e-journal
Non-Cyclic Scheduling of a Wet Station
We examine a non-cyclic scheduling problem of a wet station that performs cleaning processes for removing residual contaminants on wafer surfaces. Several chemical and rinse baths, and multiple robots for transporting jobs are linearly combined in a wet station. A wet station in a fab tends to have different types of jobs. Therefore, it is realistic to consider non-cyclic release of jobs into a wet station. We therefore examine a non-cyclic scheduling problem of a wet station that determines the task
sequence of each robot so as to minimize the makespan of a given sequence of different jobs. We develop an efficient branch and bound procedure by examining the scheduling problem. To do this, we first develop a Petri net model for the scheduling problem. By identifying deadlock prevention conditions from the Petri net model, we eliminate partial solutions in advance that eventually will lead to a deadlock. By examining the feasible transition firings or state transition behavior of the Petri net model, we branch only feasible partial solutions or nodes that correspond to feasible state transitions or transition firings. We also develop a tight lower bound based on the bottleneck workload of the baths. We prove computational efficiency of the branch and bound procedure for practical problems.
Note to Practitioners—A wet station performs wafer cleaning processes for removing residual contaminants after a wafer fabrication process. The wafer cleaning process approximately accounts for 30% of the whole wafer fabrication process and is critical to wafer quality. A wet station consists of several cleaning and rinsing baths and several lot-handling robots, and processes multiple different jobs concurrently. The jobs often require reentrant flows and have strict time constraints while there is no intermediate buffer. Due to such high complexity, the utilization of the baths and the throughput rate tend to be very low. For example, fabs process only two or three jobs concurrently, while the number of baths is eight or more. We developed an efficient scheduling method that can solve practical scheduling problems for wet stations and increase the throughput and utilization rate more than twice. The whole solution procedure from Petri net modeling for a given tool configuration and job flow data to finding optimal robot task sequences and schedules can be automated.
Index Terms—Branch and bound algorithm, cluster tool, deadlock, no-wait, Petri nets, wet station.
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