In a dual-armed cluster tool, the swap operation method that exchange a wafer on a robot arm with another wafer at a chamber has been mostly used. It is known to minimize the tool cycle time although it restricts the robot task sequence. Recent cluster tools have new scheduling requirements such as reentrant wafer flows for atomic layer deposition processes, constraints on the wafer delay times within chambers after processing, and concurrent processing of different wafer types. The restricted swap operation method may neither minimize the tool cycle time nor satisfy the wafer delay constraints, and even cause a deadlock. We examine new robot task sequences for dual-armed cluster tools that use the two robot arms more flexibly than the conventional restricted swap operation method.
In this thesis, we first examine new robot task sequences for a dual-armed cluster tool with basic scheduling requirements. We develop a systematic method of modeling the tool operational behaviors for non-swap operation sequences by using Petri nets. By examining the net model, we show that if the routing decisions on a conflict place of the model are made in cyclic order, the net is behaviorally equivalent to an event graph. We also identify conditions to prevent deadlocks to enhance computation time. From the results, we develop a mixed integer programming model for determining the optimal tool operation sequence, schedule, and cycle time. Finally, we discuss how our works can be applied to each of the additional scheduling requirements such as residency time constraints and concurrent wafer flows.
Second, we address modeling and scheduling issues for dual-armed cluster tools with reentrant job flows. There have been some researches addressing the issues, however, it is not yet clearly determined or investigated how the dual-armed robot can be fully utilized with the flow. To do this, we first propose a systematic way of modeling the tool operational behaviors with reentrant job flows that enables the robot to use each of the arms more flexibly. By investigating the model, we also present an MIP optimization model by revising the model with basic scheduling requirements. The reentrant job flow where a wafer visits the same process chamber more than once can be classified into two categories as a full reentrant and partial reentrant wafer flows. Both of the flows are prevalently used in many different manufacturing processes. By examining the reentrant wafer flows, we show that the conventional swap sequence can also be used as an optimal robot task sequence for the model with a full reentrant wafer flow. We also present systematic ways to build an event graph model with the swap sequence. Finally, we extend our works to the reentrant flows with residency time constraints.
Finally, we consider dispatching rules based on the Petri net model of dual-armed cluster tools with complex scheduling requirements. Many researches have been made for the scheduling of the cluster tools based on the cyclic scheduling approaches. They assume the robot and each processing chamber repeat identical operations in every one-wafer cycle which is defined as a period of producing one wafer by performing such repetitive tasks once. It is essential for analyzing and characterizing principles or theories about the given system. However, it has vulnerable points when the given system has complex requirements, where the predetermined sequence is not easy to be obtained, and has significant configuration changes or uncertainties. Uncertainties include the unexpected events such as malfunctions of components and delays of some activities. Such behaviors should be described by the optimization model which will considerably increase the complexity of the model to be solved to determine the optimal solution. For that reason, we study for the scheduling problems with such complex requirements using dispatching rules. We first suggest two types of deadlock prevention rules. One is based on the reachability analysis of the Petri net model. And the other is with the swap operation which is known to be an optimal robot sequence. Based on the deadlock prevention rule, we propose the general architecture of Petri net based simulation model of dual-armed cluster tools. Finally, we investigate these problems with simple dispatching rules and experiments for two specific configuration such as multi-slots cluster tools or the tool with cleaning processes of each chamber.
양팔 클러스터 장비의 스케줄링에 관한 연구는, 최적의 사이클 타임을 보장하는 것으로 알려진 스왑(Swap)작업을 기반으로 하는 스케줄링 방법이 주를 이루어 왔다. 그러나 장비의 사용이 확대되고, 반도체 제조 공정이 진화함에 따라, 재방문 물류 흐름, 챔버 내 웨이퍼 체재 시간 제약, 멀티 슬롯 클러스터 장비 등 스왑작업 만으로는 더 이상 대응하기 어려운 스케줄링 요구사항이 등장하고 있다. 따라서 로봇의 양 팔의 개별적인 작업을 허용하는 스왑 이외의 작업을 고려한 스케줄링 방법에 대한 연구가 필요하다.
본 논문에서는, 재방문 물류흐름, 웨이퍼의 체제 시간 제약, 다수의 물류흐름, 멀티슬롯 챔버, 주기적인 챔버 클리닝 등 복잡한 양팔 클러스터 장비의 스케줄링 요구사항에 대응할 수 있는 체계적이고 통합적인 스케줄링 이론 및 방법을 개발한다. 우선, 기본적인 형태의 장비를 대상으로, 양 팔의 개별적인 작업을 허용하는 로봇 작업 순서에 관한 연구를 수행한다. 이를 위해 반도체 제조 장비의 운영 형태를 모형화하기 위해 체계적인 페트리 넷(Petri Net) 모델을 개발한다. 이를 분석하여 데드락 방지를 위한 조건을 제시하고, 최적의 로봇 작업 순서 및 장비 운영을 위한 Mixed Integer Programming(MIP)을 개발한다. 이를 기반으로, 추가적인 스케줄링 요구사항에 대응할 수 있는 조건을 제시하고 각 요구사항 별 MIP모델을 개발한다. 또한 일부 재방문 물류흐름의 경우에, 기존의 스왑작업을 최적의 스케줄링 방법으로 사용할 수 있는 필요충분조건을 제시한다. 마지막으로, 앞서 개발한 페트리 넷 모형을 이용한 디스패칭 룰을 개발한다. Reachability 분석을 이용한 데드락 방지 조건과, 스왑작업의 특성을 이용한 방지 조건을 제시하고, 이를 기반으로 복잡한 스케줄링 요구사항에 대응할 수 있는 페트리넷 기반의 시뮬레이션 프레임웍을 제시한다.
