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

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 z...

Full description

Saved in:
Bibliographic Details
Published inJournal of physics. Condensed matter Vol. 34; no. 49; pp. 493001 - 493039
Main Authors de Assis, Thiago A, Dall’Agnol, Fernando F, Forbes, Richard G
Format Journal Article
LanguageEnglish
Published IOP Publishing 07.12.2022
Subjects
conducting post formula
electrostatic depolarization
field emission
field emitter electrostatics
field enhancement factor
finite element method
minimum simulation domain dimensions
Online AccessGet full text

Cover

Abstract 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.
AbstractList 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.
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.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.
Author de Assis, Thiago A
Forbes, Richard G
Dall’Agnol, Fernando F
Author_xml – sequence: 1
  givenname: Thiago A
  orcidid: 0000-0003-2332-1096
  surname: de Assis
  fullname: de Assis, Thiago A
  organization: Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação , Rua Barão de Jeremoabo s/n, 40170-115 Salvador, BA, Brazil
– sequence: 2
  givenname: Fernando F
  orcidid: 0000-0003-3551-3466
  surname: Dall’Agnol
  fullname: Dall’Agnol, Fernando F
  organization: Universidade Federal de Santa Catarina Department of Exact Sciences and Education (CEE), Campus Blumenau, Rua João Pessoa, 2514, Velha, Blumenau 89036-004, SC, Brazil
– sequence: 3
  givenname: Richard G
  orcidid: 0000-0002-8621-3298
  surname: Forbes
  fullname: Forbes, Richard G
  organization: University of Surrey Advanced Technology Institute & School of Computer Science and Electronic Engineering, Guildford, Surrey GU2 7XH, United Kingdom
BookMark eNp9kE1P5DAMhiMEEsPHnWOOHCgkbdqm3BBiWCQkLrvS3iJP6jJGbVKSDGj_PZmdFQek5WTJfl7Lfo7YvvMOGTuT4lIKra9k1ciiUfr3FdiuFLDHFp-tfbYQXV0VutPqkB3F-CKEULpSC-aWhGPPcaKUMHAc0abgY4JENl5z4AHfCN_5O6U1jzNagjHT8xoiRe4dn3yPwfE1Pa-LOeR5pNwdyFHCIq-b0KW_0DiSez5hBwOMEU__1WP2a3n38_ZH8fh0_3B781jYqq5TgWqFrQCLK73CAXoF0PSlHWAAgUNpm64vm1LoWklZVUpC268QBQiJULetrY7Z-W7vHPzrBmMyE0WbbwCHfhNN2UrV1HVX64yKHWrz3zHgYOZAE4Q_RgqzVWu2Hs3Wo9mpzZHmS8TS1ph3KQCN3wUvdkHys3nxm-CyhP_jHwvUkgQ
CODEN JCOMEL
CitedBy_id crossref_primary_10_1109_TED_2024_3476240
crossref_primary_10_1103_PhysRevB_107_075426
crossref_primary_10_1063_5_0138100
crossref_primary_10_1016_j_elstat_2023_103867
crossref_primary_10_1016_j_carbon_2024_118936
crossref_primary_10_1063_5_0153635
crossref_primary_10_1088_1361_6463_ad9616
crossref_primary_10_1116_6_0003016
crossref_primary_10_1103_PhysRevLett_130_106204
crossref_primary_10_1116_6_0002478
crossref_primary_10_1109_TED_2023_3283231
crossref_primary_10_1116_6_0002739
crossref_primary_10_1063_10_0030409
crossref_primary_10_1116_6_0002315
crossref_primary_10_1116_6_0002317
Cites_doi 10.1063/1.2996005
10.1063/1.4921709
10.1016/j.ultramic.2018.11.007
10.1016/j.physe.2019.01.005
10.1016/S0304-3991(02)00297-8
10.1088/0031-9120/24/3/309
10.1098/rspa.2013.0271
10.1016/j.ultramic.2017.10.016
10.1002/sia.2938
10.1016/j.cartre.2020.100008
10.1098/rspa.1929.0147
10.1063/1.5025694
10.1116/6.0000949
10.1063/1.5063901
10.1209/0295-5075/85/17001
10.1116/1.5063733
10.1088/1361-648X/aad84c
10.1016/j.nima.2003.11.167
10.1049/el:20045581
10.1016/0378-5963(83)90073-9
10.1103/PhysRev.102.1464
10.1016/j.diamond.2009.08.008
10.1063/1.3665390
10.1063/1.5122971
10.1063/1.2771375
10.1063/1.322600
10.1063/1.2041824
10.7567/1347-4065/ab5fef
10.1088/0031-8949/38/2/029
10.1016/S0304-3991(97)00132-0
10.1016/j.phpro.2008.07.080
10.1116/6.0000033
10.1063/1.5093416
10.1088/0022-3727/18/6/006
10.1038/s41598-022-06670-1
10.24033/asens.287
10.1046/j.1365-2818.2001.00890.x
10.1016/j.mtcomm.2022.103654
10.1016/S0304-3991(99)00098-4
10.1063/1.3253760
10.1103/PhysRev.31.900
10.1103/PhysRev.89.799
10.1098/rsos.190912
10.1116/1.4989428
10.1080/00268970410001727673
10.1063/1.3549705
10.1116/1.5144510
10.1116/1.5111455
10.1063/1.4973584
10.1116/6.0001886
10.1063/1.5041019
10.1063/1.4798926
10.1063/1.1448403
10.1063/1.3466992
10.1098/rspa.1928.0091
10.1109/JEDS.2019.2940086
10.1088/1361-648X/aadbdf
10.48550/arXiv.1504.06134
10.1116/1.5127118
10.1116/1.4953076
10.1017/S1431927615015184
10.1039/D0NR00739K
10.1088/0022-3727/48/38/385203
10.1088/0957-4484/27/44/44LT01
10.1088/1361-648X/aa8567
10.1007/BF00550007
10.1063/1.2008363
10.1103/PhysRev.92.45
10.1038/s41586-018-0223-y
10.1063/1.4940410
10.1103/PhysRev.21.419
10.1088/1361-6463/aaaba6
10.1116/1.1880072
10.1002/adma.200501267
10.1098/rsos.201986
10.1103/PhysRevLett.89.197602
10.1116/1.590857
10.1063/1.1744158
10.1116/1.3574391
10.1098/rsos.220748
10.1116/1.586867
10.1063/1.2964109
10.1007/BF01340034
10.1088/0031-8949/82/03/035602
10.1063/1.5126245
10.1063/1.1638617
10.1002/pssb.19690320103
10.1088/1742-6596/1400/5/055011
10.1134/1.1994978
10.1088/1361-648X/aaba9f
10.1109/IVNC.2017.8051530
10.1016/j.rinp.2021.104822
10.1063/1.1814439
10.1143/JJAP.43.L427
10.1063/5.0030100
10.1063/1.4961216
10.1103/PhysRevLett.92.106803
10.1088/0022-3727/11/14/003
10.1063/1.5133740
10.1063/1.5126674
10.1016/0169-4332(95)00521-8
10.1116/1.2894898
10.1098/rspa.2010.0460
10.1116/1.4971768
10.1063/1.5117289
10.1016/j.ultramic.2015.02.012
10.1142/S1793292006000112
10.1063/1.3615846
10.1016/0039-6028(80)90055-2
10.1088/0957-4484/16/1/018
10.1063/1.1430507
10.1021/nl051397d
10.1098/rspa.2007.0030
10.1063/1.5132561
10.1109/16.81650
10.1063/1.4959150
10.1063/1.5091712
10.1063/1.3097239
10.1116/1.5064403
10.1016/j.ultramic.2012.12.007
10.1002/aelm.201700295
10.1063/1.1709157
10.1103/PhysRevSeriesI.32.492
10.1063/1.4953813
10.1063/1.2188389
10.1063/1.1722347
10.1016/j.ultramic.2015.10.018
10.1016/S0360-0564(08)60526-X
10.1080/13642810208218358
10.1116/1.2188403
10.1016/j.mser.2004.12.001
10.1002/j.1538-7305.1951.tb03688.x
10.1080/13642810208218357
10.1016/j.ultramic.2021.113462
10.1103/PhysRevB.100.165421
10.1063/1.1576310
10.1063/1.332879
10.1098/rspa.2011.0025
10.1063/1.4929983
10.1039/D0TC05873D
10.1103/PhysRev.2.450
10.1002/1521-4095(200102)13:3<184::AID-ADMA184>3.0.CO;2-I
10.1117/12.451277
10.1016/j.ultramic.2021.113362
10.1116/1.3684425
10.1063/1.2799423
10.21236/AD0602844
10.1063/1.4979320
10.1016/S0042-207X(98)00302-9
10.1088/0022-3727/4/9/305
10.1063/1.1721330
10.1039/c0cs00126k
10.1063/1.4983680
10.1016/j.ultramic.2009.01.006
10.1103/PhysRevLett.9.417
10.1063/1.1713118
10.1063/1.1743515
ContentType Journal Article
Copyright 2022 The Author(s). Published by IOP Publishing Ltd
Creative Commons Attribution license.
