Petri net decomposition approach to deadlock-free and non-cyclic scheduling of dual-armed cluster tools

Semiconductor cluster tools are the integrated equipment to process a variety of silicon wafers for the fabrication of microelectronic components. The cluster tool system consists of several loadlock modules, processing chambers, and material handling armed robots for transferring wafers between them. Most scheduling problems for dual-armed cluster tools adopt cyclic scheduling with the assumption of swap sequence of the robot arm. A deadlock-free and non-cyclic scheduling is highly required to improve total throughput of cluster tools for various types of wafer flow patterns and various changes of equipment configurations. In this paper, we propose a Petri net decomposition approach to derive a near-optimal solution of deadlock-free and non-cyclic scheduling of dual-armed cluster tools to reduce the computational complexity. A timed Petri net model is introduced to represent a non-cyclic scheduling model for dual-armed cluster tools. In order to obtain a deadlock-free and non-cyclic schedule efficiently, we propose a deadlock avoidance control policy that restricts the markings to prevent unmarked siphons. Deadlock condition for the dual-armed cluster tools is characterized by the structure of Petri net model. The performance of the non-cyclic scheduling model by the proposed method is compared with that of the cyclic scheduling model. Computational results show the effectiveness of the non-cyclic scheduling model compared with the cyclic scheduling model for multiple wafer flow patterns.