Enhancement of field emission performance of graphene nanowalls: the role of compound-cathode architecture and anode proximity effect

Sarkar, Shreya; Kar, Rajib; Mondal, Jayanta; Mishra, L.; Jayaprakash, D.; Maiti, Namita; Tripathi, Rashmi; Biswas, Debabrata

doi:10.1016/j.cartre.2020.100008

Cited by 12 publications

(7 citation statements)

References 49 publications

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“…Experimentally, it is known (e.g. [146][147][148]) that such arrangements can generate a high total apex FEF. The basic physics can be understood qualitatively by considering PPP geometry and using FSEPP models for two HCP posts.…”

Section: Two-stage Field Enhancement and 'Schottky's Conjecture'mentioning

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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Section: Two-stage Field Enhancement and 'Schottky's Conjecture'mentioning

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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“…A question of basic interest is what is the total field enhancement generated by a two-stage structure, in which one protrusion stands on the apex of another. Experimentally, it is known (e.g., [142][143][144]) that such arrangements can generate a high total apex FEF. The basic physics can be understood qualitatively by considering PPP geometry and using FSEPP models for two HCP posts.…”

Section: G Two-stage Field Enhancementmentioning

confidence: 99%

“…Various other methods of investigating two-stage fieldenhancement effects and/or the limitations of eq. ( 90) have been explored in the literature, for example [109,142,144,[147][148][149][150][151][152][153][154][155][156].…”

Section: G Two-stage Field Enhancementmentioning

confidence: 99%

“…Collector adjacency effects occur when the counterelectrode (here called the collector ) is sufficiently close to the emitter that this affects the values of the apex local field and related field enhancement factors. Adjacency effects have been widely discussed in FE literature (e.g., [52,75,144,[157][158][159][160][161][162][163][164][165]), usually for PPP geometry and HCP model emitters, though also for other models.…”

Section: H Collector Adjacency Effectsmentioning

confidence: 99%

See 1 more Smart Citation

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

Assis¹,

Dall’Agnol²,

Forbes³

2022

Preprint

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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

“…Conventional field emission theory [3][4][5][6][7][8] is based on the works of Fowler-Norheim (FN) 9,10 and Murphy-Good (MG) 11 which use the free-electron model and quantum mechanical tunneling through a field dependent potential barrier. Of the two, the MG theory which includes the image charge potential 10,11 appears to be closer to physical reality 12 and is increasingly being used 13,14 . Since curvature effects do not feature in the tunneling potential in these theories, they are relevant for quasi-planar emitters.…”

Section: Introductionmentioning

confidence: 99%

Approximate universality in the tunneling potential for curved field emitters -- a line charge model approach

Ramachandran,

Biswas

2021

Preprint

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Enhancement of field emission performance of graphene nanowalls: the role of compound-cathode architecture and anode proximity effect

Cited by 12 publications

References 49 publications

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

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

Approximate universality in the tunneling potential for curved field emitters -- a line charge model approach

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