Variation modeling, analysis and control for multistage wafer manufacturing processes
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Geometric quality variables of wafers, such as BOW and WARP, are critical in their applications. A large variation of these quality variables reduces the number of conforming products in the downstream production. Therefore, it is important to reduce the variation by variation modeling, analysis and control for multistage wafer manufacturing processes (MWMPs). First, an intermediate feedforward control strategy is developed to adjust and update the control actions based on the online measurements of intermediate wafer quality measurements. The control performance is evaluated in a MWMP to transform ingots into polished wafers. However, in a complex multistage manufacturing process, the quality variables may have nonlinear relationship with the parameters of the predictors. In this case, piecewise linear regression tree (PLRT) models are used to address nonlinear relationships in MWMP to improve the model prediction performance. The obtained PLRT model is further reconfigured to be complied with the physical layout of the MWMP for feedforward control purposes. The procedure and effectiveness of the proposed method is shown in a case study of a MWMP. Furthermore, as the geometric profiles and quality variables are important quality features for a wafer, fast and accurate measurements of those features are crucial for variation reduction and feedforward control. A sequential measurement strategy is proposed to reduce the number of samples measured in a wafer, yet provide adequate accuracy for the quality feature estimation. A Gaussian process model is used to estimate the true profile of a wafer with improved sensing efficiency. Finally, we study the multistage multimode process monitoring problem. We propose to use PLRTs to inter-relate the variables in a multistage multimode process. A unified charting system is developed. We further study the run length distribution, and optimize the control chart system by considering the modeling uncertainties. Finally, we compare the proposed method with the risk adjustment type of control chart systems based on global regression models, for both simulation study and a wafer manufacturing process.