Copyright_xml – notice: 2022 The Author(s). Published by IOP Publishing Ltd
– notice: Creative Commons Attribution license.
DBID O3W
TSCCA
AAYXX
CITATION
7X8
DOI 10.1088/1361-648X/ac920a
DatabaseName Institute of Physics Open Access
IOPscience (Open Access)
CrossRef
MEDLINE - Academic
DatabaseTitle CrossRef
MEDLINE - Academic
DatabaseTitleList CrossRef
MEDLINE - Academic
Database_xml – sequence: 1
  dbid: O3W
  name: Institute of Physics Open Access Journal Titles
  url: http://iopscience.iop.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 1361-648X
ExternalDocumentID 10_1088_1361_648X_ac920a
cmac920a
GrantInformation_xml – fundername: Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil
  grantid: 310311/2020-9.
GroupedDBID ---
-~X
1JI
4.4
53G
5B3
5GY
5PX
5VS
5ZH
7.M
7.Q
AAGCD
AAGID
AAJIO
AAJKP
AATNI
ABCXL
ABHWH
ABLJU
ABQJV
ABVAM
ACAFW
ACGFS
ACHIP
ACNCT
AEFHF
AFYNE
AKPSB
ALMA_UNASSIGNED_HOLDINGS
AOAED
ASPBG
ATQHT
AVWKF
AZFZN
CBCFC
CEBXE
CJUJL
CRLBU
CS3
EBS
EDWGO
EMSAF
EPQRW
EQZZN
F5P
HAK
IHE
IJHAN
IOP
IZVLO
KOT
LAP
M45
N5L
N9A
O3W
P2P
PJBAE
RIN
RNS
RO9
ROL
RPA
SY9
TN5
TSCCA
W28
WH7
XPP
YQT
ZMT
~02
AAYXX
ADEQX
CITATION
7X8
ID FETCH-LOGICAL-c355t-e4be70aceb8befad4aa6d2cfafa0ef2c69d2620854113341a7dbee0a01ea577c3
IEDL.DBID O3W
ISSN 0953-8984
1361-648X
IngestDate Fri Jul 11 04:07:53 EDT 2025
Thu Apr 24 23:03:21 EDT 2025
Tue Jul 01 02:46:46 EDT 2025
Wed Aug 21 03:34:59 EDT 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 49
Language English
License Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c355t-e4be70aceb8befad4aa6d2cfafa0ef2c69d2620854113341a7dbee0a01ea577c3
Notes JPCM-120676.R1
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
ObjectType-Review-3
content type line 23
ORCID 0000-0002-8621-3298
0000-0003-3551-3466
0000-0003-2332-1096
OpenAccessLink https://iopscience.iop.org/article/10.1088/1361-648X/ac920a
PQID 2714655958
PQPubID 23479
PageCount 39
ParticipantIDs proquest_miscellaneous_2714655958
crossref_citationtrail_10_1088_1361_648X_ac920a
crossref_primary_10_1088_1361_648X_ac920a
iop_journals_10_1088_1361_648X_ac920a
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2022-12-07
PublicationDateYYYYMMDD 2022-12-07
PublicationDate_xml – month: 12
  year: 2022
  text: 2022-12-07
  day: 07
PublicationDecade 2020
PublicationTitle Journal of physics. Condensed matter
PublicationTitleAbbrev JPhysCM
PublicationTitleAlternate J. Phys.: Condens. Matter
PublicationYear 2022
Publisher IOP Publishing
Publisher_xml – name: IOP Publishing
References Pogorelov (cmac920abib50) 2009; 85
Gomer (cmac920abib59) 1957; 28
Forbes (cmac920abib62) 2021
Dall’Agnol (cmac920abib147) 2020; 117
Bonard (cmac920abib181) 2001; 13
Rohrbach (cmac920abib48) 1971
Dwivedi (cmac920abib13) 2021; 9
Biswas (cmac920abib44) 2018; 185
Harris (cmac920abib177) 2016; 119
Sun (cmac920abib115) 2013; 113
Langmuir (cmac920abib103) 1923; 21
Filippov (cmac920abib82) 2021; 230
de Souza (cmac920abib182) 2020; 127
Zhu (cmac920abib76) 2005; 16
de Assis (cmac920abib150) 2016; 27
Zhbanov (cmac920abib184) 2011; 110
Murata (cmac920abib173) 2001; 4510
Smith (cmac920abib175) 2009; 94
Purcell (cmac920abib108) 2022
Forbes (cmac920abib171) 1978; 11
Forbes (cmac920abib5) 2020
Forbes (cmac920abib19) 2011; 467
Chen (cmac920abib85) 2010; 18
Forbes (cmac920abib29) 2015; 8
Tanaka (cmac920abib80) 2004; 43
Kokkorakis (cmac920abib81) 2004; 95
Gröning (cmac920abib100) 1999; 17
Filippov (cmac920abib118) 2022; 233
Amorim (cmac920abib24) 2018; 30
Kokkorakis (cmac920abib64) 2002; 291
Bocharov (cmac920abib174) 2005; 50
Dyke (cmac920abib39) 1953; 24
Hii (cmac920abib167) 2006; 24
Spindt (cmac920abib8) 1976; 47
Harris (cmac920abib119) 2015; 48
Forbes (cmac920abib72) 2018
Forbes (cmac920abib129) 1980; 93
Kosmahl (cmac920abib49) 1991; 38
Forbes (cmac920abib89) 2019; 37
Morgan (cmac920abib97) 1970; 5
Masur (cmac920abib187) 2021
Russell (cmac920abib91) 1962; 9
Wang (cmac920abib164) 1982; 96
Edgcombe (cmac920abib67) 2002; 82
Fowler (cmac920abib21) 1928; 119
Vibrans (cmac920abib54) 1964; 35
Toijala (cmac920abib139) 2019; 100
Edgcombe (cmac920abib68) 1998
de Assis (cmac920abib71) 2019; 37
Nevrovskii (cmac920abib161) 1982; 27
Forbes (cmac920abib16) 2007; 463
Forbes (cmac920abib88) 2017; 110
Miller (cmac920abib113) 2007; 91
Lepetit (cmac920abib136) 2016; 120
Forbes (cmac920abib25) 2021; 8
Rose (cmac920abib38) 1956; 27
Forbes (cmac920abib46) 2003; 95
Zeng (cmac920abib78) 2009; 18
Filippov (cmac920abib117) 2019; 1400
Xu (cmac920abib168) 2006; 88
Roveri (cmac920abib79) 2016; 160
Latham (cmac920abib47) 1981
Rolland (cmac920abib34) 2015; 21
Yanagisawa (cmac920abib145) 2022; 12
Braun (cmac920abib92) 1975
Dyke (cmac920abib28) 1953; 89
Forbes (cmac920abib106) 1999; 104
Wang (cmac920abib110) 2011; 109
Bonard (cmac920abib163) 2002; 89
de Assis (cmac920abib179) 2018; 30
Tang (cmac920abib116) 2011; 110
Biswas (cmac920abib20) 2019; 37
Lauritsen (cmac920abib30) 1929
Biswas (cmac920abib42) 2018; 25
Zheng (cmac920abib120) 2020; 12
Jensen (cmac920abib159) 2019; 126
Murphy (cmac920abib15) 1956; 102
Forbes (cmac920abib52) 2016; 120
Gomer (cmac920abib40) 1955; 7
Spindt (cmac920abib107) 1983; 16
Smith (cmac920abib166) 2005; 87
Langmuir (cmac920abib102) 1913; 2
Allaham (cmac920abib18) 2022; 31
