A probabilistic approach to run-to-run control

Author

Hamby, Eric S. ; Kabamba, Pierre T. ; Khargonekar, Pramod P.

Author_Institution

Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA

Volume

11

Issue

4

fYear

1998

fDate

11/1/1998 12:00:00 AM

Firstpage

654

Lastpage

669

Abstract

This paper considers model uncertainty in the run-to-run control problem from a probabilistic viewpoint. The methodology assumes that the model parameters are stochastic and uses experimental input-output data off-line to characterize the probability distribution of the model parameters. This naturally leads to the notions of probability of stability and probability of performance as a means of evaluating run-to-run controllers. Analytic formulas for the probability of stability are given for the particular case of an EWMA controller. When considering a more general notion of performance, the Monte Carlo method is used to approximate the probability of performance to a high degree of confidence. This probabilistic approach to run-to-run control is then illustrated on a virtual plasma etching reactor. Finally, the reliability of the method is investigated

Keywords

Monte Carlo methods; integrated circuit manufacture; moving average processes; probability; robust control; sputter etching; statistical process control; uncertain systems; EWMA controller; Monte Carlo method; exponentially weighted moving average; model uncertainty; probabilistic approach; probability distribution; reliability; run-to-run control; stochastic model parameters; virtual plasma etching reactor; Etching; Inductors; Manufacturing processes; Performance analysis; Plasma applications; Plasma simulation; Process control; Robust control; Stability analysis; Uncertainty;

fLanguage

English

Journal_Title

Semiconductor Manufacturing, IEEE Transactions on

Publisher

ieee

ISSN

0894-6507

Type

jour

DOI

10.1109/66.728563

Filename

728563