Scheduling a Single-Arm Multi-Cluster Tool With a Condition-Based Cleaning Operation

As wafer circuit widths shrink less than 10 nm, stringent quality control is imposed on the wafer fabrication processes. Therefore, wafer residency time constraints and chamber cleaning operations are widely required in chemical vapor deposition, coating processes, etc. They increase scheduling complexity in cluster tools. In this paper, we focus on scheduling single-arm multi-cluster tools with chamber cleaning operations subject to wafer residency time constraints. When a chamber is being cleaned, it can be viewed as processing a virtual wafer. In this way, chamber cleaning operations can be performed while wafer residency time constraints for real wafers are not violated. Based on such a method, we present the necessary and sufficient conditions to analytically check whether a single-arm multi-cluster tool can be scheduled with a chamber cleaning operation and wafer residency time constraints. An algorithm is proposed to adjust the cycle time for a cleaning operation that lasts a long cleaning time. Meanwhile, algorithms for a feasible schedule are also derived. And an algorithm is presented for operating a multi-cluster tool back to a steady state after the cleaning. Illustrative examples are given to show the application and effectiveness of the proposed method.

     

A memetic algorithm for minimizing total weighted tardiness on parallel batch machines with incompatible job families and dynamic job arrival

This paper addresses a scheduling problem motivated by scheduling of diffusion operations in the wafer fabrication facility. In the target problem, jobs arrive at the batch machines at different time instants, and only jobs belonging to the same family can be processed together. Parallel batch machine scheduling typically consists of three types of decisions—batch forming, machine assignment, and batch sequencing. We propose a memetic algorithm with a new genome encoding scheme to search for the optimal or near-optimal batch formation and batch sequence simultaneously. Machine assignment is resolved in the proposed decoding scheme. Crossover and mutation operators suitable for the proposed encoding scheme are also devised. Through the experiment with 4860 problem instances of various characteristics including the number of machines, the number of jobs, and so on, the proposed algorithm demonstrates its advantages over a recently proposed benchmark algorithm in terms of both solution quality and computational efficiency.     

具有清洗工艺的单臂组合设备终止暂态调度

随着多品种小批量生产模式的普及,导致了组合设备频繁的暂态加工过程.为了提高组合设备的生产柔性,同时考虑晶圆驻留时间约束和腔室清洗时间约束,研究了单臂组合设备的终止暂态调度问题.首先,提出了 1-周期清洗工艺的暂态调度规则,并采用了面向资源的Petri网对单臂组合设备的终止暂态过程进行建模,引入避免死锁的变迁触发规则;其次,根据系统的终止暂态时间特性并考虑不同的调度情形,建立了终止暂态调度的线性规划模型;最后,通过实例验证了该方法的可行性.实验结果表明,与运用改进拉式策略的虚拟晶圆方案相比,该调度方案可有效地减少组合设备终止暂态的完工时间,并满足晶圆制造的工艺要求.     

Cycle time analysis for wafer revisiting process in scheduling of single-arm cluster tools

Some wafer fabrication processes performed by cluster tools require revisiting. With wafer revisiting, a cluster tool is very difficult to be scheduled due to a large number of possible schedules for the revisiting process. Atomic layer deposition (ALD) is a typical process with wafer revisiting that should be performed by cluster tools. This paper discusses the scheduling problem of single-arm cluster tools for the ALD process. In scheduling such a system, the most difficult part is to schedule the revisit...     

