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Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Manufacturing and supply chain management are becoming increasingly important in the semiconductor industry. Cluster tools are essential equipment in semiconductor production and are used for microscopic operations, such as the surface treatment of wafers. In particular, the operational parameters of cluster tools directly affect productivity, and various efforts are underway to optimize them at manufacturing sites. However, there are still many challenges in this process. In this study, we propose a framework for optimizing the operational parameters of cluster tools in semiconductor manufacturing using digital twin technology to address these challenges. The framework predicts productivity through manufacturing simulations based on operational parameters in a digital twin environment, analyzes the factors affecting productivity, and determines the optimal operational parameters. The study demonstrates that the cycle time of cluster tools in wafer fabrication can be significantly reduced through the proposed approach based on digital twins. The application of this framework is expected to contribute to cost reduction, productivity improvement, and enhancement of industrial competitiveness at semiconductor manufacturing sites.

Recently, in semiconductor manufacturing, cluster tools have to process multiple wafer types concurrently due to product customization. Different wafer types may have different processing routes, which causes deadlocks and complicates the scheduling problem of cluster tools. This work aims to develop a general method to resolve the scheduling problem of single-arm cluster tools with a general mix of wafer types. To this end, a generic Petri net model controlled by self-loops is developed to optimally avoid deadlocks. Based on the Petri net model, an earliest starting strategy is adopted to operate single-arm cluster tools once wafers enter the tools. In order to maximize the productivity, a particle swarm optimization algorithm is constructed to determine the releasing sequence of raw wafers. Numerical examples are provided to validate the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Optimal cyclic scheduling problems of wafer-residency-time-constrained dual-arm cluster tools in wafer fabrication are challenging and remain to be fully solved. Existing studies assume that all processing modules (PMs) of a required type are used to process the same type of wafers. This sometimes brings unneeded conservativeness to scheduling results, because we may be able to make a tool schedulable by reducing the number of PMs in some steps if the original one is not. In some cases, we may use fewer PMs to reach the same result if the original one is schedulable, thus saving energy and other production resources. This work selects a proper number of PMs of needed types to process wafers while ensuring the highest productivity of a wafer-residency-time-constrained dual-arm cluster tool. It proposes the necessary and sufficient conditions under which a tool is schedulable. It then develops a polynomial-complexity algorithm that finds an optimal cyclic schedule. Examples are given to show its superiority over existing ones, thus advancing this field of cluster tool scheduling greatly and helping semiconductor producers to realize the green manufacturing of wafers. [ABSTRACT FROM AUTHOR]

As the design of integrated circuits has become increasingly complicated and dense, serious wafer quality problems are observed in modern wafer fabrication facilities. Therefore, in cluster tools of leading fabs process chambers are periodically cleaned in order to eliminate residual chemicals and impurities that can damage the wafer quality. A chamber cleaning operation is mainly applied to tools in which a wafer delay has a crucial impact on the wafer quality, and hence the need of wafer delay control becomes more significant when chamber cleaning is considered. Thus, we first examine how wafer delays can be specified for cluster tools with chamber cleaning operations. We confirm that wafer delays are substantially increased when chambers are periodically cleaned, and we show that such increased wafer delays cannot be eliminated or reduced using the existing scheduling methods. In such a case, we prove that a partial loading strategy can minimise both the tool cycle time and the wafer delays by controlling the number of wafers being loaded into parallel chambers. We also present how wafer delays under the partial loading strategy can be further reduced by introducing a timing control method that regulates the start times of robot tasks. [ABSTRACT FROM AUTHOR]

