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To increase productivity, more sophisticated cluster tools are developed. To achieve this, one of the ways is to increase the number of spaces in a process module (PM) and the number of fingers on a robot arm as well, leading to a cluster tool with multi-space PMs and a multi-finger-arm robot. This paper discusses the scheduling problem of cluster tools with four-space PMs and a four-finger-arm robot, a typical tool with multi-space PMs and a multi-finger-arm robot adopted in modern fabs. With two arms in such a tool, one is used as a clean one, while the other is used as a dirty one. In this way, wafer quality can be improved. However, scheduling such cluster tools to ensure the residency time constraints is very challenging, and there is no research report on this issue. This article conducts an in-depth analysis of the steady-state scheduling for this type of cluster tools to explore the effect of different scheduling strategies. Based on the properties, four robot task sequences are presented as scheduling strategies. With them, four linear programming models are developed to optimize the cycle time of the system and find feasible schedules. The performance of these strategies is dependent on the activity parameters. Experiments are carried out to test the effect of different parameters on the performance of different strategies. It shows that, given a group of parameters, one can apply all the strategies and choose the best result obtained by one of the strategies. [ABSTRACT FROM AUTHOR]

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an arm task-constrained dual-arm cluster tool (ATC-DACT). To do this, one of the arms is identified as the dirty one and the other as the clean one. The dirty one can deal with raw wafers, while the clean one can deal with processed wafers. This requirement raises a new problem for scheduling a cluster tool. This paper discusses the scheduling problem of ATC-DACTs with RTCs. Due to the arm task constraints, the proven, effective swap strategy is no longer applicable to ATC-DACTs, making the scheduling problem difficult. To address this problem, we explicitly describe the robot waiting as an event and build a Petri net (PN) model. Then, we propose a hybrid task sequence (HTS) as an operation strategy by combining the swap and backward strategies. Based on the HTS, the necessary and sufficient conditions for schedulability are established; also, a linear programming model is developed. We then develop an algorithm using these results to optimally schedule the system. Industrial case studies demonstrate the application of this method. [ABSTRACT FROM AUTHOR]

In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a wafer into/from a space in the PM. This means that the wafer staying time in PMs is affected by both the rotation operations of the internal chambers of PMs and the robot tasks. Thus, minimizing the wafer delay time is quite challenging. In this work, for cluster tools with single-arm robots and two-space PMs, efforts are made for wafer delay minimization in scheduling the tools. Specifically, a two-wafer backward strategy is presented to operate the tools in a steady state. Then, the workloads of each processing step and the robot are analyzed. Further, to find optimal schedules with the objective of minimizing the total wafer delay time, efficient algorithms are established. Finally, case studies show that the wafer delay time at some steps can be totally eliminated by the proposed method. In the meantime, in all cases, the proposed method can work well in reducing the total wafer delay time at all steps. [ABSTRACT FROM AUTHOR]

In semiconductor manufacturing, an extremely stringent quality control is enforced for wafer fabrication processes. Consequently, cleaning operations that clear residual chemical gases and heat in the chambers are frequently performed. As one kind of cleaning operations, a purge operation which executes a cleaning operation each time a wafer is removed from a chamber is widely adopted in leading semiconductor fabrication plants. Such an operation can definitely improve the quality of wafer. However, it results in lower productivity. To make a tradeoff between quality and productivity, a condition-based chamber cleaning operation that performs a cleaning operation with the consideration of the actual state of a chamber is introduced in practice. Aiming to address the scheduling problem of time-constrained single-armed cluster tools with condition-based chamber cleaning operations, efficient scheduling approaches are proposed in this work for the first time and, algorithms for searching for a feasible schedule are also derived. Two illustrative examples are given to show the power of the approach. [ABSTRACT FROM AUTHOR]

To increase productivity, more sophisticated cluster tools are developed. To achieve this, one of the ways is to increase the number of spaces in a process module (PM) and the number of fingers on a robot arm as well, leading to a cluster tool with multi-space PMs and a multi-finger-arm robot. This paper discusses the scheduling problem of cluster tools with four-space PMs and a four-finger-arm robot, a typical tool with multi-space PMs and a multi-finger-arm robot adopted in modern fabs. With two arms in such a tool, one is used as a clean one, while the other is used as a dirty one. In this way, wafer quality can be improved. However, scheduling such cluster tools to ensure the residency time constraints is very challenging, and there is no research report on this issue. This article conducts an in-depth analysis of the steady-state scheduling for this type of cluster tools to explore the effect of different scheduling strategies. Based on the properties, four robot task sequences are presented as scheduling strategies. With them, four linear programming models are developed to optimize the cycle time of the system and find feasible schedules. The performance of these strategies is dependent on the activity parameters. Experiments are carried out to test the effect of different parameters on the performance of different strategies. It shows that, given a group of parameters, one can apply all the strategies and choose the best result obtained by one of the strategies.

