The theoretical description of plasma processing provides a formidable task that has been addressed by analytical modeling and numerical simulation for decades. Although the continuous increase in compute power has enabled simulation studies of the gas discharge physics in great detail, many open questions remain. This is reasoned by the extremely complex dynamics of multi-component plasmas facing solid surfaces, involving a large number of processes in the plasma and in the solid, as well as their plasma-surface interaction. The time and length scales of these physico-chemical processes span many orders of magnitude. Well separated scales often allow for the description of a given phenomenon on its respective scales, paired with a hierarchical coupling. This coupling is often rather static and realized via oversimplifying assumptions (e.g., tabulated coefficients), and may be biased-by-experience. Advantage can be taken from more unbiased data-driven approaches, which are derived from high fidelity data obtained from physical models at the lower scales. Moreover, the description of certain physical mechanisms may be substituted by data-driven sub-models (e.g., electric field calculation or transport parameters from a kinetic description). Correspondingly, a hierarchy of physical and data-driven models may be derived, linking global process quantities (e.g., pressure, voltage, current) to microscopic process quantities (e.g., thin film composition, electrical properties).

This approach is exemplified by the investigation of a low-pressure partially-magnetized capacitively coupled radio frequency discharge for the sputter deposition of silicon oxide thin films. The model is implemented in the OpenFOAM framework, extended by a Particle In Cell/Monte Carlo Collisions (PIC/MCC) implementation and coupled to a system of fluid equations for the neutral background. The surface evolution is described by a system of rate equations, which takes into account physical sputtering, chemisorption, physisorption, and surface diffusion of adatoms. The dynamics of physical sputtering are included using an artificial neural network model trained on surface kinetics data with varying stoichiometry from Monte Carlo simulations. It is argued that the versatility of the implementation also allows to use this model in a broader range of applications, such as plasma etching.

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 138690629 – TRR 87 and – Project-ID 434434223 – SFB 1461.

Recent developments in the field of coating technology have seen a rise in the adoption of process modeling and digital twin tools. The primary motivation for this shift is the extended duration and unpredictability of process transfers and scaling in coating applications. Moreover, these technologies are now beginning to contribute to energy reduction in coating processes.

In our previous work, we introduced a Digital Twin model for coaters, integrated into the MatSight framework by PlasmaSolve. This model demonstrated high accuracy in predicting the composition and key performance characteristics (such as hardness and residual stress) of coatings, utilizing a dataset of only eight characterized samples for training. This achievement was made possible by a hybrid process model that merges simulations of physical processes and chemistry with machine learning techniques. By incorporating knowledge of the coater's physical limitations, the model significantly reduced the need for extensive training experiments.

This contribution advances our research by tackling an inverse problem: using the Digital Twin model to create a coating recipe based on defined material specifications. These specifications include the number of layers, the thickness and composition of each layer, and the target hardness/residual stress for the complete stack. The model generates a recipe file compatible with coater operations, allowing for immediate implementation and validation of model predictions.

Furthermore, we illustrate how the Digital Twin model can be seamlessly integrated with other PVD simulation tools, offering a comprehensive view of the coating process. A case in point is the integration with the MatSight Coating Uniformity App, which enhances understanding of the coating's thickness distribution and the variations in ion bombardment and composition across a 3D object.