Optimal one-wafer cyclic scheduling analysis of transport-dominant single-arm multi-cluster tools

In semiconductor manufacturing, it is very challenging to find an optimal one-wafer cyclic schedule for a multi-cluster tool. This work aims to do so. It assumes that its bottleneck tool is transport-bound, thereby making it transport-dominant. To do so, a scheduling strategy for each individual tool is determined. Then, a Petri net model is developed to describe the dynamic behavior of the system. With the model, it is found that to coordinate the robots is to determine their waiting time. Then, we derive necessary and sufficient conditions under which a one-wafer cyclic schedule with the lower bound of cycle time exists and present an efficient algorithm to test its existence and find it if existing. One industrial example is used to show the application and effectiveness of the proposed method.