半導體產業為一個產品快速變遷的產業，其製程平均需經過300至500道製程，影響製程的因子也很多，使製程的投入－產出模型難以估計，干擾值難以某一種干擾值的分配加以估計。然而大多數的半導體廠都是利用EWMA控制器，無法隨著製程情況的改變而調整控制參數。
本研究考慮了半導體製程干擾值難以估計的情況，提出一個符合半導體製程的動態調整控制參數的比例積分（Dynamic Adjusted Proportional-Integral, DAPI）控制器架構，藉由逐批調整控制參數，可有效地解決當製程干擾值和I-O模型無法精確得知的半導體製程的控制問題。本文並以微影製程的線寬控制和減小覆蓋誤差為實證，考量了時間序列的干擾值及實際製程的干擾值等情況，並與EWMA（Exponentially Weighted Moving Average）控制器作比較，使製程產出能更接近目標值且變異更小。
另外，半導體製程在實務上經常會發生突發性的位移造成回饋控制器的錯誤判斷，以及量測站因量測不及造成堆貨，使接下來的數批貨所使用的補償值皆相同的量測時間延遲，在此情況之下，批次控制系統便無法完全發揮其原有的補償功能。本研究所提出的DAPI控制器因為不易受到製程干擾的影響而使投入值改變太大，可有解決突發性的位移和量測時間延遲的實務問題，並更接近實際半導體的生產環境。最後，實際製程干擾的線寬控制在製程能力比率有10%的改善率，變異數有11%的改善率；實際製程干擾的減小覆蓋誤差六種產品在全距平均有16%的改善率，均方根誤差平均有11%的改善率。DAPI比起EWMA控制器更能有效解決各種情境設定和二種實務問題。

Semiconductor industry and its products change fast with time. There are about 300 to 500 processes in semiconductor manufacturing, and there are many factors affecting each process. Therefore, it is hard to estimate the input-output model for one process, and also hard to estimate the process disturbance distribution or model. However, in most of fabs in semiconductor industry, they use EWMA controller to control the process, which cannot adjust the control parameter with process disturbance.
This research considers the situation that it is hard to estimate the process disturbance model, and propose a framework for the Dynamic Adjusted Proportional-Integral (DAPI) controller. By adjusting the control parameters lot by lot, we can effectively solve the problems mentioned above. And we will illustrate an empirical study of critical dimension control and overlay errors reduction of photolithography, both consider the time series disturbance model and real process disturbance. We will compare the output result with traditional EWMA (Exponentially Weighted Moving Average) controller, and show that DAPI controller can make the process closer to target and reduce the process output variance than EWMA controller.
In addition, in real semiconductor manufacturing situation, there exists process sudden Shift and metrology Delay problems, which make the controller performs worse. Since DAPI controller adjusts input value slowly, it will not be affect by process sudden Shift. We will show that DAPI controller can solve those problems, and can be used to a real semiconductor manufacturing situation. Finally, in the real process disturbance situation, for critical dimension control, DAPI can improve 10% on Process Capability Ratio and improve 11% on process standard deviation. Also, for overlay errors reduction, DAPI can improve 16% on Range and improve 11% on root Mean squared error. For all scenarios and two real problems, DAPI can perform better than EWMA controller.

第1章 緒論 1
1.1 研究背景 1
1.2 研究動機與重要性 2
1.3 研究目的與研究範圍 3
1.4 文章結構 3
第2章 文獻回顧 4
2.1 批次控制 5
2.2 批次控制器 6
2.2.1 EWMA控制器 7
2.2.2 PCC控制器 9
2.2.3 MMSE控制器 10
2.2.4 PID控制器 13
2.2.5 Self Tuning模型 15
2.2.6 LMPC模型 16
2.2.7 常用控制器的比較 18
2.3 批次控制於半導體的應用 19
第3章 研究架構 21
3.1 研究架構 22
3.2 問題定義 24
3.2.1 製程產出值的估計方法 24
3.2.2 製程干擾值的估計方法 25
3.2.3 製程投入量改變的限制 26
3.2.4 針對製程干擾值最佳化DAPI控制器的控制參數 27
3.3 估計製程I-O模型 28
3.4 DAPI控制器 29
3.5 定義評估指標 32
第4章 微影製程線寬控制驗證 33
4.1 以實驗設計找出顯著影響因子 33
4.2 迴歸模型建立 37
4.3 線寬控制評估指標 39
4.4 EWMA控制器 40
4.5 DAPI與EWMA控制器在不同製程情況的比較 40
4.5.1 虛擬製程干擾值和情境設定 40
4.5.2 實際製程干擾 48
4.5.3 三組製程干擾值分析 49
4.6 小結 51
第5章 微影製程覆蓋誤差控制驗證 52
5.1 覆蓋誤差 53
5.2 覆蓋誤差的製程I-O模型 53
5.2.1 找出顯著影響因子 53
5.2.2 曝光機台覆蓋誤差模型 56
5.3 覆蓋誤差評估指標 61
5.4 DAPI控制器 62
5.5 DAPI控制器與EWMA控制器在不同製程干擾的比較 64
5.5.1 虛擬製程干擾值和情境設定 64
5.5.2 實際製程干擾 69
5.6 小結 83
第6章 結論與未來研究 85
參考文獻 87

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