Pogorelov (cmac920abib57) 2010; 108
de Assis (cmac920abib151) 2017; 121
Miller (cmac920abib55) 1967; 38
Miller (cmac920abib162) 1984; 55
Vibrans (cmac920abib53) 1964
Harris (cmac920abib183) 2015; 5
Saito (cmac920abib14) 2022
Gomer (cmac920abib41) 1961
Li (cmac920abib112) 2022
Becker (cmac920abib37) 1951; 30
Nicolaescu (cmac920abib56) 1993; 11
Katnagallu (cmac920abib128) 2018; 51
Sanchez (cmac920abib138) 2004; 102
Forbes (cmac920abib127) 1985; 18
Egorov (cmac920abib3) 2017
Forbes (cmac920abib7) 2009
Edgcombe (cmac920abib65) 2001; 203
le Fèbre (cmac920abib169) 2008; 26
Huang (cmac920abib146) 2005; 87
Mousa (cmac920abib94) 1996; 94–95
Lepetit (cmac920abib137) 2019; 125
Jensen (cmac920abib4) 2018
Liang (cmac920abib2) 2014
Miller (cmac920abib99) 2014
Stern (cmac920abib104) 1929; 124
Forbes (cmac920abib130) 1999; 79
Biswas (cmac920abib160) 2020; 38
Forbes (cmac920abib23) 2019; 6
Watcharotone (cmac920abib114) 2008; 1
Fink (cmac920abib140) 1988; 38
Maxwell (cmac920abib31) 1891 A
Kishimoto (cmac920abib142) 2008; 40
Filippov (cmac920abib26) 2022
Eyring (cmac920abib35) 1928; 31
Vinogradova (cmac920abib126) 2021; 30
Forbes (cmac920abib172) 1998; 73
de Castro (cmac920abib135) 2019; 126
Li (cmac920abib134) 2015; 159
Rudra (cmac920abib125) 2019; 9
Ciarlet (cmac920abib69) 2002
Marcelino (cmac920abib156) 2017; 35
Jin (cmac920abib70) 2014
Shen (cmac920abib111) 2017; 3
Qin (cmac920abib132) 2011; 29
Harris (cmac920abib122) 2015; 106
Fursey (cmac920abib95) 1969; 32
Schottky (cmac920abib149) 1923; 14
Spindt (cmac920abib9) 2001
Forbes (cmac920abib27) 2013; 469
Coelho (cmac920abib36) 1971; 4
Qin (cmac920abib109) 2011; 467
Bachmann (cmac920abib87) 2017; 35
Biswas (cmac920abib124) 2018; 25
Harris (cmac920abib152) 2019; 125
Evtukh (cmac920abib1) 2015
Saito (cmac920abib10) 2010
Zhai (cmac920abib12) 2011; 40
Wang (cmac920abib133) 2008; 104
Notte (cmac920abib141) 2008; 931
Minoux (cmac920abib90) 2005; 5
Forbes (cmac920abib93) 1996
Esat (cmac920abib143) 2018; 558
Sarkar (cmac920abib43) 2019; 37
Dall’Agnol (cmac920abib74) 2021; 39
Miller (cmac920abib153) 2009; 106
Child (cmac920abib101) 1911; 32
Smith (cmac920abib165) 2005; 23
Fowler (cmac920abib32) 1936
Forbes (cmac920abib96) 2017
Miranda (cmac920abib83) 2004; 40
Ohta (cmac920abib144) 2020; 59
Dall’Agnol (cmac920abib180) 2017; 29
Edgcombe (cmac920abib66) 2002; 82
Harris (cmac920abib123) 2017; 121
Zheng (cmac920abib131) 2004; 92
Miller (cmac920abib6) 2014
Lewin (cmac920abib61) 2015
Xu (cmac920abib11) 2005; 48
Read (cmac920abib75) 2004; 519
Harris (cmac920abib157) 2019; 125
Fricker (cmac920abib63) 1989; 254
Forbes (cmac920abib17) 2019; 126
Zhong (cmac920abib154) 2002; 80
Egorov (cmac920abib121) 1999; 53
Sarka (cmac920abib148) 2021; 2
Podenok (cmac920abib77) 2006; 1
Biswas (cmac920abib45) 2019; 109
Vurpillot (cmac920abib98) 2013; 132
Barbour (cmac920abib105) 1953; 92
Biswas (cmac920abib170) 2020; 38
Gomer (cmac920abib58) 1957; 26
Jensen (cmac920abib155) 2016; 6
Forbes (cmac920abib22) 2018
Robin (cmac920abib33) 1886; 3
Feynman (cmac920abib60) 1964
Dall’Agnol (cmac920abib73) 2018; 30
Bieker (cmac920abib185) 2019; 7
Pogorelov (cmac920abib51) 2009; 109
Wisitsora-at (cmac920abib86) 2012; 35
Jo (cmac920abib178) 2003; 82
Edgcombe (cmac920abib186) 2019; 198
Cha (cmac920abib84) 2006; 18
de Carvalho Neto (cmac920abib158) 2019; 126
Harris (cmac920abib176) 2016; 34
Masur (cmac920abib188) 2022; 40
References_xml – volume: 104
  year: 1999
  ident: cmac920abib106
  article-title: Exact analysis of surface field reduction due to field emitted vacuum space-charge, in plane-parallel geometry, using simple dimensionless equations
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.2996005
– volume: 106
  year: 2015
  ident: cmac920abib122
  article-title: Shielding in ungated field emitter arrays
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.4921709
– volume: 198
  start-page: 26
  year: 2019
  ident: cmac920abib186
  article-title: Analysis of a capped carbon nanotube by linear-scaling density-functional theory
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2018.11.007
– volume: 109
  start-page: 179
  year: 2019
  ident: cmac920abib45
  article-title: The cosine law of field enhancement factor: generic emitter shapes
  publication-title: Physica E
  doi: 10.1016/j.physe.2019.01.005
– volume: 95
  start-page: 57
  year: 2003
  ident: cmac920abib46
  article-title: Some comments on models for field enhancement
  publication-title: Ultramicroscopy
  doi: 10.1016/S0304-3991(02)00297-8
– volume: 254
  start-page: 157
  year: 1989
  ident: cmac920abib63
  article-title: Why does charge concentrate on points?
  publication-title: Phys. Educ.
  doi: 10.1088/0031-9120/24/3/309
– volume: 469
  year: 2013
  ident: cmac920abib27
  article-title: Development of a simple quantitative test for lack of field emission orthodoxy
  publication-title: Proc. R. Soc. A
  doi: 10.1098/rspa.2013.0271
– volume: 185
  start-page: 1
  year: 2018
  ident: cmac920abib44
  article-title: Variation of field enhancement factor near the emitter tip
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2017.10.016
– volume: 27
  start-page: 180
  year: 1982
  ident: cmac920abib161
  publication-title: Sov. Phys. Tech. Phys.
