{"id":"https://openalex.org/W2139673612","doi":"https://doi.org/10.1155/2001/35094","title":"Approximation of the BTE by a Relaxation\u2010timeOperator: Simulations for a 50 nm\u2010channel Si Diode","display_name":"Approximation of the BTE by a Relaxation\u2010timeOperator: Simulations for a 50 nm\u2010channel Si Diode","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2139673612","doi":"https://doi.org/10.1155/2001/35094","mag":"2139673612"},"language":"en","primary_location":{"id":"doi:10.1155/2001/35094","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2001/35094","pdf_url":"https://downloads.hindawi.com/archive/2001/035094.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/2001/035094.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060931083","display_name":"Marcello Anile","orcid":null},"institutions":[{"id":"https://openalex.org/I39063666","display_name":"University of Catania","ror":"https://ror.org/03a64bh57","country_code":"IT","type":"education","lineage":["https://openalex.org/I39063666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marcello A. Anile","raw_affiliation_strings":["Dipartimento di Matematica,  Universit\u00e1 di Catania, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica,  Universit\u00e1 di Catania, Italy","institution_ids":["https://openalex.org/I39063666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022412709","display_name":"Jos\u00e9 A. Carrillo","orcid":"https://orcid.org/0000-0001-8819-4660"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]},{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["ES","US"],"is_corresponding":false,"raw_author_name":"Jose A. Carrillo","raw_affiliation_strings":["Departamento de Matematica Aplicada, Universidad de Granada, Granada 18071, Spain","Department of Mathematics, University of Texas at Austin, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matematica Aplicada, Universidad de Granada, Granada 18071, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Mathematics, University of Texas at Austin, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087543049","display_name":"Irene M. Gamba","orcid":"https://orcid.org/0000-0002-4956-2376"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Irene M. Gamba","raw_affiliation_strings":["Department of Mathematics, University of Texas at Austin, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas at Austin, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047035333","display_name":"Chi\u2010Wang Shu","orcid":"https://orcid.org/0000-0001-7720-9564"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chi-Wang Shu","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02912, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02912, USA","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047035333"],"corresponding_institution_ids":["https://openalex.org/I27804330"],"apc_list":null,"apc_paid":null,"fwci":0.4379,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71487141,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"13","issue":"1-4","first_page":"349","last_page":"354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10558","display_name":"Advancements in Semiconductor Devices and Circuit Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10558","display_name":"Advancements in Semiconductor Devices and Circuit Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11277","display_name":"Thermal properties of materials","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10624","display_name":"Silicon and Solar Cell Technologies","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dimensionless-quantity","display_name":"Dimensionless quantity","score":0.6533297300338745},{"id":"https://openalex.org/keywords/ballistic-conduction","display_name":"Ballistic conduction","score":0.6408737897872925},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6330638527870178},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5754435658454895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5752403736114502},{"id":"https://openalex.org/keywords/computational-physics","display_name":"Computational physics","score":0.5045801401138306},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.47520574927330017},{"id":"https://openalex.org/keywords/drift-velocity","display_name":"Drift velocity","score":0.4524690806865692},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3539679944515228},{"id":"https://openalex.org/keywords/electric-field","display_name":"Electric field","score":0.21866756677627563},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1908796727657318}],"concepts":[{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.6533297300338745},{"id":"https://openalex.org/C192683347","wikidata":"https://www.wikidata.org/wiki/Q4851798","display_name":"Ballistic conduction","level":3,"score":0.6408737897872925},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6330638527870178},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5754435658454895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5752403736114502},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.5045801401138306},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.47520574927330017},{"id":"https://openalex.org/C131751877","wikidata":"https://www.wikidata.org/wiki/Q909891","display_name":"Drift velocity","level":3,"score":0.4524690806865692},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3539679944515228},{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.21866756677627563},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1908796727657318},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2001/35094","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2001/35094","pdf_url":"https://downloads.hindawi.com/archive/2001/035094.