Modified EWMA controller subject to metrology delay

Abstract

The resource and capacity limitations of the metrology equipment used in the creation of integrated circuits result in delay being a common issue for the practical implementation of run-to-run control scheme. In the literature, several papers have provided the means of using metrology delay data or Virtual Metrology (VM) prediction models on the transient behavior and asymptotic stability of Exponentially Weighted Moving Average (EWMA) controllers. However, these procedures still suffer from large bias and/or variation of the process response variable. To overcome this difficulty, a modified EWMA controller is proposed that adjusts the process by using both the metrology delay data and VM information. The analytical expression of the process output of this developed controller and its long-term stability along with short-term output performance are derived. Furthermore, under some specific parameter settings, a more comprehensive study is presented to illustrate that the proposed controller has the capability to reduce the total mean square error of process response variable compared with existing controllers.

[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the Appendices to this article.]

Keywords:

• Run-to-run control
• EWMA controller
• metrology delay
• virtual metrology