Cluster tools are the key equipment in semiconductor manufacturing. For high-end chip manufacturing processes, to ensure the wafer quality, periodical cleaning operations for process chambers in such tools are required for eliminating the residual gas and chemicals. In operating a tool, the wafer processing time in a process chamber may vary within a range. It is meaningful to predict the cycle time of cluster tools with chamber cleaning operations and processing time variation. By doing so, automation material handling system can be told when a lot is completed by a cluster tool such that it can assign an overhead hoist transporter to transport this lot at the right time. This plays an important role in improving the productivity of a whole semiconductor manufacturing system. This work conducts the cycle time analysis of cluster tools with chamber cleaning operations and processing time variation. Specifically, it proposes a novel method to calculate the average cycle time of a single-arm cluster tool under which an optimal schedule can be obtained. Then, for a dual-arm cluster tool, an efficient algorithm is developed to approximate the average system cycle time under which an optimal schedule can be obtained. Experiments show that the gap between the average system cycle time obtained by simulations and the average system cycle time obtained by the proposed method is no more than 0.1% which demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The semiconductor etch cluster facility is the most used facility platform in the semiconductor manufacturing process. Optimizing cluster facilities can depend on production schedules and can have a direct impact on productivity. According to the diversity of semiconductor processes, the complexity of optimization is also increasing. Various optimization methods have been studied in many papers for optimizing such a complex cluster facility. However, there is a lack of discussion of how these methods can apply to practical semiconductor manufacturing fabs and the actual performance results. Even now, data analysis and optimal parameter derivation for maximizing the productivity of cluster manufacturing in semiconductor manufacturing fabs are continuing. In this study, we propose an automated method for data collection and analysis of the cluster, which used to be done manually. In addition, the derivation of optimization parameters and application to facilities are addressed. This automated method could improve the manual analysis methods, such as simulation through data analysis using machine learning algorithms. It could also solve the inefficiency caused by manual analysis performed within the network inside the semiconductor manufacturing fabs. [ABSTRACT FROM AUTHOR]

In this research, we examine feedback control-based cluster tool scheduling methods to maintain consistent wafer sojourn times when a tool is subject to random disruptive events. In our previous work, we proposed a feedback control design that regulates wafer sojourn times not to exceed the upper limits on wafer delays in a deterministic processing environment. Although such a feedback controller may ensure that wafer delay upper limits are always satisfied, it does not necessarily guarantee that the tool always restores its initial tool state after the occurrence of time disruptive events. This article thus further examines under which conditions a feedback controller enforces the wafer sojourn times to be stabilized in a stochastic processing environment with unexpected random time disruptions. Note to Practitioners—In semiconductor manufacturing, excessive wafer sojourn times at wafer fabrication tools increase the risk of wafer quality failures. In particular, the wafer quality fluctuates when the sojourn times are inconsistent over different wafers. Therefore, in cluster tools, wafer sojourn times are often strictly regulated to be minimized or to remain constant with an objective of reducing the risk of wafer quality degradation. In this research, we examine a cluster tool scheduling framework that enables to maintain stable tool operations even when a tool is randomly disrupted by unexpected exceptional events. [ABSTRACT FROM AUTHOR]

Nowadays, cluster tools tend to concurrently process multiple types of wafers with similar recipes in order to improve their utilization and flexibility in semiconductor manufacturing. Different wafer types may have different wafer flow patterns, resulting in that cluster tools are deadlock-prone. It is challenging to develop a general method to solve the deadlock problem of cluster tools without restriction on the wafer types. This work aims at solving such a challenging problem for single-arm cluster tools. To do so, a general Petri net model is developed for single-arm cluster tools. Given the wafer flow patterns of all wafer types to be processed in a single-arm cluster tool, such a Petri net model can be easily obtained by defining the relationship between places and transitions. Then, a control method by using self-loops is presented to prevent the model from deadlocks during the evolutions from the initial state to the final state. Furthermore, such a control method is proved to be optimal. Illustrative examples are given to verify the proposed method at last.

In wafer fabrication, it is imperative to minimize the transient process of cluster tools for the sake of on-demand and preventive maintenance. Due to the trend of multi-type and small-batch production, transient processes appear more and more frequently. Thus, the optimization problems of transient processes have gained increasing attention from both industry and academia. The requirement for wafer revisiting tend to complicate this problem significantly. However, only a few studies take such a challenge for cluster tools with wafer revisiting. This paper focuses on the schedule optimization of transient processes for dual-arm cluster tools with wafer revisiting. To accelerate transient processes, including both start-up and close-down ones, we adopt a program evaluation and review technique to analyze and harness a cluster tool’s state evolution. We then propose computationally efficient algorithms to speed up transient processes. Finally, we provide illustrative examples to show their applications and validate their effectiveness.

