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研究生:黃柏淵
研究生(外文):Bo-Yuan Huang
論文名稱:整合前饋與回饋EWMA控制器之績效表現
論文名稱(外文):A study of feed-forward feedback EWMA controllerfor multistage processes
指導教授:林建華林建華引用關係念家興念家興引用關係
指導教授(外文):Chien-Hua LinGu-Xing Nian
口試委員:廖茂原彭健育
口試日期:2011-07-12
學位類別:碩士
校院名稱:靜宜大學
系所名稱:財務與計算數學系
學門:數學及統計學門
學類:其他數學及統計學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:33
中文關鍵詞:批次控制回饋控制器前饋控制器
外文關鍵詞:Run-to-Run process controlDouble EWMA controllerfeed-forward controller
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  • 下載下載:24
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近年來,全球高科技產業的發展,其中以半導體產業為最,然而新技術的引進,使得晶圓尺寸 (wafer size) 越做越大而元件的特徵尺寸 (feature size) 越做越小,這麼精密的IC產業製程中,做好製程監控的工作是格外重要的。Exponentially Weighted Moving Average (EWMA) 控制器在半導體製程的批次控制 (Run-to-Run process control, R2R) 中扮演著極為重要的回饋控制角色,它利用製程產出值與目標值之差異來調整製程之投入變數,以達到製程監控的目的。然而,半導體的製程是一個多階段的製程,一個產品從原料到成品,需經過好幾道子製程,而且每個子製程之間都息息相關,例如,蝕刻的深度以及寬度大小,會影響沉積的時間,而沉積的厚度會影響到研磨的時間。因此,當前一站製程的資訊能夠準確獲得,而如何將此資訊加入整個批次控制中,則是一個重要的課題。
本文整合前饋控制器 (feed-forward controller) 與double EWMA回饋控制器來監控半導體中具老化現象的生產製程,藉由控制後的製程產出公式,求得此控制器之穩定性條件;接下來利用條件期望值的想法推導出製程產出的總均分差 (total mean squared error, TMSE),並利用數值解求出在不同情況下的最適折扣因子與相對應之總均方差。並將製程影響因素加入探討本文控制器的績效表現,並在double EWMA控制器的最佳折扣因子之下,討論本論文提出的整合前饋與回饋EWMA控制器與傳統 double EWMA 控制器的相對績效。當加入前一站資訊,整合前饋與回饋控制器有效的降低TMSE,所以整合前饋與回饋控制器在製程產出監控優於傳統double EWMA 控制器。 

Run-to-run (R2R) process control is well developed in semiconductor manufacturing communities. The exponentially weighted moving average (EWMA) feedback controller is a popular model-based controller which primarily uses data from past process run to adjust the input recipe for the next run. The long-term stability conditions, performance analysis, and the optimal discount factors of EWMA controller for this closed-loop system have received great attention in literatures. However, IC manufacturing is a hybrid and multistage process. Wafer fabrication includes cleaning, layering, patterning, etching, deposition, planarization, etc. Each process is highly correlated with others such as the deposition time is deeply affected by the depth and width of etching process.
Focusing on the known information (such as the depth of etching) in previous process, and assuming that the process disturbance follows a general ARIMA (p, d, q) series, we propose a systematic approach that combines feed-forward controller and double EWMA feedback controller to adjust IC process. First, the long-term stability and short-term output performance are addressed. Furthermore, under the optimal discount factor of double EWMA controller, a simulation study is presented to illustrate that the proposed controller has the capability of reducing the total mean square error (TMSE) of process response variable by comparing with double EWMA controller. Finally, a sensitivity analysis is addressed to the impacts of parameters (such as initial bias, drifted rate, the variation of previous process and so on) on the process TMSE.

目錄

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………………………………………………………3
1.4 研究架構………………………………………………………4
第二章 文獻回顧與問題描述…………………………………5
2.1 Single EWMA回饋控制器之介紹……………………………5
2.2 Double EWMA回饋控制器之介紹……………………………6
2.3 問題描述………………………………………………………7
第三章 整合前饋與回饋EWMA控制器……………………10
3.1 模型簡介………………………………………………………10
3.2 製程產出及其穩定條件………………………………………11
3.3 最佳折扣因子的選取…………………………………………14
第四章 整合前饋與回饋EWMA控制器之績效分析………18
第五章 結論與後續研究………………………………………24

附錄……………………………………………………………25
參考文獻………………………………………………………27

參考文獻

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[8] Ingolfsson, A. and Sach, E. (1993), “Stability and Sensitivity of an EWMA Controller”, Journal of Quality Technology, 25, pp. 271-287.
[9] Jin, M. and Tsung, F. ( 2009), “Smith-EWMA run-to-run control schemes for a process with measurement delay’’, IIE Transactions, 44, pp. 346-358.
[10] Sachs, E., Guo, R., Ha, S. and Hu, A. (1991), “Process Control System for VLSI Fabrication’’, IEEE Transactions on Semiconductor Manufacturing, 4, pp. 134-144.
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[12] Sullivan, M., Bulter, S. W., Hirsch, J. and Wang, C. J. (1995), “A Control-to-Target Architecture for Process Control’’, IEEE Transactions on Semiconductor Manufacturing, 7, pp. 134-148.
[13] Tseng, S. T., Chou, R. j. and Lee, S. P. (2002b), “Statistical Design of Double EWMA Controller’’, Applied Stochastic Models in Business and Industry, 18, pp. 313-322.

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