以最小平方法建構先進製程控制系統

Advanced Process Control by Using Partial Least Squares

張源融(Yuan-Jung Chang)

指導教授 ： 江行全

元智大學/工程學院/工業工程與管理學系/博士(2012年)

https://doi.org/10.6838/YZU.2012.00285

摘要

本論文以偏最小平方法(Partial Least Squares, PLS)為基礎來建構一個先進製程控制系統(Advanced Process Control, APC)， 由於在半導體的製程當中，製程參數通常有多重共線性的關係，以及量測延遲的情況發生。此兩種情形會導致製程的不穩定性增強，因此，為了解決在實務上的這兩個問題，本論文提出一個PLS-MIMO DEWMA (double exponentially weight moving average) 控制器，利用PLS為模型建構(model-building)的方法以處理製程參數之間所產生的多重共線性。再建立一個虛擬量測(Virtual Metrology, VM )系統預測產品之品質特徵值，以補償量測延遲的發生。最後，利用PLS投影後的主成份建立一個錯誤偵測系統，以提供製程當前狀態。

關鍵字

先進製程控制 ； 批次控制 ； 多重共線性 ； 虛擬量測

並列摘要

In this dissertation, an integrated Advanced Process Control (APC) system which is based on Partial Least Squares (PLS) technique is presented. Due to the property of batch processing, the semiconductor manufacturing processes frequently exhibit high multicollinearity among the process variables. This effect will typically cause variance inflation of the regression coefficient estimates which are utilized in regulating or updating the run-to run (R2R) controller. Furthermore, it is often the case that a noticeable delay exists between a process run and the process measurements from that run; inevitably, metrology delay leads to close-loop instabilities. To rectify the aforementioned difficulties that might realistically take place in practice, this dissertation proposes a PLS double exponentially weighted moving average (PLS-MIMO DEWMA) controller. It uses the PLS method as the model-building technique to help the EWMA controller to yield more consistent and robust control outputs than the Ridge Solution (RS) DEWMA controller and PLS multi-SISO DEWMA controller. To cope with metrology delays, the proposed APC system uses the pre-process metrology data to build up a Virtual Metrology (VM) system that can provide the estimation process outputs for PLS-MIMO DEWMA controller. Finally, a Fault Detection (FD) system is investigated based on the principal components of PLS which can provide the process state for VM and PLS-MIMO DEWMA controller to respond to the system errors. The simulation results show that the control outputs of the proposed APC system under the IMA (1, 1) model (which is the disturbance term follows a non-stationary time series) is more close to target and smaller deviation from the target than the other controller and VM system (proposed by Khan et al. 2008)

並列關鍵字

Adavnced process control ； partial least square ； Run-to-Run ； multicollinearity ； virtual metrology

參考文獻

Butler, S.W., and Stefani, J.A. “Supervisor run-to-run control a polysilicon gate etch using in situ Ellipsometry.” IEEE Trans. Semicond. Manuf. 7 (1994) 193-201.

Chen, J. and Patton, R.J. “Robust model-based fault diagnosis for dynamic systems”

Chen, J., and Wang, F. “PLS based dEWMA run-to-run controller for MIMO non-squared semiconductor processes.” J. Process Control, 17 (2007) 309-319.

Cheng, F.T., Chen, Y.T., Su, Y.C., and Zeng, D.L. “Evaluating reliance level of virtual metrology system” IEEE Trans. Semicond. Manuf. 21(1) (2008) 92-102.

Cherry, G.A. and Qin, S.J. “Multiblock principal component analysis based on a combined index for semiconductor fault detection and diagnosis.” IEEE Trans. Semicond. Manuf. 19(2) (2006) 159-172.