  A dynamic electrical model is introduced to investigate the hysteretic
effects in the I-V characteristics of perovskite based solar cells. By making a
simple ansatz for the polarization relaxation, our model is able to reproduce
qualitatively and quantitatively detailed features of measured I-V
characteristics. Pre-poling effects are discussed, pointing out the differences
between initially over- and under-polarized samples. In particular, the
presence of the current over-shoot observed in the reverse characteristics is
correlated with the solar cell pre-conditioning. Furthermore, the dynamic
hysteresis is analyzed with respect to changing the bias scan rate, the
obtained results being consistent with experimentally reported data: the
hysteresis amplitude is maximum at intermediate scan rates, while at very slow
and very fast ones it becomes negligible. The effects induced by different
relaxation time scales are assessed. The proposed dynamic electrical model
offers a comprehensive view of the solar cell operation, being a practical tool
for future calibration of tentative microscopic descriptions.
