基于Petri网的组合设备建模与调度综述

袁凤连; 黄波; 王际鹏; 潘春荣

doi:10.16383/j.aas.c210951

基于Petri网的组合设备建模与调度综述

doi: 10.16383/j.aas.c210951

1.
南京理工大学计算机科学与工程学院南京 210094
2.
湖北工业大学机械工程学院武汉 430068
3.
江西理工大学机电工程学院赣州 341000

详细信息

作者简介:
袁凤连：南京理工大学计算机科学与工程学院博士研究生. 主要研究方向为离散事件系统, Petri网和晶圆制造系统. E-mail: yuanfenglian@njust.edu.cn

黄波：南京理工大学计算机科学与工程学院教授. 主要研究方向为离散事件系统, Petri网, 智能制造和机器人系统. 本文通信作者. E-mail: huangbo@njust.edu.cn

王际鹏：湖北工业大学机械工程学院讲师. 主要研究方向为晶圆制造系统, 智能制造, 离散事件系统和Petri网. E-mail: wangjipeng.tpk@gmail.com

潘春荣：江西理工大学机电工程学院教授. 主要研究方向为制造系统的建模, 仿真, 调度与控制. E-mail: mailto:crpan@jxust.edu.cn

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出版历程
- 收稿日期: 2021-10-08
- 录用日期: 2022-06-07
- 网络出版日期: 2022-07-22
- 刊出日期: 2023-05-20

A Survey of Modeling and Scheduling of Cluster Tools Based on Petri Nets

1.
School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094
2.
School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068
3.
School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000

More Information

Author Bio:
YUAN Feng-Lian　Ph.D. candidate at the School of Computer Science and Engineering, Nanjing University of Science and Technology. Her research interest covers discrete event systems, Petri nets, and wafer fabrication system

HUANG Bo　Professor at the School of Computer Science and Engineering, Nanjing University of Science and Technology. His research interest covers discrete event systems, Petri nets, intelligent manufacturing, and robotic systems. Corresponding author of this paper

WANG Ji-Peng　Lecturer at the School of Mechanical Engineering, Hubei University of Technology. His research interest covers wafer fabrication system, intelligent manufacturing, discrete event systems, and Petri nets

PAN Chun-Rong　Professor at the School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology. His research interest covers modeling, simulation, scheduling, and control of manufacturing systems

摘要

摘要: 组合设备是半导体晶圆制造的核心装备, 其调度与控制优化是半导体制造领域极具挑战性的课题. Petri网因其强大的建模能力和简约的图形化表达优势, 被广泛地应用于组合设备的建模与调度. 对基于Petri网的组合设备建模与调度方法进行综述, 归纳总结了组合设备的结构类型、晶圆流模式、调度策略及Petri网建模方法, 并系统阐述组合设备的7类典型调度问题, 包括驻留时间约束、作业时间波动、晶圆重入加工、多品种晶圆加工、加工模块(Process module, PM)故障、PM清洗和组合设备群. 最后, 讨论了当前组合设备调度存在的挑战及后续可能的研究方向.
- 晶圆制造 /
- Petri网 /
- 组合设备 /
- 建模 /
- 调度
Abstract: Cluster tools are the core equipment of semiconductor wafer manufacturing. Their scheduling and controlling are challenging topics in the field of semiconductor manufacturing. Petri nets have the advantages of powerful modeling capacity and simple graphical descriptions. They are thus widely used in modeling and scheduling of cluster tools. This paper summarizes the research on cluster tools modeling and scheduling based on Petri nets. It presents structures and types of cluster tools, wafer flow patterns, scheduling strategy, and Petri net-based methods. It also addresses seven typical scheduling problems of cluster tools, including wafer residency time constraints, activity time variation, wafer revisiting, multi-type wafer flow patterns, process module (PM) failure, PM cleaning, and multi-cluster tools. Finally, the challenges existing in the cluster tools scheduling field and some possible future research directions are given.
- Wafer fabrication /
- Petri net /
- cluster tool /
- modeling /
- scheduling

HTML全文

图 1 组合设备示意图

Fig. 1 Sketch of cluster tools

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图 2 线型混合组合设备群

Fig. 2 Linear hybrid multi-cluster tools

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图 3 树型单臂组合设备群

Fig. 3 Tree-like single-arm multi-cluster tools

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图 4 组合设备不同晶圆流模式

Fig. 4 Different wafer flow patterns for cluster tools

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图 5 晶圆流为(1, 1, 1, 1)的拉式策略

Fig. 5 Backward strategy for wafer flow pattern (1, 1, 1, 1)

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图 6 晶圆流为(1, 1, 1, 1)的交换策略

Fig. 6 Swap strategy for wafer flow pattern (1, 1, 1, 1)

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图 7 不同晶圆流的POPN模型

Fig. 7 POPN models for different wafer flow patterns

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图 8 混合2-组合设备的POPN模型

Fig. 8 The POPN model for a hybrid 2-cluster tools

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图 9 单臂组合设备的ROPN模型

Fig. 9 The ROPN model for a single-arm cluster tool

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图 10 双臂组合设备的ROPN模型

Fig. 10 The ROPN model for a dual-arm cluster tool

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图 11 邻接组合设备ROPN模型

Fig. 11 The ROPN model of adjacent cluster tools

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表 1 拉式与交换策略在组合设备的应用

Table 1 Backward and swap strategy in cluster tools

调度问题	拉式/改进拉式	交换/改进交换
驻留时间约束	文献[16, 19–21, 25, 34–35]	文献[11–12, 17]
作业时间波动	文献[30, 34–36]	文献[29–33]
晶圆重入加工	文献[14, 36, 38–40, 47]	文献[41–46, 48–50]
多品种晶圆	文献[53, 56, 59, 62–63, 66, 72]	文献[54–57, 62–63]
PM故障	文献[76–77]	文献[78–79]
PM清洗	文献[69–70, 72–73]	文献[68, 70–71]