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an arm task-constrained dual-arm cluster tool (ATC-DACT). To do this, one of the arms is identified as the dirty one and the other as the clean one. The dirty one can deal with raw wafers, while the clean one can deal with processed wafers. This requirement raises a new problem for scheduling a cluster tool. This paper discusses the scheduling problem of ATC-DACTs with RTCs. Due to the arm task constraints, the proven, effective swap strategy is no longer applicable to ATC-DACTs, making the scheduling problem difficult. To address this problem, we explicitly describe the robot waiting as an event and build a Petri net (PN) model. Then, we propose a hybrid task sequence (HTS) as an operation strategy by combining the swap and backward strategies. Based on the HTS, the necessary and sufficient conditions for schedulability are established; also, a linear programming model is developed. We then develop an algorithm using these results to optimally schedule the system. Industrial case studies demonstrate the application of this method.

In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a wafer into/from a space in the PM. This means that the wafer staying time in PMs is affected by both the rotation operations of the internal chambers of PMs and the robot tasks. Thus, minimizing the wafer delay time is quite challenging. In this work, for cluster tools with single-arm robots and two-space PMs, efforts are made for wafer delay minimization in scheduling the tools. Specifically, a two-wafer backward strategy is presented to operate the tools in a steady state. Then, the workloads of each processing step and the robot are analyzed. Further, to find optimal schedules with the objective of minimizing the total wafer delay time, efficient algorithms are established. Finally, case studies show that the wafer delay time at some steps can be totally eliminated by the proposed method. In the meantime, in all cases, the proposed method can work well in reducing the total wafer delay time at all steps.

Cluster tools are the key equipment in semiconductor manufacturing systems. They have been widely adopted for many wafer fabrication processes, such as chemical and physical vapor deposition processes. Reentrant wafer flows are commonly seen in cluster tool operations for deposition processes. It is very complicated to schedule cluster tools with reentrant processes. For a dual-arm cluster tool with two-time reentering, the existing studies point out that a one-wafer periodical (1-WP) schedule can be found, and it is optimal in terms of productivity. However, for some wafer fabrication processes, wafers should be processed at some PMs more than two times. This gives rise to a question of whether there still exists a 1-WP schedule for dual-arm cluster tools with the number of reentering times being more than two such that the cycle time of a tool can reach the lower bound. This problem is still open, and this is what this work wants to tackle. For a dual-arm cluster tool with the number of reentering times being k (>2) times, if there does not exist a value f ∈ {1, 2 ...} such that k = 3f, theoretical proofs are given to show that a 1-WP schedule can be found, otherwise it does not exist. For cases with a 1-WP schedule, the cycle time can be obtained by analytical expressions. For the cases without a 1-WP schedule, two new methods for a three-wafer periodical schedule are proposed to improve the system productivity by comparing it with an existing three-wafer periodical schedule. The applications of the obtained results are demonstrated by examples. Wafer residency time constraints are required for some wafer fabrication processes. Note that the results obtained in this work cannot be directly applied to cluster tools with both reentrant wafer flows and wafer residency time constraints. Nevertheless, schedulablity and scheduling analyses for that applications can be conducted based on the obtained results in this work. [ABSTRACT FROM AUTHOR]