A cluster tool consists of several single-wafer processing chambers and a wafer handling robot. A wafer has to wait within a chamber after being processed there until it is unloaded by the robot. Such wafer delays may cause wafer quality degradation or variability due to residual gases and heat in the chamber. The tool operation schedule has to maintain identical timing patterns or schedules for each cycle so as to keep wafer delays constant for every wafer. However, at the beginning of the tool operation, the tool is in an empty state and hence we need to make the tool reach such steady schedule by loading wafers into the tool. In this article, we develop a method of scheduling the robot tasks during the start-up period of a cluster tool to reach a target steady schedule quickly as possible. To do this, we model the behaviors of a cluster tool using timed Petri nets and linear system matrices in the max-plus algebra. By analyzing the matrices, we first identify a class of steady schedules which can be reached from the empty tool. We develop the matrices that explain the schedule evolution of the start-up period before reaching the steady period. By examining the matrices, we develop a method of choosing the most desirable one from such class of reachable steady schedules that can be achieved in the minimum time. We also prove that the schedule also minimizes the time duration of the close-down. Finally, we present computational experiments. [ABSTRACT FROM AUTHOR]

We examine cyclic scheduling of single-armed and dual-armed cluster tools that concurrently process two wafer types by sharing a process module (PM). Because a PM is shared by two different wafers, the backward and swap sequences, which are prevalently used for single-armed and dual-armed tools without such complexity, respectively, are not effective. We therefore propose new sequences, called alternating backward and alternating swap sequences, for steady cycles of single-armed and dual-armed tools, respectively. We then develop optimality conditions for which the proposed sequences achieve the minimum cycle times in a fundamental cycle, and show that the optimality conditions hold for most practical cases. We also develop a condition for which a shared PM becomes the bottleneck and hence the PM sharing increases the cycle time. For general cycles, we propose heuristic scheduling methods that combine both the alternating backward (or swap) sequence and the conventional backward (or swap) sequence. Finally, we experimentally verify the efficiency and effectiveness of the proposed algorithm for dual-armed cluster tools. [ABSTRACT FROM AUTHOR]

We examine a scheduling problem for a dual-armed cluster tool that processes multiple similar wafer types concurrently. It has been recently proved that the well-known swap sequence, which is widely used for single wafer type processing, also minimizes the cycle time for concurrent processing. In this article, we wish to minimize wafer delays in a process chamber, which are critical to wafer quality degradation, while maintaining the minimum cycle time. In particular, we show that concurrent processing of wafers with different processing times complicates the analysis of wafer delays significantly, and the wafer delays can be remarkably reduced by finding a proper cycle plan which is the release sequence of different wafer types. We first characterize wafer delays for a given cycle plan by analyzing the circuits of the timed event graph (TEG) model. From this, we prove that concurrent processing of wafers may cause a significant workload imbalance between parallel chambers of a process step, and hence the wafer delays increase substantially. We present that the wafer delays are minimized by a cycle plan that evenly balances workloads between parallel chambers. We also propose how wafer loading task at each process step has to be postponed to meet wafer delay constraints while maintaining the minimum cycle time. Note to Practitioners—Wafer quality control has become an essential fab operational problem in semiconductor manufacturing industry. In cluster tools, which are dominantly being used for diverse wafer fabrication stages, it has been proven that the wafer delays within process chambers have a crucial impact on the wafer quality. Accordingly, modern fabs have introduced stringent quality control to regulate wafer delays in cluster tools. In this research, we propose a scheduling strategy to minimize the wafer delays when a cluster tool concurrently processes multiple wafer types. We first show that the release sequence of different wafer types significantly impacts the wafer delays under concurrent processing, and we then propose how these wafer delays can be minimized by finding the optimal wafer release sequence. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The semiconductor etch cluster facility is the most used facility platform in the semiconductor manufacturing process. Optimizing cluster facilities can depend on production schedules and can have a direct impact on productivity. According to the diversity of semiconductor processes, the complexity of optimization is also increasing. Various optimization methods have been studied in many papers for optimizing such a complex cluster facility. However, there is a lack of discussion of how these methods can apply to practical semiconductor manufacturing fabs and the actual performance results. Even now, data analysis and optimal parameter derivation for maximizing the productivity of cluster manufacturing in semiconductor manufacturing fabs are continuing. In this study, we propose an automated method for data collection and analysis of the cluster, which used to be done manually. In addition, the derivation of optimization parameters and application to facilities are addressed. This automated method could improve the manual analysis methods, such as simulation through data analysis using machine learning algorithms. It could also solve the inefficiency caused by manual analysis performed within the network inside the semiconductor manufacturing fabs.

