Efficient and Optimal Scheduling of Time-constrained Hybrid Multi-cluster Tools in Semiconductor Industry

Scheduling a multi-cluster tool with wafer residency time constraints is highly challenging yet important in ensuring high productivity of wafer fabrication. This paper presents a method to find an optimal one-wafer cyclic schedule for it. A Petri net is developed to model its dynamic behavior. By using this model, its schedule is found and analytically expressed as a function of robots' waiting time. In addition, this work establishes the necessary and sufficient conditions under which a feasible one-wafer cyclic schedule exists. Then, it gives efficient algorithms to find such a schedule that is optimal. These algorithms require one to determine the robots' waiting time via simple calculation and thus are efficient.