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

Daniel Brinkman; Klemens J. Fellner; Peter A. Markowich; Marie Therese Wolfram

doi:10.1142/S0218202512500625

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

Daniel Brinkman, Klemens J. Fellner, Peter A. Markowich, Marie Therese Wolfram

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English (US)
Pages (from-to)	839-872
Number of pages	34
Journal	Mathematical Models and Methods in Applied Sciences
Volume	23
Issue number	05
DOIs	https://doi.org/10.1142/S0218202512500625
State	Published - May 2013

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: 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.

ASJC Scopus subject areas

Modeling and Simulation
Applied Mathematics

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10.1142/S0218202512500625

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@article{d49c84ba38394cf59b705214bcdfbbb4,

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

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. {\textcopyright} 2013 World Scientific Publishing Company.",

author = "Daniel Brinkman and Fellner, {Klemens J.} and Markowich, {Peter A.} and Wolfram, {Marie Therese}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: 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.",

year = "2013",

month = may,

doi = "10.1142/S0218202512500625",

language = "English (US)",

volume = "23",

pages = "839--872",

journal = "Mathematical Models and Methods in Applied Sciences",

issn = "0218-2025",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "05",

}

A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme. / Brinkman, Daniel; Fellner, Klemens J.; Markowich, Peter A. et al.
In: Mathematical Models and Methods in Applied Sciences, Vol. 23, No. 05, 05.2013, p. 839-872.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme

AU - Brinkman, Daniel

AU - Fellner, Klemens J.

AU - Markowich, Peter A.

AU - Wolfram, Marie Therese

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: 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.

PY - 2013/5

Y1 - 2013/5

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/562736

UR - http://arxiv.org/abs/arXiv:1202.0817v1

UR - http://www.scopus.com/inward/record.url?scp=84874396719&partnerID=8YFLogxK

U2 - 10.1142/S0218202512500625

DO - 10.1142/S0218202512500625

M3 - Article

SN - 0218-2025

VL - 23

SP - 839

EP - 872

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 05

ER -

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

Abstract

Bibliographical note

ASJC Scopus subject areas

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