3D-to-2D Transition of Anion Vacancy Mobility in CsPbBr₃under Hydrostatic Pressure

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.Comment: 25 pages, 3 figure

Linear normal mode analysis of baroclinic instability in a meridional channel

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution March 2001Numerical solutions of the unstable, growing modes are found for the two-layer inviscid quasigeostrophic equations in a meridional channel. A steady mean flow in the N-S direction is imposed in the upper layer, and it is assumed that changes in planetary vorticity following this mean flow are balanced by the input of vorticity from an imposed wind stress curl. Thus in the two-layer system, the vertical shear, in thermal wind balance, is associated with an interface slope which provides a gradient of potential vorticity (PV) in the x-direction, of equal magnitude and opposite sign in the two layers. In the y-direction the PV gradient has the value of planetary beta, β in both layers. The unstable modes of this system exhibit a boundary-layer structure across the channel. They are intensified in the west. The growth rates of the unstable modes are of the same order as the zonal case, however the range of wavenumber and shear for which instability is possible is larger. Established cutoff criteria for the equal-layer zonal case are not applicable, and no analogous criteria has yet been found. Growing modes are found even for very weakly sheared flows, and this suggests that baroclinic instability may represent a more significant source of mid-ocean eddy energy than previously believed.This research was supported by the National Science Foundation under grant 9901654

Bayesian optimisation 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 Optimisation to minimise 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 MAPbI$_3$ that 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

Interpretation of photocurrent transients at semiconductor electrodes:Effects of band-edge unpinning

The transient photocurrent response of semiconductor electrodes to chopped illumination often shows spikes and overshoots that are usually interpreted as evidence that surface recombination is occurring. In the case of the high intensities used for light-driven water splitting, the interpretation is less straightforward since the electron transfer reactions are so slow that the minority carrier concentration at or near the surface increases to high values that modify the potential drop across the Helmholtz layer in the electrolyte, leading to ‘band edge unpinning’. In addition, changes in chemical composition of the surface or local changes in pH may also alter the potential distribution across the semiconductor/electrolyte junction. A quantitative theory of band edge unpinning due to minority carrier build up is presented, and numerical calculations of transient photocurrent responses are compared with experimental examples for n-type Fe2O3 and p-type lithium-doped CuO electrodes. It is shown that the apparently high reaction orders (up to third order) with respect to hole concentration reported for hematite photoanodes can be explained as arising from an acceleration of hole transfer by the increased voltage drop across the Helmholtz layer associated with band edge unpinning. The limitations of the band edge unpinning model are discussed considering additional effects associated with modification of the potential distribution brought about by light-induced changes in surface composition, surface dipoles and surface ionic charge.</p

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