Semiconductor fabrication lines have increasingly adopted cluster tools, each of which consists of several single wafer processing chambers and a central wafer handling robot. We investigate a scheduling problem for cluster tools for chemical vapor deposition. A chemical vapor deposition cluster tool can have diverse chamber configurations and should process diverse complicated wafer flow patterns. Further, an wafer should leave a chamber within a time limit after the processing is completed in the chamber. The cluster tool has a wafer handling robot with dual hands, and the robot operates in a swap mode such that the robot unloads a processed wafer from a chamber by using its empty hand and loads the wafer in another hand into the chamber. In such swap mode operation, a feasible robot move sequence is determined. However, since there is no intermediate buffer except the robot hands and each chamber has a strict wafer residency time constraint, the timings of the robot moves should be appropriately determined. Assuming a simple earliest starting timing control, we develop a mathematical condition on the process times at the chambers for which the resulting schedule satisfies the wafer residency time requirement. Since the process times are controllable more or less by the process engineers, the condition is used for developing a decision support system that supports the process engineers to determine the feasible process times. We also propose a way of implementing the schedule as a real-time scheduler embedded in a cluster tool controller using a finite state machine.
