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A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells

A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells
A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells
Drift-diffusion models that account for the motion of ion vacancies and electronic charge carriers are important tools for explaining the behaviour, and guiding the development, of metal halide perovskite solar cells. Computing numerical solutions to such models in realistic parameter regimes, where the short Debye lengths give rise to boundary layers in which the solution varies extremely rapidly, is challenging. Two suitable numerical methods, that can effectively cope with the spatial stiffness inherent to such problems, are presented and contrasted (a finite element scheme and a finite difference scheme). Both schemes are based on an appropriate choice of non-uniform spatial grid that allows the solution to be computed accurately in the boundary layers. An adaptive time step is employed in order to combat a second source of stiffness, due to the disparity in timescales between the motion of the ion vacancies and electronic charge carriers. It is found that the finite element scheme provides significantly higher accuracy, in a given compute time, than both the finite difference scheme and some previously used alternatives (Chebfun and pdepe). An example transient sweep of a current-voltage curve for realistic parameter values can be computed using this finite element scheme in only a few seconds on a standard desktop computer.
Perovskite solar cell; ion vacancy; drift-diffusion; finite element; finite difference; stiffness
0307-904X
329-348
Courtier, Nicola, Elizabeth
9c4e0fa1-e239-4a4b-aa70-af65f8b0a524
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Foster, Jamie M.
b93acb2c-f981-4d4b-bc01-b1bc8332facf
Courtier, Nicola, Elizabeth
9c4e0fa1-e239-4a4b-aa70-af65f8b0a524
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Foster, Jamie M.
b93acb2c-f981-4d4b-bc01-b1bc8332facf

Courtier, Nicola, Elizabeth, Richardson, Giles and Foster, Jamie M. (2018) A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells. Applied Mathematical Modelling, 63, 329-348. (doi:10.1016/j.apm.2018.06.051).

Record type: Article

Abstract

Drift-diffusion models that account for the motion of ion vacancies and electronic charge carriers are important tools for explaining the behaviour, and guiding the development, of metal halide perovskite solar cells. Computing numerical solutions to such models in realistic parameter regimes, where the short Debye lengths give rise to boundary layers in which the solution varies extremely rapidly, is challenging. Two suitable numerical methods, that can effectively cope with the spatial stiffness inherent to such problems, are presented and contrasted (a finite element scheme and a finite difference scheme). Both schemes are based on an appropriate choice of non-uniform spatial grid that allows the solution to be computed accurately in the boundary layers. An adaptive time step is employed in order to combat a second source of stiffness, due to the disparity in timescales between the motion of the ion vacancies and electronic charge carriers. It is found that the finite element scheme provides significantly higher accuracy, in a given compute time, than both the finite difference scheme and some previously used alternatives (Chebfun and pdepe). An example transient sweep of a current-voltage curve for realistic parameter values can be computed using this finite element scheme in only a few seconds on a standard desktop computer.

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courtier_num_18_accepted - Accepted Manuscript
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More information

Accepted/In Press date: 25 June 2018
e-pub ahead of print date: 3 July 2018
Published date: November 2018
Keywords: Perovskite solar cell; ion vacancy; drift-diffusion; finite element; finite difference; stiffness

Identifiers

Local EPrints ID: 422209
URI: https://eprints.soton.ac.uk/id/eprint/422209
ISSN: 0307-904X
PURE UUID: 3186dd2c-710e-468d-8d08-638abfbb6447

Catalogue record

Date deposited: 18 Jul 2018 16:31
Last modified: 13 Mar 2019 18:19

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