An Effective Problem Decomposition Method for Scheduling of Diffusion Processes Based on Mixed Integer Linear Programming

Diffusion processes in semiconductor fabrication facilities (Fabs) refer to the series of processes from wafer cleaning processes to furnace processes. Most furnace tools are batch tools, with large batch sizes, and have relatively long process times, when compared to the other processes. Strict time window constraints link cleaning processes with furnace processes for quality control. Those operational requirements for diffusion processes make their scheduling very difficult. This paper proposes an advanced scheduling approach based on a rolling horizon scheduling concept. Due to the combinatorial nature of the scheduling problem, the complexity of the problem increases exponentially, when the number of jobs and tools increase. However, the computation time allowed for the scheduler is limited in practice, because the variability in most Fabs requires schedulers to update the schedule in short intervals. We suggest an mixed integer linear programming model for diffusion processes, and propose an effective decomposition method to deal with this complexity problem. The decomposition method repeats multiple scheduling iterations, as it gradually extends the number of runs on tools, enabling the scheduler to generate near-optimal schedules in limited time intervals. The scheduler could make large improvements on key performance indicators, such as time window violation rates, batch sizes, throughput, etc. The software architecture of the scheduler implementation is also addressed in this paper.