Cluster tools are used to process a variety of silicon wafers for the fabrication of microelectronic components. The dual-armed cluster tool system consists of several loadlock modules, processing devices, and dual-armed robots for transferring wafers between them. In order to improve total throughput of cluster tools, deadlock avoidance 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 deadlock avoidance scheduling for 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 better feasible solution. Computational results show the effectiveness of the proposed method combined with the deadlock avoidance policy.