{"id":"https://openalex.org/W7220992804","doi":"https://doi.org/10.48550/arxiv.2610.07013","title":"A numerical and efficient model for thermo-field electron emission calculations","display_name":"A numerical and efficient model for thermo-field electron emission calculations","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220992804","doi":"https://doi.org/10.48550/arxiv.2610.07013"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07013","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07013","pdf_url":"https://arxiv.org/pdf/2610.07013","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.07013","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035839983","display_name":"Salvador Barranco C\u00e1rceles","orcid":"https://orcid.org/0000-0001-8154-0866","observed_orcids":["https://orcid.org/0000-0001-8154-0866"]},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210133140","display_name":"Institut Lumi\u00e8re Mati\u00e8re","ror":"https://ror.org/0323bey33","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210098836","https://openalex.org/I4210133140","https://openalex.org/I4405259976","https://openalex.org/I4405263940","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE","FR"],"is_corresponding":false,"raw_author_name":"C\u00e1rceles, Salvador Barranco","raw_affiliation_strings":["Institute Lumi\u00e8re Mati\u00e8re , Universit\u00e9 Claude Bernard Lyon 1 , Villeurbanne , France","Instute of Technology , Tartu , Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute Lumi\u00e8re Mati\u00e8re , Universit\u00e9 Claude Bernard Lyon 1 , Villeurbanne , France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210133140"]},{"raw_affiliation_string":"Instute of Technology , Tartu , Estonia","institution_ids":["https://openalex.org/I56085075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003531010","display_name":"Andreas Kyritsakis","orcid":"https://orcid.org/0000-0002-4334-5450","observed_orcids":["https://orcid.org/0000-0002-4334-5450"]},"institutions":[{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Kyritsakis, Andreas","raw_affiliation_strings":["Instute of Technology , Tartu , Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instute of Technology , Tartu , Estonia","institution_ids":["https://openalex.org/I56085075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045545049","display_name":"Anthony Ayari","orcid":"https://orcid.org/0000-0003-1654-5470","observed_orcids":["https://orcid.org/0000-0003-1654-5470"]},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210133140","display_name":"Institut Lumi\u00e8re Mati\u00e8re","ror":"https://ror.org/0323bey33","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210098836","https://openalex.org/I4210133140","https://openalex.org/I4405259976","https://openalex.org/I4405263940","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ayari, Anthony","raw_affiliation_strings":["Institute Lumi\u00e8re Mati\u00e8re , Universit\u00e9 Claude Bernard Lyon 1 , Villeurbanne , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute Lumi\u00e8re Mati\u00e8re , Universit\u00e9 Claude Bernard Lyon 1 , Villeurbanne , France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210133140"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11175","display_name":"Gyrotron and Vacuum Electronics Research","score":0.461899995803833,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11175","display_name":"Gyrotron and Vacuum Electronics Research","score":0.461899995803833,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13418","display_name":"Photocathodes and Microchannel Plates","score":0.37450000643730164,"subfield":{"id":"https://openalex.org/subfields/3105","display_name":"Instrumentation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12039","display_name":"Electron and X-Ray Spectroscopy Techniques","score":0.09690000116825104,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/electron-emission-current-density","display_name":"electron emission current density","score":0.4950000047683716},{"id":"https://openalex.org/keywords/fowler-nordheim-equation","display_name":"Fowler-Nordheim equation","score":0.8080000281333923},{"id":"https://openalex.org/keywords/wkb-approximation","display_name":"WKB approximation","score":0.9430000185966492},{"id":"https://openalex.org/keywords/neural-network-surrogate-model","display_name":"neural network surrogate model","score":0.8330000042915344},{"id":"https://openalex.org/keywords/open-source-software","display_name":"open source software","score":0.4449999928474426}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.6514000296592712},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5774999856948853},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4966999888420105},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.4851999878883362},{"id":"https://openalex.org/C207740977","wikidata":"https://www.wikidata.org/wiki/Q234072","display_name":"Current density","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.46869999170303345},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C125485243","wikidata":"https://www.wikidata.org/wiki/Q905186","display_name":"Electron