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Derivation and solution of effective medium equations for bulk heterojunction organic solar cells

Published online by Cambridge University Press:  10 January 2017

G. RICHARDSON ,
C. P. PLEASE  and
V. STYLES
G. RICHARDSON
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK email: [email protected]
C. P. PLEASE
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK email: [email protected]
V. STYLES
Affiliation:
Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK email: [email protected]
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Abstract

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A drift-diffusion model for charge transport in an organic bulk heterojunction solar cell, formed by conjoined acceptor and donor materials sandwiched between two electrodes, is formulated. The model accounts for (i) bulk photogeneration of excitons, (ii) exciton drift and recombination, (iii) exciton dissociation (into polarons) on the acceptor–donor interface, (iv) polaron recombination, (v) polaron dissociation into a free electron (in the acceptor) and a hole (in the donor), (vi) electron/hole transport and (vii) electron–hole recombination on the acceptor–donor interface. A finite element method is employed to solve the model in a cell with a highly convoluted acceptor/donor interface. The solutions show that, with physically realistic parameters, and in the power generating regime, the solution varies little on the scale of the micro-structure. This motivates us to homogenise over the micro-structure; a process that yields a far simpler one-dimensional effective medium model on the cell scale. The comparison between the solution of the full model and the effective medium (homogenised) model is very favourable for applied voltages less than the built-in voltage (the power generating regime) but breaks down as the applied voltages increases above it. Furthermore, it is noted that the homogenisation technique provides a systematic way to relate effective medium modelling of bulk heterojunctions [19, 25, 36, 37, 42, 59] to a more fundamental approach that explicitly models the full micro-structure [8, 38, 39, 58] and that it allows the parameters in the effective medium model to be derived in terms of the geometry of the micro-structure. Finally, the effective medium model is used to investigate the effects of modifying the micro-structure geometry, of a device with an interdigitated acceptor/donor interface, on its current–voltage curve.

Keywords

Shockley modeldrift diffusionasymptotic analysisphotovoltaichomogenisation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Special Issue 6: Big Data and Partial Differential Equations , December 2017 , pp. 973 - 1014
Copyright
Copyright © Cambridge University Press 2017 

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