Scheduling transient periods of dual-armed cluster tools

Modern semiconductor manufacturing industry tends to reduce the lot size; that is, a lot has a small number of identical wafers, because of demands for small lots and an increased die yield per wafer due to the larger wafer size. Therefore, cluster tools for wafer processing, mostly repeating identical work cycles, are subject to frequent lot changes. We thus examine dual-armed cluster tool scheduling problems for transient periods. We first develop a Petri net model for the tool´s operational behavior in a transient period. We then develop a mixed integer programming model for finding an optimal schedule in terms of makespan of a transient period. We also examine how to adapt the conventional swap sequence, which is mostly used for scheduling steady work cycles, for a transient period. This is important to guarantee the compatibility between schedules of steady-state and transient periods because most tools are scheduled by the swap sequence in steady-state periods. To do this, we identify a deadlock-free condition and also propose two efficient scheduling algorithms by modifying the swap sequence. Finally, we experimentally analyze the efficiency of the proposed algorithms.