Adaptive Scheduling of Cluster Tools With Wafer Delay Constraints and Process Time Variation

A cluster tool consists of several single-wafer processing chambers and a wafer-handling robot. Cluster tools are widely used for wafer fabrication in semiconductor manufacturing fabs. As the circuit width shrinks down to below 20 or even several nanometers, wafer waiting within a chamber after processing becomes more critical to wafer quality due to residual gases and heat. Conventional tool scheduling rules, such as the swap sequence and the backward sequence, may not satisfy strict upper limits on wafer delays, especially when process times fluctuate randomly. We examine a scheduling problem for cluster tools with strict upper limits on wafer delays under process time variation. We propose a new class of schedules, which not only keeps timing patterns steady as possible but also adapts timing of tasks in response to process time variation so as to satisfy wafer delay constraints robustly. We also derive conditions for which there exists such a schedule. We develop a mixed-integer programming model to find an optimal schedule among such adaptive schedules. By numerical experiments, we show that the proposed scheduling method can effectively cope with tight wafer delay constraints even under large process time variations. Note to Practitioners—As the circuit widths shrink down, residual gases and particles within chambers after processing wafers become more critical to wafer quality. In fact, leading fabs are now cleaning a chamber for each new wafer in order to reduce such quality risk. We propose a new practical method for scheduling tools that can significantly reduce such quality risk caused by wafer waiting within chambers after processing.