Cluster tools for semiconductor fabrication, each of which consists of several single-wafer processing modules and a wafer-handling robot, are increasingly used for diverse fabrication processes. They are also being adopted for recent atomic layer deposition processes, where a wafer visits a process module more than once. We examine a scheduling problem for dual-armed cluster tools with such reentrant wafer flow patterns. Conventional swap operation strategy for dual-armed cluster tools cannot be used for the case of such reentrant flow patterns due to inevitable deadlocks.
Therefore, we propose two modified strategies, a hybrid operation strategy and a modified swap strategy. The hybrid operation strategy uses simple push-and-wait operation for reentrant process modules and swap operations for all other process modules. The modified swap strategy allows swapping between two different classes of wafers at a reentrant process module, the first-visit and the second-visit wafers, while conventional swap operation exchanges two identical types of wafers. We derive the cycle times of the two strategies in closed forms. It is shown that both strategies have much shorter cycle times than the simple and greedy, push-and-wait strategy. It is also identified when one of the two proposed strategies is better than the other.