– volume: 40
  start-page: 1669
  year: 2008
  ident: cmac920abib142
  article-title: Behaviors of single CO2 molecule on pentagon at carbon nanotube tip observed by field emission microscopy
  publication-title: Surf. Interface Anal.
  doi: 10.1002/sia.2938
– volume: 2
  year: 2021
  ident: cmac920abib148
  article-title: Enhancement of field emission performance of graphene nanowalls: the role of compound-cathode architecture and anode proximity effect
  publication-title: Carbon Trends
  doi: 10.1016/j.cartre.2020.100008
– volume: 124
  start-page: 699
  year: 1929
  ident: cmac920abib104
  article-title: Further studies in the emission of electrons from cold metals
  publication-title: Proc. R. Soc. A
  doi: 10.1098/rspa.1929.0147
– year: 2018
  ident: cmac920abib72
  article-title: Physical explanation of the universal “inverse-3rd-power-of-separation” law found numerically for the electrostatic interaction between two protruding nanostructures
– volume: 25
  year: 2018
  ident: cmac920abib42
  article-title: A universal formula for the field enhancement factor
  publication-title: Phys. Plasmas
  doi: 10.1063/1.5025694
– year: 2015
  ident: cmac920abib1
– volume: 39
  year: 2021
  ident: cmac920abib74
  article-title: Determining the field enhancement factors of various field electron emitters with high numerical accuracy
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/6.0000949
– volume: 125
  year: 2019
  ident: cmac920abib137
  article-title: A three dimensional numerical quantum mechanical model of electronic field emission from metallic surfaces with nanoscale corrugation
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5063901
– volume: 85
  year: 2009
  ident: cmac920abib50
  article-title: Enhancement factor, electrostatic force and emission current in a nanoneedle emitter
  publication-title: Europhys. Lett.
  doi: 10.1209/0295-5075/85/17001
– volume: 37
  year: 2019
  ident: cmac920abib71
  article-title: Minimal domain size necessary to simulate the field enhancement factor numerically with specified precision
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.5063733
– volume: 30
  year: 2018
  ident: cmac920abib73
  article-title: Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters
  publication-title: J. Phys.: Condens. Matter
  doi: 10.1088/1361-648X/aad84c
– volume: 519
  start-page: 305
  year: 2004
  ident: cmac920abib75
  article-title: Field enhancement factors of random arrays of carbon nanotubes
  publication-title: Nucl. Instrum. Meth. Phys. Res. A
  doi: 10.1016/j.nima.2003.11.167
– volume: 40
  start-page: 1153
  year: 2004
  ident: cmac920abib83
  article-title: Method for extracting series resistance in MOS devices using Fowler–Nordheim plot
  publication-title: Electron. Lett.
  doi: 10.1049/el:20045581
– volume: 16
  start-page: 268
  year: 1983
  ident: cmac920abib107
  article-title: Field emission cathode array development for high-current-density applications
  publication-title: Appl. Surf. Sci.
  doi: 10.1016/0378-5963(83)90073-9
– volume: 102
  start-page: 1464
  year: 1956
  ident: cmac920abib15
  article-title: Thermionic emission, field emission and the transition region
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.102.1464
– volume: 18
  start-page: 1381
  year: 2009
  ident: cmac920abib78
  article-title: Numerical calculations of field enhancement and field amplification factors for a vertical carbon nanotube in parallel-plate geometry
  publication-title: Diam. Relat. Mater.
  doi: 10.1016/j.diamond.2009.08.008
– volume: 110
  year: 2011
  ident: cmac920abib184
  article-title: Screened field enhancement factor for the floating sphere model of a carbon nanotube array
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.3665390
– year: 2018
  ident: cmac920abib22
  article-title: Comparison of the Lepetit field emission current-density calculations with the Modinos–Forbes uncertainty limits
– year: 2021
  ident: cmac920abib187
  article-title: Theoretical and experimental secondary electron spin polarisation studies and 3D theory of field emission for nanoscale emitters
– start-page: pp 387
  year: 2020
  ident: cmac920abib5
  article-title: Renewing the mainstream theory of field and thermal electron emission
– volume: 126
  year: 2019
  ident: cmac920abib135
  article-title: On the quantum mechanics of how an ideal carbon nanotube field emitter can exhibit a constant field enhancement factor
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5122971
– volume: 91
  year: 2007
  ident: cmac920abib113
  article-title: Electric field distribution on knife-edge field emitters
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.2771375
– volume: 47
  start-page: 5248
  year: 1976
  ident: cmac920abib8
  article-title: Physical properties of thin-film field emission cathodes with molybdenum cones
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.322600
– volume: 87
  year: 2005
  ident: cmac920abib166
  article-title: Electron field emission from a single carbon nanotube: effects of anode location
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.2041824
– volume: 59
  year: 2020
  ident: cmac920abib144
  article-title: Study of the local barrier field variations for electron tunneling in field ionization at a step edge of W(112) with a micro-probe hole field ion microscope
  publication-title: Jpn. J. Appl. Phys.
  doi: 10.7567/1347-4065/ab5fef
– volume: 38
  start-page: 260
  year: 1988
  ident: cmac920abib140
  article-title: Point source for ions and electrons
  publication-title: Phys. Scr.
  doi: 10.1088/0031-8949/38/2/029
– start-page: pp 318
  year: 1998
  ident: cmac920abib68
  article-title: Determination of F-N parameters for carbon contamination grown nano-tip field emitters: a combined experimental and computational approach
– volume: 73
  start-page: 31
  year: 1998
  ident: cmac920abib172
  article-title: Calculation of the electrical-surface (image-plane) position for aluminium
  publication-title: Surf. Sci.
  doi: 10.1016/S0304-3991(97)00132-0
– volume: 1
  start-page: 71
  year: 2008
  ident: cmac920abib114
  article-title: Possibilities for graphene for field emission: modeling studies using the BEM
  publication-title: Phys. Proc.
  doi: 10.1016/j.phpro.2008.07.080
– volume: 38
  year: 2020
  ident: cmac920abib170
  article-title: Electrostatic shielding versus anode-proximity in large area field emitters
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/6.0000033
– volume: 125
  year: 2019
  ident: cmac920abib152
  article-title: Investigation of the Schottky conjecture for compound structures modeled with line charges
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5093416
– volume: 18
  start-page: 973
  year: 1985
  ident: cmac920abib127
  article-title: Seeing atoms: the origins of local contrast in field ion images
  publication-title: J. Phys. D: Appl. Phys.
  doi: 10.1088/0022-3727/18/6/006
– volume: 12
  start-page: 2714
  year: 2022
  ident: cmac920abib145
  article-title: Field emission microscope for a single fullerene molecule
  publication-title: Sci. Rep.
  doi: 10.1038/s41598-022-06670-1
– volume: 3
  start-page: 3
  year: 1886
  ident: cmac920abib33
  article-title: Sur la distribution de l’électricité à la surface des conducteurs fermés des conducteurs ouverts
  publication-title: Ann. Sci. Éc. Norm. Supér.
  doi: 10.24033/asens.287
– volume: 203
  start-page: 188
  year: 2001
  ident: cmac920abib65
  article-title: Microscopy and computational modelling to elucidate the enhancement factor for field electron emitters
  publication-title: J. Microsc.