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表 2 组合设备的典型问题及调度方法

Table 2 Typical problems and scheduling methods of cluster tools

调度问题	相关文献	系统特征	Petri网类型	调度方法	调度目标
驻留时间约束	[11]	双臂	POPN	变迁发射顺序	最小周期时间
	[12]	双臂	POPN	变迁发射顺序	可调度性分析
	[13]	单/双臂	POPN	TM无干涉序列	最小周期时间
	[14]	单/双臂	POPN	变迁发射顺序	最小周期时间
	[15]	双臂	POPN	混合整数规划	优化最坏情况下$k$-晶圆周期
	[16–17]	单/双臂, 加工主导	ROPN	TM等待时间	最优1-晶圆周期
	[19–21]	单臂, 暂态过程, 加工主导	ROPN	TM等待时间	优化暂态过程
	[18, 25]	单臂, 传输与加工主导	ROPN	TM等待时间	最小周期时间
作业时间波动	[26]	单/双臂, 驻留时间约束	POPN	延迟TM发射时间	稳态运行
	[27]	单臂	POPN	延迟TM发射时间	恢复到稳态
	[28]	单/双臂, 驻留时间约束	POPN	反馈控制法	最小周期时间
	[29]	双臂, 驻留时间约束	POPN	TM变迁发射顺序	可调度的充分必要条件
	[30]	单/双臂, 驻留时间约束	POPN	自适应调度	最小周期时间
	[31–36]	单/双臂, 驻留时间约束	ROPN	实时调度	最小周期时间
晶圆重入加工	[38]	单臂	POPN	库所不变量分析	稳态的性能分析
	[39]	单臂, 不同晶圆流	POPN	变迁发射顺序	最小周期时间
	[40–44]	单/双臂	ROPN	TM等待时间	最小周期时间
	[45–48]	单/双臂, 驻留时间约束	ROPN	TM等待时间	最小周期时间
	[49–50]	单/双臂, 驻留时间约束和作业时间波动	ROPN	实时调度	最小周期时间
多品种晶圆	[56]	单/双臂, 混流, PM共享	POPN	启发式调度	最小周期时间
	[57]	双臂, 混流, PM共享	POPN	变迁发射顺序	最小周期时间
	[58]	双臂/混流, 并行, 驻留时间约束	POPN	变迁发射顺序	晶圆延迟最少
	[59]	单臂/混流, 驻留时间约束	ROPN	虚拟加工	可调度性
	[53]	单臂/混流	POPN	自循环控制法	系统无死锁运行
	[62]	单/双臂, 切换, 驻留时间约束	POPN	混合整数规划	最少完成时间
	[63]	单/双臂, 切换	POPN	混合整数规划	最少完成时间
PM清洗	[68]	双臂, $m\geq 1$	POPN	启发式调度	最小周期时间
	[69–70]	单/双臂, $m=1$	POPN	部分加载	最小周期时间
	[71]	双臂, $m=1$	POPN	部分加载	最小晶圆延迟
	[72]	单臂, $m=1$, 驻留时间约束	ROPN	线性规划	最小周期时间
	[73]	单臂, $m=1$, 驻留时间约束, 暂态	ROPN	线性规划	优化暂态过程
PM故障	[76–77]	单臂, 驻留时间约束	ROPN	故障响应策略	可行调度
PM故障	[79]	双臂, 重入, 驻留时间约束	ROPN	虚拟晶圆	优化暂态过程

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表 3 不同组合设备群及调度方法

Table 3 Different multi-cluster tools and scheduling methods

相关文献	拓扑结构	系统特征	缓冲模块容量	运行状态	调度策略	模型方法	调度目标
[80, 82]	线型	单臂	1或2	加工主导	拉式	ROPN	最优1-晶圆周期
[81]	线型	单臂	1	传输主导	拉式	ROPN	最优1-晶圆周期
[83]	线型	单臂	1或2	加工主导	拉式	ROPN	最优缓冲模块配置
[84]	线型	混合	1	加工主导	拉式/交换	ROPN	最优1-晶圆周期
[85]	树型	单臂	1	加工主导	拉式	ROPN	最优1-晶圆周期
[86–87]	树型	混合	1	加工主导	拉式/交换	ROPN	最优1-晶圆周期
[88]	线型	单/双臂	1	无固定	无固定	POPN	最优k-晶圆周期
[89]	线型	混合	1或2	无固定	拉式/交换	分解法	最优k-晶圆周期
[91]	树型	单臂	1或2	无固定	拉式	递归与分解法	最小周期
[92]	线型	单臂, 驻留时间约束	2	加工主导	拉式	ROPN	最优1-晶圆周期
[93]	线型	混合, 驻留时间约束	1	加工主导	拉式/交换	ROPN	最优1-晶圆周期
[94]	线型	单臂, 驻留时间约束	2	无固定	无固定	启发式	最小化最大完工时间
[95]	线型	单/双臂, 驻留时间约束, 暂态	1	加工主导	拉式/交换	线性规划	最优1-晶圆周期
[96]	线型	双臂, 驻留时间约束, 作业时间波动	1	加工主导	交换	实时调度	最优1-晶圆周期
[97]	线型	单/双臂, 驻留时间约束	2	无固定	无固定	改进动态规划	最优Pareto
[98]	线型	单/双臂/混合, 驻留时间约束	2	无固定	无固定	POPN	最优1-晶圆周期

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