Scheduling transient period of cluster tools to reach a steady schedule

Abstract

A cluster tool consists of several single-wafer processing chambers and a wafer handling robot. A wafer should wait within a chamber after being processed there until it is unloaded by the robot. Such wafer delays may cause wafer quality degradation or variability due to residual gases and heat in the chamber. The tool operation schedule should maintain identical timing patterns or schedules for each cycle to keep wafer delays at each chamber constant for each wafer or cycle. However, we should make the tool to reach such steady schedule by loading wafers into the tool, empty at the beginning. Moreover, lots of random disruptive events, such as chamber failures, can occur while a cluster tool is operating. It is essential to make the tool to reach a steady schedule after a random disruptive event. The problem remains unsolved in view of cluster tool scheduling and the associated timed discrete event system or timed Petri net. In this paper, we develop a method of scheduling the robot tasks during the transient period of a cluster tool to reach a target steady schedule quickly as possible. To do this, we model the behaviors of a cluster tool using timed Petri nets and linear system matrices in the max-plus algebra. By analyzing the matrices, we first identify a class of steady schedules which can be reached from the empty tool. We develop the matrices that explains the schedule evolution of the start-up period before reaching the full work cycles. By examining the matrices, we develop a method of choosing the most desirable one from such class of reachable steady schedules that can be reached in the minimum time. In addition, we consider several complicate operational requirements and find out efficient scheduling methods. Moreover, the solution methods of this thesis are defined on general TEGs, and hence we expect that the methods can be extensively applied for various scheduling problems such as shop scheduling or project scheduling. Also, the method is easy to implement in practice as the solution is provided in a set of closed-form equations.