Cluster tools play a significant role in the entire process of wafer fabrication. As the width of circuits in semiconductor chips shrinks down to less than 10nm, strict operational constraints are imposed on the operations of cluster tools in order to ensure the quality of processed wafers. Particularly, wafer residency time constraints and chamber cleaning requirements are commonly seen in etching, chemical vapor deposition, coating processes, etc. They make the scheduling problem of cluster tools more challenging. This work aims to provide a solution for dual-arm cluster tools with wafer residency time constraints and chamber cleaning requirements. To do so, it proposes a novel virtual wafer-based scheduling method. By this method, under a steady state, a PM processes either a real or virtual wafer at a time. When a PM processes a virtual one, its chamber can perform a cleaning operation. In this way, we can meet not only the strict residency time constraints for real wafers, but also innovatively meet chamber cleaning requirements. Based on such a novel scheduling method, an efficient binary integer programming model is established to optimize the throughput of cluster tools. Finally, experiments are performed to show the efficiency and effectiveness of the proposed method. Note to Practitioners—To ensure wafer quality in semiconductor manufacturing, engineers have to impose wafer residency time constraints and chamber cleaning requirements on the operations of cluster tools. In order to tackle their scheduling problem with these constraints, this work proposes a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for time-constrained cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a PM processes a virtual wafer, a chamber cleaning operation can be performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. To do so, this work establishes an efficient binary integer programming model to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has a high practical value to numerous semiconductor manufacturers. [ABSTRACT FROM AUTHOR]

Nowadays, wafer fabrication in semiconductor manufacturing is highly dependent on cluster tools. A cluster tool is equipped with several process modules (PMs) and a wafer handling robot. When the tool is operating, generally each PM is processing a wafer, and the robot is responsible for delivering the wafers from one PM to another. Thus, when a wafer is completed in a PM, the robot may be busy for performing other tasks such that it cannot immediately unload the completed wafer in the PM, resulting in that the wafer has to stay there for some extra time. The processing time of a wafer together with its delay time for waiting for the robot’s arrival for unloading is defined as wafer residency time in a PM. However, a long wafer delay time may deteriorate its quality. Therefore, it is highly desired and important to reduce the wafer delay time at each step as much as possible. This work aims to tackle this important issue for single-arm cluster tools (SACTs). Specifically, by using a Petri net model, this work analyzes the steady-state operational behavior of an SACT under the backward and earliest starting strategies. It is found that there must exist wafer delay time at the steps in the upstream of the bottleneck step, and such wafer delay time can be reduced by properly adjusting the robot waiting time. Thus, three algorithms are developed to reduce the wafer delay time at each step as much as possible by properly assigning the robot idle time. Finally, the application of the proposed method is illustrated by using examples. Note to Practitioners—In a modern semiconductor fab, there are hundreds of cluster tools for wafer fabrication. To ensure wafer quality, it is important to reduce the wafer delay time in PMs of cluster tools after a wafer is processed since the high temperature, chemical gas, and particles in the PMs may damage the wafer. To do so, this work proposes three algorithms with polynomial complexity to assign the robot idle time as robot waiting time such that the wafer delay time in PMs can be reduced as much as possible. Furthermore, the obtained schedule by these algorithms is optimal in terms of the cycle time. Besides, the developed algorithms can be easily embedded into the controller of cluster tools by facility engineers. Therefore, this work has a practical value. [ABSTRACT FROM AUTHOR]

To ensure wafer quality, engineers have to impose wafer residency time constraints and chamber cleaning operations on cluster tools; this has been widely used in semiconductor manufacturing. Wafer residency time constraints and chamber cleaning operations make the scheduling problem of cluster tools more challenging. This work aims to solve such a scheduling problem for single-arm cluster tools and presents a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for single-arm cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a process module (PM) processes virtual wafers, a chamber cleaning operation is performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. With this idea, this work constructs a genetic algorithm to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has high practical value to numerous semiconductor manufacturers. Experiments were performed to show the efficiency and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In wafer manufacturing, extensive research on the operations of cluster tools under the steady state has been reported. However, with the shrinking down of wafer lot size, such tools are frequently required to switch from handling one lot of wafers to another, resulting in more transient processes, including start-up and close-down ones. Also, wafer residency time constraint is critical for many wafer fabrication processes. To cope with the transient scheduling problem of time-constrained single-arm cluster tools with parallel chambers, based on a generalized backward strategy, this paper first builds timed Petri net models for these two transient processes. Then, two linear programs are derived for the first time to search a feasible schedule with a minimal makespan. Two industrial examples are given to demonstrate the effectiveness of the obtained results at last. [ABSTRACT FROM AUTHOR]