  doi: 10.1046/j.1365-2818.2001.00890.x
– year: 2018
  ident: cmac920abib4
– volume: 31
  year: 2022
  ident: cmac920abib18
  article-title: Interpretation of field emission current-voltage data: background theory and detailed simulation testing of a user-friendly webtool
  publication-title: Mater. Today Commun.
  doi: 10.1016/j.mtcomm.2022.103654
– volume: 79
  start-page: 25
  year: 1999
  ident: cmac920abib130
  article-title: The electrical surface as centroid of the surface-induced charge
  publication-title: Ultramicroscopy
  doi: 10.1016/S0304-3991(99)00098-4
– volume: 106
  year: 2009
  ident: cmac920abib153
  article-title: Schottky’s conjecture on multiplication of field enhancement factors
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.3253760
– volume: 31
  start-page: 900
  year: 1928
  ident: cmac920abib35
  article-title: Fields currents from points
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.31.900
– volume: 89
  start-page: 799
  year: 1953
  ident: cmac920abib28
  article-title: Field emission: large current densities, space charge and the vacuum arc
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.89.799
– volume: 6
  year: 2019
  ident: cmac920abib23
  article-title: The Murphy–Good plot: a better method of analysing field emission data
  publication-title: R. Soc. Open. Sci.
  doi: 10.1098/rsos.190912
– volume: 35
  year: 2017
  ident: cmac920abib156
  article-title: Unexpected validity of Schottky’s conjecture for two-stage field emitters: a response via Schwarz–Christoffel transformation
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.4989428
– year: 2002
  ident: cmac920abib69
– volume: 102
  start-page: 1045
  year: 2004
  ident: cmac920abib138
  article-title: Field-evaporation from first-principles
  publication-title: Mol. Phys.
  doi: 10.1080/00268970410001727673
– volume: 109
  year: 2011
  ident: cmac920abib110
  article-title: Field electron emission characteristic of graphene
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.3549705
– volume: 38
  year: 2020
  ident: cmac920abib160
  article-title: Schottky conjecture and beyond
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.5144510
– start-page: pp 105
  year: 2001
  ident: cmac920abib9
  article-title: Spindt field emitter arrays
– start-page: p 159
  year: 2021
  ident: cmac920abib62
  article-title: Correction of conceptual error in Feynman’s textbook treatment of pointed-conductor electrostatics
– volume: 37
  year: 2019
  ident: cmac920abib89
  article-title: Why converting field emission voltages to macroscopic fields before making a Fowler–Nordheim plot has often led to spurious characterization results
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.5111455
– volume: 121
  year: 2017
  ident: cmac920abib151
  article-title: Trade-off between the electrostatic efficiency and mechanical stability of two-stage field emitter structures
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.4973584
– volume: 40
  year: 2022
  ident: cmac920abib188
  article-title: On modeling the induced charge in density-functional calculations for field emitters
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/6.0001886
– volume: 25
  year: 2018
  ident: cmac920abib124
  article-title: Shielding effects in random large area field emitters, the field enhancement factor distribution and current calculation
  publication-title: Phys. Plasmas
  doi: 10.1063/1.5041019
– volume: 113
  year: 2013
  ident: cmac920abib115
  article-title: Analysis of nonuniform field emission from a sharp tip emitter of Lorentzian or hyperboloid shape
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.4798926
– volume: 291
  start-page: 4580
  year: 2002
  ident: cmac920abib64
  article-title: Local electric field at the emitting surface of a carbon nanotube
  publication-title: J. Appl. Phys
  doi: 10.1063/1.1448403
– volume: 108
  year: 2010
  ident: cmac920abib57
  article-title: Corrected field enhancement factor for the floating sphere model of carbon nanotube emitter
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.3466992
– volume: 119
  start-page: 173
  year: 1928
  ident: cmac920abib21
  article-title: Electron emission in intense electric fields
  publication-title: Proc. R. Soc. A
  doi: 10.1098/rspa.1928.0091
– year: 2014
  ident: cmac920abib70
– volume: 7
  start-page: 997
  year: 2019
  ident: cmac920abib185
  article-title: Simulation-based model of randomly distributed large-area field electron emitters
  publication-title: IEEE J. Electron Devices Soc.
  doi: 10.1109/JEDS.2019.2940086
– volume: 30
  year: 2018
  ident: cmac920abib24
  article-title: Numerical analysis of the notional area in cold field electron emission from arrays
  publication-title: J. Phys.: Condens. Matter
  doi: 10.1088/1361-648X/aadbdf
– volume: 8
  start-page: 125
  year: 2015
  ident: cmac920abib29
  article-title: Fowler–Nordheim plot analysis: a progress report
  publication-title: Jordan J. Phys.
  doi: 10.48550/arXiv.1504.06134
– volume: 37
  year: 2019
  ident: cmac920abib43
  article-title: Electrostatic field enhancement on end-caps of cylindrical field-emitters
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.5127118
– volume: 34
  year: 2016
  ident: cmac920abib176
  article-title: Control of bulk and edge screening effects in two-dimensional arrays of ungated field emitters
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.4953076
– volume: 21
  start-page: 1649
  year: 2015
  ident: cmac920abib34
  article-title: A meshless algorithm to model field evaporation in atom probe tomography
  publication-title: Microsc. Microanal.
  doi: 10.1017/S1431927615015184
– volume: 12
  year: 2020
  ident: cmac920abib120
  article-title: Quantitative measurement of charge accumulation along a quasi-one-dimensional W5O15 nanowire during electron field emission
  publication-title: Nanoscale
  doi: 10.1039/D0NR00739K
– volume: 48
  year: 2015
  ident: cmac920abib119
  article-title: Modelling field emitter arrays using line charge distributions
  publication-title: J. Phys. D: Appl. Phys.
  doi: 10.1088/0022-3727/48/38/385203
– volume: 27
  start-page: 44LT01
  year: 2016
  ident: cmac920abib150
  article-title: Mechanically stable nanostructures with desirable characteristic field enhancement factors: a response from scale invariance in electrostatics
  publication-title: Nanotechnology
  doi: 10.1088/0957-4484/27/44/44LT01
– volume: 29
  start-page: 40LT01
  year: 2017
  ident: cmac920abib180
  article-title: Close proximity electrostatic effect from small clusters of emitters
  publication-title: J. Phys.: Condens. Matter
  doi: 10.1088/1361-648X/aa8567
– volume: 5
  start-page: 445
  year: 1970
  ident: cmac920abib97
  article-title: Field ion microscopy of uranium dioxide
  publication-title: J. Mater. Sci
  doi: 10.1007/BF00550007
– volume: 87
  year: 2005
  ident: cmac920abib146
  article-title: Giant field enhancement at carbon nanotube tips induced by multistage effect
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.2008363
– start-page: pp 87
  year: 2009
  ident: cmac920abib7
  article-title: Gas field ionization sources
– volume: 92
  start-page: 45
  year: 1953
  ident: cmac920abib105
  article-title: Space-charge effects in field emission
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.92.45
– volume: 558
  start-page: 573
  year: 2018
  ident: cmac920abib143
  article-title: A standing molecule as a single-electron field emitter
  publication-title: Nature
  doi: 10.1038/s41586-018-0223-y
– year: 1964
  ident: cmac920abib60
– volume: 119
  year: 2016
  ident: cmac920abib177
  article-title: Edge enhancement control in linear arrays of ungated field emitters
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.4940410
– volume: 21
  start-page: 419
  year: 1923
  ident: cmac920abib103
  article-title: The effect of space charge and initial velocities on the potential distribution and thermionic current between parallel plane electrodes
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.21.419
– volume: 51
  year: 2018
  ident: cmac920abib128
  article-title: Impact of local electrostatic field rearrangement on field ionization
  publication-title: J. Phys. D: Appl. Phys.
