Closed-Form Expressions on Lot Completion Time for Dual-Armed Cluster Tools With Parallel Processing Modules

Abstract

Cluster tools, which consist of processing modules (PMs) and a transport robot, are used for wafer fabrication processes in semiconductor manufacturing fabs. Once processing of a wafer lot containing several wafers is completed in a tool, an overhead hoist transport (OHT) unloads the lot and transports it to another tool. Since it is not easy to estimate when a wafer lot is completed, an OHT is required to wait for the wafer lot to be completed near the tool, or tools become idle due to the late delivery of wafer lots. To reduce the resulting idle time, a closed-form expression of the lot completion time is derived, especially, for a dual-armed cluster tool consisting of parallel PMs, to reflect real applications. We even consider lot switching operations where two consecutive wafer lots are processed with an overlap in analyzing the completion time. We finally show that the formulas derived can be used when there are small processing time variations experimentally. Note to Practitioners—For a dual-armed cluster tool with parallel processing modules (PMs), a closed-form expression on the lot completion time is derived. For this, we also consider lot switching operations, where the previous and next lots are temporarily processed together in a tool. With the formulas, we can send overhead hoist transports (OHTs) just-in-time to tools to unload or load wafer lots in tools, which can significantly reduce the idle time of tools and OHTs. In addition, the formulas can be used to design the number of PMs for wafer lots and assign wafer lots to tools to reduce their flow time. We believe that more efficient planning and scheduling in semiconductor manufacturing can be achieved by utilizing our results.