A Cyclic Scheduling Approach to Single-Arm Cluster Tools With Multiple Wafer Types and Residency Time Constraints

With the reduction of wafer batch size on account of the diversification and individuation of consumption demands, increasing importance has been attached to the schedulability and controllability of the cluster tools with multiple wafer types being concurrently processed, while the corresponding research is seldom and still open. This paper is devoted to addressing the steady-state scheduling of single-arm cluster tools with multiple wafer types and residency time constraints. Inspired by the definition of wafer flow pattern for the single wafer type, a novel description for the multiple wafer types is introduced. For the sake of efficiency and simplicity, the multiplex backward sequence is proposed. To balance the workload of process steps, a virtual module technology with a two-tiered architecture is implemented. Furthermore, several sufficient and necessary conditions are derived to verify the schedulability of the system. Finally, an efficient algorithm is presented to find the periodic steady-state schedule, and its practicability and availability are validated by the given illustrative examples. Note to Practitioners —Cluster tools are a kind of highly automated, flexible, and integrated equipment applied widely in diversified semiconductor fabrication processes. Due to the strictness of processing constraints and unavailability of in-built buffers, it is challenging to effectively operate cluster tools. For a higher utilization of processing modules, fabs tend to concurrently process several kinds of wafers with dissimilar recipes in a cluster tool. However, the related scheduling and control problems remain open. With residency time constraints, this paper addresses the scheduling problems of single-arm cluster tools with multiple wafer types. By dissecting the mechanism of mixed-processing of multiple wafer types, several formal conditions are obtained to test the schedulability. Based on the multiplex backward sequence, a cyclic scheduling approach to single-arm cluster tools with multiple wafer types is presented. With the proposed method, schedulability conditions can be readily checked and a periodic schedule can be found easily. Thus, it can be applied to solve practical application problems.