For a time-constrained single-robot-arm cluster tool with unfixed scheduling strategy, necessary and sufficient conditions under which a feasible cyclic schedule exists are presented in the literature. However, the results are obtained under the assumption that the activity time is deterministic. In practice, the activity time could be subject to fluctuation, leading to that an originally feasible schedule obtained based on such an assumption may be infeasible. Hence, it is critically important to reveal how the wafer residency time (WRT) varies with the variation of activity time. To solve this problem, this paper first proposes an operational strategy and a real-time control policy. Based on them, the exact upper bound of WRT delay resulted from the activity time variation (ATV) is presented, with which one can check if a given schedule is feasible. Finally, illustrative examples are given to demonstrate the application of the derived method. [ABSTRACT FROM AUTHOR]

Scheduling a cluster tool with wafer residency time constraints is challenging and important in wafer manufacturing. With a backward strategy, the scheduling problem of such single-robot-arm cluster tools is well-studied in the literature. It is much more challenging to schedule a more general case whose optimal scheduling strategy is not limited to the backward one. This work uses a timed Petri net (PN) to model the dynamic behavior of the system and presents a method to determine the optimal scheduling strategy for the system. Based on its PN model and the obtained strategy, it reveals that the key issue to schedule such a tool is to determine when and how long the robot should wait for. Based on this finding, this work establishes for the first time the necessary and sufficient conditions regarding the existence of an optimal and feasible one-wafer cyclic schedule for single-robot-arm cluster tools. It then formulates a computationally efficient linear program to find it if existing, and finally gives industrial examples to show the application and power of the proposed method. [ABSTRACT FROM AUTHOR]

Cluster tools have been increasingly used for semiconductor manufacturing. While there have been many studies on cluster tool scheduling, most of them have focused on full work cycles in which identical work cycles are repeated. However, in reality, there are significant transient periods during which an empty tool begins to process new wafers or finishes processing and becomes empty. We should minimise the lengths of transient periods, so that a cluster tool quickly enters a desirable steady schedule for full work cycles or finishes operations quickly. We should also regulate wafer delays within chambers, because they cause wafer quality variation or failures. In this paper, we propose scheduling strategies for transient periods to meet those requirements. We prove that for the close-down period, the earliest starting policy that starts each operation as soon as the preceding operations complete minimises the close-down period while regulating the wafer delays. We also show that for the start-up period, the latest starting policy that starts each operation as late as possible while meeting the deadlines specified by the starting times of the given steady schedule minimises the start-up period. Finally, we suggest a way of minimising the total makespan by optimising the steady schedule. [ABSTRACT FROM AUTHOR]

To ensure wafer quality, engineers have to impose wafer residency time constraints and chamber cleaning operations on cluster tools; this has been widely used in semiconductor manufacturing. Wafer residency time constraints and chamber cleaning operations make the scheduling problem of cluster tools more challenging. This work aims to solve such a scheduling problem for single-arm cluster tools and presents a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for single-arm cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a process module (PM) processes virtual wafers, a chamber cleaning operation is performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. With this idea, this work constructs a genetic algorithm to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has high practical value to numerous semiconductor manufacturers. Experiments were performed to show the efficiency and effectiveness of the proposed method.

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With the reduction of wafer batch size on account of the diversification and individuation of consumption demands, increasing importance has been attached to the schedulability and controllability of the cluster tools with multiple wafer types being concurrently processed, while the corresponding research is seldom and still open. This paper is devoted to addressing the steady-state scheduling of single-arm cluster tools with multiple wafer types and residency time constraints. Inspired by the definition of wafer flow pattern for the single wafer type, a novel description for the multiple wafer types is introduced. For the sake of efficiency and simplicity, the multiplex backward sequence is proposed. To balance the workload of process steps, a virtual module technology with a two-tiered architecture is implemented. Furthermore, several sufficient and necessary conditions are derived to verify the schedulability of the system. Finally, an efficient algorithm is presented to find the periodic steady-state schedule, and its practicability and availability are validated by the given illustrative examples. Note to Practitioners—Cluster tools are a kind of highly automated, flexible, and integrated equipment applied widely in diversified semiconductor fabrication processes. Due to the strictness of processing constraints and unavailability of in-built buffers, it is challenging to effectively operate cluster tools. For a higher utilization of processing modules, fabs tend to concurrently process several kinds of wafers with dissimilar recipes in a cluster tool. However, the related scheduling and control problems remain open. With residency time constraints, this paper addresses the scheduling problems of single-arm cluster tools with multiple wafer types. By dissecting the mechanism of mixed-processing of multiple wafer types, several formal conditions are obtained to test the schedulability. Based on the multiplex backward sequence, a cyclic scheduling approach to single-arm cluster tools with multiple wafer types is presented. With the proposed method, schedulability conditions can be readily checked and a periodic schedule can be found easily. Thus, it can be applied to solve practical application problems. [ABSTRACT FROM AUTHOR]

