Scheduling Single-Arm Multi-Cluster Tools with Lower Bound Cycle Time via Petri Nets

Multi-cluster tools are widely adopted in wafer fabrication. It is of paramount importance to schedule them to achieve their optimal throughput. This work intends to find their one-wafer optimal periodic schedule to attain their lower bound cycle time. A resource-oriented Petri net model is developed to describe not only their steady state behavior but also behavior of their initial and final transient processes. Based on the model, this work derives the conditions under which one-wafer cyclic schedule with lower bound of cycle exists. Then, an algorithm is given to find it by scheduling the individual cluster tools one by one, which requires simple calculation only. Also, based on the Petri net model, an effective method for the implementation of such an optimal schedule is proposed. Examples are given to show the results.