Semiconductor cluster tools are used to process a variety of silicon wafers for the fabrication of microelectronic components. The cluster tool system consists of several loadlock modules, processing devices, and material handling armed robots for transferring wafers between them. In order to improve total throughput of cluster tools, a deadlock-free scheduling is highly required for various types of wafer flow patterns or various equipment configurations. In this paper, we propose a Petri net decomposition approach to the optimization of scheduling of dual-armed cluster tools for semiconductor manufacturing. A timed Petri net model is introduced to represent scheduling problems for dual-armed cluster tools. In order to obtain a deadlock-free schedule, we develop a deadlock avoidance control policy that restricts the marking to prevent unmarked siphons. The developed control policy is combined with the Petri net decomposition approach to generate a feasible solution. Computational results show the effectiveness of the proposed method combined with deadlock avoidance policy.