Dual-armed Cluster Tools Research Articles

Scheduling Dual-Armed Cluster Tools With Chamber Cleaning Operations

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.

Scheduling and optimization of mixed-processing with multi-variety wafers in dual-armed cluster tools

ABSTRACTTo improve the efficiency of wafer fabrication, this work addresses the scheduling and control problems of mixed-processing with multiple wafer types in cluster tools. Then, based on a developed Petri net (PN) model, it presents a general model for cluster tools with multiple wafer types and the conventional swap strategy. By analyzing the coordination mechanism between wafers processing and robot tasks, necessary and sufficient conditions are established to check the schedulability of the system that is operated by using the conventional swap strategy. If the system is not schedulable checked by such schedulability conditions, a constraint-guided heuristic algorithm and a conflicts-avoiding algorithm are developed to obtain a reasonable schedule. Finally, illustrative examples are presented to show the applications of the proposed method.

Scheduling Single-Armed Cluster Tools With Chamber Cleaning Operations

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.

Polynomial approach to optimal one-wafer cyclic scheduling of treelike hybrid multi-cluster tools via Petri nets

A treelike hybrid multi-cluster tool is composed of both single-arm and dual-arm cluster tools with a treelike topology. Scheduling such a tool is challenging. For a hybrid treelike multi-cluster tool whose bottleneck individual tool is process-bound, this work aims at finding its optimal one-wafer cyclic schedule. It is modeled with Petri nets such that a onewafer cyclic schedule is parameterized as its robots’ waiting time. Based on the model, this work proves the existence of its onewafer cyclic schedule that features with the ease of industrial implementation. Then, computationally efficient algorithms are proposed to find the minimal cycle time and optimal onewafer cyclic schedule. Multi-cluster tool examples are given to illustrate the proposed approach. The use of the found schedules enables industrial multi-cluster tools to operate with their highest productivity.

Noncyclic scheduling of dual-armed cluster tools for minimization of wafer residency time and makespan

Cluster tools are used for semiconductor wafer fabrication. A cluster tool consists of several loadlock modules, processing modules, and material handling armed robots to transfer wafers between loadlocks and processing modules. Most conventional scheduling methods consider a cyclic schedule to minimize makespan. We consider noncyclic scheduling of dual-armed cluster tools. In practice, it is important to minimize wafer residency time in processing modules to maintain the surface quality of wafers. In the noncyclic operations, the cluster tool causes deadlock which may lead to excessive loss in the wafer fabrication process. We propose an efficient deadlock-free scheduling method for the noncyclic scheduling problem of a dual-armed cluster tool to minimize the residency time and makespan. The proposed method is applied to a dual-armed cluster tool with a non-revisiting process and a revisiting process. Computational results demonstrate the effectiveness of the proposed method.

Output feedback control of discrete processes under time constraint: application to cluster tools

Practical control of timed behaviours in industrial applications is difficult. One of the few efficient modelling approaches to deal with time constraints on discrete event systems is to use timed event graph (TEG), a subclass of Petri nets. The dynamic behaviour of these graphs is represented by a linear equations system over the max-plus algebra. Up to date, these models were assumed to be fully observable. In this paper, it is demonstrated that if a TEG is strongly connected, one can derive a realisable output feedback control. In other words, the control law depends solely on the control itself and the system’s outputs, considered to be the only observable events. The satisfaction of a set of constraints is addressed in the case of a single input model (i.e. having only one input transition) and the procedure to derive a realisable output feedback control law is provided. Finally, the present control method is applied to a dual-armed cluster tool, a well-known industrial practical application.

Makespan Analysis of Lot Switching Period in Cluster Tools

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.

Feedback Control of Cluster Tools for Regulating Wafer Delays

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.

Modeling, Analysis, and Scheduling of Cluster Tools With Two Independent Arms

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.

Scheduling and Analysis of Start-Up Transient Processes for Dual-Arm Cluster Tools With Wafer Revisiting

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.

Scheduling cluster tools for concurrent processing of two wafer types with PM sharing

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.

Schedulability and Scheduling Analysis of Dual-Arm Cluster Tools with Wafer Revisiting and Residency Time Constraints Based on a Novel Schedule

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.

