Petri net-based scheduling analysis of dual-arm cluster tools subject to wafer revisiting and residency time constraints

In semiconductor fabrication, it is very challenging to schedule a cluster tool with wafer revisiting and residency time constraints. For the typical wafer revisiting process of atomic layer deposition (ALD), a Petri net model is developed for the system. Then, with it and based on a 1-wafer cyclic scheduling method previously developed by the authors of this paper, schedulability conditions and scheduling algorithms are derived. The schedulability can be checked by analytical expressions. If schedulable, an optimal 1-wafer cyclic schedule can be analytically found. It is very computationally efficient. An illustrative example is given to show the application of the proposed approach.