Scheduling start-up and close-down periods of dual-armed cluster tools with wafer delay regulation

Abstract

Cluster tools have been increasingly used for semiconductor manufacturing. While there have been many studies on cluster tool scheduling, most of them have focused on full work cycles in which identical work cycles are repeated. However, in reality, there are significant transient periods during which an empty tool begins to process new wafers or finishes processing and becomes empty. We should minimise the lengths of transient periods, so that a cluster tool quickly enters a desirable steady schedule for full work cycles or finishes operations quickly. We should also regulate wafer delays within chambers, because they cause wafer quality variation or failures. In this paper, we propose scheduling strategies for transient periods to meet those requirements. We prove that for the close-down period, the earliest starting policy that starts each operation as soon as the preceding operations complete minimises the close-down period while regulating the wafer delays. We also show that for the start-up period, the latest starting policy that starts each operation as late as possible while meeting the deadlines specified by the starting times of the given steady schedule minimises the start-up period. Finally, we suggest a way of minimising the total makespan by optimising the steady schedule.