Petri net-based optimal one-wafer cyclic scheduling of hybrid multi-cluster tools in wafer fabrication

In a multi-cluster tool, there may be both single and dual-arm cluster tools. Such a multi-cluster tool is called hybrid multi-cluster tool. To operate such a multi-cluster tool, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this paper conducts a study on scheduling a hybrid multi-cluster tool with its bottleneck tool being process-bound. The tool is modeled by a kind of timed Petri net model. With this model, the scheduling problem is reduced to determining the robots' waiting time. Then, the conditions under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached are presented. Based on them, a closed-form algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. Examples are given to show the application of the proposed method.