1Modern cluster tools tend to clean the chambers each time a specified number of wafers have been processed. Such cleaning processes are intended to reduce the quality risk due to the residual chemicals within the chambers. When such cleaning processes are introduced, the conventional scheduling methods for cluster tools, such as the swap sequence for dual-armed cluster tools, are no longer effective. Therefore, we examine a cyclic scheduling problem for a dual-armed cluster tool that performs cleaning processes periodically. We first identify sufficient conditions for which the conventional backward and swap sequences give the minimum cycle time. We then develop a systematic way of generating all feasible robot task sequences, for which the cycle times can be computed. However, the number of feasible robot task sequences increases too fast to be enumerated as the cleaning cycle and the number of process steps increase. To address the complexity problem, we propose two heuristic scheduling strategies and compare them with the conventional scheduling methods and the lower bound of each schedule, respectively, to verify their effectiveness experimentally. [ABSTRACT FROM AUTHOR]

As a kind of robotic cells, cluster tools are widely used for semiconductor wafer fabrication processes since they provide a reconfigurable and efficient environment. With recent advances in new semiconductor materials, the circuit line width has continuously being shrunk down, which brings new challenges for manufacturers. They require that a wafer should be moved away from a processing chamber as soon as possible after its processing is finished. To ensure high-quality integrated circuits in a wafer, its post-processing residency time must be minimized. It is also highly desirable to maximize the throughput of robotic cluster tools. This article aims at scheduling such tools with multiple objectives subject to wafer residency time constraints. To do so, new algorithms are proposed to calculate robot waiting time delicately upon the analysis of particular events of robot waiting for dual-blade robotic tools and optimally schedule such tools. The numerical results of industrial examples show that the proposed algorithms can provide an effective method to find schedules for dual-blade cluster tools such that multiple objectives are optimized. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the problem of sequencing handler's moves in cluster tools in the semiconductor industry. A suboptimal sequence of the handler's moves usually leads to long idle times in the cluster tool's chambers and hence longer makespan and lower throughput. Therefore, an effective algorithm that minimises idle times in the cluster tool's chambers is required. An algorithm called MinBIT (minimising bottleneck idle time) is presented as a new method for sequencing the handler's moves. The MinBIT algorithm gives priority to the bottleneck stage, and thus leads to a reduction in unnecessary idle times and hence a shorter makespan. We compared the MinBIT algorithm with other algorithms. Our algorithm achieved best performance in 98% of the cases. In the other 2% of the cases it achieved second or third best performance. The computational results show that the MinBIT algorithm can improve the performance of a cluster tool by up to 10%. A comparison between the MinBIT solutions and the optimal solutions found by using branch and bound, shows that the deviation between them ranged between 0% and 0.22%, which indicates that MinBIT gives optimal or near optimal results. [ABSTRACT FROM AUTHOR]

Since last decade, the cluster tool has been mainstream in modern semiconductor manufacturing factories. In general, the cluster tool occupies 60% to 70% of production machines for advanced technology factories. The most characteristic feature of this kind of equipment is to integrate the relevant processes into one single machine to reduce wafer transportation time and prevent wafer contaminations as well. Nevertheless, cluster tools also increase the difficulty of production planning significantly, particularly for shop floor control due to complicated machine configurations. The main objective of this study is to propose a short-term scheduling model. The noteworthy goal of scheduling is to maximize the throughput within time constraints. There are two modules included in this scheduling model—arrival time estimation and short-term scheduling. The concept of the dynamic cycle time of the product’s step is applied to estimate the arrival time of the work in process (WIP) in front of machine. Furthermore, in order to avoid violating the time constraint of the WIP, an algorithm to calculate the latest time of the WIP to process on the machine is developed. Based on the latest process time of the WIP and the combination efficiency table, the production schedule of the cluster tools can be re-arranged to fulfill the production goal. The scheduling process will be renewed every three hours to make sure of the effectiveness and good performance of the schedule.

