Scheduling Time-Constrained Cluster Tools With Non-Identical Parallel Processing Chambers

As a computer-integrated manufacturing system, cluster tools are widely used for semiconductor manufacturing. To tackle their scheduling problems with parallel processing chambers, existing studies assume that the parallel processing chambers at each step are identical. However, due to machine aging, some differences among them could appear in reality. This work represents the first one to report the scheduling problems of cluster tools with non-identical parallel processing chambers. By focusing on time-constrained single and dual-armed cluster tools with non-identical parallel processing chambers, it derives the sufficient conditions under which a system is schedulable. Based on them, it develops two algorithms to obtain the feasible and optimal schedules. It also develops two linear programming models to find the feasible and optimal ones if the sufficient conditions are violated. The experimental results based on 5400 random instances show that the proposed scheduling method can be readily used to generate schedules for both time-constrained single and dual-armed cluster tools. Note to Practitioners - For cluster tools, due to machine aging, the wafer processing time at parallel processing chambers performing the same process tends to be different in practice. Such parallel processing chambers are called non-identical ones. It is tough to schedule time-constrained (with wafer residency time constraint) cluster tools with non-identical parallel processing chambers. The challenge is how to allocate robot waiting time at each step such that the wafer residency time constraint is satisfied. To ensure the high quality of finished wafers, their post-processing time at non-identical parallel processing chambers must be equal. This work offers readily applicable methods to address the problems, thereby generating a positive influence on the wafer quality and yield in the critically important field of semiconductor manufacturing.