Abstract
Run-to-run process control techniques are frequently used in semiconductor manufacturing operations. Most of the model-based studies (such as EWMA-based controllers) in literature assumed that process input-output (I-O) relationship is static and simply considers colored noise models for the process disturbance. However, the EWMA-based controllers usually lead to unsatisfactory performance when process dynamics and disturbance dynamics are occurred simultaneously. Recently, a quasi minimum mean square error (qMMSE) controller is proposed in literature, based on the assumption that process I-O model follows a combined first-order transfer function (TF)-noise model. However, it lacks of generality in practical applications. To overcome this difficulty, this study first proposes a generalized qMMSE controller when the process I-O model follows a combined general-order TF-noise model. Then, the expression of process output, the long-term stability conditions and the optimal discount factor of this controller are derived analytically. Furthermore, we use a second-order TF model to illustrate the effects of mis-identification of process I-O model (at the offline stage) on the process total mean square error (TMSE). Via a comprehensive simulation study, it demonstrates that the TMSE may even inflate more than 150% if a second-order TF-noise model with moderately large carry-over effects is wrongly identified as that of a first-order model. It means that the model identification at off-line stage is not negligible for implementing a dynamic RTR process control.