Performance analysis of single EWMA controller subject to metrology delay under dynamic models

ABSTRACT

This article mainly focuses on analyzing the performance of a closed-loop system where a single exponentially weighted moving average controller (SEWMA) subject to metrology delay is applied to regulate a semiconductor manufacturing process that exhibits input–output dynamics. Based on the Hurwitz stability criterion, the sufficient and necessary conditions for the stability of the closed-loop system are established. Based on these, it is convenient to study the effect of metrology delay on the feasible region of the weighting factor in the SEWMA controller. Later, under the stability condition, the asymptotical properties of the SEWMA controller are discussed and the performance of the closed-loop control system is analyzed in terms of the asymptotical variation and the transient deviation in the presence of several typical types of process stochastic disturbance. Then an optimization model is built to find the appropriate weighting factor to reduce the overall variation of the process output during production. Finally, extensive simulations are carried out to demonstrate the validity of our theoretical analysis in the context of chemical–mechanical planarization process.

KEYWORDS:

• Metrology delay
• process dynamics
• quality control
• run-to-run control
• statistical process control
• semiconductor manufacturing

Acknowledgement

We are grateful to the associate editor and anonymous reviewers for their valuable comments that significantly improve the presentation of this article.

Funding

This work was supported by the National Natural Science Foundation of China under grants 61203178, 61290323, and 61304214 and the Nature Science Foundation of Shanghai under grant 16ZR1416500.

Additional information

Notes on contributors

Qingsong Gong

Qingsong Gong received his B.Sc. and M.Sc. degrees in mathematics from the University of Science and Technology Beijing, People's Republic of China, in 2010 and 2012, respectively. He is now a Ph.D. candidate in the Department of Automation at Shanghai Jiao Tong University, Shanghai, People's Republic of China. His research interests include process control and optimization in semiconductor manufacturing.

Genke Yang

Genke Yang received his B.Sc. degree in mathematics from Shanxi University, People's Republic of China, in 1984; an M.Sc. degree in mathematics from Xinan Normal University, People's Republic of China, in 1987; and a Ph.D. degree in systems engineering from Xi'an Jiaotong University, People's Republic of China, in 1998. He is a full-time professor in the Department of Automation at Shanghai Jiao Tong University, Shanghai, People's Republic of China. His research interests include supply chain management, logistics, production planning and scheduling, and discrete event dynamics systems.

Changchun Pan

Changchun Pan received his Ph.D. degree in control and system engineering from the Department of Automation, Shanghai Jiao Tong University, People's Republic of China, in 2009. He is an associate professor at the School of Electronics, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of China. He was a visiting scholar at MIT, Cambridge in 2015, and a postdoctoral researcher at the Department of Chemical Engineering in Taiwan Tsinghua University, Tsinchu, Taiwan, in 2010–2011. His research interests include production scheduling and optimization, industrial process control, and big data analysis with location-based service.

Yuwang Chen

Yuwang Chen received his Ph.D. degree in control theory and control engineering from the Department of Automation, Shanghai Jiao Tong University, Shanghai, China, in 2008. He is a senior lecturer in decision sciences at the University of Manchester, Manchester, UK. Prior to his current appointment, he was a postdoctoral research associate at the Decision and Cognitive Sciences (DCS) research center of the University of Manchester and a postdoctoral research fellow at the Department of Computer Science, Hong Kong Baptist University. His research interests include multiple criteria decision analysis under uncertainties, modeling and optimization of complex systems, and risk analysis in supply chains.