Bayesian parameter estimation for characterising mobile ion vacancies in perovskite solar cells

To overcome the challenges associated with poor temporal stability of perovskite solar cells, methods are required that allow for fast iteration of fabrication and characterisation, such that optimal device performance and stability may be actively pursued. Currently, establishing the causes of underperformance is both complex and time-consuming, and optimisation of device fabrication thus inherently slow. Here, we present a means of computational device characterisation of mobile halide ion parameters from room temperature current-voltage (J-V) measurements only, requiring $\sim 2$ hours of computation on basic computing resources. With our approach, the physical parameters of the device may be reverse modelled from experimental J-V measurements. In a drift-diffusion model, the set of coupled drift-diffusion partial differential equations cannot be inverted explicitly, so a method for inverting the drift-diffusion simulation is required. We show how Bayesian Parameter Estimation (BPE) coupled with a drift-diffusion perovskite solar cell model can determine the extent to which device parameters affect performance measured by J-V characteristics. Our method is demonstrated by investigating the extent to which device performance is influenced by mobile halide ions for a specific fabricated device. The ion vacancy density $N_0$ and diffusion coefficient $D_I$ were found to be precisely characterised for both simulated and fabricated devices. This result opens up the possibility of pinpointing origins of degradation by finding which parameters most influence device J-V curves as the cell degrades

Bayesian optimization approach to quantify the effect of input parameter uncertainty on predictions of numerical physics simulations

An understanding of how input parameter uncertainty in the numerical simulation of physical models leads to simulation output uncertainty is a challenging task. Common methods for quantifying output uncertainty, such as performing a grid or random search over the model input space, are computationally intractable for a large number of input parameters represented by a high-dimensional input space. It is, therefore, generally unclear as to whether a numerical simulation can reproduce a particular outcome (e.g., a set of experimental results) with a plausible set of model input parameters. Here, we present a method for efficiently searching the input space using Bayesian optimization to minimize the difference between the simulation output and a set of experimental results. Our method allows explicit evaluation of the probability that the simulation can reproduce the measured experimental results in the region of input space defined by the uncertainty in each input parameter. We apply this method to the simulation of charge-carrier dynamics in the perovskite semiconductor methyl-ammonium lead iodide (MAPbI3), which has attracted attention as a light harvesting material in solar cells. From our analysis, we conclude that the formation of large polarons, quasiparticles created by the coupling of excess electrons or holes with ionic vibrations, cannot explain the experimentally observed temperature dependence of electron mobility

Bayesian parameter estimation for characterising mobile ion vacancies in perovskite solar cells

To overcome the challenges associated with poor temporal stability of perovskite solar cells, methods are required that allow for fast iteration of fabrication and characterisation, such that optimal device performance and stability may be actively pursued. Currently, establishing the causes of underperformance is both complex and time-consuming, and optimisation of device fabrication is thus inherently slow. Here, we present a means of computational device characterisation of mobile halide ion parameters from room temperature current–voltage ( $J-V$ ) measurements only , requiring ∼2 h of computation on basic computing resources. With our approach, the physical parameters of the device may be reverse-modelled from experimental $J-V$ measurements. In a drift-diffusion (DD) model, the set of coupled DD partial differential equations cannot be inverted explicitly, so a method for inverting the DD simulation is required. We show how Bayesian Parameter Estimation coupled with a DD perovskite solar cell model can determine the extent to which device parameters affect performance measured by $J-V$ characteristics. Our method is demonstrated by investigating the extent to which device performance is influenced by mobile halide ions for a specific fabricated device. The ion vacancy density N _0 and diffusion coefficient D _I were found to be precisely characterised for both simulated and fabricated devices. This result opens up the possibility of pinpointing origins of degradation by finding which parameters most influence device $J-V$ curves as the cell degrades