Scheduling and Control of Start-up Process for Time-Constrained Single-Arm Cluster Tools with Parallel Chambers

In wafer manufacturing, with the shrinking down of wafer lot size, cluster tools are frequently required to switch from handling one lot of wafers to another, resulting in more transient processes, including start-up and close-down processes. In the existing work, optimal scheduling of start-up process for time-constrained single-arm cluster tools has been addressed under the assumption that each processing step consists of just one process chamber. This work relaxes this strict restriction by treating that multiple process chambers could be configured for processing steps. By building Petri net model for the start-up process, a linear program is derived to search a feasible schedule with minimal makespan for time-constrained single-arm cluster tools with parallel chambers for the first time. One industrial example is given to demonstrate the effectiveness of the obtained results.