Mathematics (Jun 2024)

Wafer Delay Minimization in Scheduling Single-Arm Cluster Tools with Two-Space Process Modules

  • Chengyu Zou,
  • Siwei Zhang,
  • Shan Zeng,
  • Lei Gu,
  • Jie Li

DOI
https://doi.org/10.3390/math12121783
Journal volume & issue
Vol. 12, no. 12
p. 1783

Abstract

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In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a wafer into/from a space in the PM. This means that the wafer staying time in PMs is affected by both the rotation operations of the internal chambers of PMs and the robot tasks. Thus, minimizing the wafer delay time is quite challenging. In this work, for cluster tools with single-arm robots and two-space PMs, efforts are made for wafer delay minimization in scheduling the tools. Specifically, a two-wafer backward strategy is presented to operate the tools in a steady state. Then, the workloads of each processing step and the robot are analyzed. Further, to find optimal schedules with the objective of minimizing the total wafer delay time, efficient algorithms are established. Finally, case studies show that the wafer delay time at some steps can be totally eliminated by the proposed method. In the meantime, in all cases, the proposed method can work well in reducing the total wafer delay time at all steps.

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