Surface Polarization Model for the Dynamic Hysteresis of Perovskite Solar Cells

Abstract

The dynamic hysteresis of perovskite solar cells consists of the occurrence of significant deviations of the current density-voltage curve shapes depending on the specific conditions of measurement such as starting voltage, waiting time, scan rate, and other factors. Dynamic hysteresis is a serious impediment to stabilized and reliable measurement and operation of the perovskite solar cells. In this Letter, we formulate a model for the dynamic hysteresis based on the idea that the cell accumulates a huge quantity of surface electronic charge at forward bias that is released on voltage sweeping, causing extra current over the normal response. The charge shows a retarded dynamics due to the slow relaxation of the accompanying ionic charge, that produces variable shapes depending on scan rate or poling value and time. We show that the quantitative model provides a consistent description of experimental results and allows us to determine significant parameters of the perovskite solar cell for both the transient and steady-state performance.

Normal and Inverted Hysteresis in Perovskite Solar Cells

“…Both versions of DEM consistently reproduced experimental NH, including the dependence on the bias scan rate and the current overshoot in the reverse scan observed in several experimental studies [5,18,32], reproduced only in part by drift-diffusion based models [28]. The overshoot is consistent with a relaxation time of the polarization or charge accumulated at interfaces [30,31] at the beginning of the reverse scan measurement, indicating a relation between the pre-poling bias and the initial polarization. Furthermore, the dependence of the hysteresis on the bias scan rate is consistently described by the DEM: the hysteresis is diminished at very low and very high bias scan rates, being significant at intermediate ones; importantly, the short circuit current is enhanced with the increase of the bias scan rate.…”

“…On the other hand, the crossing was observed experimentally [26] on aged samples with Ag counter electrodes, using a forward-reverse scan protocol starting from -0.1 V, which may be the effect of a small negative bias pre-poling, although not intentionally performed. The crossing of separately measured forward and reverse characteristics was also observed [31].…”

“…al. [31] in terms of a relaxation kinetic constant determined by ion displacement, by reformulating Eq. (2) for the surface polarization voltage [Eq.…”

Interfacial Kinetics of Efficient Perovskite Solar Cells

“…Recent studies have shown that the accumulation of the ions and vacancies at interfaces changes the interfacial charge concentration and recombination rates, as well as the net photovoltage by setting up an electrostatic potential in addition to the built-in potential [23][24][25]. Since the electrostatic and built-in potentials have the same polarity (backward scan), the net open circuit voltage (VOC) of PSC devices is the sum of these potentials [24,26]. A generalized single diode model of a PSC, including the built-in and electrostatic potential formed due to the accumulation of ions and charges, is placed in a model previously discussed by Gottesman and others (Figure 1b) [24,26,27].…”

The Influence of the Relaxation Time on the Dynamic Hysteresis in Perovskite Solar Cells

“…(2), which describes the time evolution of P nl using a single relaxation time τ. A condition of the same type was used for the surface polarization voltage in the model proposed by Ravishankar et al [6], where it was conjectured that the cation migration together with an accumulation of holes is responsible for the hysteretic effects. According to Eq.…”