A physics-informed Run-to-Run control framework for semiconductor manufacturing

Abstract For decades, Run-to-Run (R2R) controllers have been widely implemented in semiconductor manufacturing. They operate over key process parameters on the basis of the metrological measurements acquired from the process and their deviations from the target setpoints. Conventionally, R2R controllers have been implemented independently of the actual equipment condition, which is obviously affecting the process stability and performance. Therefore, both equipment signals and process states shall be considered to make the R2R controllers more robust to the equipment condition drifts. In this paper, we propose a novel physics-informed framework to integrate the real-time equipment condition, based on the Fault Detection and Classification (FDC) data, into the R2R controllers. By utilizing Dynamic Bayesian Networks (DBN), the implicit relationship structure between metrology measurements, FDC indicators, and R2R regulators can be learned and reviewed explicitly. The structure shall be further reviewed to valid with the existing relationships and expert knowledge. Infeasible causalities on the structure will be constrained via setting up the blacklist at the structure learning stage. The proposed framework consists of the offline modeling stage, which incorporates the process, equipment variables, and the expert knowledge in the structure learning, and the online control stage, which constructs the Structured R2R controller (SRC) based on the relationship structure. As a result, the model is consistent by design with empirically known relationships and fundamental physical laws. The proposed SRC not only optimizes the operation with respect to the target control values but also considers the equipment and process states simultaneously. The effectiveness of SRC and the derivative control strategy are validated through a real dataset of a Chemical-Mechanical Polishing (CMP) process, and two simulated studies.