Performance models for dual-arm cluster tools

Cluster tools with a dual-arm wafer transport robot are common in semiconductor wafer manufacturing. However, existing modeling methods suffer either from computational complexity (e.g., Petri nets, detailed simulation) and the resulting dearth of insight or from simplicity and its attendant loss of accuracy and expression (e.g., Ax+B models). Looking toward application in tool configuration optimization, performance evaluation and fab-wide simulation models, we develop expressive and computationally tractable equations and recursions for the cycle time of such cluster tools. The models include transient periods and robot behavior to express nonlinearities in tool performance. The models incorporate the affinity of such tools toward lots with certain numbers of wafers. We conduct simulations of dual-arm cluster tools to assess the quality of our models and compare performance and computational complexity between various approximation methods.