Transient scheduling of single armed cluster tools: Algorithms for wafer residency constraints

The wafer handling robot actions in cluster tools used for semiconductor manufacturing should serve to maximize throughput while maintaining good wafer quality. Since excessive delay in a process chamber may cause deterioration in wafer quality, wafer delays should be maintained in an acceptable range, or preferably, should be minimized. We focus on addressing these concerns for all wafers in a lot, including those in both the transient and possibly cyclic regime. As the general problem is computationally complex, we first assume that the robot sequence is given and develop a multistage linear programming (LP) model to minimize the total makespan, subject to wafer residency constraints, and subsequently the average delay. Forging into less tractable territory, we next develop a branch and bound algorithm to find an optimal robot sequence with minimum wafer delay. This approach enables us to solve problems that were not previously solvable. Simulation studies demonstrate that when the number of process modules grows to more than five, the branch and bound algorithm may fail to find an optimal solution due to computational complexity. In this case, we suggest a transient sequence based on cyclic policies together with the LP model; it is within 2% of optimal.