Petri Net Modeling And Optimal Scheduling Of Multi-Cluster Tools

In semiconductor manufacturing for VLSI (Very Large Scale Integrated) chips, the size of wafers is becoming larger and larger, which requires a highly automated production system such as cluster tools. Cluster tool with single wafer processing technology is adopted to semiconductor manufacturing more and more widely in the recent two decades. It is composed of a transport module (robot) and several processing modules. A new trend in the recent years of cluster tools is to adopt multi-cluster tools due to its greater efficiency. It is connected by several single-cluster tools with shared buffering modules to form a multi-cluster tool with linear or tree topology. It is one of the most complicated manufacturing systems. The interconnected buffers result in interactions among cluster tools. When the cycle time of one cluster tool fluctuates, it will propagate to the others, thus, the synchronization of multiple robots becomes extremely difficult. Hence, the schedule of multi-cluster tools is very challenging. Considering the moving times of robots, we focus on the schedule of a type of process-dominant multi-cluster tool which is equipped with single-arm robots and single-space buffers. It is widely used in semiconductor manufacturing industry practice. For such a multi-cluster tool, existing studies show that a one-wafer cyclic schedule cannot obtain the cycle time equal to the lower-bound. Furthermore, there is an optimal k-wafer cyclic schedule for it, which cannot obtain lower-bound cycle time in some cases. In the literature, there is no uniform model to analyze the initial transient process, steady process, and final transient process. For such a multi-cluster tool, this thesis investigates its Petri Nets (PN) modeling and an optimal1-wafer cyclic scheduling, mainly focusing on the following three problems.Its modeling. A Resource-oriented PN model is developed for it, where the robots’ waiting events are modeled explicitly. The sharing and competition of buffers are solved by colored tokens and controlled transitions in the PN model. A single model can describe the initial transient process, steady process and final transient process by introducing a special token representing a virtual wafer. With this PN model, it is derived that the cycle time of an individual cluster tool is a function of processing times of modules and robot moving/loading/unloading times, which uncovers that how the robot’s waiting times affects the cycle time.Linear topology multi-cluster tool scheduling. The sufficient and necessary conditions for the existence of1-wafer cyclic schedule is derived by the PN model, upon which an algorithm to obtain the robots’waiting times are found. By such known robots’waiting times, an optimal schedule by pull strategy to reach lower-bound cycle time is determined. Furthermore, when lower-bound cycle time cannot be obtained, the existence of a1-wafer schedule is shown, then, it is found that an increase in the cycle time of upstream cluster tools will influence the wafer sojourn time at buffer modules of downstream cluster tools. A small increment in the cycle time of upstream tools will make a large increment in the wafer sojourn time at a buffer of downstream tools. Such buffers are further propogated from the loadlock such that large increment in wafer sojourn time at them is accumulated, which can be calculated by some analytical expressions. With a smallest increment in the cycle time, an algorithm is developed to adjust the robot’s waiting times which can determine an optimal schedule.Tree-like topology multi-cluster tool scheduling. By decomposing a tree-like multi-cluster tool into several linear multi-cluster tools, the schedule of the former can be reduced to schedule of the latter. The schedulability conditions of1-wafer cyclic schedule are derived. Then, algorithms are proposed to check if a tree-like multi-cluster tool can be scheduled to obtain lower-bound cycle time, which can figure out the robots’waiting times to determine an optimal1-wafer schedule.In summary, this study reveals the conditions to reach lower-bound cycle time for a linear multi-cluster tool, and how to obtain an optimal schedule if the lower-bound of cycle time cannot be reached. In addition, it reveals the conditions to reach lower-bound cycle time for tree-like ones and corresponding algorithms are presented. The1-wafer cyclic schedule obtained by the proposed methods is preferred by the industry due to its simplicity and reliability and thus, it is very valuable in practice. The proposed algorithms use analytical expressions to find a schedule. Thus, they are efficient and will help the manufacturer of multi-cluster tools to improve the throughput. Compared with the existing studies, this thesis makes new discovery and methods which has not been seen. Such results will enlighten our future work on the schedule of multi-cluster tools.