Analysis of circular cluster tools: Transient behavior and semiconductor equipment models

A cluster tool consists of a collection of wafer processing chambers housed in a chassis about a wafer transport robot. Cluster tools are of increasing importance in semiconductor wafer manufacturing. While much effort has been focused on the modeling and optimization of such tools in steady state, less attention has been paid to transient modeling. It is anticipated that there will be smaller lot sizes, more product changeovers and an increase in setups brought about by the transition to 450mm wafer diameters and product customization. As such, transient behavior may become the norm rather than the exception. In this paper we conduct a rigorous analysis of the cycle time of wafers that includes transient behavior, diverse process times and robot movement. The results extend existing analyzes, provide justification of existing approximations and allow us to develop more expressive and simple approximations for the cycle time. The models, which include the robot as a resource, can be used to replace the common affine Ax+B tool model in fab level simulations. A study of the quality and computational complexity of various transient models is conducted.