Optimal Cyclic Scheduling of Wafer-Residency-Time-Constrained Dual-Arm Cluster Tools by Configuring Processing Modules and Robot Waiting Time

Optimal cyclic scheduling problems of wafer-residency-time-constrained dual-arm cluster tools in wafer fabrication are challenging and remain to be fully solved. Existing studies assume that all processing modules (PMs) of a required type are used to process the same type of wafers. This sometimes brings unneeded conservativeness to scheduling results, because we may be able to make a tool schedulable by reducing the number of PMs in some steps if the original one is not. In some cases, we may use fewer PMs to reach the same result if the original one is schedulable, thus saving energy and other production resources. This work selects a proper number of PMs of needed types to process wafers while ensuring the highest productivity of a wafer-residency-time-constrained dual-arm cluster tool. It proposes the necessary and sufficient conditions under which a tool is schedulable. It then develops a polynomial-complexity algorithm that finds an optimal cyclic schedule. Examples are given to show its superiority over existing ones, thus advancing this field of cluster tool scheduling greatly and helping semiconductor producers to realize the green manufacturing of wafers.