Petri net-based optimal one-wafer scheduling of single-arm multi-cluster tools in semiconductor manufacturing

In operating a multi-cluster tool, it needs to coordinate the activities of multiple robots. Thus, it is very challenging to schedule it. This paper conducts a study on one-wafer cyclic scheduling for multi-cluster tools whose bottleneck cluster tool is process-bound. The system is modeled by a Petri net. With this model, conditions under which a one-wafer cyclic schedule exists are developed. Based on them, it is shown that, for any multi-cluster tool whose bottleneck cluster tool is process-bound, there is always a one-wafer cyclic schedule. Then, a method is presented to find the minimal cycle time and the optimal one-wafer cyclic schedule. It is computationally efficient. Illustrative examples are used to show the applications and effectiveness of the proposed method.