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

Systematic derivation of a surface polarisation model for planar perovskite solar cells
Systematic derivation of a surface polarisation model for planar perovskite solar cells
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.
perovskite, solar cell, ion vacancy, drift-diffusion, asymptotic analysis
0956-7925
1-31
Courtier, Nicola, Elizabeth
9c4e0fa1-e239-4a4b-aa70-af65f8b0a524
Foster, Jamie M.
7cf00fd5-1568-4021-b15f-7e6aeb7cce2f
O'Kane, Simon
e438f569-9deb-4da8-8bb3-685d4d15e376
Walker, Alison
4d255ac5-1772-4562-b116-b7e6608123d9
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Courtier, Nicola, Elizabeth
9c4e0fa1-e239-4a4b-aa70-af65f8b0a524
Foster, Jamie M.
7cf00fd5-1568-4021-b15f-7e6aeb7cce2f
O'Kane, Simon
e438f569-9deb-4da8-8bb3-685d4d15e376
Walker, Alison
4d255ac5-1772-4562-b116-b7e6608123d9
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91

Courtier, Nicola, Elizabeth, Foster, Jamie M., O'Kane, Simon, Walker, Alison and Richardson, Giles (2018) Systematic derivation of a surface polarisation model for planar perovskite solar cells. European Journal of Applied Mathematics, 1-31. (doi:10.1017/S0956792518000207).

Record type: Article

Abstract

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.

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Accepted/In Press date: 24 March 2018
e-pub ahead of print date: 22 April 2018
Keywords: perovskite, solar cell, ion vacancy, drift-diffusion, asymptotic analysis

Identifiers

Local EPrints ID: 420085
URI: https://eprints.soton.ac.uk/id/eprint/420085
ISSN: 0956-7925
PURE UUID: 6c3743e5-4732-447c-afd2-b3aa86985a4f

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Date deposited: 26 Apr 2018 16:30
Last modified: 23 Sep 2019 17:01

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