在半導體製程中，批次間控制通常用於消除擾動對產品品質的影響，以減少其與目標值的差異。然而製程擾動的形式未知且複雜多變，必須要對其有一定的瞭解，才能透過調整擾動預測濾波器的參數設置來提供最佳的輸入配方，從而使批次間控制維持良好運作。
本論文開發了一種基於半導體製程實際輸出入數據的批次間程序鑑別方法，以獲得擾動模型參數和輸入相關的程序增益。根據該方法，可以設計出一個強健最佳批次間控制器。首先，針對確定性與隨機性擾動的常見形式進行探討，發現確定性擾動多為製程偏移或漂移，隨機性擾動往往具有ARIMA (自回歸積分移動平均)動態。因此，可以通過R語言提供的Arima()函數將擾動模型和程序增益同時鑑別為具有ARIMA誤差的回歸模型(regression with ARIMA error)，並使用殘差分析來證明模型的準確性。接著，提出了一種基於ARIMA擾動模型參數和程序增益的批次間控制器設計方法。由於採用內模控制架構，批次間控制器的設計可轉化為擾動預測濾波器的設計，並選用三階濾波器來處理確定性製程漂移與複雜多變的隨機性擾動。
為了簡化三階濾波器的最佳設計，本論文開發了暫態和漸近性能指標的閉合形表示式，來分別代表確定性和隨機性擾動的影響，可以同時處理ARIMA、IMA和ARMA隨機性擾動，並以結合兩指標的權衡性能指標來評估濾波器的整體性能。最後，本論文討論批次間控制器的強健最佳設計，藉由奈氏圖建立並分類強健穩定性圖形，可以輕易地獲得滿足指定增益邊界並且最小化權衡性能指標的批次間控制器設計。

In semiconductor processing, run-to-run control is commonly used to eliminate the impact of disturbances on product quality to reduce its variations from target values. However, the forms of process disturbances are unknown and complicated, and some understanding of them is necessary to provide the best input recipe by adjusting the parameter settings of the disturbance prediction filter, so that the control can perform well.
This thesis develops a run-to-run process identification method based on the actual output and input data of a semiconductor process to obtain disturbance model parameters and an input-dependent process gain. According to this method, a robust optimal run-to-run controller can be designed. First, the common forms of deterministic and stochastic disturbances are investigated, and it is found that the deterministic disturbances are mostly shifts or drifts, and the stochastic disturbances often possess ARIMA (Autoregressive Integrated Moving Average) dynamics. Therefore, the disturbance model and process gain can be simultaneously identified as a regression model with ARIMA error through the Arima() function provided by the R language, and the accuracy of the model can be proved by residual analysis. Then, a run-to-run controller design method based on the ARIMA disturbance model parameters and process gain is proposed. Due to the internal model control structure, the design of the run-to-run controller can be translated into the design of a disturbance prediction filter.
To simplify the optimal design of the filter, closed-form expressions of transient and asymptotic performance indices are developed in this thesis to represent the effects of deterministic and stochastic disturbances, respectively, which can cope with ARIMA, IMA, and ARMA perturbations simultaneously. The overall performance of the filter is assessed by a trade-off performance index combining the two indices. Finally, this thesis discusses the robust optimal design of the run-to-run controller. By establishing and classifying robust stability diagrams based on Nyquist plots, the run-to-run controller design that satisfies specified gain margins and minimizes the trade-off performance index can be easily obtained.

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