To effectively solve the scheduling problems of dual-blade cluster tools with parallel processing chambers and reentrancy constraints in semiconductor manufacturing, this article introduces a scheduling method centering on optimal searching. Firstly, according to the optimization search rule (FIFO), a mathematical programming model of 4-chamber dual-blade cluster tools with parallel processing chambers and reentrancy constraints was built to minimize the makespan of the system. Combined with the concept of virtual buffer module, an optimum searching algorithm was proposed based on the robot swap strategy. Finally, simulation experiments were conducted for the proposed algorithm, and the results indicate that the algorithm is feasible and effective.

Cluster tools are widely used for semiconductor manufacturing. A multi-cluster tool consists of several single cluster tools which are interconnected with each other. The multi-cluster tool causes a deadlock due to non-existence of intermediate buffer. Deadlock is a serious problem leading decrease of throughput and deterioration of wafers. In this paper, the optimal supervisor proposed by Chen et al. (2011) is applied to a Petri net model of the multi-cluster tools. From the comparison of performance with the conventional deadlock prevention policies, we find that the maximally permissive supervisor does not always produce a better scheduling performance. We propose a design method of a Petri net supervisor to improve the scheduling performance. Our main idea is to eliminate legal markings that may eventually cause the increase of makespan. The proposed method is applied to the two-connected multi-cluster tool. The results indicate that the scheduling performance can be improved by the proposed method without lowering maximal permissivity.

In semiconductor manufacturing, with the shrinking down of wafer circuit widths, a strict quality control is required for wafer fabrication processes, resulting in that after a wafer being processed and removed from a chamber, a cleaning operation that takes significant time is performed for eliminating the chemical residual. Such a cleaning operation makes a traditional backward strategy for single-arm cluster tools inefficient. By the existing studies, it is shown that the productivity can be improved if some numbers of chambers at a step are kept empty. With this idea, an extended backward strategy is proposed by deciding the optimal number of empty chambers. Based on such a strategy, this paper studies the challenging problem for scheduling a single-arm cluster tool with both chamber cleaning operations and wafer residency time constraint for the first time. By building a timed Petri net model for the system, two linear programs are proposed to determine the minimal cycle time and test the existence of a feasible schedule and find it if existing. At last, two industrial examples are used to demonstrate the obtained results. [ABSTRACT FROM AUTHOR]

A robotic cluster tool involves many activities whose time is subject to some disturbance, thus leading to the activity time variation. It results in wafer sojourn time fluctuation in a process module, which may in turn violate wafer residency time constraints. Some wafer fabrication requires a revisiting process. With wafer revisiting, the effect of activity time variation on wafer sojourn time fluctuation is so complicated that no analysis was reported to the best knowledge of the authors. It is vitally important to accurately analyze it. To do so, this paper adopts a Petri net model to describe the dynamical behavior of cluster tools. With this model, a real-time control policy is proposed to offset the effect of the activity time variation on wafer sojourn time fluctuation as much as possible. Then, the wafer sojourn time delay is analyzed and algorithms are developed to calculate its exact upper bound. With the proposed method, one can check if a given schedule is feasible under bounded activity time variation. Some practical examples are given to show the application of the proposed approach. [ABSTRACT FROM PUBLISHER]

