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

TL;DR

This paper develops a simplified surface polarization model for planar perovskite solar cells by asymptotically analyzing the drift-diffusion equations, capturing ion-induced effects and hysteresis phenomena.

Contribution

It introduces a novel asymptotic derivation of a surface polarization model that replaces slow ion dynamics with interfacial capacitances, simplifying analysis of perovskite solar cells.

Findings

The model accurately reproduces numerical solutions across various conditions.

Large Debye layers store significant charge near interfaces.

The approach effectively captures hysteresis effects in current-voltage curves.

Abstract

Increasing evidence suggests that the presence of mobile ions in perovskite solar cells can cause a current-voltage curve hysteresis. Steady state and transient current-voltage characteristics of a planar metal halide CH$_3$NH$_3$PbI$_3$ perovskite solar cell 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 $\sim$2nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer ($\sim$600nm) 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 dynamic are replaced by interfacial (nonlinear) 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.