Nonlinear Dynamics Modeling of Correlated Functional Process Variables for Condition Monitoring in Chemical–Mechanical Planarization

This paper aims to investigate correlation mechanism among functional process variables (FPVs) for condition monitoring in chemical-mechanical planarization (CMP). During wafer polishing, critical process variables such as coefficient of friction and pad temperature vary with time and present in the shape of functional curves. Our previous work has demonstrated that correlation patterns among these FPVs could be related to polishing conditions. Since correlation is affected by both amplitude fluctuations and phase variability in FPVs, further study of timing correlation of FPVs measured in different units could bring more insight into the physical interactions and thereby enhance CMP condition monitoring. Existing research on FPVs in CMP mainly focuses on individual effects of FPVs and statistical correlations through experimental and theoretical analyses. In this paper, we intend to specifically reveal the timing correlation patterns in CMP. Using nonlinear dynamics, we first established a dynamic phase model to define the strength and patterns of FPV interaction. By monitoring the extracted patterns, we then developed a novel method of detecting CMP condition change and demonstrated the approach via a CMP experiment. The results show that the proposed method has a promising application in identifying the process changes that may not be easily detected otherwise.