Multi-cluster tools are automated equipment which is increasingly used in semiconductor manufacturing. The scheduling of multi-cluster tools is much more challenging than single-cluster tools due to multi-robot coordination and increasing chambers. In this paper, we develop a mixed integer programming (MIP) model which manages to formulate the multi-robot coordination for cyclic scheduling of multi-cluster tools. Three reformulations of the model are implemented: 1) linearization; 2) eliminating integer variables; and 3) tightening constraints. The first reformulation is designed to make the MIP model solvable by commercial solvers while the other two are intended for promoting computational efficiency which is critical when chambers increase. The proposed model can meet various practical scheduling requirements such as dual-armed robots, wafer residency time constraints, parallel and reentrant processes in multi-cluster tools. Experimental results demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the trends of larger wafer diameters and smaller lot sizes, cluster tools need to switch from processing one lot of wafers to another frequently. This leads to more transient periods in wafer fabrication, which includes startup and close-down processes. Their efficient scheduling and control problems become more and more important. They become very difficult to solve especially when wafer residency time constraints must be considered. Most previous studies focused on the steady periodic schedule for cluster tools. Little research was on the transient processes of cluster tools despite their increasing importance. In order to optimize a startup transient process, this work develops a Petri net model to describe its behavior for a single-arm cluster tool. Then, based on the model, for the case that the workloads among the steps can be properly balanced, this work proposes a scheduling algorithm to find an optimal and feasible schedule for the startup process. For the other cases schedulable at the steady state, a linear programming model is developed to find an optimal and feasible schedule for the startup process. Finally, illustrative examples are given to show the applications of the proposed method. [ABSTRACT FROM PUBLISHER]

Queueing models can be used to evaluate the performance of manufacturing systems. Due to the emergence of cluster tools in contemporary production systems, proper queueing models have to be derived to evaluate the performance of machines with complex configurations. Job cascading is a common structure among cluster tools. Because of the blocking and starvation effects among servers, queue time analysis for a cluster tool with job cascading is difficult in general. Based on the insight from the reduction method, we proposed the approximate model for the mean queue time of a cascading machine subject to breakdowns. The model is validated by simulation and performs well in the examined cases. [ABSTRACT FROM AUTHOR]

In semiconductor manufacturing, wafer residency time constraints make the scheduling problem of cluster tools complicated. A process module (PM) in cluster tools is prone to failure. It is crucial to deal with any such failure in a proper and timely manner. If there are feasible periodic schedules in operating a cluster tool before and after a PM failure, it is desired to make it operate continuously when such a failure occurs. However, due to wafer residency time constraints, it is highly challenging to control a tool such that it can be correctly transferred from a feasible schedule before failure to another after it. To solve this problem, a Petri net model is developed to describe the dynamic behavior of a single-arm cluster tool and failure response policies are proposed. The proposed policies are formulated via simple control laws for their easy implementation. Examples are given to show them. [ABSTRACT FROM PUBLISHER]

The trends of increasing wafer diameter and smaller lot sizes have led to more transient periods in wafer fabrication. For some wafer fabrication processes, such as atomic layer deposition, wafers need to visit some process modules for a number of times, instead of once, thus leading to a so-called revisiting process. Most previous studies on cluster tool scheduling focus on steady state at which cluster tools repeat identical cycles. Research on transient processes of dual-arm cluster tools with wafer revisiting processes becomes urgently needed for high-performance wafer fabrication. In order to speed up start-up transient processes, this paper adopts a program evaluation and review technique for the analysis of start-up transient processes and develops optimization algorithms for their scheduling of dual-arm cluster tools. Then, their complexity is analyzed. Finally, illustrative examples are given to show the applications of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the scheduling problem of single-arm cluster tools with both wafer residency time constraints and activity time variation in semiconductor manufacturing. Based on a Petri net model developed in our previous work, polynomial algorithms are proposed to obtain the exact upper bound of the wafer sojourn time delay for the first time. With the obtained results, one can check the feasibility of a given schedule or find a feasible and optimal one if it exists. Illustrative examples are given to show the applications of the proposed method. [ABSTRACT FROM PUBLISHER]

Some wafer fabrication processes require a wafer to visit some processing modules in a cluster tool multiple times, leading to a wafer revisiting process. They may pose wafer residency time constraints, i.e., a wafer can stay in a module for a limited time after it is processed. Although techniques exist for scheduling cluster tools with either wafer residency time constraints or wafer revisiting, it is much more challenging to schedule tools with both of them. Considering that atomic layer deposition is a typical wafer revisiting process, this paper intends to schedule a dual-arm cluster tool dealing with it. Based on the analysis of such a tool’s properties, a novel scheduling strategy called modified 1-wafer cyclic scheduling is derived. With this strategy, necessary and sufficient schedulability conditions are presented. If schedulable, highly efficient scheduling algorithms are developed to obtain a feasible and optimal schedule together with a way to implement the obtained one. Illustrative examples are given to show the application of the proposed approach. [ABSTRACT FROM PUBLISHER]

