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.

Spin-orbit coupling in the electronic states of solution-processed hybrid metal halide perovskites forms complex spin-textures in the band structures and allows for optical manipulation of the excited state spin-polarizations. Here, we report that motional narrowing acts on the photoexcited spin-polarization in CH3NH3PbBr3 thin films, which are doped at percentage-level with Mn2+ ions. Using ultrafast circularly polarized broadband transient absorption spectroscopy at cryogenic temperatures, we investigate the spin population dynamics in these doped hybrid perovskites and find that spin relaxation lifetimes are increased by a factor of 3 compared to those of undoped materials. Using quantitative analysis of the photoexcitation cooling processes, we reveal increased carrier scattering rates in the doped perovskites as the fundamental mechanism driving spin-polarization-maintaining motional narrowing. Our work reports transition-metal doping as a concept to extend spin lifetimes of hybrid perovskites.

Understanding perovskite solar cell physics through combining modelling and machine learningAlison Walker a, Samuel McCallum b, Jamie Lerpiniere aa Department of Physics University of Bath, BA2 7AY, UKb Department of Mathematical Sciences, University of Bath, BA2 7AY, UKInternational Conference on Hybrid and Organic PhotovoltaicsProceedings of International Conference on Hybrid and Organic Photovoltaics (HOPV24)València, Spain, 2024 May 12th - 15thOrganizer: Bruno EhrlerInvited Speaker Session, Alison Walker, presentation 100DOI: https://doi.org/10.29363/nanoge.hopv.2024.100Publication date: 6th February 2024This talk will cover our recent work combining machine learning and simulation methodologies to produce much faster and more direct characterisation of materials and devices. We have created a virtual model through a combination of device transport models and machine learning. This combination can be used to test hypotheses about the physical processes within these devices. These processes include the role of interfaces where charge accumulation/depletion can occur and traps where nonradiative recombination takes place are often located. I will show how we address outstanding questions on charge transport in lead halide perovskites. My main topic will concern how machine learning can solve the inverse parameter problem, where a device model (here the drift-diffusion code IonMonger) is combined with Bayesian parameter estimation to deduce the input parameters for the device model from experimental measurements of the device characteristics [1]. This approach allows us to pinpoint causes of features seen in the measurements using only a few hours of computation. The virtual model can be continuously updated to reflect the current output of a fabricated laboratory device. Through these updates the materials processes underlying changes in the devices' outputs can be identified. Accurately and rapidly simulating the function and performance of the lab device opens up the possibility of pinpointing the origins of degradation and allows improvements to be made much more quickly in future device iterations. The talk will also describe how we efficiently search the input space using Bayesian optimization to minimize the difference between the simulation output from our mesoscale simulations with the code BoltMC, and a set of experimental results. BoltMC uses Boltzmann transport theory implemented via ensemble Monte Carlo to provide insight into mobility-limiting mechanisms [2]. 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. References:[1] McCallum, S. G.; Nicholls, O.; Jensen, K. O.; Cowley, M. V.; Lerpinière, J. E.; Walker A. B. Bayesian parameter estimation for characterising mobile ion vacancies in perovskite solar cells J Physics: Energy 2024, 6, 015005[2] McCallum, S. G.; Lerpinière, J. E.; Jensen, K. O.; Friederich, P.; Walker A. B. Bayesian optimisation approach to quantify the effect of input parameter uncertainty on predictions of numerical physics simulations APL Machine Learning 2023, 1 046106Acknowledgements:We thank the UK Engineering and Physical Sciences Research Council (EPSRC) for a doctoral training partnership studentship (JEC) and for a Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa) studentship (SGM). © FUNDACIO DE LA COMUNITAT VALENCIANA SCITOnanoGe is a prestigious brand of successful science conferences that are developed along the year in different areas of the world since 2009. Our worldwide conferences cover cutting-edge materials topics like perovskite solar cells, photovoltaics, optoelectronics, solar fuel conversion, surface science, catalysis and two-dimensional materials, among many others.MATSUSPreviously nanoGe Spring Meeting (NSM) and nanoGe Fall Meeting (NFM), MATSUS is a multiple symposia conference focused on a broad set of topics of advanced materials preparation, their fundamental properties, and their applications, in fields such as renewable energy, photovoltaics, lighting, semiconductor quantum dots, 2-D materials synthesis, charge carriers dynamics, microscopy and spectroscopy semiconductors fundamentals, etc.International Conference on Hybrid and Organic PhotovoltaicsInternational Conference on Hybrid and Organic Photovoltaics (HOPV) is celebrated yearly in May. The main topics are the development, function and modeling of materials and devices for hybrid and organic solar cells. The field is now dominated by perovskite solar cells but also other hybrid technologies, as organic solar cells, quantum dot solar cells, and dye-sensitized solar cells and their integration into devices for photoelectrochemical solar fuel production.Asia-Pacific International Conference on Perovskite, Organic Photovoltaics and OptoelectronicsThe main topics of the Asia-Pacific International Conference on Perovskite, Organic Photovoltaics and Optoelectronics (IPEROP) are discussed every year in Asia-Pacific for gathering the recent advances in the fields of material preparation, modeling and fabrication of perovskite and hybrid and organic materials. Photovoltaic devices are analyzed from fundamental physics and materials properties to a broad set of applications. The conference also covers the developments of perovskite optoelectronics, including light-emitting diodes, lasers, optical devices, nanophotonics, nonlinear optical properties, colloidal nanostructures, photophysics and light-matter coupling.International Conference on Perovskite Thin Film Photovoltaics Perovskite Photonics and OptoelectronicsThe International Conference on Perovskite Thin Film Photovoltaics Perovskite Photonics and Optoelectronics (NIPHO) is the best place to hear the latest developments in perovskite solar cells as well as on recent advances in the fields of perovskite light-emitting diodes, lasers, optical devices, nanophotonics, nonlinear optical properties, colloidal nanostructures, photophysics and light-matter coupling.