Optimal Integrated Schedule of Entire Process of Dual-blade Multi-cluster Tools From Start-up to Close-down

Multi-cluster tools are widely used in majority of wafer fabrication processes in semiconductor industry. Smaller lot production, thinner circuit width in wafers, larger wafer size, and maintenance have resulted in a large quantity of their start-up and close-down transient periods. Yet, most of existing efforts have been concentrated on scheduling their steady states. Different from such efforts, this work schedules their transient and steady-state periods subject to wafer residency constraints. It gives the schedulability conditions for the steady-state scheduling of dual-blade robotic multi-cluster tools and a corresponding algorithm for finding an optimal schedule. Based on the robot synchronization conditions, a linear program is proposed to figure out an optimal schedule for a start-up period, which ensures a tool to enter the desired optimal steady state. Another linear program is proposed to find an optimal schedule for a close-down period that evolves from the steady state period. Finally, industrial cases are presented to illustrate how the provided method outperforms the existing approach in terms of system throughput improvement.      

腔室清洗的单臂组合设备初始暂态调度

为了提升腔室洁净度,晶圆厂需对组合设备腔室进行清洗操作,从而提高晶圆的加工质量.考虑腔室清洗时间和晶圆驻留时间的约束条件下,本文研究了单臂组合设备的初始暂态调度问题.首先,提出了机械手的初始暂态活动规则,并对机械手活动序列进行描述,实现了系统的初始暂态可调度性;其次,对机械手在初始暂态和稳态的活动时间进行了建模;然后,根据系统的时间特性,建立了初始暂态调度的线性规划模型;最后,通过实例验证了该方法的有效性.与已有的虚拟晶圆方法相比,该调度方法能有效减少初始暂态的完工时间,提高了组合设备的晶圆生产效率.     

基于eM-Plant的虚拟晶圆制造自动组合装置

针对难以用解析法验证半导体加工装置的调度可行性问题,提出仿真建模研究的新方法。利用仿真软件eM-Plant建立晶圆制造中单臂自动组合装置的参数化仿真模型,构建一个虚拟的晶圆制造系统。该系统为研究自动组合装置控制问题提供有效手段,是验证半导体制造生产调度可行性的仿真平台。     

具有多品种晶圆混合加工的单臂组合设备调度

为了提高晶圆制造中组合设备的生产效率,在考虑晶圆驻留时间约束条件下,研究没有共享加工模块的多品种晶圆混合加工的单臂组合设备调度问题.首先,采用面向资源的Petri网模型描述多种晶圆产品的混合加工过程,引入控制变迁避免模型的死锁,采用赋时库所和赋时变迁模拟系统资源的活动时间.其次,通过虚拟加工的方法平衡工序的负载,基于系统Petri网模型和拉式调度策略,推导出单臂组合设备在多品种晶圆混合加工情形下的可调度性判定条件,并以解析形式描述.最后,提出了系统稳态调度求解算法并以实例验证了算法的有效性和可行性.     

Decomposition-based classified ant colony optimization algorithm for scheduling semiconductor wafer fabrication system

Due to its typical features, such as large-scale, multiple re-entrant flows, and hybrid machine types, the semiconductor wafer fabrication system (SWFS) is extremely difficult to schedule. In order to cope with this difficulty, the decomposition-based classified ant colony optimization (D-CACO) method is proposed and analyzed in this paper. The D-CACO method comprises decomposition procedure and classified ant colony optimization algorithm. In the decomposition procedure, a large and complicate scheduling problem is decomposed into several subproblems and these subproblems are scheduled in sequence. The classified ACO algorithm then groups all of the operations of the subproblems and schedules them according to machine type. To test the effect of the method, a set of simulations are conducted on a virtual fab simulation platform. The test results show that the proposed D-CACO algorithm works efficiently in scheduling SWFS.     

