Electrical Instability
Anomalous Hysteresis
Hysteresis is simply the dependency of a state of a system on its history. For elastic bands, a hysteresis curve can be seen from its force against extensions plot, as seen in Fig. 1. Here, the relationship between the extension of the band and the force applied to it is effected by whether a load is being applied to the band, or if one is being taken off. In the case of perovskite solar cell, this hysteresis effect is seen from the current-voltage plots. Depending on the bias direction, (whether or not the current-voltage sweep is being measured from forward to reverse bias or the other way round), different measurements are obtained in measuring efficiencies. Moreover, the scan rate of the measurements seemingly has an effect on the observed hysteresis for the device, with a slower scan rate achieving a lesser hysteresis effect. Whilst not inherently degrading the solar cell, this phenomenon leads to complications in regards to the potential applications of perovskite solar cells. During real operating conditions, the maximum power point will vary throughout the day, as a results a precise measurement into the efficiencies of the performing cell will be unknown. In order to address this issue, the precise origins of the hysteresis effect within perovskite solar cells need to be understood, and what this can tell us about the electrical properties of the material.
Ferroelectric Contributions
A possible explination to the observed hysteresis effect may be in the ferroelectric properties of perovskites. Ferroelectrics are materails capable of sustaining a permanent magnetic diople, in the absence of an external magnetic field. Furthermore, the direction of polarization in ferromagnetic materials can be switched, with an applied mangetic field.
Although the precise origin of ferroelectricity within perovskites is not completely known, it is likely to result from the structural properties of its lattice; due to rotaion and disorder. The tolerance factor, t, is a relatively simple however evidently useful equation used to demonstrate this phenomenon. Relating a compounds structual properites in relation to its stability, the Goldsmidt tolerance factor is given by;
t
where this = this etc.
We see that when t > 1, the A-O bond sites are underbonded, and as a result there is a roatation of the octahedral cage of the perovskite structure, throughout its lattice. Likewise, when t < 1, the B-O bond sites are underbonding, which leads to the movement of the cation within the cage in order to compensate. It is to be noted that when t = 1, corrosponds to the structure that exhibits stability with a pefectly cubic structure.
From the experimental evidenece collected so far ref ref ref, we see that not only do almost all peroskites follow this trend predeiceted by the tolerance factor, but almost all with a tolerance factor less than one are ferromagnetic, whilst almost all with one greater than one not. It is evident to see that the ferroelectric properties and the roation of the octahedra cage seemingly compete with, and surpress eachother, whilst the movement of the cation within the cage creates a polar moment, contributing the the ferroelectricity.