Deducing transport properties of mobile vacancies from perovskite solar cell characteristics

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 N₀ 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 MAPbI₃ (MAPI) where MA is methylammonium, CH₃NH₃, 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 TiO₂ or SnO₂. For the third and fourth structures, the perovskite layer is FAPbI₃ (FAPI) where FA is formamidinium, HC(NH₂)₂, or MAPbBr₃ (MAPBr) and in both cases the HTL is spiro and the ETL is SnO₂. 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, N₀ and parameters determining free charge recombination.