Scheduling and Control of Startup Process for Single-Arm Cluster Tools with Residency Time Constraints

Due to the trends of larger wafer diameters and smaller lot sizes, cluster tools need to switch from processing one lot of wafers to another frequently. This leads to more transient periods in wafer fabrication, which includes startup and close-down processes. Their efficient scheduling and control problems become more and more important. They become very difficult to solve especially when wafer residency time constraints must be considered. Most previous studies focused on the steady periodic schedule for cluster tools. Little research was on the transient processes of cluster tools despite their increasing importance. In order to optimize a startup transient process, this work develops a Petri net model to describe its behavior for a single-Arm cluster tool. Then, based on the model, for the case that the workloads among the steps can be properly balanced, this work proposes a scheduling algorithm to find an optimal and feasible schedule for the startup process. For the other cases schedulable at the steady state, a linear programming model is developed to find an optimal and feasible schedule for the startup process. Finally, illustrative examples are given to show the applications of the proposed method.