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.5299","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.5299","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.math.tu-berlin.de/pub/pdgl/tmr/ps/defiwce.ps","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:428cba97cffe427aa13afed014a512d2","is_oa":false,"landing_page_url":"https://doaj.org/article/428cba97cffe427aa13afed014a512d2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"VLSI Design, Vol 13, Iss 1-4, Pp 349-354 (2001)","raw_type":"article"},{"id":"pmh:oai:zenodo.org:14454730","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2001/35094","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1155/2001/35094","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2001/35094","pdf_url":"https://downloads.hindawi.com/archive/2001/035094.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8299999833106995}],"awards":[{"id":"https://openalex.org/G1224758599","display_name":null,"funder_award_id":"ECS-9627849","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3286829029","display_name":null,"funder_award_id":"DAAG55-97-1-0318","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3624984764","display_name":null,"funder_award_id":"ECS-9906606","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4915241927","display_name":null,"funder_award_id":"DAAG55-97-1-0318.","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5446830966","display_name":"Semiconductor Device Modeling, Numerical Methods and Simulations","funder_award_id":"9906606","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6445561921","display_name":null,"funder_award_id":"DMS 9971779","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7030765071","display_name":"Modeling and Numerical Methods for Device Simulations","funder_award_id":"9627849","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7535558615","display_name":"Mathematical Issues in the Modeling and Simulation of Self-Consistent Charge Particle Transport","funder_award_id":"9971779","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2139673612.pdf","grobid_xml":"https://content.openalex.org/works/W2139673612.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1973481688","https://openalex.org/W2018311843","https://openalex.org/W2039150507","https://openalex.org/W2067700446","https://openalex.org/W2107378853","https://openalex.org/W2144923759","https://openalex.org/W2316678504","https://openalex.org/W2610542513","https://openalex.org/W2798640573","https://openalex.org/W4230373105","https://openalex.org/W4250571781","https://openalex.org/W6660089719"],"related_works":["https://openalex.org/W2393220471","https://openalex.org/W3035214572","https://openalex.org/W2990133497","https://openalex.org/W3097484052","https://openalex.org/W2727503437","https://openalex.org/W4389287092","https://openalex.org/W2767303085","https://openalex.org/W2610797193","https://openalex.org/W2008079860","https://openalex.org/W2759487628"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3],"present":[4],"comparisons":[5],"between":[6],"DSMC":[7,43],"simulations":[8,15,44],"of":[9,16,62,69],"the":[10,36,50,67,70,77,85,89,94],"full":[11],"BTE":[12],"and":[13,59,65,99],"deterministic":[14,71],"a":[17,21,28],"relaxation\u2010time":[18,72],"approximation":[19],"for":[20,45],"nowadays":[22],"size":[23],"Si":[24],"diode.":[25],"We":[26,48,74],"assume":[27],"field":[29],"dependent":[30],"relaxation":[31,90],"time":[32,91],"fitted":[33],"to":[34,79,87],"give":[35],"same":[37],"drift":[38],"speed":[39],"(mean":[40],"velocity)":[41],"as":[42],"bulk":[46],"Si.":[47],"compute":[49],"density,":[51],"mean":[52],"velocity,":[53],"force":[54],"field,":[55],"potential":[56],"drop,":[57],"energy":[58],"I\u2010V":[60],"curves":[61],"both":[63],"models":[64,82],"plot":[66],"pdf":[68],"model.":[73],"also":[75],"compare":[76],"results":[78],"augmented":[80],"drift\u2010diffusion":[81],"proposed":[83],"in":[84,93],"literature":[86],"approximate":[88],"system":[92],"quasi\u2010ballistic":[95,98],"regime.":[96],"The":[97],"ballistic":[100],"regimes":[101],"are":[102],"distinguished":[103],"by":[104],"using":[105],"local":[106],"dimensionless":[107],"parameters.":[108]},"counts_by_year":[{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}