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Fast movement strategies for a step‐and‐scan wafer stepper
Author(s) -
Kuijpers C. M. H.,
Hurkens C. A. J.,
Melissen J. B. M.
Publication year - 1997
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00037
Subject(s) - stepper , wafer , travelling salesman problem , simulated annealing , stepper motor , computer science , look ahead , grid , integrated circuit , photolithography , algorithm , mathematical optimization , mathematics , engineering , materials science , mechanical engineering , nanotechnology , electrical engineering , geometry , operating system
We describe algorithms for the determination of fast movement strategies for a step‐and‐scan wafer stepper, a device that is used for the photolithographic processing of integrated circuits. The proposed solution strategy consists of two parts. First, we determine the maximum number of congruent rectangular chips that can be packed on a wafer, subject to the restriction that the chips are placed in a rectangular grid. Second, we find fast movement strategies for scanning all chips of a given packing, given the mechanical restrictions of the wafer stepper. The corresponding combinatorial optimization problem is formulated as a generalized asymmetric traveling salesman problem. We show how feasible scan strategies are determined, and how these strategies are improved by local search techniques, such as iterative improvement based on 2‐ and 3‐exchanges, and simulated annealing based on 2‐exchanges.