Analysis of Interaction Structure Among Multiple Functional Process Variables for Process Control in Semiconductor Manufacturing

Our previous work has shown that complex interaction patterns among functional process variables (FPVs) in semiconductor manufacturing processes can indicate process condition changes. We developed a nonlinear dynamics model to describe interactions among FPVs, which was further used to monitor process condition changes. However, the interaction structure among three or more FPVs has not been thoroughly investigated for the purpose of process control. In this work, we first extend our previously developed nonlinear dynamics model by considering the autocorrelation in each FPV. A generalized least square (GLS) method is applied to estimate the extended model. The interaction structure among FPVs is represented as a complex network in which the directionality and strength of interaction are discovered from the extended nonlinear dynamics model. To validate the proposed method, we first conduct simulation study using van del Pol oscillators. Then two sets of real experimental data from chemical mechanical planarization process are used to investigate the interaction structure change over a polishing cycle. The results show that the extracted patterns of interaction structure among FPVs aid to uncover the polishing mechanisms and provide more insights for condition monitoring and diagnosis.