FaJun Yang

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.

Optimal One-Wafer Cyclic Scheduling of Single-Arm Multicluster Tools With Two-Space Buffering Modules

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.

Scheduling of Single-Arm Cluster Tools for an Atomic Layer Deposition Process With Residency Time Constraints

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.

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.

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.

Optimal scheduling of single-arm multi-cluster tools with two-space buffering modules

A multi-cluster tool is composed of a number of single-cluster tools linked by buffering modules. The capacity of a buffering module can be one or two. Aiming at finding an optimal one-wafer cyclic schedule, this work explores the effect of two-space buffering modules on the performance of a multi-cluster tool. The tool is modeled by a kind of Petri nets. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well captured by the net model. With the model, this work shows that there is always a one-wafer cyclic schedule that reaches the lower bound of the cycle time of a process-dominant tool. Furthermore, a constant-time algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. An illustrative example is given to show the application and power of this new method.

Optimal one-wafer cyclic scheduling analysis of hybrid multi-cluster tools with one-space buffering module

A multi-cluster tool with both single and dual-arm individual cluster tools is called a hybrid multi-cluster tool. To operate it, 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 work studies its scheduling when its bottleneck individual tool is process-bound. With a timed Petri net model, the scheduling problem is reduced to determine the waiting time of robots. Then, the conditions are presented, under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached. Based on them, an efficient algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. An example is given to show its effectiveness.

Optimal scheduling of time-constrained single-arm cluster tools with wafer revisiting

It is very difficult to schedule a single-arm cluster tool with wafer revisiting such that wafer residency time constraints are satisfied. This paper conducts a study on this challenging problem for a single-arm cluster tool with atomic layer deposition (ALD) process. With a so called p-backward strategy being applied, a Petri net model is developed to describe the dynamic behavior of the system. Based on the model, existence of a feasible schedule is analyzed, schedulability conditions are derived, and a scheduling algorithm is presented if there is a schedule. A schedule is obtained by simply setting the robot waiting time and it is very computationally efficient. The obtained schedule is shown to be optimal. Illustrative examples are given to demonstrate the proposed approach.

Optimal One-Wafer Cyclic Scheduling of Hybrid Multirobot Cluster Tools With Tree Topology

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.

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.