A cluster tool consists of several single-wafer processing chambers and a wafer-handling robot. Cluster tools are widely used for wafer fabrication in semiconductor manufacturing fabs. As the circuit width shrinks down to below 20 or even several nanometers, wafer waiting within a chamber after processing becomes more critical to wafer quality due to residual gases and heat. Conventional tool scheduling rules, such as the swap sequence and the backward sequence, may not satisfy strict upper limits on wafer delays, especially when process times fluctuate randomly. We examine a scheduling problem for cluster tools with strict upper limits on wafer delays under process time variation. We propose a new class of schedules, which not only keeps timing patterns steady as possible but also adapts timing of tasks in response to process time variation so as to satisfy wafer delay constraints robustly. We also derive conditions for which there exists such a schedule. We develop a mixed-integer programming model to find an optimal schedule among such adaptive schedules. By numerical experiments, we show that the proposed scheduling method can effectively cope with tight wafer delay constraints even under large process time variations. Note to Practitioners—As the circuit widths shrink down, residual gases and particles within chambers after processing wafers become more critical to wafer quality. In fact, leading fabs are now cleaning a chamber for each new wafer in order to reduce such quality risk. We propose a new practical method for scheduling tools that can significantly reduce such quality risk caused by wafer waiting within chambers after processing. [ABSTRACT FROM AUTHOR]

As the order size for modern fabs tends to be smaller, fabs wish to process a class of similar wafer lots at a tool concurrently to reduce the work-in-progress lots as well as the total manufacturing lead time. We examine a scheduling problem for a dual-armed cluster tool that simultaneously produces multiple wafer types with identical wafer flow patterns but different process times. We prove that the conventional swap sequence, which is optimal and prevalently being used for single-wafer-type processing, is also optimal for such concurrent processing. We then propose a way of determining a release sequence of wafer types into the tool, called cycle plan, that maximizes the utilization of parallel chambers and hence increases the tool throughput rate. We present conditions for which the parallel chambers are shared by all wafer types and their workloads are evenly balanced so as to maximize the throughput rate. We also report the experimental results. Note to Practitioners—This paper suggests how to operate cluster tools for concurrent processing of similar wafer types. The results ensure that the conventional swap sequence is still effective for concurrent processing. We also provide a simple strategy of mixing different wafer types and the optimal release sequence for the wafers. We confirm that the tool throughput can be significantly improved when the release sequence of wafers is properly determined. [ABSTRACT FROM AUTHOR]

Complex multi-cluster tools have been extensively used in semiconductor manufacturing. It is crucial to increase their productivity by their effective operation. With structural complexity, multiple robots, and the interaction among individual tools, it is very challenging to schedule a tree-like multi-cluster tool. This paper investigates the scheduling problem of such a tool whose bottleneck individual tool is process-bound. The system is modeled by well-known discrete-event models, i.e., resource-oriented Petri nets. Based on the models, for the first time, this work develops necessary and sufficient conditions under which a one-unit (wafer) periodic schedule exists and shows that an optimal one-unit periodic schedule can always be found. Algorithms with polynomial complexity are presented to find the optimal cycle time and the one-unit periodic schedule. Industrial examples are used to illustrate the proposed method, and they show that a significant reduction in cycle time can be obtained in comparison with the existing method.

The paper investigates the options to increase the production yield of temperature compensated surface acoustic wave (SAW) devices with a defined range of operational frequencies. The paper focuses on the preparation of large wafers with SiO2 and AlN/Si3N4 depositions. Stability of the intermediate SiO2 layer is achieved by combining high power density UV radiation with annealing in high humidity environment. A uniform thickness of the capping AlN layer is achieved by local high-rate etching with a focused ion beam emitted by the FALCON ion source. Operation parameters and limitations of the etching process are discussed.