Petri Net Decomposition Approach to Deadlock-Free and Non-Cyclic Scheduling of Dual-Armed Cluster Tools

Semiconductor cluster tools are the integrated equipment to process a variety of silicon wafers for the fabrication of microelectronic components. The cluster tool system consists of several loadlock modules, processing chambers, and material handling armed robots for transferring wafers between them. Most scheduling problems for dual-armed cluster tools adopt cyclic scheduling with the assumption of swap sequence of the robot arm. A deadlock-free and non-cyclic scheduling is highly required to improve total throughput of cluster tools for various types of wafer flow patterns and various changes of equipment configurations. In this paper, we propose a Petri net decomposition approach to derive a near-optimal solution of deadlock-free and non-cyclic scheduling of dual-armed cluster tools to reduce the computational complexity. A timed Petri net model is introduced to represent a non-cyclic scheduling model for dual-armed cluster tools. In order to obtain a deadlock-free and non-cyclic schedule efficiently, we propose a deadlock avoidance control policy that restricts the markings to prevent unmarked siphons. Deadlock condition for the dual-armed cluster tools is characterized by the structure of Petri net model. The performance of the non-cyclic scheduling model by the proposed method is compared with that of the cyclic scheduling model. Computational results show the effectiveness of the non-cyclic scheduling model compared with the cyclic scheduling model for multiple wafer flow patterns.

Petri Net-Based Polynomially Complex Approach to Optimal One-Wafer Cyclic Scheduling of Hybrid Multi-Cluster Tools in Semiconductor Manufacturing

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.

Schedule Restoration for Single-Armed Cluster Tools

The idle time between two consecutive tasks may seriously affect the wafer quality in some wafer fabrication processes requiring high temperature and pressure. Hence, a cluster tool provides high wafer quality and predictability when operated at a steady schedule, which means that every cycle repeats the same pattern considering not only a sequence but also timing. However, multiple process modules per step can cause the fluctuation of wafer quality even under the same sequence since different modules have different wafer delays. It is known that a dual-armed cluster tool can always have a steady schedule that can be established via a timed event graph and (max, +) algebra. We extend this result to a single-armed cluster tool and generalize the method to establish its steady schedule. Although a cluster tool is initially set on a steady schedule, the schedule can become unsteady after disruptive events, such as wafer alignment failures, and it cannot always return to it. We develop strategies that change the system dynamics of a cluster tool by appropriately delaying some tasks such that any disrupted schedule pattern is stabilized in a finite time. Finally, we examine how they help to flatten wafer delays after a disruption or when tasks have stochastic time fluctuation.

Petri Net-Based Optimal One-Wafer Cyclic Scheduling of Hybrid Multi-Cluster Tools in Wafer Fabrication

In a multi-cluster tool, there may be both single and dual-arm cluster tools. Such a multi-cluster tool is called hybrid multi-cluster tool. To operate such a multi-cluster tool, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this paper conducts a study on scheduling a hybrid multi-cluster tool with its bottleneck tool being process-bound. The tool is modeled by a kind of timed Petri net model. With this model, the scheduling problem is reduced to determining the robots' waiting time. Then, the conditions under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached are presented. Based on them, a closed-form algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. Examples are given to show the application of the proposed method.

Cycle time analysis of dual-arm cluster tools for wafer fabrication processes with multiple wafer revisiting times

For some wafer fabrication processes, the wafers need to visit some processing modules for a number of times, which is referred to as the revisiting process. With wafer revisiting, it is very complicated to analyze the cycle time of a dual-arm cluster tool. Due to the fact that atomic layer deposition (ALD) process is a typical revisiting process in the semiconductor industry, study is conducted on cycle time analysis of dual-arm cluster tools for the ALD process with multiple revisiting times. The system is modeled by a type of Petri net. With this model, it is revealed that the system may never reach a steady state. Based on this finding, a method is presented to analyze the cycle time and analytical expressions are derived to calculate the cycle time for different cases. Several illustrative examples are given to show the applications of the proposed approach.

Scheduling of Dual-Arm Cluster Tools With Wafer Revisiting and Residency Time Constraints

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.

Scheduling algorithm of dual-armed cluster tools with residency time and reentrant constraints

To solve the scheduling problem of dual-armed cluster tools for wafer fabrications with residency time and reentrant constraints, a heuristic scheduling algorithm was developed. Firstly, on the basis of formulating scheduling problems domain of dual-armed cluster tools, a non-integer programming model was set up with a minimizing objective function of the makespan. Combining characteristics of residency time and reentrant constraints, a scheduling algorithm of searching the optimal operation path of dual-armed transport module was presented under many kinds of robotic scheduling paths for dual-armed cluster tools. Finally, the experiments were designed to evaluate the proposed algorithm. The results show that the proposed algorithm is feasible and efficient for obtaining an optimal scheduling solution of dual-armed cluster tools with residency time and reentrant constraints.

Scheduling Lot Switching Operations for Cluster Tools

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.