Because of residency time constraints and activity time variation for cluster tools, it is very challenging to schedule them. This chapter addresses their real-time scheduling issues and conducts their schedulability analysis in considering residency time constraints and bounded activity time variation. A Petri Net (PN) model, called Resource-Oriented PN (ROPN) is developed to model them. Such formal models describe not only the behavior of both initial transient and steady state processes of cluster tools but also determine the robot activity sequence with robot waits included. They are very compact, independent of wafer flow pattern, and useful for discrete-event control. It is due to the proposed models that scheduling cluster tools are converted into determining robot wait times. A two-level operational architecture is proposed to include an off-line periodic schedule and real-time controller. The former determines when a wafer should be placed into a process module for processing, while the latter regulates robot wait times on-line in order to reduce the effect of activity time variation on wafer sojourn times in process modules. Therefore, the system can adapt to random activity time variation. Based on the PN model, real-time operational architecture, and real-time control policy, it analyzes the effect of activity time variation on wafer sojourn time delay at a process module and presents its upper bounds. The upper bounds are given in an analytical form and can be easily evaluated. Then, it derives schedulability conditions that are in closed form expressions. If schedulable, an algorithm is developed to obtain an off-line periodic schedule. This schedule together with the real-time control policy forms a real-time schedule. It is optimal in terms of cycle time and can be analytically computed, which represents significant advance in this area. Several examples are used to show the applications of the proposed approach.
A Resource-Oriented Petri Net Approach to Scheduling and Control of Time-Constrained Cluster Tools in Semiconductor Fabrication