  doi: 10.1088/1361-6463/aaaba6
– volume: 23
  start-page: 632
  year: 2005
  ident: cmac920abib165
  article-title: Effect of aspect ratio and anode location on the field emission properties of a single tip based emitter
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.1880072
– volume: 18
  start-page: 553
  year: 2006
  ident: cmac920abib84
  article-title: Field-emission behavior of a carbon-nanotube-implanted Co nanocomposite fabricated from pearl-necklace-structured carbon nanotube/Co powders
  publication-title: Adv. Mater.
  doi: 10.1002/adma.200501267
– year: 2014
  ident: cmac920abib99
– volume: 8
  year: 2021
  ident: cmac920abib25
  article-title: The pre-exponential voltage-exponent as a sensitive test parameter for field emission theories
  publication-title: R. Soc. Open Sci.
  doi: 10.1098/rsos.201986
– volume: 89
  year: 2002
  ident: cmac920abib163
  article-title: Field emission of individual carbon nanotubes in the scanning electron microscope
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.89.197602
– year: 1975
  ident: cmac920abib92
  article-title: Progress with the application of a high-resolution field electron spectrometer to semiconductors
– volume: 17
  start-page: 1970
  year: 1999
  ident: cmac920abib100
  article-title: Field emission properties of nanocrystalline chemically vapor-deposited diamond films
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.590857
– year: 2014
  ident: cmac920abib6
– volume: 28
  start-page: 457
  year: 1957
  ident: cmac920abib59
  article-title: Field emission from mercury whiskers
  publication-title: J. Chem. Phys.
  doi: 10.1063/1.1744158
– volume: 29
  year: 2011
  ident: cmac920abib132
  article-title: Electric potential of a metallic nanowall between cathode and anode planes
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.3574391
– year: 2022
  ident: cmac920abib26
  article-title: Field emission: calculations supporting a new methodology of comparing theory with experiment
  doi: 10.1098/rsos.220748
– volume: 11
  start-page: 392
  year: 1993
  ident: cmac920abib56
  article-title: Physical basis for applying the Fowler–Nordheim J–E relationship to experimental I–V data
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.586867
– volume: 104
  year: 2008
  ident: cmac920abib133
  article-title: Image potentials of single-walled carbon nanotubes in the field emission condition
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.2964109
– volume: 14
  start-page: 63
  year: 1923
  ident: cmac920abib149
  article-title: Über kalte und warme elektronenentladungen
  publication-title: Z. Phys.
  doi: 10.1007/BF01340034
– volume: 18
  year: 2010
  ident: cmac920abib85
  article-title: Nonlinear characteristics of the Fowler–Nordheim plots of carbon nanotube field emission
  publication-title: Phys. Scr.
  doi: 10.1088/0031-8949/82/03/035602
– volume: 126
  year: 2019
  ident: cmac920abib158
  article-title: Analytical proof of Schottky’s conjecture for multi-stage field emitters
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5126245
– volume: 95
  start-page: 1468
  year: 2004
  ident: cmac920abib81
  article-title: Enhancement factor of open thick-wall carbon nanotubes
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1638617
– volume: 32
  start-page: 23
  year: 1969
  ident: cmac920abib95
  article-title: Field emission from p-type Si
  publication-title: Phys. Status Solidi
  doi: 10.1002/pssb.19690320103
– volume: 1400
  year: 2019
  ident: cmac920abib117
  article-title: Investigation of the emission properties of a silicon blade-type cathode
  publication-title: J. Phys: Conf. Ser.
  doi: 10.1088/1742-6596/1400/5/055011
– volume: 50
  start-page: 944
  year: 2005
  ident: cmac920abib174
  article-title: Effect of screening on the emissivity of field electron emitters based on carbon nanotubes
  publication-title: Tech. Phys.
  doi: 10.1134/1.1994978
– volume: 30
  year: 2018
  ident: cmac920abib179
  article-title: Evidence of universal inverse-third power law for the shielding-induced fractional decrease in apex field enhancement factor at large spacings: a response via accurate Laplace-type calculations
  publication-title: J. Phys.: Condens. Matter
  doi: 10.1088/1361-648X/aaba9f
– year: 2017
  ident: cmac920abib96
  article-title: Comments on the relationship between voltage loss, reduction in field enhancement factor and saturation effects in Fowler–Nordheim plots
  doi: 10.1109/IVNC.2017.8051530
– volume: 30
  year: 2021
  ident: cmac920abib126
  article-title: Effect of dielectrics on the field emission characterisrics in the diode system modelling
  publication-title: Results Phys.
  doi: 10.1016/j.rinp.2021.104822
– volume: 96
  start-page: 6752
  year: 1982
  ident: cmac920abib164
  article-title: Model calculation for the field enhancement factor of carbon nanotube
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1814439
– volume: 43
  start-page: L427
  year: 2004
  ident: cmac920abib80
  article-title: Comparison of capped carbon nanotube with open-ended one for field emission
  publication-title: Jpn. J. Appl. Phys.
  doi: 10.1143/JJAP.43.L427
– start-page: pp 127
  year: 2022
  ident: cmac920abib108
  article-title: Field emission from the edges of single-layer graphene
– volume: 117
  year: 2020
  ident: cmac920abib147
  article-title: Looped carbon nanotube fibers as cathodes with giant field enhancement factors
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/5.0030100
– volume: 120
  year: 2016
  ident: cmac920abib136
  article-title: Static electric field enhancement in nanoscale structures
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.4961216
– year: 1891 A
  ident: cmac920abib31
– volume: 92
  year: 2004
  ident: cmac920abib131
  article-title: Quantum-mechanical investigation of field-emission mechanism of a micrometer-long single-walled carbon nanotube
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.92.106803
– volume: 11
  start-page: L161
  year: 1978
  ident: cmac920abib171
  article-title: Negative work-function correction at a positively charged surface
  publication-title: J. Phys. D: Appl. Phys.
  doi: 10.1088/0022-3727/11/14/003
– volume: 127
  year: 2020
  ident: cmac920abib182
  article-title: A classical first-principles study of depolarization effects in small clusters of field emitters
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5133740
– year: 2015
  ident: cmac920abib61
  article-title: High-voltage breakdown, lightning, sparks, St-Elmo’s fire
– year: 2017
  ident: cmac920abib3
– volume: 9
  year: 2019
  ident: cmac920abib125
  article-title: Verification of shielding effect predictions for large area field emitters
  publication-title: AIP Adv.
  doi: 10.1063/1.5126674
– volume: 94–95
  start-page: 129
  year: 1996
  ident: cmac920abib94
  article-title: Electron emission from carbon fibre tips
  publication-title: Appl. Surf. Sci.
  doi: 10.1016/0169-4332(95)00521-8
– volume: 26
  start-page: 724
  year: 2008
  ident: cmac920abib169
  article-title: Field emission at nanometer distances for high resolution positioning
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.2894898
– volume: 467
  start-page: 1029
  year: 2011
  ident: cmac920abib109
  article-title: Analytical treatment of cold field electron emission from a nanowall emitter, including quantum confinement effects
  publication-title: Proc. R. Soc. A
  doi: 10.1098/rspa.2010.0460
– volume: 35
  start-page: 0C2103
  year: 2017
  ident: cmac920abib87
  article-title: Extraction of the characteristics of current-limiting elements from field emission measurement data
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.4971768
– volume: 126
  year: 2019
  ident: cmac920abib17
  article-title: Comments on the continuing widespread and unnecessary use of a defective emission equation in field emission related literature
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5117289
– volume: 159
  start-page: 162
  year: 2015
  ident: cmac920abib134
  article-title: Density functional theory for field emission from carbon nano-structures
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2015.02.012
– year: 2014
  ident: cmac920abib2
– volume: 1
  start-page: 87
  year: 2006
  ident: cmac920abib77
  article-title: Electric field enhancement factors around a metallic end-capped cylinder
  publication-title: Nanotechnol. Rev.
