ASML designs extremely advanced lithography machines. When designing a new machine or one of its components, the behavior of the machine must be calculated and analyzed at system level to ensure that both static and dynamic requirements are met. Because meeting these requirements can be quite challenging, the design process often requires multiple iterations. Due to the size and complexity of these machines, the Finite Element Method (FEM) model is too large to solve in its entirety. Therefore, ASML uses a substructuring approach, in which multiple substructures are defined within the machine. For each of these, a Reduced Order Model (ROM) is created. This is a simplified representation of a complex model, which significantly reduces its size. To calculate the static and dynamic behavior at system level, the ROMs of the individual substructures are then connected.
Generating these ROMs is very time-consuming and they cannot be reused when parameters change. As a result, whenever a substructure is modified during one of the many iterations, a new ROM must be generated for that substructure. This significantly increases the overall duration of the design process. To address this issue, ASML is interested in methods that allow parameter changes to be applied directly within a ROM. Therefore, the aim of this research was to explore such techniques, assess how they could be integrated into ASML’s design process, and evaluate the extent to which they can help to speed it up. The scope of this research was limited to techniques used for static analysis. In line with this goal and scope, the following main research question was introduced: “To what extent can techniques that enable parametric changes within Reduced Order Models for static analysis contribute to speeding up ASML's design process?”.
The research followed the Design Science Research Methodology, including a literature review, interviews with ASML engineers, practical testing, and a case study. From this, it was ultimately concluded that the technique Proper Orthogonal Decomposition Radial Basis Function (POD-RBF) approximation can indeed help speed up ASML’s design process. However, an important limitation is that its constraints make the technique suitable only for scenarios where the coupling between the interface Degrees of Freedom (DOFs) in the substructuring context is minimal and the DOFs in a structure respond fairly linearly in relation to one another when certain parameter changes. The reason why the POD-RBF approximation can speed up the design process in these specific scenarios is not, as initially expected, due to skipping the reduction step, but rather because it also skips the regeneration of the FEM model. The resulting time savings are therefore much smaller than the potential gains from skipping the reduction step for dynamic analysis, which was found to take considerably longer than in static analysis. It is therefore recommended that future research focuses on this area.