Polynomial time optimal algorithm for stencil row planning in e-beam lithography
Guo, Daifeng
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https://hdl.handle.net/2142/50492
Description
Title
Polynomial time optimal algorithm for stencil row planning in e-beam lithography
Author(s)
Guo, Daifeng
Issue Date
2014-09-16
Director of Research (if dissertation) or Advisor (if thesis)
Wong, Martin D.F.
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
E-beam
Stencil Planning
1D Character Placement
Abstract
Electron beam lithography (EBL) is a very promising candidate for integrated circuit (IC) fabrication beyond the 10 nm technology node. To address its throughput issue, the Character Projection (CP) technique has been proposed, and its stencil planning can be optimized with awareness of overlapping characters. However, the top-level 2D stencil planning problem has been proven to be an NP-hard problem. As its most essential step, the 1D row ordering is believed hard as well, and no polynomial time optimal solution has been provided so far. Previous research formulates the problem as the travelling salesman problem, which is NP-hard and solves it by heuristics. In this thesis, we formulate the problem as a matching problem and propose a polynomial time optimal algorithm, which serves as the major subroutine for the entire stencil planning problem. The optimality of the algorithm is proved, and experimental results are also provided to show that our work makes a great improvement in efficiency and correctness to solve the row ordering problem.
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