Time-Dependent Drift-Diffusion Modelling of Perovskite Solar Cells with Moving Ions

Alison Walker^a, Timo Peltola^a, Simon O'Kane^a, Jamie Foster^b, Giles Richardson^b

^aUniversity of Bath, Department of Physics, Claverton Down, Bath BA2 7AY, United Kingdom

^bDepartment of Mathematical Sciences, University of Southampton, University of Southampton, Southampton, SO17 1BJ, United Kingdom

International Conference on Hybrid and Organic Photovoltaics
Proceedings of International Conference on Hybrid and Organic Photovoltaics 2015 (HOPV15)

Roma, Italy, 2015 May 11th - 13th

Organizer: Filippo De Angelis

Oral, Simon O'Kane, presentation 053
Publication date: 5th February 2015

The presence of mobile ions within the bulk methylammonium lead tri-iodide (CH₃NH₃PbI₃) active layer of perovskite solar cells has been suggested as a possible cause of the hysteresis [1,2] observed in these devices. Impedance spectroscopy measurements point towards the existence of mobile ions [3]. Drift-diffusion models provide a possible mechanism for testing this hypothesis. In previous work, the steady-state drift-diffusion model of Foster et al. [4] was adapted to create a “frozen ion” model that predicted hysteresis, although the predicted forward and reverse current-voltage curves intersect, which is not observed in measurements (see attached figure). The assumption of Shockley-Read-Hall recombination was found to be the cause of both the hysteresis and the intersection. In this work, the time-dependent drift-diffusion model of Foster et al. [4] is adapted to also include drift-diffusion equations for mobile ions. Using this improved model, the possible effects of moving ions are explored and compared with hysteresis measurements reported in the literature [1,2].
Current-voltage curves simulated using a ‘frozen ion’ steady-state model, where the ionic charge density is assumed to take the form of a hyperbolic sine distribution with opposite directions corresponding to the forward and reverse scans. The dotted line is the current-voltage curve obtained with zero ionic charge.
[1] Henry Snaith et al., J. Phys. Chem. Lett., vol. 5, no. 9, pp. 1511-1515, March 2014 [2] Rafael Sanchez et al., J. Phys. Chem. Lett., vol. 5, no. 13, pp. 2357-2363, June 2014 [3] Adam Pockett et al., J. Phys. Chem. C, in press, early 2015 [4] Jamie Foster et al., SIAM J. Appl. Math., vol. 74, no. 6, pp. 1935-1966, Dec. 2014

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