; Assis, Thiago A. de

doi:10.1088/1361-648x/aa8567

Cited by 15 publications

(15 citation statements)

References 30 publications

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“…Cold field electron emission (CFE) by a conducting surface, when a strong electrostatic field is applied, is a phenomenon that has led to scientific and technological developments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Recently, great attention has been given by field emission community to the research of the electrostatics behind single or small cluster of emitters [17][18][19][20][21][22][23][24][25][26][27], aiming to understand the emitter's interaction that leads to charge-transfer and neighbor-field effects [22]. Particularly, an important Field Emission (FE) characterization parameter is the apex-field enhancement factor (FEF) [4].…”

Section: Introductionmentioning

confidence: 99%

Discrepancies and universality in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters

Assis

DallrAgnol

2018

2018 31st International Vacuum Nanoelectronics Conference (IVNC)

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Numerical simulations are important when assessing the many characteristics of field emission related phenomena. In small simulation domains, the electrostatic effect from the boundaries is known to influence the calculated apex field enhancement factor (FEF) of the emitter, but no established dependence has been reported at present. In this work, we report the dependence of the lateral size, L, and the height, H, of the simulation domain on the apex-FEF of a single conducting ellipsoidal emitter. Firstly, we analyze the error, ε, in the calculation of the apex-FEF as a function of H and L. Importantly, our results show that the effects of H and L on ε are scale invariant, allowing one to predict ε for ratios L/h and H/h, where h is the height of the emitter. Next, we analyze the fractional change of the apex-FEF, δ, from a single emitter, γ1, and a pair, γ2. We show that small relative errors in γ1 (i.e., ε ≈ 0.5%), due to the finite domain size, are sufficient to alter the functional dependence δ(c), where c is the distance from the emitters in the pair. We show that δ(c) obeys a recently proposed power law decay [R. G. Forbes, J. of Appl. Phys. 120, 054302 (2016)], at sufficient large distances in the limit of infinite domain size (ε = 0, say), in contrast to a long time established exponential decay [J.-M. Bonard et al. Advanced Materials 13, 184 (2001)]. We also shown that this functional dependence is respected for various systems which includes infinity arrays and small clusters of emitters with different shapes. Thus, power law functional dependence, −δ ∼ c −m , with m = 3, is suggested to be a universal signature of the charge-blunting (CB) effect in small clusters or arrays, at sufficient large distances between emitters with any shape. These results explain the origin of the discrepancies in the literature and improves the scientific understanding of the field electron emission theory, for accurate characterization of emitters in small clusters or arrays. Finally, our results reinforce that the consequences of CB for a small cluster of emitters are also expected for infinity arrays.

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Section: Introductionmentioning

confidence: 99%

Discrepancies and universality in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters

Assis

DallrAgnol

2018

2018 31st International Vacuum Nanoelectronics Conference (IVNC)

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“…This is responsible for a nonuniform emission along the LAFE [27]. These aspects have motivated theoretical studies based on the electrostatic interaction between emitters in small clusters [28][29][30][31][32][33]. In addition, an interesting phenomenon, called Close Proximity Electrostatic Effect (CPEE), has been recently reported [28,29,32,33].…”

Section: Introductionmentioning

confidence: 99%

“…These aspects have motivated theoretical studies based on the electrostatic interaction between emitters in small clusters [28][29][30][31][32][33]. In addition, an interesting phenomenon, called Close Proximity Electrostatic Effect (CPEE), has been recently reported [28,29,32,33]. It is generally expected that the FEF of two emitter sites, in a small cluster or in an array, would be reduced when they are close to each other.…”

Section: Introductionmentioning

confidence: 99%

“…It is generally expected that the FEF of two emitter sites, in a small cluster or in an array, would be reduced when they are close to each other. The CPEE, differently from the electrostatic shielding, consists of an increasing of the characteristic local FEF, as long as the emitter sites become closer to each other in some specific interval [28,29,32,33]. Since the CPEE was recently reported and there are just a few works concerning this effect in the literature, it is not yet clear whether any kind of geometry would be able to provide CPEE.…”

Section: Introductionmentioning

confidence: 99%

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Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation

Marcelino,

de Assis,

de Castilho

2017

Preprint

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It is well known that sufficiently strong electrostatic fields are able to change the morphology of Large Area Field Emitters (LAFEs). This phenomenon affects the electrostatic interactions between adjacent sites on a LAFE during field emission and may lead to several consequences, such as: the emitter's degradation, diffusion of absorbed particles on the emitter's surface, deflection due to electrostatic forces and mechanical stress. These consequences are undesirable for technological applications, since they may significantly affect the macroscopic current density on the LAFE. Despite the technological importance, these processes are not completely understood yet. Moreover, the electrostatic effects due to the proximity between emitters on a LAFE may compete with the morphological ones. The balance between these effects may lead to a non trivial behavior in the apex-Field Enhancement Factor (FEF). The present work intends to study the interplay between proximity and morphological effects by studying a model amenable for an analytical treatment. In order to do that, a conducting system under an external electrostatic field, with a profile limited by two mirror-reflected triangular protrusions on an infinite line, is considered. The FEF near the apex of each emitter is obtained as a function of their shape and the distance between them via a Schwarz-Christoffel transformation. Our results suggest that a tradeoff between morphological and proximity effects on a LAFE may provide an explanation for the observed reduction of the local FEF and its variation at small distances between the emitter sites.

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“…It should be noted that approximation (19) may fail for very small s-values, certainly when s 0.05. In this case, the functional dependence of the fractional reduction ρ will be significantly affected by additional electrostatic effects that, depending on the geometry of the system, can be related to the "close proximity electrostatic effect" [10,11].…”

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confidence: 99%

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Dall’Agnol

Assis

Forbes

2018

J. Phys.: Condens. Matter

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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 [Formula: see text] (c being the separation and h is the height of the emitters) and large separations ([Formula: see text]) 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%.

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Close proximity electrostatic effect from small clusters of emitters

Cited by 15 publications

References 30 publications

Discrepancies and universality in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters

Discrepancies and universality in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters

Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

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