應用RLS控制器適應地調整時變的量測時延

Adaptive Adjustment Scheme of Time-Varying Metrology Delay using RLS-type Controllers

羅仂君(Le-Chun Lo)

指導教授 ： 范書愷

元智大學/工程學院/工業工程與管理學系/碩士(2007年)

https://doi.org/10.6838/YZU.2007.00177

摘要

在半導體產業中，批次控制技術(Run-to-Run Control)已經受到極大的關注，例如應用在線上品質管制上。比較常見的控制法則包括了指數加權移動平均控制器EWMA(Exponentially Weighted Moving Average)、雙重指數加權移動平均控制器double EWMA、和遞迴式最小平方控制器RLS(Recursive Least Squares)。在產品的製造與量測之間，經常會發生明顯的時延情況，而且不可避免地，這些量測時延會導致閉環控制的不穩定。這篇論文整理了大量有關量測時延的研究，資料中指出處理時變性的量測時延(例如從0批到5批之間)具有相當大的挑戰性。Wang和Qin(2003, 2005)等人提出了RLS-type控制器，本論文則將其中的RLS-LT控制器加以改良，提出了“結合移動平均值管制圖與區間測試法則的RLS-LT控制器”，用來適應地調整時變性的量測時延。將本論文所提出之研究方法和原來的EWMA-type控制器和RLS-type控制器作比較，結果能使製程穩定於其目標值而且產出值有較小的標準誤差和均方誤差。在時變性的量測時延以及受限於噪音干擾和製程飄移(老化)的單進單出Single-input Single-output(SISO)系統之下，經由大量的實驗模擬可以發現本論文所提出之控制方法，無論是在短期的還是長期的操作中，都能有良好的控制績效。此外，將此控制方法應用於線性的SISO化學機械研磨Chemical-Mechanical Polishing(CMP)製程上，控制器也提供了不錯的控制績效。

關鍵字

線上品質管制 ； 批次控制 ； 單進單出系統 ； 時變的量測時延 ； 遞迴最小平方演算法 ； 區間測試 ； 移動平均值管制圖 ； 化學機械研磨

並列摘要

RtR control technique has received tremendous interest, such as on-line quality control, in semiconductor manufacturing industry. The well-known methods are EWMA, dEWMA, and RLS controllers. It is often the case that a significant delay exists between a process run and the process measurements from that run; inevitably, metrology delay leads to close-loop instabilities. This thesis arranged a great deal of researches of metrology delay. It is a great challenge for the current controllers to deal with if metrology delay is dynamically dapping between 0 and 5. Under the RLS-type controllers proposed by Wang and Qin et al. (2003, 2005), a practicable method “RLT-LT controller using zone tests with MA control chart” is presented to adaptively predict the time-varying metrology delays. The proposed method is able to drive the process outputs accurately on target with smaller error variance and MSE than the “original” RLS-type and EWMA-type estimates. As evidenced by a variety of simulations, for time-varying metrology delay SISO system which was subject to noise and drift, the proposed control method was demonstrated that performing well in the short-run and long-run simulations. Furthermore, a linear SISO CMP process is given to demonstrate the proposed control method.

並列關鍵字

On-line Quality Control ； Run-to-Run Control ； Single-input Single-output System ； Time-Varying Metrology Delay ； Recursive Least Squares ； Zone Tests ； Moving Average Control Chart ； Chemical Mechanical Polishing

參考文獻

[1] Astrom, K. J. (1970), Introduction to Stochastic Control, Academic press, New York, NY.

[2] Astrom, K. J. and Wittenmark, B. (1973), “On self Tuning Regulators,” Automatica, 9(2), pp. 185-199.

[4] Astrom, K. J., Borisson, U., Ljung, L. and Wittenmark, B. (1977), “Theory and applications of self-tunings regulators,” Automatica, 13(5), pp. 457-476.

[6] Box, G. E. P. and Jenkins, G. M. (1974), Time Series Analysis, Forecasting, and Control, Revised edition, Holden Day, Oakland, CA.

[7] Box, G. E. P. and MacGregor, J. F. (1976), “Parameter Estimation with Close-Loop Operating Data,” Technometrics, 18, pp. 371-380.