J =  J  exp     qV

− 1 − 1 − J_ph,                                               (2)

where J_s is the saturation current density (A·cm−2, where the

Figure 6. PSC J−V curve in both bias scan directions (50 mV·s−1) under 100

area is that of the electrodes); q is the elementary charge; k_BT is the thermal voltage, m is the dimensionless diode ideality factor; and J_ph is the photocurrent (A·cm−2, where the area is the light-absorbing). Each one of these parameters, in addition to others not included in equation 1 (e.g. series and shunt resistances), describes different mechanisms whose analysis constitutes a powerful tool for understanding the complete device.

Typically, for obtaining the experimental patterns that equation 2 describes -and hence calculate PCE via equation 1- a bias is applied across the device terminals sweeping the proper voltage range while current through an external circuit is been measured in the steady-state power output condition. However, it seems that such steady-state power output condition is not so easy to hold for MAPbI₃-based solar cells.

As described in the early work by Snaith and co-workers [158], the hysteresis phenomenon consists in the appearance of different J − V curves depending on the scan direction and rate at which the bias is swept. For instance, as in Figure 6, we can label FR (forward to reverse) to the scan direction from open circuit to short-circuit and RF (reverse to forward) to the opposite bias sweep. In that convention it is apparent that the maxim output power when FR is larger than the corresponding in RF, as illustrated with the corresponding squares P_maxRF < P_maxFR in Figure 6. Consequently, the reliability of the efficiency reports is not warrantied. Among the subsequent important contributions to the phenomenon description, Unger and co-workers [159] concluded that measurement delay time, and light and voltage bias conditions prior to measurement can all have a significant impact upon the shape of the measured J − V curve, and by utilizing alternative selective contacts found that the contact interfaces have a big effect on transients in MAPbI₃-absorber devices. More successive descriptions and typical behaviors were reported, as nicely mW·cm−2 (AM1.5G) of illumination. The red (blue) gray square illustrates the corresponding maximum output power for the RF (FR) bias scan direction.

The absolute current in the range between open circuit and short-circuit is often large when FR than when RF.

 

Regarding the clarifications for the hysteresis, Snaith and co-workers [158] first proposed three possible explanations: (i) filling and emptying of trap states, (ii) migration of excess ions, as interstitial defects (iodide or methylammonium), and/or (iii) ferroelectric effect. Accordingly, a lot of research contributed, and attempt to contribute yet, with evidence supporting one or another issue. However, at this point the most general criteria agreed in the cooperative confluence of dynamic and complex interactions between (i) electronic trapping and (ii) ionic mechanisms, leaving the (iii) ferroelectric effect as a possibly negligible factor.

Yet, favouring the ferroelectric behaviour, for example, Chen et al. [163] affirmed that the greater magnitude of hysteresis in the case of a planar heterojunction and Al₂O₃ scaffolds in comparison to mesoporous TiO₂ structures indicates the significance of the bulk property of perovskites rich in ferroelectric domains as an origin of hysteresis. A theoretical support to this hypothesis was afforded by Frost et al. [164,165] through ab initio molecular dynamics numerical simulations and also by Wei et al. [166] that interpreted the scan range and rate dependency as it is well explained by the ferroelectric diode model.

Other of those milestones worthy of mention in this race for the truth behind hysteresis, is Kim & Park’s suggestion [167] that the origin of hysteresis is due to the characteristic capacitance C of MAPbI₃ by correlating the amount of hysteresis with the size of perovskite and mesoporous TiO₂ layers thickness. In other direction, Sanchez et al. [168] showed that the hysteresis is enhanced at high sweep rates (scan velocity dV/dt ), and hence it could be a capacitive current effect:

summarized by Ravishankar et al. [160]. Still without J

the proper understanding of the mechanisms behind this phenomenon, a first necessary step was to suggest special

cap =

dt = C dt ,                                                                          (3)

measurement protocols for avoiding unfeasible PCE reports. About this latter issue, the works by Kamat and co-workers

[161] and Schmidt-Mende and co-workers [162] are of utmost significance.

which is a widely recognized feature in liquid electrolyte dye solar cells (DSCs). Importantly, as in equation 3, J_cap can be negative or positive depending on the charging or discharging given by the bias scan direction. In addition,

Almora et al. [169, 170] studied the J_cap capacitive trend, but in dark conditions, linking the hysteretic behaviour with the capacitance excess observed at low frequencies, that correlated with ionic electrode polarization (see Figure 7). In addition, they checked the charging response of thick MAPbI₃ pellets revealing an interfacial double layer electrical structure formed by mobile ions at non-interacting Au contacts [171].