Analysis of circular cluster tools

Abstract

Cluster tools are used as semiconductor manufacturing equipment. An understanding of cluster tools is essential in this industry. While much effort has been focused on the modeling and simulating of tools in a steady state, less attention has been paid to transient modeling. The transition of the wafer size from 300mm to 450mm has brought with it the desire for smaller lot sizes. As the lot size becomes progressively smaller, a transient state becomes more important. In this paper, we focus on a circular cluster tool with a single-armed robot. We apply a backward sequence to control the robot. This sequence can be applied both a steady state and a transient state. We prove the feasibility of this approach when we use the backward sequence in a transient state. We also find a unique optimal region to minimize the cycle time when we use the backward sequence in a steady state. We find the fastest robot control in a transient state to attain a steady state when the workload is balanced, and we develop computationally reduced equations by conducting a rigorous analysis of the cycle time. This provides an exact transient analysis. To reduce the computation further, we developed a simpler and more accurate approximation of 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.