Assessing Measurement Noise Effect in Run-to-Run Process Control: Extends EWMA Controller by Kalman Filter

Abstract

Recently, the Exponentially Weighted Moving Average (EWMA) controller has become a popular control method in Run-to-Run (RtR) process control, but the issue of measurement noise from metrology tools has not been addressed in RtR EWMA controllers yet. This paper utilizes a Kalman Filter (KF) controller to deal with measurement noise in RtR process control and investigates the output properties for steady-state mean and variance, and for closed-loop stability. Five disturbance models modeling semiconductor process disturbances are investigated. These disturbance models consist of Deterministic Trend (DT), Random Walk with Drift (RWD), Integrated Moving Average process (IMA(1,1)), AutoRegressive Moving Average (ARMA(1,1)), and Autoregressive Integrated Moving Average (ARIMA(1,1,1)). Analytical results show that a KF controller can be considered as an extended version of a RtR EWMA controller. In particular, the EWMA controller is a special case of KF in a filtering form without the capability of measuring noise. Simulation results also show that the KF has a better ability to deal with measurement noise than the EWMA controller.