Modeling Film Conductivity for Ion Migration Analysis in Perovskite Solar Cells

Ion migration under stress is a major degradation challenge for commercialization of perovskite solar cells. This paper presents three different approaches to model the conductivity variation in perovskite films at elevated temperature, prolonged irradiation levels and strain induced in the lattice. The conductivity variation under any of these stressing conditions can represent ion migration across the perovskite layer because the conductivity is related to mobility and carrier densities. Ion migration can elevate the density of electrons/holes across the film if the stress condition reduce/lift the activation energy at the interface of the film and smoothens the ion passivation to the perovskite layer. In addition, the conductivity of the film is related to device metrics (e.g. fill factor) and also to materials properties (e.g. mobility and bandgap) and, therefore, it can be a significant measure of stress impact on device stability. For example, the conductivity falls under stress which represents the ion migration enhancement. In our modeling, we have shown that the conductivity is inversely related to temperature and strain (sigma proportional to 1/kT, sigma proportional to 1/epsilon) but is directly related to irradiation level (sigma proportional to xi(1/2)). We have fitted our modeling to experimental data reported in the literature and extracted the activation energy of ion migration mechanism under every stress condition. The band diagrams of the mechanism are presented and it is shown that stress can foster the ion migration by reducing the activation energy at the interfaces of the perovskite layer. However, the impact of heating is worse on film conductivity, whereas irradiation and strain have a moderate or slight effect on it, respectively. Our findings may provide a practical solution to obtain a measure of ion migration in perovskite solar cells for aging analysis of the cell stability and recovery rates under different stressing conditions.