  doi: 10.1142/S1793292006000112
– volume: 110
  year: 2011
  ident: cmac920abib116
  article-title: Analysis of electric field screening by the proximity of two knife-edge field emitters
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.3615846
– volume: 93
  start-page: 192
  year: 1980
  ident: cmac920abib129
  article-title: An array model for the field adsorption of helium on tungsten (111)
  publication-title: Surf. Sci.
  doi: 10.1016/0039-6028(80)90055-2
– year: 1971
  ident: cmac920abib48
– volume: 16
  start-page: 88
  year: 2005
  ident: cmac920abib76
  article-title: Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films
  publication-title: Nanotechnology
  doi: 10.1088/0957-4484/16/1/018
– volume: 80
  start-page: 506
  year: 2002
  ident: cmac920abib154
  article-title: Universal field-emission model for carbon nanotubes on a metal tip
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.1430507
– volume: 5
  start-page: 2135
  year: 2005
  ident: cmac920abib90
  article-title: Achieving high-current carbon nanotube emitters
  publication-title: Nano Lett.
  doi: 10.1021/nl051397d
– volume: 463
  start-page: 2907
  year: 2007
  ident: cmac920abib16
  article-title: Reformulation of the standard theory of Fowler–Nordheim tunnelling and cold field electron emission
  publication-title: Proc. R. Soc. A
  doi: 10.1098/rspa.2007.0030
– volume: 126
  year: 2019
  ident: cmac920abib159
  article-title: Analytic model of a compound thermal-field emitter and its performance
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5132561
– volume: 38
  start-page: 1534
  year: 1991
  ident: cmac920abib49
  article-title: Analytic evaluation of field emission enhancement factors for ellipsoidal cones and elliptic cross-section wedges
  publication-title: IEEE Trans. Electron Devices
  doi: 10.1109/16.81650
– volume: 120
  year: 2016
  ident: cmac920abib52
  article-title: Physical electrostatics of small field emitter arrays/clusters
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.4959150
– volume: 125
  year: 2019
  ident: cmac920abib157
  article-title: Verifications of Schottky’s conjecture
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.5091712
– volume: 94
  year: 2009
  ident: cmac920abib175
  article-title: Maximizing the electron field emission performance of carbon nanotube arrays
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.3097239
– volume: 37
  year: 2019
  ident: cmac920abib20
  article-title: Curvature correction to the field emission current
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.5064403
– volume: 132
  start-page: 152
  year: 2013
  ident: cmac920abib98
  article-title: A model to predict image formation in atom probe tomography
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2012.12.007
– volume: 3
  year: 2017
  ident: cmac920abib111
  article-title: An analytical modeling of field electron emission for a vertical wedged ordered nanostructure
  publication-title: Adv. Electron. Mater.
  doi: 10.1002/aelm.201700295
– volume: 38
  start-page: 4501
  year: 1967
  ident: cmac920abib55
  article-title: Change in field intensification factor β of an electrode projection (whisker) at short gap lengths
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1709157
– volume: 32
  start-page: 492
  year: 1911
  ident: cmac920abib101
  article-title: Discharge from hot CaO
  publication-title: Phys. Rev. I
  doi: 10.1103/PhysRevSeriesI.32.492
– volume: 6
  year: 2016
  ident: cmac920abib155
  article-title: Schottky’s conjecture, field emitters and the point charge model
  publication-title: AIP Adv.
  doi: 10.1063/1.4953813
– year: 2022
  ident: cmac920abib14
– volume: 88
  year: 2006
  ident: cmac920abib168
  article-title: Geometrical enhancement of field emission of individual nanotubes studied by in situ transmission electron microscopy
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.2188389
– start-page: pp 173
  year: 2022
  ident: cmac920abib112
  article-title: Theoretical coherent field emission of graphene
– volume: 27
  start-page: 215
  year: 1956
  ident: cmac920abib38
  article-title: On the magnification and resolution of the field emission electron microscope
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1722347
– volume: 160
  start-page: 247
  year: 2016
  ident: cmac920abib79
  article-title: Simulation of the enhancement factor from an individual 3D hemisphere-on-post field emitter by using finite elements method
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2015.10.018
– year: 1936
  ident: cmac920abib32
– volume: 7
  start-page: 93
  year: 1955
  ident: cmac920abib40
  article-title: Field emission microscopy and some applications to catalysis and chemisorption
  publication-title: Adv. Catal.
  doi: 10.1016/S0360-0564(08)60526-X
– volume: 82
  start-page: 1009
  year: 2002
  ident: cmac920abib67
  article-title: Experimental and computational study of field emission characteristics from amorphous carbon single nanotips grown by carbon contamination. II. Theory
  publication-title: Phil. Mag. B
  doi: 10.1080/13642810208218358
– volume: 24
  start-page: 1081
  year: 2006
  ident: cmac920abib167
  article-title: Characterising field emission from individual carbon nanotubes at small distances
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.2188403
– volume: 48
  start-page: 47
  year: 2005
  ident: cmac920abib11
  article-title: Novel cold cathode materials and applications
  publication-title: Mater. Sci. Eng. R
  doi: 10.1016/j.mser.2004.12.001
– volume: 30
  start-page: 907
  year: 1951
  ident: cmac920abib37
  article-title: The use of the field emission electron microscope in adsorption studies of W on W and Ba on W
  publication-title: Bell System Tech. J.
  doi: 10.1002/j.1538-7305.1951.tb03688.x
– volume: 82
  start-page: 987
  year: 2002
  ident: cmac920abib66
  article-title: Experimental and computational study of field emission characteristics from amorphous carbon single nanotips grown by carbon contamination. I. Experiments and computation
  publication-title: Phil. Mag. B
  doi: 10.1080/13642810208218357
– year: 1929
  ident: cmac920abib30
  article-title: Electron emission from metals in intense electric felds
– volume: 233
  year: 2022
  ident: cmac920abib118
  article-title: Properties of blade-like field emitters
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2021.113462
– volume: 100
  year: 2019
  ident: cmac920abib139
  article-title: Ab initio calculation of field emission from metal surfaces with atomic-scale defects
  publication-title: Phys. Rev. B
  doi: 10.1103/PhysRevB.100.165421
– volume: 82
  start-page: 3520
  year: 2003
  ident: cmac920abib178
  article-title: Effect of length and spacing of vertically aligned carbon nanotubes on field emission properties
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.1576310
– volume: 55
  start-page: 158
  year: 1984
  ident: cmac920abib162
  article-title: Influence of gap length on the field increase factor β of an electrode projection (whisker)
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.332879
– volume: 467
  start-page: 2927
  year: 2011
  ident: cmac920abib19
  article-title: Transmission coefficients for the exact triangular barrier: an exact general analytical theory that can replace Fowler & Nordheim’s 1928 theory
  publication-title: Proc. R. Soc. A
  doi: 10.1098/rspa.2011.0025
– volume: 5
  year: 2015
  ident: cmac920abib183
  article-title: Dependence of optimal spacing on applied field in ungated field emitter arrays
  publication-title: AIP Adv.
  doi: 10.1063/1.4929983
– volume: 9
  start-page: 2620
  year: 2021
  ident: cmac920abib13
  article-title: The rise of carbon materials for field emission
  publication-title: J. Mater. Chem. C
  doi: 10.1039/D0TC05873D
– volume: 2
  start-page: 450
  year: 1913
  ident: cmac920abib102
  article-title: The effect of space charge and residual gases on thermionic currents in high vacuum
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.2.450
– volume: 13
  start-page: 184
  year: 2001
  ident: cmac920abib181
  article-title: Tuning the field emission properties of patterned carbon nanotube films
  publication-title: Adv. Mater.
