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

Masaru Sakai,Tatsushi Nishi

doi:10.1177/1687814017693217

Abstract

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.

Highlights

In the semiconductor industry, manufacturers utilize cluster tools to produce silicon wafers
We show the application to the noncyclic scheduling of cluster tools with revisiting processes
We have proposed a heuristic algorithm for noncyclic scheduling of dual-armed cluster tools with revisiting processes to minimize wafer residency time and makespan

Summary

Introduction

Manufacturers utilize cluster tools to produce silicon wafers. The authors have addressed a mixedinteger linear programming model for bi-objective optimization of makespan and total wafer residency time.[22] In this article, we propose a mixed-integer formulation of noncyclic scheduling of dual-armed cluster tools that requires less computational effort. The scheduling problem treated in this article is to find a deadlock-free and an optimal operational sequence and timing of the TM to minimize the makespan and the residency time for the 25 wafers which are identical. We develop the mixed-integer linear programming formulation of the noncyclic scheduling problem of a dual-armed cluster tool with two objectives to minimize the makespan (J1) and the residency time of wafer (J2). The mixed-integer programming (IP) formulation of the noncyclic scheduling problem for dual-armed cluster tool is written as follows.

E2 E3 E4 E5 E6

E2 E3 E4 E5 E6 E7 E8 E9 E10

Findings

Conclusion