Using density functional theory and kinetic modeling, we investigate the relationship between imposed biaxial strain and Br- and Cs-vacancy diffusion in orthorhombic (Pnma) CsPbBr3, in the dilute limit. We calculate the activation energies for the hopping of vacancies between all pairs of nearest-neighbor lattice sites and use the resulting values to parametrize a kinetic scheme and thereby to calculate vacancy diffusivity tensors. Our results indicate that the relationship between strain and vacancy diffusion is significantly more complex than previously thought - activation energies for vacancy hopping may increase or decrease for both negative (compressive) or positive (tensile) imposed biaxial strain, depending both on the plane in which strain is imposed and the particular pair of sites between which the vacancy hops, and the relationships are nonlinear in general and often nonmonotonic. Furthermore, we find that the influence of imposed biaxial strain on the diffusivity is significantly greater for Cs vacancies than for Br vacancies, and in particular, that values of Cs-vacancy diffusivity approach those of Br-vacancy diffusivity under certain conditions.

Despite record-breaking devices, interfaces in perovskite solar cells are still poorly understood, inhibiting further progress. Their mixed ionic-electronic nature results in compositional variations at the interfaces, depending on the history of externally applied biases. This makes it difficult to measure the band energy alignment of charge extraction layers accurately. As a result, the field often resorts to a trial-and-error process to optimize these interfaces. Current approaches are typically carried out in a vacuum and on incomplete cells, hence values may not reflect those found in working devices. To address this, a pulsed measurement technique characterizing the electrostatic potential energy drop across the perovskite layer in a functioning device is developed. This method reconstructs the current-voltage (JV) curve for a range of stabilization biases, holding the ion distribution "static" during subsequent rapid voltage pulses. Two different regimes are observed: at low biases, the reconstructed JV curve is "s-shaped", whereas, at high biases, typical diode-shaped curves are returned. Using drift-diffusion simulations, it is demonstrated that the intersection of the two regimes reflects the band offsets at the interfaces. This approach effectively allows measurements of interfacial energy level alignment in a complete device under illumination and without the need for expensive vacuum equipment.

