Erratum: “The image-charge correction for curved field emitters” [Phys. Plasmas <b>24</b>, 073107 (2017)]

Biswas, Debabrata; Ramachandran, Rajasree

doi:10.1063/1.4994272

Cited by 8 publications

(6 citation statements)

References 1 publication

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“…The strides achieved in the past decades in our ability to pattern arrays of pointed emitters [3][4][5] and the discovery of carbon nanotubes (CNT) as a suitable material 6,7 for stable operation, have led to vigorous research activity in this direction. These efforts are supported by theoretical studies on large area field emitters (LAFE) [8][9][10][11][12][13][14] and corrections for nano-tipped emitters [15][16][17] to the planar Fowler-Nordheim (FN) formula for current density [18][19][20][21] . Despite this progress, there are several challenges in our ability to predict theoretically, the current emitted by a single emitter or a cluster of emitters placed randomly or in an array.…”

Section: Introductionmentioning

confidence: 99%

Shielding effects in random large area field emitters, the field enhancement factor distribution, and current calculation

Biswas

Rudra

2018

Physics of Plasmas

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A finite-size uniform random distribution of vertically aligned field emitters on a planar surface is studied under the assumption that the asymptotic field is uniform and parallel to the emitter axis. A formula for field enhancement factor is first derived for a 2-emitter system and this is then generalized for N -emitters placed arbitrarily (line, array or random). It is found that geometric effects dominate the shielding of field lines. The distribution of field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area field emitter.

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Section: Introductionmentioning

confidence: 99%

Shielding effects in random large area field emitters, the field enhancement factor distribution, and current calculation

Biswas

Rudra

2018

Physics of Plasmas

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“…78 The uniform emitter surface may be a valid assumption in some cases, but emitters with the tip apex radius of curvature r tip of a few nanometers down to single-atom 75 will require the consideration of the bulk and surface band structure. Comparing to the impact of such three-dimensional-shape effects on the current-voltage characteristics of field emitters, [79][80][81][82] their influences on the wave function are not much studied yet. Interestingly, the estimated full width at the half maximum of the wave function at the surface of a "point" emitter equal to 0.7 nm (at the surface field of 5 GV/m, with the corresponding r 0 ¼ 0.42 nm) is consistent with the sub-nanometer resolution of the field emission microscope for sub-nanometer-r tip emitters based on the electron optical analysis 23,83 and agrees with the values observed in the experiments.…”

Section: F Further Discussionmentioning

confidence: 99%

Transverse structure of the wave function of field emission electron beam determined by intrinsic transverse energy

Tsujino

2018

Journal of Applied Physics

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The average transverse energy of field emission electrons at the cathode surface is one of the key factors that determines the virtual source size, hence the transverse spatial coherence of field emitters. In the past, the subject has been intensively studied by classical electron optics analysis but its wave optical studies are rare. In this work, we therefore aim to elucidate the influence of the transverse momentum in solid on the transverse structure of the wave function of field emission electrons. From the calculation extending the standard field emission theory within the WKB approximation for model planar free-electron metal, we obtained a Gaussian-beam-type wave function that exhibits a minimum transverse width at the cathode surface as determined by the average transverse energy and propagates the first few nanometers with a limited transverse spread. At far field, the wave function spreads as the electron propagates away from the cathode surface. Comparison with classical results indicated that, in the present planar field emitter model, the neglect of the three-dimensional potential around the tip apexes of actual field emitters underestimates the transverse spread up to a factor of 2. However, when the cathode size is finite and the electrons in the solid are phase-coherent within the source area, the transverse spread is much smaller than that of the point-source wave function. Our result indicates that the intrinsic transverse emittance of a finite size fully coherent field emitter is much smaller than the value predicted by classical analysis. Published by AIP Publishing. https://doi.

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“…In general, both the image and external potential get modified. The image potential takes the form [13][14][15] −…”

Section: Curvature Correctionsmentioning

confidence: 99%

“…With the increasing use of nanostructured materials such as carbon nanotubes, nanowires and nanocones [1][2][3][4][5] in field emission cathodes, the need for an extension to the Fowler-Nordheim (FN) formalism [6][7][8][9][10][11] to deal with emission from nano-tipped emitters is recognized [12][13][14][15][16] . For emitters with apex radius of curvature R a in the nanometer regime, there are competing influences that determine the net field emission current from an isolated emitter.…”

Section: Introductionmentioning

confidence: 99%

Curvature correction to the field emission current

Biswas

Ramachandran

2019

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

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The curvature of field emitter tips leads to an altered tunneling potential that assumes significance when the radius of curvature is small. We provide here an analytical curvature-corrected formula for the field emission current from smooth vertically aligned emitter tips and test its applicability across a range of apex radius, R a , and local electric field, E a . It is found to give excellent results for R a > 10nm with errors generally less than 10%. Surprisingly, for the uncorrected potential, we find the errors to be high even at R a = 100 nm (> 35% at E a = 3 V/nm) and conclude that curvature correction is essential for apex radius less than a micron.

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Erratum: “The image-charge correction for curved field emitters” [Phys. Plasmas 24, 073107 (2017)]

Cited by 8 publications

References 1 publication

Shielding effects in random large area field emitters, the field enhancement factor distribution, and current calculation

Shielding effects in random large area field emitters, the field enhancement factor distribution, and current calculation

Transverse structure of the wave function of field emission electron beam determined by intrinsic transverse energy

Curvature correction to the field emission current

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