批次控制 (run-to-run control) 在半導體生產製程中扮演極重要的製程監控角色。當生產製程的投入變數對產出變數具有遷移效應 (carry-over effect) 的 transfer function (TF) model 時，文獻上有quasi MMSE控制器被提出來監控此類動態生產製程，唯此控制器僅在製程干擾項服從 IMA(1,1) 模型下被建構出來。因此當製程干擾項服從一般化的 ARIMA(p,1,q) 模型時，其製程的穩定條件及total mean square error (TMSE) 之表現並不甚理想。針對此缺點，本論文提出修正的quasi MMSE動態回饋控制器，並分別推導出此控制器下的製程產出公式、製程穩定條件及製程產出之漸近分配。最後，當實際製程為二階動態模型 TF(2,2) 且其干擾項服從 ARIMA(2,1,2) 時，本文亦探討此控制器與現存控制器之績效表現；結果顯示，本文提出的控制器之優點是不僅能將製程產出值更快速地調整到目標值，同時亦可使製程的TMSE大幅降低。

Run-to-run (R2R) control plays a vital role in monitoring or adjusting the integrated-circuit (IC) manufacturing process. Recently, a dynamic quasi MMSE (qMMSE) controller has been proposed in literature to address R2R problem when the process dynamics and disturbance dynamics exit simultaneously. The controller, however, was constructed only based on a transfer function (TF) model with the process disturbance follows an IMA(1,1) model. Therefore, its control performances on stability conditions and total mean square error (TMSE) may not perform satisfactorily when the true process disturbance follows a general ARIMA(p,1,q) model. To overcome this difficulty, this article first proposed a modified dynamic quasi MMSE (qMMSE) controller and then, the corresponding long-term stability conditions and its limiting distribution are derived. Furthermore, when the process I-O model follows a second-order transfer function (TF) model with the ARIMA(2,1,2) disturbance, we also compared the control performance of our proposed controller with that of existing controllers by using a simulation study. The results demonstrates that using wrong controllers usually cause serious effects on the performances of stability conditions and total mean square error (TMSE).

第一章 簡介 1
1.1 前言 1
1.2 批次控制簡介 2
1.3 研究動機 5
1.4 研究架構 6
第二章 文獻回顧 8
2.1 轉換函數模型 (Transfer Function Models) 8
2.2 製程干擾項為IMA (1,1) 的qMMSE控制器之文獻探討 10
2.3 問題描述 11
第三章 動態qMMSE回饋控制器分析 13
3.1 動態qMMSE回饋控制器之建構 13
3.2 動態qMMSE回饋控制器控制後產出公式 15
3.3 動態qMMSE回饋控制器的穩定條件 18
3.4當r+p+1 < q時控制器之績效分析 20
3.5 小結 23
第四章 控制器模擬分析 25
4.1 動態qMMSE回饋控制器在CMP製程之應用 25
4.2 當預測模型發生誤判時，對控制器績效之影響 28
4.3 當預測模型發生誤判時，影響控制器績效之模擬分析 34
4.4樣本數大小對製程穩定條件之影響 36
第五章 結論與後續研究 39
附錄 41
附錄1：一般化qMMSE控制器證明 41
附錄2：定理3.1證明 43
附錄3：定理3.2證明 45
參考文獻 54

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