{"id":"https://openalex.org/W4200394255","doi":"https://doi.org/10.1038/s41598-021-03760-4","title":"Thermopower, figure of merit and Fermi integrals","display_name":"Thermopower, figure of merit and Fermi integrals","publication_year":2021,"publication_date":"2021-12-21","ids":{"openalex":"https://openalex.org/W4200394255","doi":"https://doi.org/10.1038/s41598-021-03760-4","pmid":"https://pubmed.ncbi.nlm.nih.gov/34934116","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/8692468"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-021-03760-4","doi":"https://doi.org/10.1038/s41598-021-03760-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-021-03760-4","pdf_url":"https://www.nature.com/articles/s41598-021-03760-4.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-021-03760-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004964343","display_name":"Patrice Limelette","orcid":"https://orcid.org/0000-0003-4311-8589","observed_orcids":["https://orcid.org/0000-0003-4311-8589"]},"institutions":[{"id":"https://openalex.org/I110017253","display_name":"Universit\u00e9 de Tours","ror":"https://ror.org/02wwzvj46","country_code":"FR","type":"education","lineage":["https://openalex.org/I110017253"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4405262765","display_name":"GREMAN, Mat\u00e9riaux, Micro\u00e9lectronique, Acoustique, Nanotechnologies","ror":"https://ror.org/051qnm298","country_code":"FR","type":"facility","lineage":["https://openalex.org/I110017253","https://openalex.org/I1294671590","https://openalex.org/I4210143826","https://openalex.org/I4405262765"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Patrice Limelette","raw_affiliation_strings":["GREMAN, UMR 7347 CNRS-INSA-Universit\u00e9 de Tours, Parc de Grandmont, 37200, Tours, France. patrice.limelette@univ-tours.fr","GREMAN (mat\u00e9riaux, micro\u00e9lectronique, acoustique et nanotechnologies)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GREMAN, UMR 7347 CNRS-INSA-Universit\u00e9 de Tours, Parc de Grandmont, 37200, Tours, France. patrice.limelette@univ-tours.fr","institution_ids":["https://openalex.org/I110017253","https://openalex.org/I1294671590","https://openalex.org/I4405262765"]},{"raw_affiliation_string":"GREMAN (mat\u00e9riaux, micro\u00e9lectronique, acoustique et nanotechnologies)","institution_ids":["https://openalex.org/I4405262765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004964343"],"corresponding_institution_ids":["https://openalex.org/I110017253","https://openalex.org/I1294671590","https://openalex.org/I4405262765"],"apc_list":{"value":1990,"currency":"USD","value_usd":1990},"apc_paid":{"value":1990,"currency":"USD","value_usd":1990},"fwci":0.2136,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.36726041,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"11","issue":"1","first_page":"24323","last_page":"24323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10440","display_name":"Advanced Thermoelectric Materials and Devices","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10440","display_name":"Advanced Thermoelectric Materials and Devices","score":1.0,"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/T11277","display_name":"Thermal properties of materials","score":0.0,"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/T13251","display_name":"Electrical and Thermal Properties of Materials","score":0.0,"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/seebeck-coefficient","display_name":"Seebeck coefficient","score":0.8399999737739563},{"id":"https://openalex.org/keywords/figure-of-merit","display_name":"figure of merit","score":0.9850000143051147},{"id":"https://openalex.org/keywords/fermi-integrals","display_name":"Fermi integrals","score":0.9929999709129333},{"id":"https://openalex.org/keywords/thermoelectric-efficiency","display_name":"thermoelectric efficiency","score":0.9150000214576721},{"id":"https://openalex.org/keywords/transport-properties","display_name":"transport properties","score":0.8700000047683716},{"id":"https://openalex.org/keywords/electrical-conductivity","display_name":"electrical conductivity","score":0.890999972820282},{"id":"https://openalex.org/keywords/thermal-conductivity","display_name":"thermal conductivity","score":0.9990000128746033},{"id":"https://openalex.org/keywords/power-system-expansion","display_name":"power system expansion","score":0.7829999923706055}],"concepts":[{"id":"https://openalex.org/C130277099","wikidata":"https://www.wikidata.org/wiki/Q3676605","display_name":"Figure of merit","level":2,"score":0.7715392112731934},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7689208388328552},{"id":"https://openalex.org/C112625512","wikidata":"https://www.wikidata.org/wiki/Q1091448","display_name":"Seebeck coefficient","level":3,"score":0.7674094438552856},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5490567684173584},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.47980359196662903},{"id":"https://openalex.org/C26057338","wikidata":"https://www.wikidata.org/wiki/Q431335","display_name":"Fermi energy","level":3,"score":0.4629972577095032},{"id":"https://openalex.org/C63024428","wikidata":"https://www.wikidata.org/wiki/Q552456","display_name":"Thermoelectric effect","level":2,"score":0.42473143339157104},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42265287041664124},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36676958203315735},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.238479346036911},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22623443603515625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22417867183685303},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11887261271476746},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.10218214988708496},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.09607407450675964}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1038/s41598-021-03760-4","doi":"https://doi.org/10.1038/s41598-021-03760-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-021-03760-4","pdf_url":"https://www.nature.com/articles/s41598-021-03760-4.