钙钛矿太阳电池电荷输运有限体积格式的数值分析
Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells
摘要：
在本文中，我们考虑了钙钛矿太阳能电池的漂移扩散电荷传输模型，其中电子和空穴可以线性扩散（玻尔兹曼近似）或非线性扩散（例如，由于费米-狄拉克统计）。为了结合体积排阻效应，我们依赖于费米-狄拉克积分的顺序-1时，建模移动的钙钛矿层内的阴离子空位夹在电子和空穴传输层。无量纲化后，我们首先证明了模型的一个连续的熵耗散不等式。然后，我们在Voronoi网格上构造了相应的两点通量有限体积格式，并给出了类似的离散熵耗散不等式。利用Brouwer的不动点定理的一个推论和一个凸泛函的极小化，这个不等式帮助我们证明了非线性离散系统的离散解的存在性.最后，我们验证了我们的理论证明的属性数值，模拟一个现实的设备设置，并显示指数衰减的时间相对于L^2误差以及物理和分析意义的相对熵。
英文摘要：
In this paper, we consider a drift-diffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly (e.g. due to Fermi-Dirac statistics). To incorporate volume exclusion effects, we rely on the Fermi-Dirac integral of order -1 when modeling moving anionic vacancies within the perovskite layer which is sandwiched between electron and hole transport layers. After non-dimensionalization, we first prove a continuous entropy-dissipation inequality for the model. Then, we formulate a corresponding two-point flux finite volume scheme on Voronoi meshes and show an analogous discrete entropy-dissipation inequality. This inequality helps us to show the existence of a discrete solution of the nonlinear discrete system with the help of a corollary of Brouwer's fixed point theorem and the minimization of a convex functional. Finally, we verify our theoretically proven properties numerically, simulate a realistic device setup and show exponential decay in time with respect to the L^2 error as well as a physically and analytically meaningful relative entropy.
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