NDLI: Graph-Based Subfield Scheduling for Electron-Beam Photomask Fabrication

Content Provider	IEEE Xplore Digital Library
Author	Shao-Yun Fang Wei-Yu Chen Yao-Wen Chang
Copyright Year	1982
Abstract	Electron beam lithography has shown great promise in photomask fabrication; however, its successive heating process centralizing in a small region may cause a severe problem of critical dimension (CD) distortion. Consequently, subfield scheduling that reorders the sequence of the writing process is needed to avoid successive writing of neighboring subfields. In addition, the writing process of a subfield raises the temperature of neighboring regions and may block other subfields for writing. This paper presents the first work to solve the subfield scheduling problem while considering blocked regions by formulating the problem into a constrained maximum scatter traveling salesman problem (constrained MSTSP). To tackle the constrained MSTSP that can be shown to be NP-complete in general, we identify a special case thereof with points on two parallel lines and solve it optimally in linear time. We then decompose the constrained MSTSP into subproblems conforming to the special case, solve each subproblem optimally and efficiently by a graph-based algorithm, and then merge the subsolutions into a complete scheduling solution. We also extend our algorithm to handle the cases when the moving time of an e-beam writing head is comparable with the writing time of a subfield. Experimental results show that our algorithms are effective and efficient in finding good subfield scheduling solutions that can alleviate the successive heating problem (and thus reduce CD distortion) for e-beam photomask fabrication.
Sponsorship	IEEE Council on Electronic Design Automation IEEE Circuits and Systems Society
Starting Page	189
Ending Page	201
Page Count	13
File Size	9689454
File Format	PDF
ISSN	02780070
Volume Number	32
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Writing Heating Fabrication Optimal scheduling Throughput Job shop scheduling subfield scheduling Design for manufacturability electron beam lithography photomask fabrication
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Electrical and Electronic Engineering Software

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