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

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.