Scheduling of Single-Arm Cluster Tools Handling Multiple Wafer Types Based on Double-Layer Configuration of Processing Modules

With the rapid changes and diversity of market demand, fabs have to produce wafers in many varieties and small batches. This brings a great challenge to the scheduling of wafer-residency-time-constrained cluster tools that concurrently process multiple types of wafers. Existing practice tends to employ all processing modules (PMs) of a required type to process wafers, and adopt a virtual module technology to balance PM workload for different types of wafers. However, since the virtual module technology may fail to well balance the natural workload of each processing step of a type of wafers, the corresponding scheduling results can be too conservative for the cluster tools to reach their optimal productivity. Can we improve their schedulability by choosing the most appropriate number of PMs to process wafers instead of all PMs? Under what conditions, may we use fewer PMs in a cluster tool to reach the same cycle time reached by using all PMs, thus saving resources and reducing energy consumption? This work presents a PM dual-layer configuration method. The first configuration is performed to decide the proper number of PMs, and the second one is done for so-called virtual PMs that are not physically existing PMs. It derives necessary and sufficient conditions for the schedulability of a cluster tool, which are more relaxed than all the existing ones. Furthermore, this work presents a polynomial-complexity algorithm to find an optimal cyclic schedule, and its superiority over existing ones is shown via several examples.
Note to Practitioners
—This paper addresses the cyclic scheduling problem of wafer-residency-time-constrained single-arm cluster tools handling multiple wafer types, and gives an efficient method to configure PMs for processing wafers. Through the method, we can balance not only the PM workload for different types of wafers, but also the PM workload for each step of a type of wafers. Based on it, a cyclic scheduling approach is presented, which is readily applied to industrial wafer manufacturing. By using our method, the schedulability of the tool can be greatly improved, and some energy and resource consumption can be eliminated to make wafer fabrication greener than the existing methods.