Modeling, Scheduling And Control Of Cluster Tools In Semiconductor Manufacturing

Wafer fabrication is one of the most advanced and complicated manufacturing industries. In order to ensure high quality and precision, cluster tools have been widely used to process wafers in semiconductor manufacturing. Such a tool is a piece of integrated and automated equipment. It consists of several process modules, a transport module (a robot with single arm or dual arms), and two loadlocks for wafer loading/unloading. Since a cluster tool is very expensive, it is important to find an efficient way to schedule and control it such that it can be effectively operated.In scheduling a cluster tool, there are a variety of constraints, they include: 1) wafer residency time constraints. For some wafer fabrication processes, such as low pressure chemical-vapor deposition, wafer residency time constraints should be satisfied. It requires that a wafer should be unloaded from a process module within a limited time after it is processed, otherwise it would be damaged due to the high temperature and chemical gas. Without immediate buffer between the process modules in a cluster tool, it is very complicated to schedule a tool such that the constraints can be met; 2) activity time variation. In practice, some abnormal events may happen in cluster tool operation, leading to activity time disturbance, such as wafer alignment failure and retrial, wafer processing time delay, and computer processing time delay. With wafer residency time constraints, the activity time variation can result in the wafer residency time fluctuation such that a feasible schedule obtained under the assumption of deterministic activity time becomes infeasible; 3) wafer revisiting processes. Some wafer fabrication processes require the wafers to revisit some processing steps more than once. For instance, the atomic layer deposition is such a typical process. With wafer revisit, a cluster tool is no longer a flow-shop. Furthermore, often a wafer fabrication process with revisit in cluster tools is deadlock-prone. It is highly complicated to schedule a deadlock-prone system; 4) process modules subject to failure. With wafer residency time constraints, when one of the parallel process modules at a step fails, it is very difficult and complicated to find a way to schedule the cluster tool such that it can keep working without violating the residency time constraints.With the consideration of the above mentioned constraints, it is very complicated to schedule cluster tools. In fact, scheduling a cluster tool is a NP-hard problem. Thus, it is singnificant in the sense of both theory and practical applications to find an efficient way to schedule and control cluster tools in semiconductor manufacturing. With efficient schedule and control methods, it guarantees the stabalbility of the performence of cluster tools, improves quality of wafers, increases productivity, and reduces resource waste. Therefore, it can be put into use in practice. Thus, this thesis focuses on the scheduling and control problem of cluster tools. Since Petri net can describe concurrency well in discrete event systems, it has been widely used to model manufacturing systems, such as automated manufacturing systems. This thesis uses Petri net to model cluster tools as well. Based on the developed Petri net models, the following studies are conducted:1) Scheduling analysis of single-arm cluster tools with wafer residency time constraints and activity time variation. First, a Petri net model is developed to describe the behavior of cluster tools. Then, a real-time control policy is proposed to offset the effect caused by the activity time variation as much as possible. Based on the Petri net model and real-time control policy, the wafer sojourn time delay is analyzed and analytical expressions are given to compute its upper bound. With the upper bound of the wafer sojourn time delay, schedulability conditions and scheduling algorithms are developed. If the system is found to be schedulable by the schedulability conditions, an optimal off-line schedule can be obtained by the scheduling algorithms. The off-line schedule together with the real-time control policy forms a real-time schedule. As the scheduling algorihms consist of some simple expressions, it is very efficient. Finally, illustrative examples are given to show the application of the proposed methods;2) Scheduling analysis of time-constrainted dual-arm cluster tools with wafer revisiting. First, a Petri net model is developed for the system. Then, this thesis proposes a novel scheduling method called one-wafer cyclic schedule. Based on the Petri net model and the one-wafer cyclic schedule, necessary and sufficient schedulability conditions and scheduling algorithms are developed. If it is schedulable, an optimal schedule can be obtained by the proposed scheduling algorithms. The scheduling algorithms are composed of several analytical expressions. Therefore, it is very efficient. Finally, illustrative examples are given to show the application of the proposed methods;3) Response policies to process module failure of time-constrainted single-arm cluster tools. First, Petri net models are developed. Based on them, the failure response policies are proposed. With the proposed response policies, when one of the parallel process modules fails, the system can enter into a desired steady state from the original steady state without violating residency time constraints. The proposed policies are formulated via simple control laws for their easy implementation. Finally, illustrative examples are given to show their application.