A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme

Handle URI:
http://hdl.handle.net/10754/562736
Title:
A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme
Authors:
Brinkman, Daniel; Fellner, Klemens J.; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Wolfram, Marie Therese
Abstract:
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson's equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
World Scientific Publishing
Journal:
Mathematical Models and Methods in Applied Sciences
Issue Date:
May-2013
DOI:
10.1142/S0218202512500625
ARXIV:
arXiv:1202.0817
Type:
Article
ISSN:
02182025
Sponsors:
The authors acknowledge support from King Abdullah University of Science and Technology (KAUST) Award Number: KUK-I1-007-43. P. A. M. also acknowledges support from the Fondation Sciences Mathematique de Paris, in form of his Excellence Chair 2011, and from the Royal Society through his Wolfson Research Merit Award. M.-T.W. acknowledges financial support from the Austrian Science Foundation (FWF) via the Hertha Firnberg project TU56-N23. K. F. acknowledges the support of NaWi Graz.
Additional Links:
http://arxiv.org/abs/arXiv:1202.0817v1
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBrinkman, Danielen
dc.contributor.authorFellner, Klemens J.en
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorWolfram, Marie Thereseen
dc.date.accessioned2015-08-03T11:03:47Zen
dc.date.available2015-08-03T11:03:47Zen
dc.date.issued2013-05en
dc.identifier.issn02182025en
dc.identifier.doi10.1142/S0218202512500625en
dc.identifier.urihttp://hdl.handle.net/10754/562736en
dc.description.abstractWe present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson's equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.en
dc.description.sponsorshipThe authors acknowledge support from King Abdullah University of Science and Technology (KAUST) Award Number: KUK-I1-007-43. P. A. M. also acknowledges support from the Fondation Sciences Mathematique de Paris, in form of his Excellence Chair 2011, and from the Royal Society through his Wolfson Research Merit Award. M.-T.W. acknowledges financial support from the Austrian Science Foundation (FWF) via the Hertha Firnberg project TU56-N23. K. F. acknowledges the support of NaWi Graz.en
dc.publisherWorld Scientific Publishingen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1202.0817v1en
dc.subjectasymptotic methodsen
dc.subjectdrift-diffusion-reaction equationsen
dc.subjectfinite element methodsen
dc.subjectPhotovoltaicsen
dc.titleA drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element schemeen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalMathematical Models and Methods in Applied Sciencesen
dc.contributor.institutionDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdomen
dc.contributor.institutionInstitute for Mathematics and Scientific Computing, University of Graz, Heinrichgasse 36, 8010 Graz, Austriaen
dc.contributor.institutionDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdomen
dc.contributor.institutionDepartment of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austriaen
dc.identifier.arxividarXiv:1202.0817en
kaust.authorMarkowich, Peter A.en
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