We examine a scheduling problem of cluster tools that concurrently process two wafer types in a cyclic operational sequence. Whereas the process steps for different wafer types are assigned to different processing modules (PMs), the wafer loading and unloading tasks at the PMs are performed by a single robot. For a given cycle plan, which is a mix of different wafers for each cycle, we wish to determine the robot task sequence so as to minimize the tool cycle time. When a single wafer type is processed, the backward and swap sequences are optimal for single-armed and dual-armed tools, respectively. They are being prevalently used because of their simplicity and robustness. To maintain such advantages in concurrent processing, we introduce and define the concurrent backward and swap sequences (CBSs and CSSs, respectively). We then develop conditions on process times, robot task times, and the number of wafers produced in a cycle for which such CBSs and CSSs are still optimal for concurrent processing. We also show that, for some special cases, the two wafer types can achieve their maximum throughput rates as if each wafer type exclusively uses the tool regardless of other wafer types in progress. When the developed conditions do not hold, an effective mixed integer programming (MIP) model based on the CBSs and CSSs is used for robot task sequencing. Finally, we experimentally verify its efficiency and effectiveness by comparing to the existing scheduling methods for optimal scheduling of cluster tools. [ABSTRACT FROM PUBLISHER]

In its fabrication, a wafer must meet its residency time constraints, i.e., it must leave its process chamber within a certain time after its process is done. It may need to visit some processing steps for a number of times, called wafer revisiting. For the typical wafer revisiting process of atomic layer deposition (ALD), this paper studies the scheduling problem of dual-arm cluster tools with both residency time constraints and wafer revisiting. To do so, a Petri net model is developed for the system. Then, with the Petri net model and based on a one-wafer cyclic scheduling method previously developed by the authors of this paper, schedulability conditions and scheduling algorithms are derived. The schedulability can be checked by analytical expressions. If schedulable, an optimal one-wafer cyclic schedule can be found by simple calculation. Thus, the proposed approach is very efficient. In addition, with the Petri net model, a simple way is presented to implement the obtained schedule. Illustrative examples are given to show the application of the proposed approach. [ABSTRACT FROM PUBLISHER]

A cluster tool that consists of several processing modules, a transport robot, and loadlocks is widely used for wafer processing in the semiconductor industry. The cluster tool repeats an identical operational sequence for processing wafers in a lot, and such a cyclic operation sequence is determined by the wafer flow pattern and process times of a wafer lot. When a wafer lot changes, the tool operation sequence should be switched accordingly. Switching from a cyclic tool operation sequence to another is subject to deadlocks and unnecessary task delays to avoid scheduling complexity. Hence, it is necessary to have a scheduling method for such frequent lot switchings that prevents a deadlock and reduces the switching time. In this paper, we first develop a Petri net model for lot switching operations and then utilize a mixed integer programming model for an optimal schedule. However, since its practical value is limited, we develop effective heuristic methods for lot switching in single-armed and dual-armed cluster tools. The scheduling strategies adapt prevalent cyclic tool scheduling rules, such as backward and swap sequences. By computational experiments, we prove the efficiency and effectiveness of the proposed scheduling rules. [ABSTRACT FROM AUTHOR]

For some wafer fabrication processes, such as an atomic layer deposition (ALD) process, the wafers need to visit some process modules for a number of times. Using the existing swap-based strategy scheduling method in such systems leads to a 3-wafer cyclic schedule. Unfortunately, it is not optimal in the sense of cycle time. Aiming at searching for a better schedule, this paper models the system by a timed Petri net. With this model, the properties of the 3-wafer schedule are analyzed. Then, based on the analysis, it is found that, to improve the performance, it is necessary to reduce the number of wafers completed in a cycle. Hence, a 1-wafer schedule is developed by using a new swap-based strategy. By using the Petri net model, its cycle time is analyzed and shown to be optimal. Also, an effective method is presented to implement it. Illustrative examples are given to verify the research results obtained in this paper. [ABSTRACT FROM PUBLISHER]

