Optimal Scheduling of Transient Cycles for Single-Armed Cluster Tools With Parallel Chambers

摘要

Cluster tools have been extensively used for many semiconductor manufacturing processes such as lithograph, etching, deposition, and testing. Most previous studies on cluster tool scheduling have focused on steady cycles in which cluster tools repeat identical work cycles. However, the proportion of noncyclic transient operation cycles such as start-up cycles and close-down cycles becomes larger as the lot size tends to be smaller. We examine optimal transient scheduling for a single-armed cluster tool, in which there are parallel chambers and a process chamber is a bottleneck, while minimizing the makespan of a lot. To do this, we first identify fundamental properties of noncyclic transient cycles in a tool by analyzing resource workloads. We then propose a simple robot task sequence, a generalized backward sequence, which performs backward operations incrementally for start-up cycles and decrementally for close-down cycles. We also develop workload-based conditions for which the generalized backward sequence has the minimum makespan for single-armed cluster tools with parallel chambers. Finally, we develop a linear programming model to find the minimum makespan of the generalized backward sequence for the cases in which the conditions are not met and show its effectiveness. Note to Practitioners-Scheduling transient cycles such as start-up, close-down, and lot-switching cycles is an important issue for cluster tools due to frequent lot switchings, cleaning, and machine breakdown. In this paper, we propose a generalized backward sequence to schedule a wafer lot from the start-up cycle to the close-down cycle in a single-armed cluster tool with parallel chambers. The workload-based analysis is used for computing a lower bound on the makespan of a lot. We prove that the generalized backward sequence has an optimal makespan in most practical cases. Process engineers can adjust the workloads of process steps to improve the tool productivity based on our results. Even though the optimality conditions are not satisfied, we show that the generalized backward sequence still provides a reasonable makespan experimentally.