QingHua Zhu

Petri Net-Based Optimal One-Wafer Scheduling of Single-Arm Multi-Cluster Tools in Semiconductor Manufacturing

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.

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.

Optimal Scheduling of Complex Multi-Cluster Tools Based on Timed Resource-Oriented Petri Nets

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

Petri net modeling and one-wafer scheduling of single-arm multi-cluster tools

It is very challenging to schedule a multi-cluster tool for it needs to coordinate the activities of multiple robots. This paper studies one-wafer cyclic scheduling for multi-cluster tools whose bottleneck cluster tool is process-bound. A Petri net model is developed to describe the system. Based on the model, 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. The method requires only simple calculation. An example illustrates the application and effectiveness of the proposed method.

Scheduling of single-arm multi-cluster tools to achieve the minimum cycle time

It is very challenging to schedule a multi-cluster tool to maximize its throughput. This work studies its one-wafer optimal periodic schedule. It is found that the key to schedule it is to determine its robots waiting times. A resource-oriented Petri net model is developed for it such that the robot waiting times are well modeled. Based on the model, optimality conditions are derived and the scheduling problem is reduced to the determination of robot waiting times. By the derived conditions, an optimal one-wafer optimal periodic schedule for a multi-cluster tool can be obtained by scheduling its individual cluster tools one by one. Then, a highly efficient algorithm is proposed to compute it for an entire multi-cluster tool.

Petri Net Modeling and Scheduling of a Close-Down Process for Time-Constrained Single-Arm Cluster Tools

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

Wafer Sojourn Time Fluctuation Analysis of Time-Constrained Dual-Arm Cluster Tools With Wafer Revisiting and Activity Time Variation

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.

Petri net modeling and one-wafer scheduling of single-arm tree-like multi-cluster tools

It is very challenging to obtain a one-wafer cyclic schedule for the widely used multi-cluster tools in semiconductor manufacturing. This work studies the scheduling problem for a single-arm tree-like multi-cluster tool that is process-dominant. A resource-oriented Petri net (PN) model is developed to describe its operation behavior by explicitly modeling robot waiting. Based on it, sufficient and necessary conditions are for the first time established to find a one-wafer periodic schedule. By determining robot waiting time, efficient algorithms are proposed to find such a schedule with the minimal cycle time. An example is used to show its application.

Scheduling and Control of Startup Process for Single-Arm Cluster Tools With Residency Time Constraints

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.

Scheduling Close-Down Processes Subject to Wafer Residency Constraints for Single-Arm Cluster Tools

High-mix and low-volume wafer fabrication leads to more and more lot switches in cluster tools. Practitioners must thus deal with more transient processes during such switches, including start-up and close-down. To obtain higher throughput, it is critical to shorten these processes. Much effort has been put into the steady state modeling and scheduling of cluster tools and some for start up processes. However, no attention is paid to a close-down process for single-arm cluster tools with wafer residency constraints. This work aims to do so by 1) developing a Petri net model to analyze their properties and 2) proposing Petri net-based methods to solve their close-down optimal scheduling problems under different workloads among their process steps. An industrial example is given to illustrate their application.