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

• Published in: European journal of applied mathematics Vol. 30; no. 3; pp. 427 - 457
• Main Authors: COURTIER, N. E., FOSTER, J. M., O'KANE, S. E. J., WALKER, A. B., RICHARDSON, G.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.06.2019
• Subjects: Applied mathematics; Asymptotic properties; Carrier density; Charge density; Charge transport; Current carriers; Current voltage characteristics; Ion dynamics; Metal halides; Perovskites; Photovoltaic cells; Polarization; Simplified surfaces; Solar cells; Stiffness; Transient current; Vacancies; asymptotic analysis; drift-diffusion; perovskite; ion vacancy; solar cell
• ISSN: 0956-7925; 1469-4425
• DOI: 10.1017/S0956792518000207

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.