Asymptotic Solution of a Model for Bilayer Organic Diodes and Solar Cells

Handle URI:
http://hdl.handle.net/10754/597624
Title:
Asymptotic Solution of a Model for Bilayer Organic Diodes and Solar Cells
Authors:
Richardson, Giles; Please, Colin; Foster, Jamie; Kirkpatrick, James
Abstract:
Organic diodes and solar cells are constructed by placing together two organic semiconducting materials with dissimilar electron affinities and ionization potentials. The electrical behavior of such devices has been successfully modeled numerically using conventional drift diffusion together with recombination (which is usually assumed to be bimolecular) and thermal generation. Here a particular model is considered and the dark current-voltage curve and the spatial structure of the solution across the device is extracted analytically using asymptotic methods. We concentrate on the case of Shockley-Read-Hall recombination but note the extension to other recombination mechanisms. We find that there are three regimes of behavior, dependent on the total current. For small currents-i.e., at reverse bias or moderate forward bias-the structure of the solution is independent of the total current. For large currents-i.e., at strong forward bias-the current varies linearly with the voltage and is primarily controlled by drift of charges in the organic layers. There is then a narrow range of currents where the behavior undergoes a transition between the two regimes. The magnitude of the parameter that quantifies the interfacial recombination rate is critical in determining where the transition occurs. The extension of the theory to organic solar cells generating current under illumination is discussed as is the analogous current-voltage curves derived where the photo current is small. Finally, by comparing the analytic results to real experimental data, we show how the model parameters can be extracted from the shape of current-voltage curves measured in the dark. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Richardson G, Please C, Foster J, Kirkpatrick J (2012) Asymptotic Solution of a Model for Bilayer Organic Diodes and Solar Cells. SIAM Journal on Applied Mathematics 72: 1792–1817. Available: http://dx.doi.org/10.1137/110825807.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
15-Nov-2012
DOI:
10.1137/110825807
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
The second author’s work was supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology, and by the EPSRC through grant EP/I01702X/1. The first and third authors’ work was supported by the EPSRC through grant EP/I01702X/1. This author’s work was supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology, and a James Martin fellowship.
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Full metadata record

DC FieldValue Language
dc.contributor.authorRichardson, Gilesen
dc.contributor.authorPlease, Colinen
dc.contributor.authorFoster, Jamieen
dc.contributor.authorKirkpatrick, Jamesen
dc.date.accessioned2016-02-25T12:43:15Zen
dc.date.available2016-02-25T12:43:15Zen
dc.date.issued2012-11-15en
dc.identifier.citationRichardson G, Please C, Foster J, Kirkpatrick J (2012) Asymptotic Solution of a Model for Bilayer Organic Diodes and Solar Cells. SIAM Journal on Applied Mathematics 72: 1792–1817. Available: http://dx.doi.org/10.1137/110825807.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/110825807en
dc.identifier.urihttp://hdl.handle.net/10754/597624en
dc.description.abstractOrganic diodes and solar cells are constructed by placing together two organic semiconducting materials with dissimilar electron affinities and ionization potentials. The electrical behavior of such devices has been successfully modeled numerically using conventional drift diffusion together with recombination (which is usually assumed to be bimolecular) and thermal generation. Here a particular model is considered and the dark current-voltage curve and the spatial structure of the solution across the device is extracted analytically using asymptotic methods. We concentrate on the case of Shockley-Read-Hall recombination but note the extension to other recombination mechanisms. We find that there are three regimes of behavior, dependent on the total current. For small currents-i.e., at reverse bias or moderate forward bias-the structure of the solution is independent of the total current. For large currents-i.e., at strong forward bias-the current varies linearly with the voltage and is primarily controlled by drift of charges in the organic layers. There is then a narrow range of currents where the behavior undergoes a transition between the two regimes. The magnitude of the parameter that quantifies the interfacial recombination rate is critical in determining where the transition occurs. The extension of the theory to organic solar cells generating current under illumination is discussed as is the analogous current-voltage curves derived where the photo current is small. Finally, by comparing the analytic results to real experimental data, we show how the model parameters can be extracted from the shape of current-voltage curves measured in the dark. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThe second author’s work was supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology, and by the EPSRC through grant EP/I01702X/1. The first and third authors’ work was supported by the EPSRC through grant EP/I01702X/1. This author’s work was supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology, and a James Martin fellowship.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAsymptotic analysisen
dc.subjectDrift diffusionen
dc.subjectPhotovoltaicen
dc.subjectShockley modelen
dc.titleAsymptotic Solution of a Model for Bilayer Organic Diodes and Solar Cellsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionUniversity of Southampton, Southampton, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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