Most cluster tool scheduling studies assume identical access times between chambers or do not discuss the impact of access times. However, the optimal scheduling rule and the cycle time can depend on the access times or physical configuration of parallel chambers. Therefore, we examine cyclic scheduling problems for cluster tools that have nonidentical access times. We first develop Petri net models for tool behaviors and analyze the cycle time by identifying the workloads of the process steps. We prove that the conventional backward and swap sequencing strategies are still optimal for single-armed and dual-armed cluster tools, respectively, when a process step is the bottleneck and the tool repeats a minimal cyclic work cycle. We also present a closed-form formula for the cycle time and identify a coprime condition on the number of parallel chambers for which the cycle time is independent of the order of using parallel chambers. Finally, we develop a mixed integer programming model for cases in which the coprime requirement is not satisfied. [ABSTRACT FROM PUBLISHER]

With wafer residency time constraints, it is crucial to schedule a cluster tool in semiconductor fabrication such that the wafer sojourn time in a processing module is in a given range. However, because of the activity time variation in wafer fabrication by cluster tools, a feasible schedule obtained under the assumption of deterministic activity times may become infeasible. To solve this problem, it is critically important to reveal the wafer sojourn time fluctuations with bounded activity time variation. This paper targets at single-arm cluster tools. They are modeled by a Petri net to describe the fabrication processes. Based on the net, a real-time control policy is proposed such that its use offsets the effect of the activity time variation as much as possible. Then, the wafer sojourn time delay is analyzed and analytical expressions are given to calculate the upper bound. With the proposed method, we can check if a given schedule is feasible under bounded activity time variation. Examples are given to show the applications of the research results. [ABSTRACT FROM PUBLISHER]

Because of residency time constraints and activity time variation of cluster tools, it is very difficult to operate such integrated semiconductor manufacturing equipment. This paper addresses their real-time operational issues. To characterize their schedulability and achieve the minimum cycle time at their steady-state operation, Petri net (PN) models are developed to describe them, which are very compact, and independent of wafer flow pattern. It is due to the proposed models that scheduling cluster tools is converted into determining robot wait times. A two-level operational architecture is proposed to include an offline periodic schedule and real-time controller. The former determines when a wafer should be placed into a process module for processing, while the latter regulates robot wait times online in order to reduce the effect of activity time variation on wafer sojourn times in process modules. Therefore, the system can adapt to activity time variation. A cluster tool derived as a not-always-schedulable system by the existing methods is shown to be always-schedulable by using the proposed novel method. [ABSTRACT FROM PUBLISHER]

With wafer residency time constraint of cluster tools in semiconductor manufacturing, activity time variation can make an originally feasible schedule infeasible. Thus, it is difficult to schedule them and schedulability is a vitally important issue. With bounded activity time variation considered, this paper addresses their real-time scheduling issues and conducts their schedulability analysis. A Petri net (PN) model and a control policy are presented. Based on them, this paper derives closed-form schedulability conditions. If schedulable, an algorithm is developed to obtain an offline periodic schedule. This schedule together with the control policy forms a real-time schedule. It is optimal in terms of cycle time and can be analytically computed, which represents significant advance in this area. [ABSTRACT FROM PUBLISHER]

To improve the productivity of cluster tools in semiconductor fabrications, on the basis of stating scheduling problems, a try and error-based scheduling algorithm was proposed with residency time constraints and an objective of minimizing Makespan for the wafer jobs in cluster tools. Firstly, mathematical formulations of scheduling problems were presented by using assumptions and definitions of a scheduling domain. Resource conflicts were analyzed in the built scheduling model, and policies to solve resource conflicts were built. A scheduling algorithm was developed. Finally, the performances of the proposed algorithm were evaluated and compared with those of other methods by simulations. Experiment results indicate that the proposed algorithm is effective and practical in solving the scheduling problem of the cluster tools. [ABSTRACT FROM AUTHOR]

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 revisiting process such that the cycle time is minimized. Thus, this paper studies the revisiting process of ALD with revisiting times k = 3, 4, and 5, and analytical expressions are obtained to calculate the cycle time for the k possible schedules. Then, the schedule with the minimal cycle time is the optimal one. In this way, the scheduling problem of such a revisiting process becomes very simple and this is a significant improvement in scheduling cluster tools with wafer revisiting. Illustrative example is presented to show the application of the proposed method. [ABSTRACT FROM AUTHOR]