density","level":3,"score":0.4618000090122223},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.45509999990463257},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.4528999924659729},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.42899999022483826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3978999853134155},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3952000141143799},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.36309999227523804},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3325999975204468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29829999804496765},{"id":"https://openalex.org/C148837635","wikidata":"https://www.wikidata.org/wiki/Q1742397","display_name":"Sawtooth wave","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28189998865127563},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.26339998841285706},{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2506999969482422}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2610.07013","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07013","pdf_url":"https://arxiv.org/pdf/2610.07013","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05795910v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05795910","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2610.07013","doi":"https://doi.org/10.48550/arxiv.2610.07013","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07013","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.07013","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07013","pdf_url":"https://arxiv.org/pdf/2610.07013","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321090","display_name":"Eesti Teadusagentuur","ror":"https://ror.org/00jjeja18"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220992804.pdf","grobid_xml":"https://content.openalex.org/works/W7220992804.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1971044734","https://openalex.org/W1982392480","https://openalex.org/W2025323342","https://openalex.org/W2050009459","https://openalex.org/W2060132873","https://openalex.org/W2065825828","https://openalex.org/W2082835850","https://openalex.org/W2161606023","https://openalex.org/W2519847273","https://openalex.org/W2998639709","https://openalex.org/W4210809556","https://openalex.org/W4318309321","https://openalex.org/W4385329382","https://openalex.org/W4393045573","https://openalex.org/W4406146930","https://openalex.org/W4415243031"],"related_works":["https://openalex.org/W2773486175","https://openalex.org/W2139718135","https://openalex.org/W2020974557","https://openalex.org/W4403125336","https://openalex.org/W4415243031","https://openalex.org/W2967818816","https://openalex.org/W2093411055","https://openalex.org/W4241154161","https://openalex.org/W2148665541","https://openalex.org/W2886154174"],"abstract_inverted_index":{"As":[0],"electron":[1,20,106,198],"sources":[2],"are":[3,31],"reduced":[4,118],"in":[5,8,108,136],"size,":[6],"fabricated":[7],"new":[9],"materials,":[10],"or":[11],"pushed":[12],"for":[13,18,40,77,175],"performance,":[14],"the":[15,36,60,70,92,110,114,126,132,146,149,152,158,168],"analytical":[16],"formulations":[17],"thermo-field":[19],"emission,":[21],"namely":[22],"Fowler-Nordheim":[23],"and":[24,27,80,97,155,177,182,186,192,201],"Murphy-Good":[25],"equations":[26],"their":[28],"JWKB-based":[29],"extensions,":[30],"increasingly":[32],"applied":[33],"out":[34],"of":[35,38,59,112,148,151,167,184],"range":[37],"conditions":[39],"which":[41],"they":[42],"were":[43],"derived.":[44],"We":[45],"present":[46],"GETELEC-3,":[47],"an":[48,100],"open-source":[49],"code":[50,172],"that":[51,103],"replaces":[52],"them":[53],"with":[54,91,99,188],"a":[55,120,139,165,189],"direct":[56],"numerical":[57],"solution":[58,93],"one-dimensional":[61],"time-independent":[62],"Schr\u00f6dinger":[63],"equation":[64],"(1D-TISE).":[65],"Several":[66],"methods":[67],"to":[68,75,88,119,125,195],"solve":[69],"1D-TISE":[71],"have":[72],"been":[73,143],"implemented":[74],"test":[76],"speed,":[78,134],"robustness,":[79],"solution's":[81],"uncertainty.":[82],"The":[83,171],"Noumerov":[84],"algorithm":[85],"is":[86,117,173],"found":[87],"be":[89],"quickest,":[90],"uncertainty":[94],"below":[95],"1%,":[96],"together":[98],"optimised":[101],"kernel":[102],"advances":[104],"all":[105],"energies":[107],"parallel,":[109],"cost":[111],"calculating":[113],"current":[115,159],"density":[116,160,183],"few":[121],"milliseconds":[122],"-":[123],"comparable":[124],"JWKB":[127],"evaluation.":[128],"To":[129],"further":[130],"boost":[131],"calculation":[133],"especially":[135],"complicated":[137],"barriers,":[138],"neural":[140],"network":[141],"has":[142],"trained":[144],"on":[145],"residual":[147],"logarithm":[150],"semiclassical":[153],"reference":[154],"it":[156],"reproduces":[157],"better":[161],"than":[162],"0.4%":[163],"at":[164],"fraction":[166],"computational":[169],"cost.":[170],"developed":[174],"metals":[176],"semiconductors,":[178],"accepts":[179],"arbitrary":[180],"potentials":[181],"states,":[185],"comes":[187],"user-friendly":[190],"interface":[191],"compiled":[193],"executable":[194],"democratise":[196],"rigorous":[197],"emission":[199],"calculations":[200],"data":[202],"analysis.":[203]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