Scheduling Dual-Arm Cluster Tools With Multiple Wafer Types and Residency Time Constraints

Accompanying the unceasing progress of integrated circuit manufacturing technology, the mainstream production mode of current semiconductor wafer fabrication is featured with multi-variety, small batch, and individual customization, which poses a huge challenge to the scheduling of cluster tools with single-wafer-type fabrication. Concurrent processing multiple wafer types in cluster tools, as a novel production pattern, has drawn increasing attention from industry to academia, whereas the corresponding research remains insufficient. This paper investigates the scheduling problems of dual-arm cluster tools with multiple wafer types and residency time constraints. To pursue an easy-to-implement cyclic operation under diverse flow patterns,we develop a novel robot activity strategy called multiplex swap sequence. In the light of the virtual module technology, the workloads that stem from bottleneck process steps and asymmetrical process configuration are balanced satisfactorily. Moreover, several sufficient and necessary conditions with closed-form expressions are obtained for checking the system's schedulability. Finally, efficient algorithms with polynomial complexity are developed to find the periodic scheduling, and its practicability and availability are demonstrated by the offered illustrative examples.     

Post-Processing Time-Aware Optimal Scheduling of Single Robotic Cluster Tools

Integrated circuit chips are produced on silicon wafers. Robotic cluster tools are widely used since they provide a reconfigurable and efficient environment for most wafer fabrication processes. Recent advances in new semiconductor materials bring about new functionality for integrated circuits. After a wafer is processed in a processing chamber, the wafer should be removed from there as fast as possible to guarantee its high-quality integrated circuits. Meanwhile, maximization of the throughput of robotic cluster tools is desired. This work aims to perform post-processing time-aware scheduling for such tools subject to wafer residency time constraints. To do so, closed-form expression algorithms are derived to compute robot waiting time accurately upon the analysis of particular events of robot waiting for single-arm cluster tools. Examples are given to show the application and effectiveness of the proposed algorithms.      

Dynamic scheduling in flexible assembly system based on timed Petri nets model

This paper investigates a scheduling model for optimal production sequencing in a flexible assembly system. The system features a set of machines working together in the same workspace, with each machine performing a subset of operations. Three constraints are considered: (1) the precedence relation among the operations specified by the assembly tree; (2) working space that limits concurrent operations; and (3) the variation of process time. The objective is to find both a feasible assignment of operations to machines and schedule tasks in order to minimize the completion time for a single product or a batch of products. The assembly process is modeled using timed Petri nets and task scheduling is solved with a dynamic programming algorithm. The method calculates the time required precisely. A detailed case study is discussed to show the effectiveness of the model and algorithm.     

基于Petri网的组合设备建模与调度综述

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.     

晶圆重入加工的组合设备终止暂态的调度与分析

晶圆重入是半导体组合设备加工中典型的复杂加工工艺,分析和优化暂态加工过程对于晶圆重入加工具有重要意义.为了满足加工需求和提高组合设备的加工性能,基于稳态重入加工的双臂组合设备Petri网模型和1-晶圆周期调度策略,采用虚拟晶圆的加工模式分析了系统的终止暂态过程,讨论了系统终止暂态的加工时间分布,并给出相应的解析式进行描述.利用eM-Plant仿真平台建立了重入加工的双臂组合设备终止暂态的仿真模型,并用例子验证了1-晶圆周期调度的可行性及解析式的有效性,为研究晶圆重入加工过程的优化提供了有效方法和手段.     

应用离散事件系统控制理论求解生产调度的新方法

众所周知, 生产调度问题属组合优化问题, 一般来说不存在求得精确最优解的多项式算法. 因此, 对于大规 模调度问题, 人们应用启发式算法和元启发式算法以企求得满意解. 在实际的应用中, 许多工业过程需要满足严格 的工艺约束. 对于这类过程的调度问题, 很难应用启发式算法和元启发式算法, 因为这些方法难于保证所求得调度 的可行性. 为了解决这一问题, 本文以半导体芯片制造中组合设备的调度问题作为例子, 介绍了一种基于离散事件 系统控制理论的生产调度新方法. 利用Petri网建模, 任何违反约束的状态均被描述为非法状态, 而使非法状态出现 的调度则是不可行调度. 通过可行调度的存在性分析, 该方法获得可行解空间并将调度问题转化为连续优化问题, 从而可以有效求解. 并且指出, 该方法可以应用于其他应用领域.     

