Run-to-Run model parameter estimation of multi-step batch process based on history data analysis

Abstract

In this study, a method is proposed that estimates the parameters of a quality prediction model for a batch process using previous batch data. The focus is on multistep batch processing, particularly the lithography process in a semiconductor manufacturing system . In this process, the appropriate model parameter input values exhibit a strong dependency on the prior processing history of the feed (hereafter called the control thread), e.g. the material conditions or equipment used in the previous processing steps. In such cases, it is common practice to use the data from the previous runs with an identical thread as the new batch run. However, as the process becomes more complicated in modern manufacturing systems, the variety of the control thread is increased and consequently the opportunity to locate recent data with an identical thread is reduced. In order to combat the shortage of usable data in an identical thread, it is important to enable the utilization of the data from the identical thread history data as well as that from runs of similar threads. This study addresses this need in a practical manner. Using multivariate analyses of variance, the statistical similarities among the parameter values of the previous history data for different threads can be evaluated and substitutable sets of threads can be identified. The results from the statistical analyses can increase the amount and recency of the data used in the input parameter calculation. Furthermore, some specific rules for searching through the available previous history data are proposed that consider both the thread similarity and time-immediacy. Moreover, two different estimation methods and their results are compared. The proposed methodology is tested using simulated data and real manufacturing industrial data; the results demonstrate the practical viability and significant potential of the proposed method.