We present a drift–diffusion model of a perovskite solar cell (PSC) in which carrier transport in the charge transport layers (TLs) is not based on the Boltzmann approximation to the Fermi–Dirac (FD) statistical distribution, in contrast to previously studied models. At sufficiently high carrier densities the Boltzmann approximation breaks down and the precise form of the density of states function (often assumed to be parabolic) has a significant influence on carrier transport. In particular, parabolic, Kane and Gaussian models of the density of states are discussed in depth and it is shown that the discrepancies between the Boltzmann approximation and the full FD statistical model are particularly marked for the Gaussian model, which is typically used to describe organic semiconducting TLs. Comparison is made between full device models, using parameter values taken from the literature, in which carrier motion in the TLs is described using (I) the full FD statistical model and (II) the Boltzmann approximation. For a representative TiO 2 /MAPI/Spiro device the behaviour of the PSC predicted by the Boltzmann-based model shows significant differences compared to that predicted by the FD-based model. This holds both at steady-state, where the Boltzmann treatment overestimates the power conversion efficiency by a factor of 27%, compared to the FD treatment, and in dynamic simulations of current–voltage hysteresis and electrochemical impedance spectroscopy. This suggests that the standard approach, in which carrier transport in the TLs is modelled based on the Boltzmann approximation, is inadequate. Furthermore, we show that the full FD treatment gives a more accurate representation of the steady-state performance, compared to the standard Boltzmann treatment, as measured against experimental data reported in the literature for typical TiO 2 /MAPI/Spiro devices.

Despite current–voltage hysteresis in perovskite solar cells (PSCs) having been the subject of significant research over the past decade, inverted hysteresis (IH), although frequently observed, is still not properly understood. Several mechanisms, based on numerical simulations, have been proposed to explain it but a satisfactory description of the underlying cause remains elusive. To rectify this omission, we analyze a drift-diffusion model of a planar three-layer PSC, using asymptotic techniques, to show how inverted hysteresis comes about. The asymptotic analysis of the drift-diffusion model yields a simple approximate model that shows excellent agreement with numerical simulations of the full drift-diffusion model provides fundamental insights into the causes of IH and reconciles the alternative explanations found in the literature. This approximate model is analyzed further to isolate the material properties and external conditions that contribute to inverted hysteresis and constitutes a diagnostic tool in which the appearance of IH can be used to infer properties of the cell.

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.

A combination of experimental studies and drift‐diffusion modeling has been used to investigate the appearance of inverted hysteresis, where the area under the J–V curve for the reverse scan is lower than in the forward scan, in perovskite solar cells. It is found that solar cells in the p–i–n configuration show inverted hysteresis at a sufficiently high scan rate, whereas n–i–p solar cells tend to have normal hysteresis. By examining the influence of the composition of charge transport layers, the perovskite film crystallinity and the preconditioning treatment, the possible causes of the presence of normal and inverted hysteresis are identified. Simulated current–voltage measurements from a coupled electron–hole–ion drift‐diffusion model that replicate the experimental hysteresis trends are presented. It is shown that during current–voltage scans, the accumulation and depletion of ionic charge at the interfaces modifies carrier transport within the perovskite layer and alters the injection and recombination of carriers at the interfaces. Additionally, it is shown that the scan rate dependence of the degree of hysteresis has a universal shape, where the crossover scan rate between normal and inverted hysteresis depends on the ion diffusion coefficient and the nature of the transport layers.

Reduction of the carbon footprint of historic buildings is urgent, given their exceptionally large energy demand. In this study, the performance and cost of a roof mounted photovoltaic system has been simulated for Bath Abbey, a grade I listed building, to test the financial viability of installing such a system. The electrical output of the panels was generated by the software package PVsyst with inputs such as the known dimensions of the Abbey, historical weather data, the orientation of the Abbey's roof, module azimuthal and tilt angles and shading by the spire and roof features. An important result is that even though the roof is not shadowed by other buildings, shading causes a 19% loss of peak power. This model was used to determine a recommended configuration comprising 164 solar panels, separated into two subsystems located on two parts of the roof, each with an inverter. Its predicted electrical output, 45 ± 2 MWh generated in the first year of operation, formed the basis of a cost–benefit analysis. This system will become profitable after 13.3 ± 0.6 years and provide a profit of £139,000 ± £12,000 over its 25‐year lifetime. Financial stress tests were performed for key assumptions to ensure that this result was true in all likely scenarios. This result shows that it is likely to make financial sense to install a photovoltaic system on a historic grade I listed building.

