On the Insight Provided by Asymptotic Analysis in Perovskite Solar Cell Modelling #

Will Clarke, Giles Richardson

12:10 Monday in 4Q07.

Part of the Mathematics of energy session.

Abstract #

Perovskite solar cells (PSCs) are an exciting new green energy technology that first emerged in 2012. They have since experienced an unprecedented rise in efficiency and are now comparable to the leading commercial technology (silicon solar cells). Furthermore, silicon-perovskite tandem cells now exceed 30% efficiency, surpassing records for both technologies separately, and are one of the most promising candidates in the quest for cheap and large-scale solar energy production as governments aim to slash carbon emissions in the years to come. Throughout their development, PSCs have perplexed the photovoltaic community, with standard characterisation methods often rendered useless by the appearance of long-timescale current transients on the order of seconds to minutes. Since their inception, therefore, significant modelling efforts have accompanied the experimental breakthroughs and have been used to investigate the underlying physics of these devices. The first significant modelling triumph was the identification of slow ion migration in the perovskite material as the cause of the long-lived transients. Since then, the exact nature of the ionic migration and its possible impact on characterisation measurements and cell efficiency has been hotly debated. A perovskite solar cell can be modelled by a three-layer mixed ionic-electronic drift-diffusion model. This comprises a large system of highly nonlinear PDEs. Many groups have tackled this problem directly by employing numerical methods, tailored for the significant spatial and temporal stiffness in the model. However, the large number of material parameters in the model results in a high-dimensional parameter space which, coupled to the complexity of the model, renders meaningful interpretation problematic. Progress has, however, also been made by adopting an approach based on formal asymptotic methods. In particular, major breakthroughs in the physical understanding of these devices, through a combined experimental and numerical approach, have been accompanied by asymptotic results that have provided the clarity and insight often lacking from the numerical studies. In summary, whilst numerical methods dominate applied mathematical modelling, due to the power of modern computers, matched asymptotic analysis still has a significant role to play as illustrated by its effectiveness in aiding the development of this exciting new renewable energy technology.