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Systematic derivation of a surface polarisation model for planar perovskite solar cells

Published online by Cambridge University Press:  22 April 2018

N. E. COURTIER ,
J. M. FOSTER ,
S. E. J. O'KANE ,
A. B. WALKER  and
G. RICHARDSON
N. E. COURTIER
Affiliation:
Mathematical Sciences, University of Southampton, SO17 1BJ, UK emails: nc4g14@soton.ac.uk, G.Richardson@soton.ac.uk
J. M. FOSTER
Affiliation:
Department of Mathematics, University of Portsmouth, PO1 3HF, UK email: jamie.michael.foster@gmail.com
S. E. J. O'KANE
Affiliation:
Department of Physics, University of Bath, BA2 7AY, UK emails: A.B.Walker@bath.ac.uk, S.E.J.O'Kane@bath.ac.uk
A. B. WALKER
Affiliation:
Department of Physics, University of Bath, BA2 7AY, UK emails: A.B.Walker@bath.ac.uk, S.E.J.O'Kane@bath.ac.uk
G. RICHARDSON
Affiliation:
Mathematical Sciences, University of Southampton, SO17 1BJ, UK emails: nc4g14@soton.ac.uk, G.Richardson@soton.ac.uk
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Abstract

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Increasing evidence suggests that the presence of mobile ions in perovskite solar cells (PSCs) can cause a current–voltage curve hysteresis. Steady state and transient current–voltage characteristics of a planar metal halide CH3NH3PbI3 PSC are analysed with a drift-diffusion model that accounts for both charge transport and ion vacancy motion. The high ion vacancy density within the perovskite layer gives rise to narrow Debye layers (typical width ~2 nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer (~600 nm) and (II) the ion vacancy density and the charge carrier densities motivate an asymptotic approach to solving the model, while the stiffness of the equations renders standard solution methods unreliable. We derive a simplified surface polarisation model in which the slow ion dynamics are replaced by interfacial (non-linear) capacitances at the perovskite interfaces. Favourable comparison is made between the results of the asymptotic approach and numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.

Keywords

perovskitesolar cellion vacancydrift-diffusionasymptotic analysis

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 3 , June 2019 , pp. 427 - 457
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2018

Footnotes

NEC is supported by an EPSRC funded studentship from the CDT in New and Sustainable Photovoltaics. SEJO'K was supported by EPSRC grant EP/J017361/1. ABW acknowledges funding from the European Union Horizon 2020 research and innovation programme under Grant no. 676629.

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