Multi-cluster Tools Research Articles

Scheduling Dual-Arm Multi-Cluster Tools With Residency Time Constraints Beyond Swap-Based Strategies and Module-Bound Regions

Scheduling Dual-Arm Multi-Cluster Tools With Residency Time Constraints Beyond Swap-Based Strategies and Module-Bound Regions

Scheduling a Single-Arm Two-Cluster Tool With a Process Module Failure Subject to Wafer Residency Time Constraints

Multi-cluster tools are widely adopted in semiconductor manufacturing. When a process module (PM) at a step fails, a multi-cluster tool cannot complete the process recipe of work-in-process wafers and must be forced to enter a closedown process to be empty. To increase the throughput of a wafer fab, it is economically significant to shorten the failure-closedown process. However, due to the wafer residency time constraints, it is highly challenging to respond to a PM failure and find a corresponding optimal schedule. By assuming no parallel PM at a step, this work is the first to study this important issue for scheduling multi-cluster tools. We analyze the task sequences and synchronization conditions for robot activities to avoid deadlock in a shared buffer module. Upon these analyses, for process-dominant multi-cluster tools whose optimal steady-state schedule is known, algorithms are proposed to synthesize the proper sequences for robots in case of PM failures, then, a nonlinear program model is proposed to find an optimal schedule for the corresponding closedown process or decide no feasible solutions. The proposed model can uniformly deal with different scenarios of PM failures. Examples are given to illustrate the application of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In a wafer fab, there are hundreds, even thousands, of cluster tools. It is common that a failure of a processing module happens in a cluster tool. How to intelligently respond to such a random failure in a multi-cluster tool is an important issue in real-world production. This paper studies the scheduling problem of a multi-cluster tool in case of a failure at a PM. For a multi-cluster tool in case of a failure module, the proposed method can significantly reduce the loss of work-in-process wafers and shorten the closedown process.

Scheduling a Single-ARM Multi-Cluster Tool with a Condition-Based Cleaning Operation

Scheduling a Single-ARM Multi-Cluster Tool with a Condition-Based Cleaning Operation

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

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

Optimally Scheduling Dual-Arm Multi-Cluster Tools to Process Two Wafer Types

To satisfy the requirements of high-mix integrated-circuit chip production, multiple wafer types are grouped into a lot to be fabricated concurrently in a multi-cluster tool system. However, the existing studies do not solve the scheduling problem of multi-cluster tools with multiple wafer types being processed and wafer residency time constraints being imposed. This study aims to find a feasible steady-state schedule for a process-dominant multi-cluster tool that processes two wafer types concurrently. A novel robot cycle, called one-wafer-per-type cycle, and a two-swap robot sequence are defined, under which the minimal cycle time can be achieved. Further, the schedulability for individual cluster tools with two wafer types is proved upon closed-form derivations. The schedulability conditions of a one-wafer-per-type schedule for the system are proposed. With such conditions, an efficient algorithm is established to obtain a schedule in a two-swap sequence. Several instances show the application and effectiveness of the proposed method.

Noncyclic Scheduling of Multi-Cluster Tools With Residency Constraints Based on Pareto Optimization

Multi-cluster tools are widely used in semiconductor manufacturing. When the lot size of wafers tends to be quite small, a cyclic scheduling strategy is not suitable. However, the noncyclic scheduling of multi-cluster tools is much more challenging due to multi-robot coordination and the increasing number of chambers. This paper focuses on the noncyclic scheduling problem of multi-cluster tools with residency constraints. We construct a universal model to describe such problem to fit both single-armed and dual-armed robots, where serial flow, parallel flow and reentrant flow are all considered. Correspondingly, an improved dynamic programming algorithm is proposed. Specifically, a sequential constraint is first added to deal with the chronological conflicts brought by multi-robot coordination together with a normalization rule to improve searching efficiency. Meanwhile, considering the residency constraints, a path deleting method is also introduced to remove the infeasible solutions. Besides, the theoretical analysis of computation efficiency is also discussed. Numerical experiments demonstrate that the proposed algorithm can meet various practical scheduling requirements, while achieving distinctive improvements in efficiency.

