Prediction of time-varying metrology delay for dEWMA and RLS-LT controllers

This paper investigates how to adaptively predict the time-varying metrology delay that can realistically occur in the semiconductor manufacturing practice. In the presence of metrology delays, the expected asymptotic double exponentially weighted moving average (dEWMA) control output, by using the EWMA and recursive least squares prediction methods, is derived. It has been found that the relationships between the expected control output and target in both estimation methods are equivalent, and six cases are addressed. Within the context of time-varying metrology delay, a new time update scheme to the recursive least squares-linear trend (RLS-LT) controller, combined with zone tests and the moving average (MA) control chart, is proposed. Simulated single input–single output (SISO) run-to-run processes subject to two time-varying metrology delay scenarios are used to assess the effectiveness of the proposed controller.