论文标题
钙钛矿太阳能电池中电荷传输的有限体积方案的数值分析
Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells
论文作者
论文摘要
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，在该电池中，电子和孔可能线性扩散（玻尔兹曼近似）或非线性（例如，由于费米 - 迪拉克统计）。为了结合体积的排除效应，我们依赖于订单-1的费米 - 迪拉克积分 - 建模在钙钛矿层中移动阴离子空位，该钙钛矿层中的夹层和孔传输层之间。在非二敏化后，我们首先证明该模型的连续熵散失不平等。然后，我们在Voronoi网格上制定了相应的两点磁通量体积方案，并显示出类似的离散熵 - 散落不等式。这种不平等有助于我们借助Brouwer的固定点定理和最小化凸函数来展示非线性离散系统的离散解决方案的存在。最后，我们通过数值验证我们的理论证明的属性，模拟逼真的设备设置，并在l^2误差以及物理和分析有意义的相对熵方面及时显示指数衰减。
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.