Polycrystalline solids can exhibit material properties that differ significantly from those of equivalent single-crystal samples, in part, because of a spontaneous redistribution of mobile point defects into so-called space-charge regions adjacent to grain boundaries. The general analytical form of these space-charge regions is known only in the dilute limit, where defect-defect correlations can be neglected. Using kinetic Monte Carlo simulations of a three-dimensional Coulomb lattice gas, we show that grain boundary space-charge regions in nondilute solid electrolytes exhibit overscreening-damped oscillatory space-charge profiles-and underscreening-decay lengths that are longer than the corresponding Debye length and that increase with increasing defect-defect interaction strength. Overscreening and underscreening are known phenomena in concentrated liquid electrolytes, and the observation of functionally analogous behavior in solid electrolyte space-charge regions suggests that the same underlying physics drives behavior in both classes of systems. We therefore expect theoretical approaches developed to study nondilute liquid electrolytes to be equally applicable to future studies of solid electrolytes.

The formation of polarons due to the interaction between charge carriers and lattice ions has been proposed to have wide-ranging effects on charge carrier dynamics in lead halide perovskites. The hypothesis underlying many of those proposals is that charge carriers are 'protected' from scattering by their incorporation into large polarons. Following the approach of Kadanoff for scattering due to polar optical phonons, we derive expressions for the rates of scattering of polarons by acoustic phonons and ionized impurities, and compute the energy and angular dependent rates for electrons and holes in MAPbI(3), MAPbBr(3), and CsPbI3. We then use the ensemble Monte Carlo method to compute polaron distribution functions which satisfy a Boltzmann transport equation incorporating the same three scattering mechanisms, from which we extract mobilities for temperatures in the range 50-500 K. A comparison of the results with those of analogous calculations for bare band carriers indicates that polaronic effects on the scattering and mobilities of charge carriers in lead halide perovskites are more limited than has been suggested in some parts of the recent literature.

We study the effects of hydrostatic pressure in the range 0.0–2.0 GPa on anion mobility in the orthorhombic Pnma phase of CsPbBr_3. Using density functional theory and the climbing nudged elastic band method, we calculate the transition states and activation energies for anions to migrate both within and between neighbouring PbBr_3 octahedra. The results of those calculations are used as input to a kinetic model for anion migration, which we solve in the steady state to determine the anion mobility tensor as a function of applied pressure. We find that the response of the mobility tensor to increasing pressure is highly anisotropic, being strongly enhanced in the (010) lattice plane and strongly reduced in the direction normal to it at elevated pressure. These results demonstrate the potentially significant influence of pressure and strain on the magnitude and direction of anion migration in lead–halide perovskites.

Anion vacancy migration in the orthorhombic Pnma phase of the lead-halide perovskite CsPbBr3 under hydrostatic pressure is studied computationally. Density functional theory calculations are used to determine transition states, activation enthalpies, and attempt frequencies for vacancies to hop between nearby lattice sites, under pressure in the range 0.0-2.0 GPa. The resulting data are used to parametrize a kinetic model of vacancy migration under the influence of an electric field, which is solved in the steady state to determine the anion vacancy mobility tensor as a function of pressure. It is found that the mobility tensor becomes increasingly anisotropic with increasing pressure, such that at 2.0 GPa, the mobility within the (010) lattice plane is 3 orders of magnitude greater than the mobility normal to it. The results demonstrate the potentially significant influence of pressure, and by extension, other forms of stress, on defect migration in lead-halide perovskites.