Scheduling of Time-Constrained Single-Arm Cluster Tools with Two-Space Process Modules in Semiconductor Manufacturing

In semiconductor manufacturing, to improve the throughput of cluster tools,
process modules
(PMs) are designed to have multiple spaces such that more than one wafers can be processed in a PM concurrently. For multiple-space PMs, the internal chamber of a PM can rotate to make a wafer correctly loaded/unloaded into/from a space at the door of the PM. This makes that the wafer residency time in PMs is affected by both rotation operations of the internal chambers of PMs and the robot tasks. Also, satisfying constraints on the residency time of wafers is quite challenging in this kind of tools. Thus, with a single-arm robot and two-space PMs, this work is conducted to solve the challenging scheduling problems of cluster tools. To do so, by a presented two-wafer backward strategy, the properties of the system are presented. According to those properties, sufficient and necessary schedulability conditions under the two-wafer backward strategy are established and theoretical proofs are given. Also, if such a tool is schedulable, an optimal schedule can be found by an efficient algorithm developed in this work. Finally, case studies are carried out to show the applications of the proposed method.