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Litho Machine Scheduling With Convex Hull Analyses

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The increasing pressure to meet demand are forcing semiconductor manufacturers to seek efficient scheduling methods. Lithography, with a limited number of expensive resources and the reentrant nature of the fabrication processes, is a major bottleneck. This paper presents a litho machine scheduling
formulation for high-volume and low-variety manufacturing over a day, with novel modeling of resource setups, reticle expirations, and future stacking layer load balancing. The problem is believed to be NP hard. After linearization and simplification, it is solved by using the branch-and-cut method by exploiting problem linearity. Near-optimal solutions for practical problems, however, are still difficult to obtain efficiently. Through detailed analyses, it was discovered that the convex hull of the problem is difficult to delineate andmany low-efficient branching operations are needed.
A two-phase approach is therefore established. In the first phase, a simplified problem with certain complicating constraints dropped is efficiently solved by exploiting linearity to reduce ranges of
decision variables. The problem with the full set of constraints is then solved in the second phase with a much reduced decision space. Numerical testing shows that this two-phase approach can generate near-optimal schedules within reasonable amounts of computation time. This two-phase approach is generic, and will have major implications on other semiconductor scheduling problems and beyond.
Note to Practitioners—Lithography is a major bottleneck in semiconductor manufacturing. This paper addresses the scheduling of litho machines and reticles over a day for high-volume and low-variety lots to meet daily targets of different products. A scheduling formulation with novel modeling of resource setups, reticle expirations, and future stacking layer load balancing is presented. The problem is solved by using a standard commercial solver that exploits problem linearity. Near-optimal schedules,
however, are difficult to obtain efficiently for practical problems. Through detailed analyses, it was discovered that the difficulty is caused by certain constraints in the formulation. A two-phase
approach is therefore developed. In the first phase, a simplified problem with complicating constraints dropped is efficiently solved to reduce ranges of decision variables. The problem with the full set of constraints is then solved in the second phase with a much reduced decision space. This method can obtain near-optimal schedules for practical litho machine scheduling problems within reasonable amounts of computation time.
Index Terms—Branch-and-cut, convex hull, litho machine scheduling, mixed-integer optimization, semiconductor manufacturing, two-phase approach.

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Informasi Detail

Judul Seri

IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING

No. Panggil

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Penerbit

New York : IEEE., 2013

Deskripsi Fisik

IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 10, NO. 4, OCTOBER 2013

Bahasa

English

ISBN/ISSN

1545-5955

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

VOL. 10, NO. 4, OCTOBER 2013

Subjek

TEKNIK

Info Detail Spesifik

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Pernyataan Tanggungjawab

Yuli/Agus

Versi lain/terkait

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