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:8692468","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8692468","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sci Rep","raw_type":"Text"},{"id":"pmid:34934116","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34934116","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific reports","raw_type":"Journal Article"},{"id":"pmh:oai:HAL:hal-04884198v1","doi":null,"is_oa":true,"landing_page_url":"https://univ-tours.hal.science/hal-04884198","pdf_url":"https://univ-tours.hal.science/hal-04884198v1/file/limelette-2021-s41598-021-03760-4.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scientific Reports, 2021, 11 (1), pp.24323. ⟨10.1038/s41598-021-03760-4⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-03581368v1","doi":null,"is_oa":false,"landing_page_url":"https://univ-tours.hal.science/hal-03581368","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":"Scientific Reports, 2021, 11 (1), pp.24323. ⟨10.1038/s41598-021-03760-4⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:3edac7eb415849a5adfb669a8e6acbfc","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/3edac7eb415849a5adfb669a8e6acbfc","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1038/s41598-021-03760-4","doi":"https://doi.org/10.1038/s41598-021-03760-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-021-03760-4","pdf_url":"https://www.nature.com/articles/s41598-021-03760-4.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2147824529","display_name":null,"funder_award_id":"ANR-17-CE05","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7807244557","display_name":"Anisotropic polymer thermoelectric materials","funder_award_id":"ANR-17-CE05-0012","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200394255.pdf","grobid_xml":"https://content.openalex.org/works/W4200394255.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1821638546","https://openalex.org/W1994312980","https://openalex.org/W2001566902","https://openalex.org/W2004378275","https://openalex.org/W2016216868","https://openalex.org/W2023452791","https://openalex.org/W2045934560","https://openalex.org/W2052607266","https://openalex.org/W2055833929","https://openalex.org/W2062932347","https://openalex.org/W2068838120","https://openalex.org/W2071317896","https://openalex.org/W2072766245","https://openalex.org/W2078996162","https://openalex.org/W2096480321","https://openalex.org/W2148596493","https://openalex.org/W2294278699","https://openalex.org/W2550840417","https://openalex.org/W2626557369","https://openalex.org/W2727784010","https://openalex.org/W2747813204","https://openalex.org/W2798977091","https://openalex.org/W2811047282","https://openalex.org/W2944719179","https://openalex.org/W2946303686","https://openalex.org/W3025197323","https://openalex.org/W3113102942","https://openalex.org/W3136817013","https://openalex.org/W3141978509","https://openalex.org/W4238083559","https://openalex.org/W4254624278"],"related_works":["https://openalex.org/W3136817013","https://openalex.org/W2044864373","https://openalex.org/W2301012080","https://openalex.org/W52594017","https://openalex.org/W2058963391","https://openalex.org/W3156442765","https://openalex.org/W2997725215","https://openalex.org/W2078996162","https://openalex.org/W1981153869","https://openalex.org/W2016893430"],"abstract_inverted_index":{"The":[0],"thermoelectric":[1,75,175],"efficiency":[2],"accounting":[3],"for":[4,102,146],"the":[5,16,26,28,31,63,93,107,114,124,147,154,174,178,184,195,199],"conversion":[6],"of":[7,18,46,68,106,109,116,123,177,186],"thermal":[8,32],"energy":[9,196],"into":[10],"electricity":[11],"is":[12,67,81],"usually":[13],"given":[14],"by":[15,161],"figure":[17,108],"merit":[19,110],"which":[20,49,66,111],"involves":[21],"three":[22],"transport":[23,94,155,200],"coefficients,":[24],"with":[25],"thermopower,":[27],"electrical":[29],"and":[30,91,180],"conductivities.":[33],"These":[34,168],"coefficients":[35,95,156],"can":[36,87,96,157],"be":[37,89,97,159],"defined":[38],"at":[39],"a":[40,44,103,129,137,142],"semi-classical":[41],"level":[42],"as":[43],"function":[45],"Fermi":[47,85,125],"integrals":[48,86,126],"only":[50],"allow":[51,191],"analytical":[52],"approximations":[53],"in":[54,70,133,198],"either":[55],"highly":[56],"degenerate":[57],"or":[58],"strongly":[59],"non-degenerate":[60],"regimes.":[61],"Otherwise,":[62],"intermediate":[64,148],"regime":[65],"interest":[69,117],"order":[71,134],"to":[72,135,141,192],"describe":[73],"high":[74,164,188],"performance":[76],"requires":[77],"numerical":[78,119],"calculations.":[79,120],"It":[80,150],"shown":[82],"that":[83,92,153,183],"these":[84],"actually":[88],"calculated":[90],"reformulated":[98],"accordingly.":[99],"This":[100,121],"allows":[101],"new":[104,143,171],"definition":[105],"covers":[112],"all":[113],"regimes":[115],"without":[118],"formulation":[122],"also":[127],"provides":[128],"good":[130],"starting":[131],"point":[132,181],"perform":[136],"power":[138],"expansion":[139],"leading":[140],"approximation":[144],"relevant":[145],"regime.":[149],"turns":[151],"out":[152,182],"then":[158],"expanded":[160],"revealing":[162],"their":[163,187],"temperatures":[165,189],"asymptotic":[166],"behaviors.":[167],"results":[169],"shed":[170],"light":[172],"on":[173],"properties":[176],"materials":[179],"analysis":[185],"behaviors":[190],"characterize":[193],"experimentally":[194],"dependence":[197],"integrals.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2021-12-31T00:00:00"}