Wafer sojourn time fluctuation analysis for time-constrained dual-arm multi-cluster tools with activity time variation

ABSTRACT 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.

Optimal integrated schedule of entire process of dual-blade multi-cluster tools from start-up to close-down

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

An equivalent conversion method for dual-armed multi-cluster tool scheduling problems with multi-wafer types

Due to the trend towards 450 mm diameter wafers and customisation, an increase in wafer diversity and transient operation are anticipated for multi-cluster tools in wafer fabrication. While most previous studies focus on steady state scheduling problem of cluster tools, research on multi-cluster tools scheduling problems with transient operations is still at early stage. This article addresses the dual-armed multi-cluster tools scheduling problem with transient operations and multiple wafer types. The problem is subject to residency constraints and makespan is adopted as the performance metrics. A non-linear mathematical model of the problem is established. To solve this problem, a time constraint sets-based heuristic algorithm, called the TB algorithm, is proposed in this article. Based on SWAP strategy, this article proposed the conception of virtual buffer modules, thus the TB algorithm converts the dual-armed multi-cluster tool scheduling problem into single-armed multi-cluster tools scheduling problem equivalently. Experimental results indicate that the proposed algorithm is feasible and efficient.

An equivalent conversion method for dual-armed multi-cluster tool scheduling problems with multi-wafer types

An equivalent conversion method for dual-armed multi-cluster tool scheduling problems with multi-wafer types

Investigation of the influence of the number of modules of a multicluster technological complex and the operations performed by them on the overall performance of the installation using simulation simulations

Variety of compositions of multicluster tools determines the development of methods aimed at analysis and search of feasible compositions, which meet the requirements and optimal performance (throughput) criteria. Very often in the industry, there is a task to find optimum utilization of the cluster tool. To find a solution various approaches are used, such as input in the system several flows of the semifinished products, increasing overall number of the arms of the robot, etc. In this article cluster tool and throughput dependence on quantity of performed operations of the least loaded module are investigated. It is shown, that with the help of this approach one can easily simplify both finding the solution of the task to composite cluster tool with flows of two different types of wafers and determining schedule of the wafers for maximum and minimum throughput. Relevance of the article is stipulated by substantive and complex choices of both finding optimal composition of the cluster tool and scheduling semifinished products flows (in accordance with variations of the operations in modules) at both the design and exploitation stage.

An Efficient Deadlock Prevention Policy for Noncyclic Scheduling of Multicluster Tools

Scheduling of multicluster tools has received much attention due to its complexity of interaction among cluster tools. A cluster tool comprises several modules such as processing modules, a transfer module with a single or dual-armed handling robot, and loadlock modules. A multicluster tool comprises two, three, or more cluster tools that are interconnected with each other. In this paper, we propose a deadlock prevention policy for noncyclic scheduling of dual-armed multicluster tools. The proposed deadlock prevention policy is effective for generating an efficient schedule for two or three-connected multicluster tools with a single or a dual-path flow. This is proven by analyzing the strict minimal siphon of the Petri net model. The performance of the proposed method is compared with that of a maximal permissible deadlock prevention policy. The results demonstrate that the proposed method is computationally efficient for larger state spaces and more suitable than conventional deadlock prevention policies for generating effective schedules for noncyclic scheduling of multicluster tools. Note to Practitioners —Scheduling of multicluster tools has recently attracted attention in the growing semiconductor manufacturing industry. Most conventional studies on multicluster tools focus on cyclic scheduling to minimize cycle time with swap strategy. The challenge addressed by this paper is to derive a deadlock-free schedule for multicluster tools with noncyclic operations. We propose a simple deadlock prevention policy that can be applied to large-scale timed Petri net (PN) model of general multicluster tools without enumeration of siphon computations or solution of mixed integer programming. A timed PN model is developed for noncyclic operations of dual-armed multicluster tools with a dual ath. The computational results show that the approximately 10% of the total throughput of the proposed method is better than those of the conventional methods. It enables more efficient operations for noncyclic scheduling under transient periods including cleaning operations.

