A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells

Drift-diffusion models that account for the motion of both electronic and ionic charges are important tools for explaining the hysteretic behaviour and guiding the development of metal halide perovskite solar cells. Furnishing numerical solutions to such models for realistic operating conditions is challenging owing to the extreme values of some of the parameters. In particular, those characterising (i) the short Debye lengths (giving rise to rapid changes in the solutions across narrow layers), (ii) the relatively large potential differences across devices and (iii) the disparity in timescales between the motion of the electronic and ionic species give rise to significant stiffness. We present a finite difference scheme with an adaptive time step that is posed on a non-uniform staggered grid that provides second order accuracy in the mesh spacing. The method is able to cope with the stiffness of the system for realistic parameters values whilst providing high accuracy and maintaining modest computational costs. For example, a transient sweep of a current-voltage curve can be computed in only a few minutes on a standard desktop computer.Comment: 22 pages, 8 figure

Systematic derivation of a surface polarization model for planar perovskite solar cells

Increasing evidence suggests that the presence of mobile ions in perovskite solar cells can cause a current-voltage curve hysteresis. Steady state and transient current-voltage characteristics of a planar metal halide CH$_3$NH$_3$PbI$_3$ perovskite solar cell are analysed with a drift-diffusion model that accounts for both charge transport and ion vacancy motion. The high ion vacancy density within the perovskite layer gives rise to narrow Debye layers (typical width $\sim$2nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer ($\sim$600nm) and (II) the ion vacancy density and the charge carrier densities motivate an asymptotic approach to solving the model, while the stiffness of the equations renders standard solution methods unreliable. We derive a simplified surface polarisation model in which the slow ion dynamic are replaced by interfacial (nonlinear) capacitances at the perovskite interfaces. Favourable comparison is made between the results of the asymptotic approach and numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.Comment: 32 pages, 7 figure

Intensification of single cell storms prior to lightning onset

Single cell storms in the UK can produce lightning, despite apparently only having developed to towering cumulus rather than cumulonimbus. Such marginal thunderstorms still present severe weather hazards but are difficult to identify and predict and therefore provide a warning. Observations from the Met Office radar mosaic and ATDNet (Arrival Time Difference Network) show that these single cell storms demonstrate a characteristic increase in the area of high reflectivity storm core during the 15 minutes prior to the first lightning. By using the Met Office Unified Model to investigate reflectivity development in modelled storms, a microphysical explanation for the observed reflectivity increase is identified. During a rapid reflectivity increase, the updraft area at the melting layer, the peak updraft velocity and the storm graupel mass increase. The three quantities examined are linked to each other and to the generation of charge within the storm. The production of graupel is promoted by the increase in updraft area and charge separation is enhanced by the faster peak updraft velocity. This explains some of the physical differences between single cell storms that produce lightning and apparently similar storm systems which do not. It also provides a new basis with which to predict lightning hazard for marginal storms

IonMonger: a free and fast planar perovskite solar cell simulator with coupled ion vacancy and charge carrier dynamics

Details of an open-source planar perovskite solar cell simulator, that includes ion vacancy migration within the perovskite layer coupled to charge carrier transport throughout the perovskite and adjoining transport layers in one dimension, are presented. The model equations are discretised in space using a finite element scheme and temporal integration of the resulting system of differential-algebraic equations is carried out in MATLAB. The user is free to modify device parameters, as well as the incident illumination and applied voltage. Time-varying voltage and/or illumination protocols can be specified, e.g. to simulate current-voltage sweeps, or to track the open-circuit conditions as the illumination is varied. Typical simulations, e.g. current-voltage sweeps, only require computation times of seconds to minutes on a modern personal computer. An example set of hysteretic current-voltage curves is presented

ACTIVE: a randomised feasibility trial of a behavioural intervention to reduce fatigue in women undergoing radiotherapy for early breast cancer: study protocol

Background Fatigue is rated as the most distressing side effect of radiotherapy treatment for curable breast cancer. About four in ten women treated experience fatigue, which can last for years after treatment. The impact of this debilitating tiredness is loss of independence and impaired physical and mental function. Our study will take a behavioural intervention with demonstrated effect in treating fatigue in a mixed group of chemotherapy patients and adapt it for women undergoing radiotherapy for early breast cancer. The purpose of this trial is to evaluate the feasibility of delivering the intervention in the radiotherapy pathway for patients at a high risk of fatigue and to explore participants’ experiences of the trial and intervention. Methods A pragmatic single-site non-blinded feasibility trial of a behavioural intervention. Main inclusion criteria are prescription of the UK standard 40 Gy in 15 fractions over 3 weeks of radiotherapy (± tumour bed boost) for early (stage 0–IIIa) breast cancer. The total projected sample size after attrition is 70. A previously developed fatigue risk score tool will be used to predict individual’s likelihood of experiencing fatigue. Thirty women predicted to be at a high risk of experiencing significant fatigue will be allocated in the ratio 2:1 to the behavioural intervention or education trial arms, respectively. These feasibility trial participants will be assessed at baseline, after 10 and 15 fractions of radiotherapy and 10 days, 3 weeks and 6 months after radiotherapy. A further 40 women predicted to be at a lower risk of fatigue will join a risk score validation group. Measures to assess feasibility include recruitment, retention and completion rates and variation in implementation of the intervention. Process evaluation with intervention providers and users includes fidelity and adherence checks and qualitative interviews to understand how changes in behaviour are initiated and sustained. Discussion This feasibility study collates data to both inform the progression to and design of a future definitive trial and to refine the intervention

Radiological-pathological correlation of pleomorphic liposarcoma of the anterior mediastinum in a 17-year-old girl

Liposarcoma is a soft-tissue sarcoma typically seen in adults. It is extremely rare in children. It most often occurs in the extremities or in the retroperitoneum. We present a very rare case of an anterior mediastinal liposarcoma of the pleomorphic subtype in a 17-year-old girl, along with radiological and pathological correlation. The location, patient age and histological subtype are exceedingly uncommon for this tumor

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 neighboring 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 migration 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 the 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, 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, where FA is formamidinium, HC (NH 2) 2, or MAPbBr 3, 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 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. </p