This work presents a mathematical model describing the thin film formation during the co-evaporation of elements by PVD process for the production of CIGS type thin film photovoltaic cells. We propose a one-dimensional system of cross-diffusion Partial Differential Equations (PDEs) defined in a time-dependent space domain and introduce a numerical scheme for the discretization of the system. We calibrate our model on true experimental measurements using a dual approach. Then, in order to achieve certain targeted final concentration profiles, we consider an optimization problem that allows controlling the external atomic fluxes injected during the process. Despite its simplicity, the proposed model shows promising results towards a quantitatively predictive model. For instance, novel atomic fluxes obtained as solutions of the optimization problem could represent alternatives to the classical three-stage process. In this paper, a mathematical model describing the thin film formation during the co-evaporation PVD process for the production of CIGS type thin film photovoltaic cells is proposed.

这项工作提出了一个数学模型，描述了通过PVD工艺共蒸镀元素以生产CIGS型薄膜光伏电池时的薄膜形成过程。我们提出了一个时空空间域中定义的一维交叉扩散偏微分方程（PDE）系统，并为该系统的离散化引入了一种数值方案。我们使用对偶方法在真实的实验测量值上校准模型。然后，为了获得某些目标最终浓度曲线，我们考虑了一个优化问题，该问题允许控制过程中注入的外部原子通量。尽管其简单性，但所提出的模型在定量预测模型方面显示出令人鼓舞的结果。例如，作为最优化问题的解决方案而获得的新型原子通量可以代表经典三阶段过程的替代方案。本文提出了一种数学模型，描述了在共蒸镀PVD过程中用于生产CIGS型薄膜光伏电池的薄膜形成过程。