Perovskite solar cells (PSCs) have attracted the interest of the scientific community in the last few years due to their high performance produced by interesting physical effects and low cost solutions. In spite of the spectacular advances in cell efficiency, many aspects of this system are poorly understood. One interesting phenomenon is the hysteresis response observed in current-voltage curves upon illumination. Recently, the origin of these hysteresis cycles has been associated to capacitive effects and the movement of ions [1], pointed that the transport in perovskite is a mixed ionic-electronic conduction. The movement of ions can be assisted by anion and cation vacancies. First-principle studies in MAIPb prevskites have shown that the most diffusive species is the iodide anion [2]. In the literature, the movement of ions is modeled in different ways. In some cases, anions and cations are considered to move at the same time [3]. Other works consider only the movement of iodide cation vacancies [2]. The nature of semiconductor is also modeled differently. Some authors assume the perovskite to be intrinsic [2], [3]. Others question the intrinsic nature of the perovskite semiconductor. All these questions can be solved with the comparison between experiments and the simulation of the PSCs. 

In this work, we have systematically analyzed the effect of the distribution of mobile ions and their vacancies on p-type, n-type, or intrinsic PSCs under illumination by means of the drift-diffusion transport equations. They include ion charges at the bulk and at the perovskite/electrode interfaces. We study the profiles of the ion, electron and hole densities, at different applied voltages. In particular, the analysis is focused on the short-circuit and open-circuit regimes of the solar cell. We distinguish between the movement of single and both type of ions. The distribution of mobile ions modifies the band bending in the bulk and close to the perovskite-metal interfaces. Different distributions of mobile ions appear in the cases under study. In general they act as if the doping of the semiconductor is changed. However, not all of them produce an accumulation of free charge carriers at the interfaces which can be the origin of the hysteresis phenomena observed in experiments [4].

[1]. B. Chen et al. J. Phys. Chem. Lett. 2015, 6, 4693-47002.

[2]. P. Calado et al. Nature Comunications, 2016, 7, 138313.

[3]. S. Reenen et al. J. Phys. Chem. Lett. 2015, 6, 3808-38144.

[4]. R. Gottesman et al. Chem, 1, 776-789 (2016)