Performance Analysis of EWMA Controllers Subject to Metrology Delay

Metrology delay is a natural problem in the implementation of advanced process control scheme in semiconductor manufacturing systems. It is very important to understand the effect of metrology delay on performance of advanced process control systems. In this paper, the influences of metrology delay on both the transient and asymptotic properties of the product quality are analyzed for the case when a linear system with an initial bias and a stochastic autoregressive moving average (ARMA) disturbance is under an exponentially weighted moving average (EWMA) run-to-run control. Tuning guidelines are developed based on the study of numerical optimization results of the analytical closed-loop output response. In addition, effective metrology delay of a variable time delay system is analyzed based on the resampling technique implemented to a randomized time delay system. A virtual metrology technique is a possible solution to tackle the problem of metrology delay. The tradeoff between additional error of virtual metrology and reduction in time delay is studied. The results are illustrated using an example of control of the tungsten deposition rate in a tungsten chemical-vapor deposition reactor. The basic conclusion is that metrology delay is only important for processes that experience nonstationary stochastic disturbance. In such a case, use of virtual metrology is justified if the error of the virtual metrology method is less than the error caused by stochastic process noise. The accuracy of the virtual metrology noise with respect to the traditional metrology is not critical, provided that the error due to metrology is much less than that due to process disturbances.