Scheduling Close-Down Processes Subject to Wafer Residency Constraints for Single-Arm Cluster Tools

High-mix and low-volume wafer fabrication leads to more and more lot switches in cluster tools. Practitioners must thus deal with more transient processes during such switches, including start-up and close-down. To obtain higher throughput, it is critical to shorten these processes. Much effort has been put into the steady state modeling and scheduling of cluster tools and some for start up processes. However, no attention is paid to a close-down process for single-arm cluster tools with wafer residency constraints. This work aims to do so by 1) developing a Petri net model to analyze their properties and 2) proposing Petri net-based methods to solve their close-down optimal scheduling problems under different workloads among their process steps. An industrial example is given to illustrate their application.