批次控制在半導體生產製程的監控工作中扮演極重要的角色。傳統EWMA-based 批次控制器大多假設製程的投入-產出模型為靜態模型下進行研究；然而當生產製程存在 carry-over effect現象時，此類以製程靜態模型所發展出來的控制器通常無法獲得令人滿意之監控效果。最近Tseng and Mi (2014) 提出Quasi MMSE (qMMSE) 控制器來監控動態的生產製程，它雖可克服前述 EWMA控制器之缺點，唯其較不足之處是此控制器僅針對製程的投入-產出模型為一階動態模型下進行研究，故較缺乏一般化的結論。為了克服此問題，本論文首先建構出新的qMMSE控制器來處理製程的投入-產出為一般化動態模型之製程監控工作。其次可分別推導出製程產出公式、製程穩定條件 (stability conditions) 及決定此控制器之最適折扣因子。 最後文中亦探討此控制器與現存控制器執行批次控制之績效比較，結果顯示，當二階 (Second-order) 動態效應較顯著時，現存控制器較本研究所提出的控制器有高達約156%的製程總均方誤差(TMSE)，即使用本文之控制器可有效改善製程。

Run-to-run process control techniques are frequently used in semiconductor manufacturing operations. Most of the model-based studies (such as EWMA-based controllers) in literature assumed that process input-output (I-O) relationship is static and simply considers colored noise models for the process disturbance. However, the EWMA-based controllers usually lead to unsatisfactory performance when process dynamics and disturbance dynamics are occurred simultaneously. Recently, a quasi minimum mean square error (qMMSE) controller is proposed in literature, based on the assumption that process I-O model follows a combined first-order transfer function (TF)-noise model. However, it lacks of generality in practical applications. To overcome this difficulty, this study first proposes a generalized qMMSE controller when the process I-O model follows a combined general-order TF-noise model. Then, the expression of process output, the long-term stability conditions and the optimal discount factor of this controller are derived analytically. Furthermore, we use a second-order TF model to illustrate the effects of mis-identification of process I-O model (at the offline stage) on the process total mean square error (TMSE). Via a comprehensive simulation study, it demonstrates that the TMSE may even inflate more than 150% if a second-order TF-noise model with moderately large carry-over effects is wrongly identified as that of a first-order model. It means that the model identification at off-line stage is not negligible for implementing a dynamic RTR process control.

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