  doi: 10.1002/1521-4095(200102)13:3<184::AID-ADMA184>3.0.CO;2-I
– volume: 4510
  start-page: 156
  year: 2001
  ident: cmac920abib173
  article-title: Computer simulation of electric field analysis for vertically aligned carbon nanotubes (1)—simulation method and computing model
  publication-title: Proc. SPIE
  doi: 10.1117/12.451277
– year: 1961
  ident: cmac920abib41
– year: 2010
  ident: cmac920abib10
– volume: 230
  year: 2021
  ident: cmac920abib82
  article-title: Numerical simulations of field emission characteristics of open CNT
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2021.113362
– start-page: pp 58
  year: 1996
  ident: cmac920abib93
  article-title: The electron energy distribution from very sharp field emitters
– volume: 35
  year: 2012
  ident: cmac920abib86
  article-title: Advanced nanodiamond emitter with pyramidal tip-on-pole structure for emission self-regulation
  publication-title: J. Vac. Sci. Technol. B
  doi: 10.1116/1.3684425
– year: 1981
  ident: cmac920abib47
– volume: 931
  start-page: 489
  year: 2008
  ident: cmac920abib141
  article-title: An introduction to the helium ion microscope
  publication-title: AIP Conf. Proc.
  doi: 10.1063/1.2799423
– year: 1964
  ident: cmac920abib53
  article-title: Field emission in vacuum voltage breakdown
  doi: 10.21236/AD0602844
– volume: 110
  year: 2017
  ident: cmac920abib88
  article-title: The theoretical link between voltage loss, reduction in field enhancement factor and Fowler–Nordheim-plot saturation
  publication-title: Appl. Phys. Lett.
  doi: 10.1063/1.4979320
– volume: 53
  start-page: 295
  year: 1999
  ident: cmac920abib121
  article-title: Optimization of multi-tip field emission electron source
  publication-title: Vacuum
  doi: 10.1016/S0042-207X(98)00302-9
– volume: 4
  start-page: 1266
  year: 1971
  ident: cmac920abib36
  article-title: Properties of the tip-plane configuration
  publication-title: J. Phys. D: Appl. Phys.
  doi: 10.1088/0022-3727/4/9/305
– volume: 24
  start-page: 570
  year: 1953
  ident: cmac920abib39
  article-title: The field emitter: fabrication, electron microscopy and electric field calculations
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1721330
– volume: 40
  start-page: 2986
  year: 2011
  ident: cmac920abib12
  article-title: One-dimensional inorganic nanostructures: synthesis, field-emission and photodetection
  publication-title: Chem. Soc. Rev.
  doi: 10.1039/c0cs00126k
– volume: 121
  year: 2017
  ident: cmac920abib123
  article-title: Practical considerations in the modeling of field emitter arrays with line charge distributions
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.4983680
– volume: 109
  start-page: 373
  year: 2009
  ident: cmac920abib51
  article-title: Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle
  publication-title: Ultramicroscopy
  doi: 10.1016/j.ultramic.2009.01.006
– volume: 9
  start-page: 417
  year: 1962
  ident: cmac920abib91
  article-title: Direct measurement of the energy of electrons obtained from the surface of silicon by field emission
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.9.417
– volume: 35
  start-page: 2855
  year: 1964
  ident: cmac920abib54
  article-title: Vacuum voltage breakdown as a thermal instability of the emitting protrusion
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1713118
– volume: 26
  start-page: 1333
  year: 1957
  ident: cmac920abib58
  article-title: Field emission from mercury whiskers
  publication-title: J. Chem. Phys.
  doi: 10.1063/1.1743515
SSID ssj0004834
Score 2.5196352
SecondaryResourceType review_article
Snippet This review of the quantitative electrostatics of field emitters, covering analytical, numerical and ‘fitted formula’ approaches, is thought the first of its...
This review of the quantitative electrostatics of field emitters, covering analytical, numerical and 'fitted formula' approaches, is thought the first of its...
SourceID proquest
crossref
iop
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 493001
SubjectTerms conducting post formula
electrostatic depolarization
field emission
field emitter electrostatics
field enhancement factor
finite element method
minimum simulation domain dimensions
Title Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling
URI https://iopscience.iop.org/article/10.1088/1361-648X/ac920a
https://www.proquest.com/docview/2714655958
Volume 34
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3dS8MwEA_bRPBF_MT5MSLogw9x65o2qT6JOKYP6oPDvZV8XHGg3bDb_28ujRNRxLdCr9dy1yS_5O5-R8iJETbLdCGZBRUzDhaY1m482sTjgQxD7phtcZ8OR_xunIwb5HJZCzOdhan_3F3WRMG1CUNCnOxGcRqxlMtxVxmny4GjlVimEndeD_HzV1Gk9CFl5FNjMpM8xCh_0_BtTWq69_6YmP1qM9gg6wEm0qv6ozZJA8otsurTNU21TcoBJp5ReJtgMQ4NvWywOMjdvqCK1hUpFE9ZaVW3mHfSsxdVTSo6Lembb4FGkayYzd5Dnx1aTBCBMqhTyr2Qp-zeIaPBzdP1kIXOCcw4_DBnwDWInjKgpYZCWa5UavumUIXqQdE3aWaRiF4mPHJ7VB4pYTVAT_UiUIkQJt4lrXJawh6hShsw1jkUDHdgy2YgC4faHAwpRMwFb5Pup-1yE2jFsbvFa-7D21LmaO0crZ3X1m6Ts-UTs5pS4w_ZU-eOPIyr6g-540-H5W58YNBDlTBdVHlfREgRlyVy_5-6DshaH2scMGdFHJLW_H0BRw55zHWHNG8fHjv-P_sAbcHV4Q
linkProvider IOP Publishing
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1NT9wwELVgEYgLAkrFAqVGag89uLvZOLHDrYKuoK2AQxF7s_wxFitBNiK7_x-PY6gqEOIWKRMnmontl8zMe4R8scJVlfGSOdA54-CAGRPmoysiHqgw5Y7VFhfl2TX_NSkmSec09sLMmrT0fw-HHVFw58JUECcHWV5mrORyMtA2jKUHjfPLZKXIyxK1Gy7zm3-NkTKmlZFTjclK8pSnfG2U__al5XDvF4tz3HHGm2QjQUX6o3uwLbIE9TZZjSWbtv1A6jEWn1G4n2JDDk16NtggFE4fU027rhSKf1pp28nMB-vmVrfTls5qeh9l0CgSFrPmIWntUD9FFMqgKyuPRpG2e4dcj3_-PTljST2B2YAh5gy4ATHUFow04LXjWpduZL32egh-ZMvKIRm9LHgWvlN5poUzAEM9zEAXQtj8I-nVsxp2CdXGgnUhqGB5AFyuAukDcgtQxIucC94ngyffKZuoxVHh4k7FFLeUCr2t0Nuq83affHu-ouloNd6w_RrCodLcat-wO3oKmApzBBMfuobZolUjkSFNXFXIvXeO9ZmsXZ2O1Z_zi9_7ZH2ELQ9YwiIOSG_-sIBPAYjMzWF82R4BmizYxw
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Field+emitter+electrostatics%3A+a+review+with+special+emphasis+on+modern+high-precision+finite-element+modelling&rft.jtitle=Journal+of+physics.+Condensed+matter&rft.au=de+Assis%2C+Thiago+A&rft.au=Dall%27Agnol%2C+Fernando+F&rft.au=bes%2C+Richard+G&rft.date=2022-12-07&rft.issn=1361-648X&rft.eissn=1361-648X&rft.volume=34&rft.issue=49&rft_id=info:doi/10.1088%2F1361-648X%2Fac920a&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0953-8984&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0953-8984&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0953-8984&client=summon