Search

In modern semiconductor manufacturing, the computer-integrated manufacturing system plays an essential role in automation with plenty of software systems. Among them, the equipment automation program (EAP) is one of the fundamental systems to support the interconnection of various types of equipment. For the traditional EAP, the communication and logic models are tightly coupled. The occurrence of any exception in EAP may make the EAP power down such that no equipment is reachable. Additionally, it can handle a couple of manufacturing tools only. The extension of manufacturing tools in a semiconductor fab makes the investment in EAP unbearable. Thus, fabs are highly desired to solve such problems of the traditional EAP. To do so, this work designs a new framework for a distributed EAP system with new technologies being adopted to enhance the usage and stability of EAP. Additionally, this design philosophy makes the distributed EAP system more compatible and expansible. Further, this EAP system can be upgraded as communication and big data technologies advance. Experiments are carried out to verify the stability of the designed distributed EAP system. [ABSTRACT FROM AUTHOR]

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]

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]

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]

A kind of facilities for wafer fabrication, cluster tools (CTs) need to close down to an idle state from time to time because of periodical maintenance and switches from one type of lots to another, which is called a normal close-down process (NCDP). It is crucial to optimize such a transient process since it tends to occur more and more frequently due to customization. Also, process modules (PMs) in CTs are known to be failure-prone. Once a PM failure occurs, a tool needs to close down to an idle state as well, which is different from NCDP and is called a failure close-down process (FCDP). With wafer residency time constraints (WRTCs) being imposed, close-down process optimization for such a tool is challenging, since one needs to not only finish this process as soon as possible but also meet WRTCs during this transient process. In order to tackle this problem, this article first introduces steady state scheduling problems. Then, with a presented backward robot task sequence, a linear programming model is first proposed to optimize NCDP. To deal with the PM failures, efficient PM failure response policies are formulated for the cases in which a PM fails. Then, four linear programs are proposed to optimize an FCDP. Finally, industrial case studies are given to show the usefulness of the proposed approaches. [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]

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]

In semiconductor manufacturing systems, a time-constrained multi-cluster tool should be scheduled such that a wafer stays in a process chamber in a given time range to satisfy a wafer residency time constraint. In practice, activity time is subject to variation. It could lead to some fluctuation of wafer residency time in a process chamber. Hence, it is crucial to analyze how wafer residency time varies with activity time variation. This issue is especially challenging for multi-cluster tools. This work focuses on determining the exact upper bound of wafer sojourn time delay resulted from activity time variation for dual-arm multi-cluster tools. After discussing their dynamic behaviours, it presents a two-level real-time operational architecture and a real-time control policy. Based on them, this work derives for the first time an efficient algorithm to calculate the exact upper bound of wafer sojourn time delay in a process chamber. As a result, engineers can test whether a given schedule is feasible. Several examples of industrial significance are used to demonstrate the application of the proposed approach. [ABSTRACT FROM AUTHOR]

In LED semiconductor manufacturing, it is important to evaluate the wafer reflectance in order to validate the quality of wafers. In this work, a learning model based on ${K}$ -means clustering and neural networks is proposed to analyze the relationship between etching parameters and wafer reflectance under a complex etching environment. The implemented clustering algorithm is used to cluster historical data and reduce the effect caused by different processing environments. Then, for each obtained cluster, a neural network is developed to learn the relationship between etching parameters and wafer reflectance. Finally, a real case study from an LED semiconductor fab is conducted to show the application of the proposed method. Experiments show that the proposed method achieves much better performance in comparison with support vector machine for mapping the relationship between etching parameters and wafer reflectance. Also, by the proposed method, the average prediction accuracy of the wafer reflectance can be improved by up to 9.38%, and the mean square error is reduced by 21.64% compared with the methods without clustering. [ABSTRACT FROM AUTHOR]

