Scheduling single-armed cluster tools with reentrant wafer flows

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A cluster tool for semiconductor manufacturing consists of several single-wafer processing chambers and a wafer-handling robot in a closed environment. The use of cluster tools is extended to reentrant processes such as atomic layer deposition, where a wafer visits a processing chamber more than once. Such a reentrant wafer flow complicates scheduling and control of the cluster tool and often causes deadlocks. We examine the scheduling problem for a single-armed cluster tool with various reentrant wafer flows. We develop a convenient method of modeling tool operational behavior with reentrant wafer flows using Petri nets. By examining the net model, we then develop a necessary and sufficient condition for preventing a deadlock. We also show that the cycle time for the asymmetric choice Petri net model for a reentrant wafer flow can be easily computed by using the equivalent event graph model. From the results, we systematically develop a mixed integer programming model for determining the optimal tool operation sequence, schedule, and cycle time. We also extend a workload measure for cluster tools with reentrant wafer flows. Finally, we discuss how our results can be used for engineering a cluster tool. We compare two proposed strategies, sharing and dedicating, of operating the parallel processing chambers for identical process steps.
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