Robotized cluster tools for semiconductor wafer fabrication may have a wafer wait within a processing chamber after processing there until the wafer is unloaded from the chamber by a robot. Such wafer delays cause wafer quality degradation or variability due to residual gases and heats within the chamber. There have been numerous works on characterizing wafer delays and scheduling under upper limits on wafer delays while presuming that the tools are operated by well-known simple robot task sequences such as swap or backward sequences. However, when the wafer delay constraints are tight, there may not be feasible schedules for such sequences. We wish to know whether there can be alternative robot task sequences which can satisfy such tight wafer delay constraints. In this paper, we identify a new class of robot task sequences that can better satisfy tight wafer delay constraints than the conventional swap or backward sequences while keeping the same minimum tool cycle time. By examining the circuits of timed event graph (TEG) models for the tool operation behaviors in many different robot task sequences, we identify that such robot task sequences do not make interferences between the work cycles of the resources such as the robot and chambers. The resource interference can cause delays in the work cycles, and hence increase the wafer delays or the tool cycle time. To prove this, we examine circuits in an extended TEG model, a negative event graph, which incorporates time constraints as negative places and tokens. From this, we derive closed-form conditions for which such sequences are feasible against given wafer delay constraints. By experiments, we show that the proposed new sequences have shorter wafer delays, and hence better satisfy tight wafer delay constraints than conventional sequences. Note to Practitioners—As circuit widths shrink down to several nanometers, cluster tools for semiconductor fabrication require extreme process quality control. Even wafer delays within processing chambers of cluster tools can cause wafer quality degradation and variability. Therefore, it is desirable for cluster tools to have much shorter wafer delays. However, conventional sequences such as the swap and backward sequences, which are being prevalently used in practice, may not satisfy tight wafer delay constraints. Our proposed sequences, which are as simple as the conventional sequences, have much shorter wafer delays while keeping the same minimum tool cycle time. [ABSTRACT FROM AUTHOR]

Circuit widths and nodes of semiconductor wafers have been continually shrinking down to less than 20 nm. Therefore, modern wafer fabs enforce extremely strict process control to prevent wafer quality failures. A wafer processing chamber is now frequently cleaned to remove residual chemicals and impurities. Yu et al. show that such cleaning operations significantly change the tool operation of single-armed cluster tools, and they suggest an idea of partial wafer loading to improve the tool throughput under cleaning requirements. However, little is known about how a dual-armed tool could be effectively scheduled when chamber cleaning exists. A dual-armed robot allows more flexible tool operational sequences, and hence, the scheduling problem becomes further complicated and challenging. In this paper, we propose a scheduling method by which the dual arms can be properly exploited for better tool productivity. We show that the suggested hybrid sequence significantly reduces the tool cycle time as compared to previously developed scheduling methods. Through this research, we conclude that the productivity gain of the dual arms against single arm is more significant when chambers are cleaned. Note to Practitioners—This paper is motivated by the scheduling issues of cluster tools with chamber cleaning requirements. Though an efficient scheduling method for single-armed cluster tools is presented by Yu et al., its performance is not sufficiently close to the optimal when a dual-armed robot is considered. More specifically, we cannot expect any productivity improvement from adopting a dual-armed robot, although it allows more flexible tool operations and is known to have higher throughput than a single-armed robot. Thus, we propose a novel scheduling method for dual-armed cluster tools that require chamber cleaning operations. The experimental results show that the suggested method achieves optimal tool throughput in most of the practical tool conditions. [ABSTRACT FROM AUTHOR]

In wafer fabrication, a robotic cluster tool is required to be closed down in order for engineers to perform its on-demand and preventive maintenance and switch between different wafer lots. They often deal with a close-down process subject to wafer residency time constraints, i.e., a wafer must exit from a processing chamber before its quality degradation within a certain time limit. To obtain higher yield, it is very important to optimize a close-down process for a cluster tool. Yet the existing literature pays no or little attention to this issue. By focusing on a time-constrained single-arm cluster tool, this paper intends: 1) to build its Petri net model to analyze its schedulability and 2) to develop computationally efficient algorithms to find an optimal and feasible schedule for its closing-down process under different workloads at its steps. Industrial examples are used to illustrate the application of the proposed method. [ABSTRACT FROM PUBLISHER]

We consider the serial batching scheduling problem in which a group of machines can process multiple jobs continuously to reduce the processing times of the second and subsequent jobs. The maximum batch size is finite. Since all jobs in the same batch are loaded and unloaded simultaneously, a completed job has to wait for the others. We examine how to schedule all jobs to minimize the total completion time. If the batch size is only one, i.e., a single job per batch, the total processing time will be longer, since no reduction in processing time is possible. As a consequence, the total completion time will also be longer. On the other hand, if the batch size is large, the total completion time can be large. Each job has to wait until all jobs in the same batch are completed. We identify several optimality properties of the optimal batching sequence. These properties are used to develop a dynamic programming algorithm to optimize the batching sequences efficiently. The complexity of the proposed method depends only on the maximum batch size and the number of jobs. The improvement achieved with the proposed method when compared with two other batching rules is illustrated using two practical applications.

