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

机译:一种求解电荷载流子模型的快速而稳健的数值方案   钙钛矿太阳能电池中的迁移和离子空位运动

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摘要

Drift-diffusion models that account for the motion of both electronic andionic charges are important tools for explaining the hysteretic behaviour andguiding the development of metal halide perovskite solar cells. Furnishingnumerical solutions to such models for realistic operating conditions ischallenging owing to the extreme values of some of the parameters. Inparticular, those characterising (i) the short Debye lengths (giving rise torapid changes in the solutions across narrow layers), (ii) the relatively largepotential differences across devices and (iii) the disparity in timescalesbetween the motion of the electronic and ionic species give rise to significantstiffness. We present a finite difference scheme with an adaptive time stepthat is posed on a non-uniform staggered grid that provides second orderaccuracy in the mesh spacing. The method is able to cope with the stiffness ofthe system for realistic parameters values whilst providing high accuracy andmaintaining modest computational costs. For example, a transient sweep of acurrent-voltage curve can be computed in only a few minutes on a standarddesktop computer.
机译:考虑到电子和阴离子电荷运动的漂移扩散模型是解释滞后行为和指导金属卤化物钙钛矿太阳能电池发展的重要工具。由于某些参数的极值,为实际操作条件提供此类模型的数值解决方案极具挑战性。尤其是那些表征(i)短德拜长度(在狭窄层中的溶液中出现快速变化),(ii)跨装置的相对较大电位差以及(iii)电子和离子物质运动之间的时间尺度差异给出的特征,变得明显的刚度。我们提出了具有自适应时间步长的有限差分方案,该步长被置于非均匀交错网格上,该网格在网格间距中提供了二阶精度。该方法能够满足系统对于实际参数值的刚度,同时提供高精度并保持适度的计算成本。例如,在标准台式计算机上仅需几分钟即可计算出电流-电压曲线的瞬态扫描。

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