Extensions and performance/robustness tradeoffs of the EWMArun-to-run controller by using the internal model control structure

We consider the run-to-run (RtR) correction of input recipes for semiconductor manufacturing processes using measurement information from previous runs. A RtR control algorithm that has been experimentally tested by industry and academia is the EWMA (exponentially weighted moving average) RtR controller. In this paper we provide extensions to this algorithm to address some of its drawbacks and also provide a rigorous theoretical analysis of its properties based on discrete control theory. By formulating the RtR control problem in the internal model control (IMC) structure used in feedback process control, we are able to extend the algorithm to completely eliminate offsets due to unmodeled process drifts, which is a common problem in semiconductor manufacturing. We also develop conditions for robustness with respect to modeling error and measurement delays. Tradeoffs between robustness guarantees and fast RtR response as well as handling of measurement noise are developed and presented in the form of plots that can be used for tuning the parameters of the RtR-IMC controller to accomplish the objectives set by the process engineer. The results are illustrated through several simulations including control of film deposition uniformity in an epitaxial reactor and tungsten deposition rate in a tungsten CVD reactor