Note to Practitioners— Machines with job cascading (or cluster tools) are commonly seen in semiconductor manufacturing processes. While meeting production move targets is a common goal for the nondelayed jobs, catching up with the schedule is an important task for the delayed jobs to achieve higher customer service level. From the viewpoint of scheduling, reducing the delay is equivalent to reducing completion time. Hence, we propose scheduling algorithms to reduce the completion time by taking advantage of the special structure of a cascading machine. In contrast to existing scheduling theory, the proposed algorithm can be efficient due to the small maximum batch size of real cascading machines. In addition to the theoretical contributions, this paper aims at solving practical problems through a rigorous approach. The finding and insight from this paper can be used to enhance shop floor control in a semiconductor fab. [ABSTRACT FROM PUBLISHER]

We analyze the completion time of wafer lots in single-armed cluster tools with parallel processing modules (PMs) by considering the lot switching operation. To effectively assign wafer lots and dispatch overhead hoist transports (OHTs) to manufacturing tools, it is crucial to obtain the completion time of wafer lots. However, estimating the completion time is not straightforward, due to the concurrent processing of two consecutive wafer lots during lot switching operation, which often increases wafer sojourn times in PMs. In this paper, we derive closed-form expressions of the completion time of wafer lots in single-armed cluster tools with parallel PMs. We assume that the robot unloads wafers in the order of their loading sequence. We then experimentally show that the formulas derived can be used even when processing time variation exists or another robot task sequence, which is of first-in first-out (FIFO), is assumed.

Note to Practitioners—Due to the larger wafer size and circuit width reduction, cluster tools often perform the lot switching operation with each pair of consecutive wafer lots. In addition, since most tools are operated with parallel chambers, concurrent processing with two different wafer lots occurs frequently. Such transient periods in operating tools make it hard to estimate the completion time of wafer lots. In this paper, we derive closed-form expressions to obtain the completion time of wafer lots in single-armed cluster tools with parallel chambers. We further show that the formulas can be used with processing time variation or the FIFO rule. With the formulas, OHTs can be sent just-in-time to tools to load or unload wafer cassettes, and wafer lots can be assigned while minimizing the transient periods. In addition, the estimated completion time can be utilized in the planning and scheduling of wafer fabrication processes. [ABSTRACT FROM PUBLISHER]

In semiconductor manufacturing, there are wafer fabrication processes with wafer revisiting. Some of them must meet wafer residency time constraints. Taking atomic layer deposition (ALD) as a typical wafer revisiting process, this paper studies the challenging scheduling problem of single-arm cluster tools for the ALD process with wafer residency time constraints. It is found that there are only several scheduling strategies that are applicable to this problem and one needs to apply each of them to decide whether a feasible schedule can be found or not. This work, for each applicable strategy, performs the schedulability analysis and derives the schedulability conditions for such tools for the first time. It proposes scheduling algorithms to obtain an optimal schedule efficiently if such conditions are met. It finally gives illustrative examples to show the application of the proposed concepts and approach. [ABSTRACT FROM PUBLISHER]

A conventional robot sequence of a single-armed cluster tool pursues a backward strategy for efficiency; the strategy is optimal when identical work cycles are repeated. However, we cannot guarantee the strategy is optimal under some abnormal situations, such as breakdowns or during auto-cleaning (periodic cleaning for preventive maintenance). In this paper, we focus on undesirable but predictable auto-cleaning, which cleans the chambers of a cluster tool each time a predefined number of wafers has been processed to prevent deterioration of wafer quality caused by residual chemicals. For auto-cleaning, we suggest alternative cleaning frequencies of a single-armed cluster tool that periodically clean the inside of process modules based on the Theory of Constraints. Additionally, we derive its heuristic robot scheduling from Petri-net models, because finding the optimal robot sequence in real time is impossible. Finally, we examine the effectiveness of our suggestions by simulation. [ABSTRACT FROM AUTHOR]

We consider a scheduling problem of a robotized cluster tool for semiconductor manufacturing, which should control wafer delays within a chamber so as not to exceed a specified limit under time variation. The prior research has proposed a p^+-time event graph, an extension of Petri nets, for modeling the scheduling problem and developed a method of verifying whether a cyclic p^+-time event graph or a cluster tool, which repeats identical work cycles, can satisfy the time constraints under time variation. In this paper, we extend and simplify the schedulability analysis method in the prior research for a noncyclic event graph or a cluster tool which performs start-up and close-down operation for a lot or lot switching, and obtain specialized results. We assume that a robot task sequence or firing sequence of transitions is given. Based on the schedulability analysis, we also propose a way of modifying a not always schedulable noncyclic p^+-time event graph with some qualifications to be always schedulable, that is, we prolong token holding times at some places or equivalently delay firings of some transitions so as to be always feasible. [ABSTRACT FROM PUBLISHER]