稳态调度下单臂组合设备时间延迟分析与优化

在半导体晶圆制造过程中,驻留时间延迟过长对晶圆质量具有消极影响.本文研究单臂组合设备稳态调度中如何合理地分配机械手等待时间,抵消驻留时间延迟的问题.首先,采用Petri网模型描述晶圆制造过程,分析了单臂组合设备稳态调度的时间特性,获得了稳态下工序驻留时间延迟计算表达式.其次,通过解构机械手等待时间对驻留时间延迟的影响机理,提出了一种机械手等待时间分配优先级规则.进一步,将虚拟瓶颈工序用于辅助分配机械手等待时间,结合优先级规则,提出了一种单臂组合设备稳态调度启发式算法.最后,通过例子验证了算法的可行性与有效性.与传统拉式策略和尽早加工策略对比,该算法能有效地减少单臂组合设备稳态调度下的驻留时间延迟并能满足晶圆制造的严格要求.     

有滞留时间约束的集束型装备在线调度问题研究

针对半导体制造中有滞留时间约束的集束型装备,研究了临时晶网到达时的在线调度问题,描述了调度问题域.建立了问题的数学模型,并根据模型提出了两层调度方法.外层算法通过粒子群优化过程求解临时晶网的加工顺序;内层算法在给定加工顺序的基础上,采用前向和后向递推方法获得口,行解窄问,并从可行解窄问获得最优完工时间.从理论上证明了算...     

Scheduling Dual-Arm Multi-Cluster Tools With Regulation of Post-Processing Time

As wafer circuit width shrinks down to less than ten nanometers in recent years, stringent quality control in the wafer manufacturing process is increasingly important. Thanks to the coupling of neighboring cluster tools and coordination of multiple robots in a multi-cluster tool, wafer production scheduling becomes rather complicated. After a wafer is processed, due to high-temperature chemical reactions in a chamber, the robot should be controlled to take it out of the processing chamber at the right time. In order to ensure the uniformity of integrated circuits on wafers, it is highly desirable to make the differences in wafer post-processing time among the individual tools in a multi-cluster tool as small as possible. To achieve this goal, for the first time, this work aims to find an optimal schedule for a dual-arm multi-cluster tool to regulate the wafer post-processing time. To do so, we propose polynomial-time algorithms to find an optimal schedule, which can achieve the highest throughput, and minimize the total post-processing time of the processing steps. We propose a linear program model and another algorithm to balance the differences in the post-processing time between any pair of adjacent cluster tools. Two industrial examples are given to illustrate the application and effectiveness of the proposed method.

     

A time-decomposition method for sequence-dependent setup schedulingunder pressing demand conditions

This paper develops a method for continuous-time scheduling problems in flexible manufacturing systems. The objective is to find the optimal schedule subject to different production constraints: precedence constraints (bills of materials), sequence-dependent setup times, finite machine capacities, and pressing demands. Differential equations along with mixed constraints are used to model production and setup processes in a canonical form of optimal control. The proposed approach to the search for the optimal solution is based on the maximum principle analysis and time-decomposition methodology. To develop fast near-optimal solution algorithms for sizable problems, we replace the general problem with a number of sub-problems so that solving them iteratively provides tight lower and upper estimates of the optimal solution     

基于MapReduce模型带任务分割的平行机调度优化

研究一类基于MapReduce模型的两阶段平行机调度问题.该模型中的每个工件包含Map和Reduce两道工序,前一工序的任务可以划分并同步加工,而后一工序不可划分,结合工件的到达时间、交货时间等约束,以最大完工时间和总延迟时间的加权和作为优化目标构建混合整数规划模型,设计采用差分变异策略和逐维角度扰动机制的改进鲸鱼优化算法求解模型.数值仿真实验结果表明,所设计的算法相对于经典的鲸鱼优化算法、粒子群算法的求解效果有显著的提升,验证了模型和所设计算法的有效性.