Scheduling and timing control of time-constrained cluster tools

Abstract

A cluster tool consists of several single-wafer processing chambers and a wafer handling robot. Cluster tools have been increasingly used for diverse wafer fabrication processes. Some processes such as low pressure chemical vapor deposition processes require strict timing control, called by wafer residency time constraints. Unless a wafer processed at a chamber for such a process leaves the chamber within a specified time limit, the wafer is subject to quality problems due to residual gases and heat. Therefore, it has been challenging to schedule and control operations of cluster tools that have such wafer residency time constraints. We examine scheduling and timing control problems for dual-armed cluster tools that have wafer residency time constraints. We first discuss scheduling problems for the case when the process times and the robot task times have no random variation. We propose a systematic method of determining the schedulable process time range for which there exists a feasible schedule that satisfies the wafer residency time constraints. We explain how to select the desirable process times within the schedulable process time range. We present a method of determining the steady state tool operation schedule, called a stable schedule, that keeps the tool operation timings steady and satisfies the wafer residency time constraints. To better cope with restrictive wafer residency time constraints, we propose a modification of the conventional swap operation method that allows wafer delay on a robot arm during a swap operation. We compare the performance of the new swap strategy with that of the conventional swap strategy. Next, we discuss the case where the process times or robot task times are subject to random variation within some bounded ranges. Tool engineers wish to know a robust scheduling method for cluster tools under bounded time variation. In order to model the cluster tool operation under bounded time variation, we propose a modification of...