Exponentially weighted moving average (EWMA) 回饋控制器為半導體科技產業中常被使用的製程批次控制手法。現存文獻大多針對單一機台生產單一產品的生產型態下，探討控制器之績效表現及分析。然而目前國內積體電路 (IC)製程大多採用多產品的混合生產型態 (mixed-run production)。針對此類混合生產型態，文獻上雖已有學者提出 tool-based (TB)、 product-based (PB) 、 cycle resetting (CR) 及 modified tool-based (MTB) 等回饋控制器，但上述控制器皆未考慮具有線性漂移 (linear drift)的製程，致使當製程發生線性漂移現象時，製程產出值的 total sum square error (TSSE) 有過大之現象，因此績效並不理想。針對具有線性漂移的製程，已有論文提出 modified tool-based of drifted-version (DMTB) 回饋控制器來處理上述問題，並能有效地降低切換產品後前幾期之製程產出值與目標值的偏差量，但是在連續相同產品製程中，製程產出期望值並不會收斂在目標值上，針對此項不足，本文建構出 modified tool-based with double EWMA (簡稱 MTB-dEWMA) 控制器來改善這個問題。本文推導出此新控制器製程產品切換後第一期產出公式及穩定條件，並以模擬實驗探討 MTB-dEWMA 與 DMTB 、 MTB 及 CR 控制器之 TSSE 績效分析及偏差問題，結果顯示 MTB-dEWMA 控制器的表現優於 DMTB 、 MTB 及 CR 控制器。

Exponentially weighted moving average (EWMA) feedback controller has been widely used in semiconductor manufacturing processes. The long-term stability and short-term performance of EWMA control scheme have been addressed by several studies in the literatures. Most of the controllers emphasize on the case of a single-tool with single-product production situation. However, in advanced manufacturing, multiple-product production situations are common for the practical implementation of run-to-run (R2R) control scheme. Recently, tool-based (TB), product-based (PB), cycle resetting (CR) and modified tool-based (MTB) controllers have been proposed to handle the mixed-run R2R control problem. These controllers are developed under the scenarios of non-drifted processes. For drifted-processes, these control schemes may suffer from a larger total sum square error (TSSE). The drifted-version MTB (DMTB) controller partially solves this problem, leading to a smaller TSSE (of output) but still having a non-ignorable bias during the same product production run. To overcome this issue, this thesis propose a modified DMTB with an extra controller to compensate for drift, called MTB-dEWMA. The stability conditions of MTB-dEWMA controller under the assumption that the process disturbance follows general time series are discussed. Furthermore, a simulation is conducted to examine the performance of MTB-dEWMA controller with existing competitors, including DMTB, MTB and CR. The results show that MTB-dEWMA controller outperforms other competitors in terms of TSSE criterion.

第一章 緒論 1
1.1 前言 1
1.2 批次控制簡介 2
1.3 EWMA 控制器簡介 4
1.4 批次生產型態簡介 6
1.5 研究動機 6
1.6 研究架構 7
第二章 文獻回顧與問題描述 8
2.1 多產品之混合生產製程控制器簡介 8
2.1.1 PB 控制器 9
2.1.2 CR 控制器 11
2.1.3 TB 控制器 12
2.1.4 MTB 控制器 14
2.1.5 DMTB 控制器 15
2.2 實例說明與問題描述 17
第三章 雙產品 MTB-dEWMA 控制器之分析 20
3.1 雙產品 MTB-dEWMA 控制器之建構 20
3.2 雙產品 MTB-dEWMA 控制器的製程產出及穩定性質 22
3.3 MTB-dEWMA 控制器與 DMTB 控制器之績效分析 32
3.4 MTB-dEWMA 控制器之整體績效分析 34
第四章 總結 37
4.1 結論與後續研究 37
4.2 三產品 MTB-dEWMA 控制器之建構 38
參考文獻 41
附錄 43
A 引理3.1 的證明 43
B 定理3.1 情況2的證明 48

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