Deducing transport properties of mobile vacancies from perovskite solar cell characteristics

Abstract

The absorber layers in perovskite solar cells possess a high concentration of mobile ion vacancies. These vacancies undertake thermally activated hops between neighbouring lattice sites. The mobile vacancy concentration N 0 is much higher and the activation energy E A for ion hops is much lower than is seen in most other semiconductors due to the inherent softness of perovskite materials. The timescale at which the internal electric field changes due to ion motion is determined by the vacancy diffusion coefficient D v and is similar to the timescale on which the external bias changes by a significant fraction of the open circuit voltage at typical scan rates. Therefore hysteresis is often observed in which the shape of the current-voltage, J-V, characteristic depends on the direction of the voltage sweep. There is also evidence that this defect motion plays a role in degradation. By employing a charge transport model of coupled ion-electron conduction in a perovskite solar cell, we show that E A for the ion species responsible for hysteresis can be obtained directly from measurements of the temperature variation of the scan-rate dependence of short-circuit current and of the hysteresis factor H. This argument is validated by comparing E A deduced from measured J-V curves for four solar cell structures with density functional theory calculations. In two of these structures the perovskite is MAPbI 3 (MAPI) where MA is methylammonium, CH 3 NH 3 , the hole transport layer (HTL) is spiro (spiro-OMeTAD, 2,2',7,7'tetrakis[N,N-di(4-methoxyphenyl) amino]-9,9'-spirobifluorene) and the electron transport layer (ETL) is TiO 2 or SnO 2 . For the third and fourth structures, the perovskite layer is FAPbI 3 (FAPI) where FA is formamidinium, HC(NH 2 ) 2 , or MAPbBr 3 (MAPBr) and in both cases the HTL is spiro and the ETL is SnO 2 . For all four structures, the hole and electron extracting electrodes are Au and FTO (fluorine doped tin oxide) respectively. We also use our model to predict how the scan rate dependence of the power conversion efficiency varies with E A , N 0 and parameters determining free charge recombination.

Quantification of Efficiency Losses Due to Mobile Ions in Perovskite Solar Cells via Fast Hysteresis Measurements

“…Motivated by the successful reproduction of experimental observation by the simulations, we varied the ion density (Figure 1d) and diffusion coefficient (Figure 1e) to study the effect on the JV curves and the PCE difference between the forward and reverse scan. As discovered earlier by others, [ 44 ] we see that the hysteresis is absent at fast and slow scan speeds. Moreover, the timescale at which the maximum JV hysteresis (which we call “peak hysteresis”) occurs, appears to depend primarily on the ion diffusion coefficient (the larger D ion the higher the scan speed to resolve the maximum hysteresis) and to a lesser degree on the ion density.…”

“…The results demonstrate a maximum amplitude of the hysteresis at scan speeds of 10 V s −1 (or 100 ms per scan), while the hysteresis is absent at lower and significantly higher scan speeds. [ 44 ] As we will demonstrate in detail in this manuscript, the PCE at the fastest scan speeds is approximately equal to the PCE in the absence of mobile ions. Hence, one can use the point at high scan speeds where the forward and reverse scan merge again to estimate the “ion‐free” PCE and the difference between the steady‐state PCE (i.e., at low scan speed) and the fast scan to determine the losses due to the mobile ions.…”

“…[28,29,35,37,42] In addition, numerical simulations have shown that the influence of ions on the performance does not only depend on their density but also on the physical properties of the perovskite and the transport layers, i.e., the dielectric constant, doping density, as well as on the recombination processes and the device built-in voltage (V BI ). [2,43,44] Therefore, even if the diffusion coefficient and ion density were to be measured precisely, there is currently no easy method to know how much they influence the performance of the solar cells.…”

Effect of Ion Vacancy Migration on Open‐Circuit Voltage of Perovskite Solar Cells

“…In contrast, a lower scan rate can provide more time for ion vacancies to migrate. [36] This explains the downward shift of the rapid changing region with increasing E a .…”

Influences of dielectric constant and scan rate on hysteresis effect in perovskite solar cell with simulation and experimental analyses

“…Recent modeling studies on PSC devices have mainly focused on (1) the mechanism of ion accumulation, (2) how ion accumulation affects hysteresis, and (3) the effects of different factors of perovskite on hysteresis 23 , 23 – 27 . To simplify the model, some assumptions have been made about the transport layer of carrier injection with heavily acceptor/donor doping in previous works 28 – 33 . However, existing doping techniques cannot be applied in the organic transport layer, and some studies have shown that the organic material is an essential factor in the hysteresis behavior 34 .…”