Simulation-Based Model of Randomly Distributed Large-Area Field Electron Emitters

Bieker, Johannes; Forbes, Richard G.; Wilfert, Stefan; Schlaak, Helmut F.

doi:10.1109/jeds.2019.2940086

Cited by 17 publications

(4 citation statements)

References 35 publications

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“…Note, the emitter dimensions used for calculation of the theoretical FEFs are given in table S1 of the supplementary material. The FEFs extracted from the emitter dimensions are slightly larger than the values derived from the FE measurements, which may be explained by electrical field screening among neighboring emitters in the real field emitter array leading to the suppression of the geometrical field enhancement effect [39,52]. To estimate the influence of mutual depolarization in the investigated emitter arrays, the screening factor was extracted as the ratio of the effective FEF derived from the FE data (γ eff ) to the theoretical FEF calculated with the model for an isolated single emitter from the mean emitter dimensions (γ theory ).…”

Section: Field Emission Properties Of Zno Nanowiresmentioning

confidence: 83%

Field emission characteristics of ZnO nanowires grown by catalyst-assisted MOCVD on free-standing inorganic nanomembranes

Haugg¹,

Hedrich²,

Zierold³

et al. 2022

J. Phys. D: Appl. Phys.

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ZnO field emitters on freely suspended inorganic nanomembranes were synthesized by catalyst-assisted metal organic chemical vapor deposition (MOCVD) using the precursors zinc acetylacetonate hydrate and oxygen. The morphology and the possibly involved growth mechanisms of the randomly distributed ZnO nanostructures were investigated by scanning electron microscopy (SEM) and by energy-dispersive x-ray spectroscopy (EDX). The findings indicate a growth process that involves the vapor-liquid-solid as well as the vapor-solid-solid mechanism. The field emission properties of such ZnO nanowire samples showed to be highly reproducible and independent of the investigated Si-based substrate types. Herein, a new type of flexible substrate for the MOCVD process has been introduced that allows for the direct growth of ZnO nanowires on free-standing membranes for potential field emission-based sensor applications. A turn-on field of 4.1 V µm-1 was detected for a macroscopic emission current density of 10 µA cm-2 and the stability test revealed fluctuations of only 9 % around the mean emission current over a duration of 3 h proving a reliable and stable operation of such devices. Moreover, approaches were identified to further enhance the field emission characteristics of the ZnO nanowires by variation of the synthesis parameters and by enlargement of the nanomembrane area.

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Section: Field Emission Properties Of Zno Nanowiresmentioning

confidence: 83%

Field emission characteristics of ZnO nanowires grown by catalyst-assisted MOCVD on free-standing inorganic nanomembranes

Haugg¹,

Hedrich²,

Zierold³

et al. 2022

J. Phys. D: Appl. Phys.

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“…Exceptions to this thinking are a few papers (some already cited) that have carried out numerical simulations on finite regular arrays, and some papers on random arrays that explore some of the specific issues involved. For the random arrays, we note in particular the numerical analysis of RB [75], the analysis of Biswas and Rudra [124] and the conceptual discussion by Bieker et al [185].…”

Section: Multi-emitter Depolarization Effects: Clusters and Arraysmentioning

confidence: 99%

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Assis

Dall’Agnol

Forbes

2022

J. Phys.: Condens. Matter

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This review of the quantitative electrostatics of ﬁeld emitters, covering analytical, numerical and “ﬁtted formula” approaches, is thought to be the ﬁrst of its kind in the 100 years of the subject. The review relates chieﬂy to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is “polarity independent”, so the review applies to both ﬁeld electron and ﬁeld ion emitters. It also applies more generally to charged, pointed electron-conductors—which exhibit the “electrostatic lightning-rod eﬀect”, but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than ﬁelds) becomes apparent. Space and time limitations have meant the review cannot be comprehensive in both detail and scope. Rather, it focuses chieﬂy on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called “screening” or “shielding”). Core to the review are discussions of the “minimum domain dimensions” method for implementing eﬀective ﬁnite-element-method electrostatic simulations, and of the variant that leads to very precise estimates of dimensionless ﬁeld enhancement factors (error typically less than 0.001 % in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many “related considerations” relevant to the electrostatic situations, methods and results described. Many areas of ﬁeld emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

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“…Exceptions to this thinking are a few papers (some already cited) that have carried out numerical simulations on finite regular arrays, and some papers on random arrays that explore some of the specific issues involved. For the random arrays, we note in particular the numerical analysis of Read and Bowring [72], the analysis of Biswas and Rudra [120] and the conceptual discussion by Bieker et al [180].…”

Section: F Multi-emitter Depolarization Effects: Clusters and Arraysmentioning

confidence: 99%

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Assis¹,

Dall’Agnol²,

Forbes³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

This review of the quantitative electrostatics of field emitters, covering analytical, numerical and "fitted formula" approaches, is thought the first of its kind in the 100 years of the subject. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is "polarity independent", so that the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors-which exhibit the "electrostatic lightning-rod effect", but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than fields) becomes apparent. Space and time limitations have meant that the review cannot be comprehensive in both detail and scope. Rather, it focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called "screening" or "shielding"). Core to the review are discussions of the "minimum domain dimensions" method for implementing effective finite-element-method electrostatic simulations, and of the variant of this that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001 % in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many "related considerations" that are relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

show abstract

Simulation-Based Model of Randomly Distributed Large-Area Field Electron Emitters

Cited by 17 publications

References 35 publications

Field emission characteristics of ZnO nanowires grown by catalyst-assisted MOCVD on free-standing inorganic nanomembranes

Field emission characteristics of ZnO nanowires grown by catalyst-assisted MOCVD on free-standing inorganic nanomembranes

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

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