Petri net modeling and one-wafer scheduling of single-arm tree-like multi-cluster tools

It is very challenging to obtain a one-wafer cyclic schedule for the widely used multi-cluster tools in semiconductor manufacturing. This work studies the scheduling problem for a single-arm tree-like multi-cluster tool that is process-dominant. A resource-oriented Petri net (PN) model is developed to describe its operation behavior by explicitly modeling robot waiting. Based on it, sufficient and necessary conditions are for the first time established to find a one-wafer periodic schedule. By determining robot waiting time, efficient algorithms are proposed to find such a schedule with the minimal cycle time. An example is used to show its application.