In semiconductor manufacturing, a process module (PM) failure in cluster tools (CTs) happens from time to time. To effectively operate a CT, such a failure should be handled in a proper and timely manner. This issue becomes much more complicated because wafer residency time constraints (WRTCs) must be met to ensure the quality for some wafer fabrication processes. With such constraints, if a tool is operated under a periodic schedule and a PM fails, it is desired that the tool can still operate under a periodic schedule if it is possible. Nevertheless, the periodic schedule after a PM failure must be different from that before its failure since in this case the tool is degraded. Thus, there must be a transient process between them. It is a great challenge to operate a tool such that it can go through such a transient process with WRTCs being always satisfied. This paper aims to solve this problem by proposing PM failure response policies which can successfully transfer a CT to the feasible schedule after failure from the one before a failure. Then, efficient algorithms are developed to improve these response policies. The proposed policies are composed of simple control laws such that they can be realized in real time and online. Illustrative examples are presented to show their applications. [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]

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]

Wafer revisiting and residency time constraints complicate the scheduling problem of cluster tools in semiconductor manufacturing. Random disturbance to the activity time in operating a tool further complicates such a scheduling problem. To solve this challenging problem, this paper proposes a robust real-time schedule which consists of a real-time controller (RTC) and an off-line schedule. The former is developed to offset the activity time disturbance such that the wafer sojourn time fluctuation in a process module is minimized. With the RTC, to find the off-line schedule, necessary and sufficient schedulability conditions under which a feasible schedule exists are derived and these conditions can be easily checked. Then, the off-line schedule can be efficiently found by the proposed algorithms based on nondisturbed activity time if a feasible schedule exists. With the obtained real-time schedule, it is shown that the productivity of the system is maximized. Finally, examples are used to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

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]

A hybrid multirobot cluster tool is composed of both single and dual-arm robotic cluster tools. Since the behavior of different individual tools is different, it is very challenging to coordinate their activities in such a tool and to schedule it optimally. To find a one-wafer cyclic schedule to reach the shortest cycle time for a treelike hybrid multirobot cluster tool whose bottleneck tool is process-bound, this paper extends resource-oriented Petri nets to model it such that a schedule can be parameterized by its robots’ waiting time. Based on the model, this paper then establishes the conditions under which there is a one-wafer cyclic schedule such that the shortest cycle time can be obtained. An efficient algorithm is also given to test the existence of such a schedule and to find it if existing. At last, examples are used to illustrate the proposed approaches. [ABSTRACT FROM AUTHOR]

Scheduling a multicluster tool with wafer residency time constraints is highly challenging yet important in ensuring high productivity of wafer fabrication. This paper presents a method to find an optimal one-wafer cyclic schedule for it. A Petri net is developed to model the dynamic behavior of the tool. By this model, a schedule of the system is analytically expressed as a function of robots’ waiting time. Based on this model, this paper presents the necessary and sufficient conditions under which a feasible one-wafer cyclic schedule exists. Then, it gives efficient algorithms to find such a schedule that is optimal. These algorithms require determining the robots’ waiting time via simple calculation and thus are efficient. Examples are given to show the application and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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]

This work studies the scheduling problem of a single-arm multicluster tool with a linear topology and process-bound bottleneck individual tool. The objective is to find a one-wafer cyclic schedule such that the lower bound of cycle time is reached by optimally configuring spaces in buffering modules that link individual cluster tools. A Petri net (PN) model is developed to describe the dynamic behavior of the system by extending resource-oriented PNs such that a schedule can be parameterized by robots’ waiting time. Based on this model, conditions are presented under which a one-wafer cyclic schedule with the lower bound of cycle time can be found. With the derived conditions, an algorithm is developed to find such a schedule and optimally configure buffer spaces. The algorithm requires only simple calculation to set the robots’ waiting time and buffer size. Illustrative examples are presented to demonstrate the proposed method. [ABSTRACT FROM PUBLISHER]

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]