Cluster tools each of which consists of processing modules, a transport robot, and loadlocks perform most wafer fabrication processes in semiconductor manufacturing. Recently, the lot size has been decreasing from 25 wafers to even 7–8 wafers due to the larger wafer size and circuit width reduction especially in large-scale integration manufacturing. Hence, the lot switching operation between two consecutive wafer lots occurs frequently. In this paper, we derive closed-form expressions of the makespan of the lot switching period in single-armed and dual-armed cluster tools with the given robot task sequences for the first time. With this research, the completion time of a wafer lot can be easily estimated even though its preceding or next lot is processed together during the lot switching period. Hence, the makespan can be used for integrating operation of overhead hoist transports and cluster tools and assigning wafer lots to cluster tools while minimizing the lot switching period. [ABSTRACT FROM AUTHOR]

Dual-armed cluster tools for semiconductor manufacturing typically have had two arms fixed in opposite directions. Recently, new cluster tool robot systems with two independent robot arms have been introduced with the expectation that the arms’ flexibility will improve the throughput. However, the productivity gain has yet to be examined. Accordingly, we examine under which circumstances and the extent to which productivity gains can be achieved and how the robot task sequences should be scheduled to maximize the throughput. For this purpose, we develop a Petri net model that represents the tool behavior. We show that the well-known swap sequence, which is known to be optimal for conventional dual-armed tools, is not always optimal. Instead, we identify two other sequences that are optimal under certain conditions. We define the workloads for each process step and the transport module to derive conditions for optimality of the sequences, based on the Petri net model and the workload. We also develop a mixed integer programming (MIP) model to determine optimal sequences among one-cyclic schedules for the cases in which the proposed sequences are not optimal. Furthermore, we analyze and demonstrate how the two independent arms can increase the throughput in comparison to a conventional dual-armed robot. [ABSTRACT FROM AUTHOR]

Robotized cluster tools for semiconductor manufacturing have strict time constraints such that a wafer processed at a processing chamber should be unloaded within a specified time limit. Otherwise, it has a serious quality problem due to residual gases and heat within the chamber. Even though there have been studies on identifying a feasible tool operation schedule over such time constraints on wafer delays, such a schedule is subject to timing disruptions or time variation, and thus may violate the time constraints. In this study, we propose a more robust method of regulating wafer delays against timing disruptions not to exceed a specified limit. We first model the discrete-event behavior of a tool by a timed event graph. We then develop a feedback controller for single-armed and dual-armed cluster tools that can satisfy the time constraints by regulating wafer delays. To do this, we develop a feedback controller for the timed event graph by analyzing the timing behavior in a linear system model based on the max-plus algebra. The feedback controller postpones an event or firing of a transition, i.e., loading a wafer into a chamber, until a properly determined time elapses after an associated preceding event occurs. Finally, we present examples of feedback control and show that the feedback control is quite robust even under persistent time variation. [ABSTRACT FROM AUTHOR]

Purge operations are widely used to remove residual chemicals and impurities in chambers of wafer fabrication systems to ensure wafer quality. However, such operations lead to more start-up transient processes and wafer delays. In addition, wafer residency time constraints must be met to ensure the wafer quality. Thus, the system scheduling problem with such considerations will become more complicated. This work aims to optimize the start-up transient process of a single-arm cluster tool with purge operations and wafer residency time constraints by using resource-oriented Petri net (ROPN) models. Based on the models, we dynamically depict the behavior of the steady state and start-up transient processes of a single-arm cluster tool with purge operations. Then, a scheduling method that dynamically adjusts the robot waiting time is proposed to find an optimal schedule for such systems with purge operations and wafer residency time constraints. Finally, some examples are tested to illustrate the effectiveness of our method. • Two ROPNs are developed for the steady state and start-up transient process with purge operations. • The temporal properties of the steady state process and start-up transient process can be analyzed. • It finds an optimal schedule considering purge operations and wafer residency time constraints. [ABSTRACT FROM AUTHOR]