{"volume":6,"date_updated":"2021-01-12T08:15:47Z","type":"journal_article","has_accepted_license":"1","publication_identifier":{"eissn":["22969039"],"issn":["22969020"]},"author":[{"last_name":"Fellner","first_name":"Klemens","full_name":"Fellner, Klemens"},{"id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","last_name":"Kniely","orcid":"0000-0001-5645-4333","full_name":"Kniely, Michael","first_name":"Michael"}],"doi":"10.1007/s41808-020-00068-8","_id":"7866","publication_status":"published","publication":"Journal of Elliptic and Parabolic Equations","abstract":[{"text":"In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation.","lang":"eng"}],"article_processing_charge":"No","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). The second author has been supported by the International Research Training Group IGDK 1754 “Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian Science Fund (FWF) under grant number [W 1244-N18].","department":[{"_id":"JuFi"}],"citation":{"apa":"Fellner, K., &#38; Kniely, M. (2020). Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. <i>Journal of Elliptic and Parabolic Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41808-020-00068-8\">https://doi.org/10.1007/s41808-020-00068-8</a>","chicago":"Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” <i>Journal of Elliptic and Parabolic Equations</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s41808-020-00068-8\">https://doi.org/10.1007/s41808-020-00068-8</a>.","ista":"Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 6, 529–598.","ieee":"K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model,” <i>Journal of Elliptic and Parabolic Equations</i>, vol. 6. Springer Nature, pp. 529–598, 2020.","mla":"Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” <i>Journal of Elliptic and Parabolic Equations</i>, vol. 6, Springer Nature, 2020, pp. 529–98, doi:<a href=\"https://doi.org/10.1007/s41808-020-00068-8\">10.1007/s41808-020-00068-8</a>.","ama":"Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. <i>Journal of Elliptic and Parabolic Equations</i>. 2020;6:529-598. doi:<a href=\"https://doi.org/10.1007/s41808-020-00068-8\">10.1007/s41808-020-00068-8</a>","short":"K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020) 529–598."},"date_created":"2020-05-17T22:00:45Z","month":"12","page":"529-598","project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","call_identifier":"FWF","name":"FWF Open Access Fund"}],"status":"public","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2020-11-25T08:59:59Z","oa":1,"intvolume":"         6","file":[{"checksum":"6bc6832caacddceee1471291e93dcf1d","date_created":"2020-11-25T08:59:59Z","relation":"main_file","file_name":"2020_JourEllipticParabEquat_Fellner.pdf","success":1,"access_level":"open_access","date_updated":"2020-11-25T08:59:59Z","creator":"dernst","file_id":"8802","content_type":"application/pdf","file_size":8408694}],"language":[{"iso":"eng"}],"title":"Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model","scopus_import":"1","quality_controlled":"1","oa_version":"Published Version","publisher":"Springer Nature","article_type":"original","year":"2020","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"01","date_published":"2020-12-01T00:00:00Z"}