Dependence of optimal spacing on applied field in ungated field emitter arrays

Harris, John R.; Jensen, Kevin L.; Shiffler, D.

doi:10.1063/1.4929983

Cited by 47 publications

(31 citation statements)

References 34 publications

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“…As an example, recently, Forbes has shown that the rate at which the FEF from a pair of spherical emitters tend toward the FEF of a single sphere is given by a power law decay as a function of the separation center to center [16]. Prior to his work, many authors were assuming an exponential-type decay [17][18][19][20][21][22]. This power law was an important realization in the physical mechanism governing the FEF.…”

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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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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“…[14][15][16][17][18][19] We can analyze these geometries in terms of nearest-neighbor emitter attributes by comparing each of the four configurations considered in this paper. Notably, linear and square arrays, quite obviously, share common geometrical attributes that influence the overall field enhancement of the arrays.…”

Section: Aip Advances 6 095007 (2016)mentioning

confidence: 99%

“…Hence, in previous work, we explored the emission characteristics of two-and four-fiber arrays of carbon emitters in a carefully prepared, simple geometry. [13][14][15][16][17][18][19] Our configuration allows a much more pristine and straightforward experimental geometry for isolating and interpreting the electric field screening from other effects such as work function variation across the cathode surface or statistical inhomogeneities in the geometry of the individual emitters that comprise the array.…”

Section: Introductionmentioning

confidence: 99%

Field emission characteristics of a small number of carbon fiber emitters

et al. 2016

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This paper reports an experiment that studies the emission characteristics of small number of field emitters. The experiment consists of nine carbon fibers in a square configuration. Experimental results show that the emission characteristics depend strongly on the separation between each emitter, providing evidence of the electric field screening effects. Our results indicate that as the separation between the emitters decreases, the emission current for a given voltage also decreases. The authors compare the experimental results to four carbon fiber emitters in a linear and square configurations as well as to two carbon fiber emitters in a paired array. Voltage-current traces show that the turn-on voltage is always larger for the nine carbon fiber emitters as compared to the two and four emitters in linear configurations, and approximately identical to the four emitters in a square configuration. The observations and analysis reported here, based on Fowler-Nordheim field emission theory, suggest the electric field screening effect depends critically on the number of emitters, the separation between them, and their overall geometric configuration.

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“…Recently, Forbes [1] proved that, in the "floating sphere at emitter-plane potential (FSEPP)" model, at sufficiently large separations c between the sphere centres, the fractional reduction ρ in apex FEF falls off with a power law decay of c −3 , rather than the exponential decay usually assumed (e.g. [3][4][5]) prior to this work. This means that the interaction effect (which is a form of electrostatic depolarization) persists to larger separations than originally assumed.…”

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confidence: 90%

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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Dependence of optimal spacing on applied field in ungated field emitter arrays

Cited by 47 publications

References 34 publications

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

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

Field emission characteristics of a small number of carbon fiber emitters

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

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