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.

Design of a Petri net supervisor for multi-cluster tools to improve scheduling performance

Design of a Petri net supervisor for multi-cluster tools to improve scheduling performance

Petri Net-Based Efficient Determination of Optimal Schedules for Transport-Dominant Single-Arm Multi-Cluster Tools

It is a great challenge to find an optimal one-wafer cyclic schedule for a single-arm multi-cluster tool that is widely adopted in semiconductor fabrication. Aiming to tackle this significant problem, an optimal scheduling strategy is determined first for each individual tool under the condition that the bottleneck individual tool is transport-bound. Then, by developing a Petri net model with robot waiting being explicitly described to reveal the properties of the entire system, this paper shows that to schedule such a tool optimally is to allocate the robot waiting time properly. Then, this paper presents the necessary and sufficient conditions for the existence of an optimal one-wafer cyclic schedule. Thereafter, an efficient algorithm is developed to check the given conditions and find such a schedule efficiently if existing. Finally, two industrial examples are used to verify that the proposed method is applicable and effective.

Cyclic Scheduling of Multi-Cluster Tools Based on Mixed Integer Programming

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.

Optimal One-Wafer Cyclic Scheduling of Time-Constrained Hybrid Multicluster Tools via Petri Nets

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.

Scheduling Transient Processes for Time-Constrained Single-Arm Robotic Multi-Cluster Tools

Multi-cluster tools are highly productive yet expensive wafer fabricating facility in semiconductor industry. Current competitive business trend requires high-mix and low-volume production of wafers. The size of a wafer lot is becoming smaller and wafer lots change more frequently. This brings up with many start-up and close-down processes. It is thus more and more important to control these transient processes to ensure the highest utilization of expensive facility. Since many wafer fabrication processes have strict residency time constraints after a wafer’s processing, this work aims to schedule optimally the transient processes of single-arm multi-cluster tools subject to such constraints. For such tools whose optimal steady state schedules can be found, we propose linear programs to find the optimal schedules for start-up and close-down processes for the first time. The obtained schedules make the transitions between transient and steady states seamlessly. Examples are presented to illustrate how the proposed method outperforms the existing ones by about 10% throughput.

マルチクラスタツールの最適スーパーバイザの導出とスケジューリング性能への影響

Multi-cluster tools are widely used for semiconductor manufacturing. Multi-cluster tools can cause a deadlock due to resource conflicts. The deadlock may cause a serious decrease of throughput and a deterioration of quality of product. Therefore, the deadlock prevention method is necessary. In this paper, the optimal supervisor of multi-cluster tools is derived by reachability analysis of Petri nets for deadlock prevention. The effects of the optimal deadlock-free model is evaluated from the viewpoint of the scheduling performance.

Optimal scheduling for sequentially connected cluster tools with dual-armed robots and a single input and output module

We examine a cyclic scheduling problem of sequentially connected cluster tools with a single input and output module, which includes multi-cluster tools and linear cluster tools. Every component tool has a dual-armed robot, and chambers are parallelised for a long process step. An intermediate buffer between each pair of adjacent component tools has a limited capacity, and all processed wafers should return to the input and output module. To examine the scheduling problem, we first compute workloads of the process steps and robots to obtain a lower bound on the tool cycle time. We then identify a rule of assigning the chambers to the process steps that makes the tool cycle time independent of the order of using the parallel chambers. We also propose a simple robot task sequence which is modified from the well-known swap sequence for each component tool. We prove that the modified swap sequence is optimal when one of the process steps, not a robot, is the bottleneck. We also present a scheduling strategy which controls robot task timings to deal with interference of wafer flows between each pair of adjacent component tools. Finally, we perform numerical experiments to show the performance of the proposed sequence.