Two-Level Nested Control Chart for Batch Process in the Semiconductor Manufacturing

Traditional variables control charts assume that process data is independently identically normally distributed (IIND). Some real-world processes, however, do not obey this convenient assumption. The semiconductor industry is very familiar with non-IIND distributions. The batch processes in the semiconductor manufacturing involve nested variation sources. The variation sources are between-batch variation, the within-batch (or between-wafers) variation in each batch, and the within-wafer variation in each wafer. First, it is proved that the application of traditional mean control chart in the batch process would result in too many false alarms. In addition, some kinds of control charts proposed in previous studies either cannot be used to monitor all the three variation sources or contain too many control charts. In this paper, we propose a new control chart named as two-level nested control chart, composing of four control charts for synthetically monitoring the batch process, which can monitor all the three variation sources. Finally, it was proved by practical application in the process of phosphorus diffusion that this new control chart can be used to monitor all the three variation sources of batch processes.