半導體製程中modified-EWMA批次間控制之應用

A modified EWMA run-to-run control in its application to semiconductor manufacturing

徐仁國(Jen-Kuo Hsu)

指導教授 ： 黃孝平

國立臺灣大學/工學院/化學工程學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.01532

摘要

在各種半導體產業製程中 (如化學機械研磨、微影製程…等)，因為品質量測必須要在晶片出機台後才得進行，因此根據量測所進行控制只能反應在下一片晶片上，這種控制方式被稱為批次控制或片間控制。在上述批次控制中，EWMA (Exponential weighted moving average) 控制是經常被使用的一種控制作法。在 EWMA 控制中通常是將製程視為可用簡單的線性關係 (如: Yt = a+bUt-1)表示。但是在實際程序中因外界擾動或負荷的影響可能會使得程序批次間產生一個自我相關 (Autoregressive term, 簡稱為AR)。而忽略此一自我相關的存在使得模式不夠精確進而使得控制效果不如預期。此篇論文中我們針對模式中考慮加入自我相關項以便對實際擾動情況做較好的描述，其次對EWMA控制作法加以配合修訂使得批次間的控制能產生較佳的效果與更寬廣的應用範圍。

關鍵字

批次間控制 ； 半導體製程

並列摘要

In the fabrication of semiconductors, run-to-run control (or wafer-to-wafer control) algorithms are generally applied to compensate for disturbance changes to maintain the product qualities. The EWMA control is a most popular one among them. In EWMA control, it assumes that the process can be represented by a simple linear model without dynamics. However, in some cases, external disturbances could introduce an autoregressive dynamics into the system. Ignoring this autoregressive dynamics will lead to an imprecise model representation and result in unsatisfactory control results. In this thesis, a model with first order dynamics is adopted to derive a modified EWMA (Abbr. m-EWMA) control algorithm. By considering the autoregressive effect as a dynamic ingredient, it is found that this m-EWMA control provides a better framework to deal with more varieties of disturbances.

並列關鍵字

EWMA control ； semiconductor ； run-to-run control

參考文獻

Argon, C. and Guo, R.S., “Age-Based Double EWMA controller and Its Application to CMP Processes”, IEEE Transactions on Semiconductor Manufacturing, vol.14, pp.11-19, 2001

Bode, C.A., Ko, B.S., and Edgar, T.F., “Run-to-Run Control and Performance Monitoring of Overlay in Semiconductor Manufacturing”, Control Engineering Practice, 12, pp.893-900,2004

Box, G.E.P., and Kramer, T., “Statistical Process Control and Automated Process Control-A Discussion”, Technometrics, vol. 34, pp.251-267, Aug. 1992

Butler, S.W., and Stefani, J.A., ”Supervisory Run-to-Run Control of a Polysilicon Gate Etch Using In Situ Ellipsometry”, IEEE Transactions on Semiconductor Manufacturing, 7, 2, pp.193-201, 1994

Del Castillo, E., and Hurwitz, A., “Run-to-Run Process Control: A Review and Some Extensions”, Journal of Quality Technology ,29, 2, pp.184-196, 1997