Modeling and optimization of the fabrication process of thin-film solar cells by multi-source physical vapor deposition

Abstract 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.