This paper studies the challenging problem of scheduling single-arm multi-cluster tools with wafer residency time constraints. They have a linear topology and their bottleneck tool is process-bound. This work aims to find an optimal one-wafer cyclic schedule. With the Petri net model developed in our previous work and the minimal cycle time for a multicluster tool without wafer residency time constraints, it derives the necessary and sufficient schedulability conditions for multicluster tools with wafer residency time constraints for the first time. Then, it gives an algorithm to find an optimal one-wafer cyclic schedule if schedulable. This is done by simply setting the robots’ waiting time for each tool. Thus, it is very computationally efficient and applicable to practical problems. An example is presented to illustrate the proposed method. [ABSTRACT FROM PUBLISHER]

A multi-cluster tool is composed of a number of individual cluster tools linked by buffering modules (BMs). The capacity of a BM can be one or two. Aiming at finding an optimal one-wafer cyclic schedule, this paper explores the effect of two-space BMs on the performance of a multi-cluster tool. A Petri net (PN) model is developed to model it by extending resource-oriented PNs. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well described by the model. This paper shows that there is always a one-wafer cyclic schedule that reaches the lower bound of the cycle time of a process-bound tool. Furthermore, a closed-form algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. Illustrative examples are given to show the application and power of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the different behavior of single-arm and dual-arm cluster tools, it is challenging to schedule a hybrid multi-cluster tool containing both of them. This paper aims to find an optimal one-wafer cyclic schedule for such a multi-cluster tool. It is assumed that the bottleneck individual cluster tool in it is process-bound, thereby making it process-dominant. To do so, this paper models a hybrid multi-cluster tool with Petri nets. With this model, it derives the conditions under which individual cluster tools can operate in a paced way. Based on these conditions, this paper shows that for any process-dominant hybrid multi-cluster tool there is always a one-wafer cyclic schedule. Then, it develops the algorithms to find the minimal cycle time and the optimal one-wafer cyclic schedule. It is computationally efficient and easy-to-implement in practice. Examples are given to show the application and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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]

In operating a multi-cluster tool, it needs to coordinate the activities of multiple robots. Thus, it is very challenging to schedule it. This paper conducts a study on one-wafer cyclic scheduling for multi-cluster tools whose bottleneck cluster tool is process-bound. The system is modeled by a Petri net. With this model, conditions under which a one-wafer cyclic schedule exists are developed. Based on them, it is shown that, for any multi-cluster tool whose bottleneck cluster tool is process-bound, there is always a one-wafer cyclic schedule. Then, a method is presented to find the minimal cycle time and the optimal one-wafer cyclic schedule. It is computationally efficient. Illustrative examples are used to show the applications and effectiveness of the proposed method. [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]

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]

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]

For some wafer fabrication processes in cluster tools, e.g., atomic layer deposition (ALD), wafer revisiting is required. Typically, in such processes, wafers need to visit two consecutive processing steps several times. Such a revisiting process can be denoted as (mi, mi + 1)^h, where i means the ith-step and mi and mi + 1 mean the corresponding quantity of the processing modules in i and (i+1)th steps, and h the number of visiting times. This paper conducts a study for scheduling single-arm cluster tools with such a wafer revisiting process. The system is modeled by Petri nets (PNs) to guarantee the feasibility of robot activities. Based on the model, a deadlock avoidance policy is presented. With the control policy, cycle time analysis for the revisiting process is made. With the fact that wafer processing times are much longer than robot movement times in cluster tools, it is shown that, when mi = mi + 1 = 1, i.e., each step has only one processing module, the optimal one-wafer cyclic schedule is deterministic and unique, and the minimal cycle time can be calculated by an analytical expression. It is also shown that, when mi = 1 and mi + 1 = 2 or mi= 2 and mi + 1 = 1, the optimal one-wafer cyclic schedule can be obtained by finding h deterministic schedules and the one with the least cycle time. A novel analytical method is finally presented to schedule the overall system containing such reentrant wafer flow. This represents a significant advance in single-arm cluster equipment automation. [ABSTRACT FROM AUTHOR]