在半導體批次製程中，常運用批次間控制來調整每個批次的輸入配方，以減少由擾動造成的產品品質變化。然而，因為不正確的控制器結構、不適當的性能標準及不足的強健性，批次間控制器往往無法於最佳狀況下運作。本論文針對多種擾動與不同的固定量測時延，發展適合的權衡性能指標與有效的強健穩定性分析方法，以建立批次間控制器之強健最佳設計流程。
批次製程常遭遇確定性與隨機性擾動，本論文探討偏移與漂移兩種類型的確定性擾動，並以自回歸滑動平均模型來描述隨機性擾動。批次間控制器的設計則以內模控制為基礎架構，可利用二階濾波器來處理偏移擾動，亦可利用三階濾波器來處理漂移擾動。本論文接著發展暫態性能指標來評估確定性擾動的影響，並且提供漸近性能指標來評估隨機性擾動的長期影響，最後結合暫態與漸近性能指標形成權衡性能指標，作為評估控制器整體表現的標準。
當兩控制器設計擁有同樣的增益邊限時，因為奈氏圖的形式不同會導致控制性能的差異。一般而言，在強健最佳的設計下，批次間控制器經強健性設限後的奈氏圖應與未設限最佳控制的奈氏圖相似。因此，本論文藉由建立強健穩定性的投影圖形，提供一個依據奈氏圖分類的強健性分析方法，然後利用權衡性能指標與強健穩定性圖形，發展出強健最佳批次間控制器的完整設計流程。模擬結果顯示，所得二階和三階濾波器分別優於傳統EWMA與double EWMA濾波器。

In semiconductor batch processes, run-to-run control is commonly utilized to adjust the input recipe of each run so as to reduce the variability in the product quality caused by disturbances. However, because of inaccurate controller structures, inappropriate performance criteria, and poor robustness, many run-to-run controllers cannot operate optimally. In this thesis, a suitable tradeoff performance index and an efficient analysis method for robust stability are developed to establish a robust optimal design procedure for run-to-run controllers subject to various disturbances and different fixed metrology delays.

This thesis investigates deterministic disturbances of shift and drift types, and describes stochastic disturbances by auto-regressive and moving average models. The design of a run-to-run controller is based on the internal model control framework, which involves second-order and third-order filters to cope with shift and drift disturbances respectively. Subsequently, transient performance indices are developed to assess the effects of deterministic disturbances and asymptotic performance indices are provided to assess the long-term effects of stochastic disturbances. Finally, a tradeoff performance index is formed by combining a transient and an asymptotic performance index, which can serve as a criterion to assess the overall performance of the controller.

When two controller designs possess the same gain margins, their Nyquist plots may still differ in shape, thus making a difference in control performance. In general, under the robust optimal design, the run-to-run controller with robustness constraints should have a Nyquist plot that is similar to that given by the unconstrained optimal control. Therefore, a robustness analysis method based on the classification of Nyquist plots is furnished by establishing the projected diagrams for robust stability. As a result, a complete design procedure for the robust optimal run-to-run controller is developed utilizing the tradeoff performance index and robust stability diagrams. Simulation studies manifest that the derived second-order and third-order filters are superior to the conventional EWMA and double EWMA filters respectively.

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