Operational modeling and scheduling of cluster tools

Abstract

A cluster tool is considered as a key equipment for agile semiconductor manufacturing industry. The cluster tool consists of a wafer handling robot and several wafer processing chambers as usually a radial configuration. As many chip processes adopt the single-wafer processing technology, the cluster tools are broadly used for various types of processes. There are many types of operation characteristics including various wafer flow patterns, parallelization of processing chamber to reduce the cycle time, and pipeline configuration in a cell type working area. We investigate such operational properties and scheduling issues through formal modeling approaches. We use the Petri Net formalism as modeling tool to develop a performance evaluation and analysis the transient control. There are two problems, one is to find a optimal robot work cycle to guarantee the minimal cycle time to produce a wafer, the other is to check schedulability whether the configuration of processing times satisfy the time window constraints. The time window constraint is very crucial factor to determine the wafer quality. Therefore, we develop a directed graph which takes second weight factor for representing the number of chamber duplications. A polynomial time algorithm can be devised to check the processing time could satisfy the given timing constraints, based on the directed graph model. Also, we investigate the scheduling issues arising at cluster tool domain with time window and without time window constraints. Our event graph models the parallelized chamber as duplication tokens. This token duplication has the same modeling and analysis capabilities with the complicated event graph model. The cycle time formulae and functional characteristics are investigated by the circuit analysis. The circuit analysis is an important method to analyze the characteristics of system. All the results from event graph models and scheduling algorithms can be applied to develop a real-time scheduler a...