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With wafer residency time constraints for some wafer fabrication processes, such as low pressure chemical--vapor deposition, the schedulability and scheduling problems are still open. This paper aims to solve both problems. A Petri net (PN) model is developed for the system. This model describes when the robot should wait and a robot wait is modeled as an event in an explicit way. Thus, to schedule a single-arm cluster tool with wafer residency time constraint is to decide how long a robot wait should be. Based on this model, for the first time, we present the necessary and sufficient conditions under which a single-arm cluster tool with residency time constraints is schedulable, which can be checked analytically. Meanwhile, a closed form scheduling algorithm is developed to find an optimal periodic schedule if it is schedulable. Also, a simple method is presented for the implementation of the periodic schedule for steady state, which is not seen in any previous work. Index Terms--Automated manufacturing system, cluster tool, Petri nets (PN), schedulability, scheduling, semiconductor manufacturing.

This paper studies the challenging problem of scheduling single-arm multi-cluster tools with wafer residency time constraints. They have a linear topology and their bottleneck tool is process-bound. This work aims to find an optimal one-wafer cyclic schedule. With the Petri net model developed in our previous work and the minimal cycle time for a multicluster tool without wafer residency time constraints, it derives the necessary and sufficient schedulability conditions for multicluster tools with wafer residency time constraints for the first time. Then, it gives an algorithm to find an optimal one-wafer cyclic schedule if schedulable. This is done by simply setting the robots’ waiting time for each tool. Thus, it is very computationally efficient and applicable to practical problems. An example is presented to illustrate the proposed method. [ABSTRACT FROM PUBLISHER]

In a multi-cluster tool, there may be both single and dual-arm cluster tools. Such a multi-cluster tool is called hybrid multi-cluster tool. To operate such a multi-cluster tool, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this paper conducts a study on scheduling a hybrid multi-cluster tool with its bottleneck tool being process-bound. The tool is modeled by a kind of timed Petri net model. With this model, the scheduling problem is reduced to determining the robots' waiting time. Then, the conditions under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached are presented. Based on them, a closed-form algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. Examples are given to show the application of the proposed method. [ABSTRACT FROM PUBLISHER]

With wafer residency time constraints, it is crucial to schedule a cluster tool in semiconductor fabrication such that the wafer sojourn time in a processing module is in a given range. However, because of the activity time variation in wafer fabrication by cluster tools, a feasible schedule obtained under the assumption of deterministic activity times may become infeasible. To solve this problem, it is critically important to reveal the wafer sojourn time fluctuations with bounded activity time variation. This paper targets at single-arm cluster tools. They are modeled by a Petri net to describe the fabrication processes. Based on the net, a real-time control policy is proposed such that its use offsets the effect of the activity time variation as much as possible. Then, the wafer sojourn time delay is analyzed and analytical expressions are given to calculate the upper bound. With the proposed method, we can check if a given schedule is feasible under bounded activity time variation. Examples are given to show the applications of the research results. [ABSTRACT FROM PUBLISHER]