Open AccessParametric analytical model for off-axis illumination sources based on Sigmoid function
Author(s) -
Wei Liu,
Shiyuan Liu,
Xiaofei Wu,
Chuanwei Zhang
Publication year - 2011
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.60.054213
Subject(s) - sigmoid function , parametric statistics , distortion (music) , fourier series , fourier transform , scaling , parametric model , kernel (algebra) , function (biology) , resolution (logic) , tilt (camera) , basis (linear algebra) , optics , representation (politics) , computer science , physics , mathematical analysis , geometry , mathematics , artificial intelligence , artificial neural network , political science , law , amplifier , computer network , statistics , bandwidth (computing) , combinatorics , evolutionary biology , politics , biology
This paper proposes a parametric analytical source model for overall representation of the physical distribution property of off-axis illumination sources in lithographic tools. A Sigmoid function is adopted as a kernel function to construct the analytical model for the multiple mainstream off-axis sources. Corrected parametrical terms are subsequently presented for characterization of different physical distortions and deviations of real illumination sources. The corrected parametrical terms can be decomposed into Fourier series which have the special physical meaning of respectively indicating different distortion types including shift of the center, tilt, ellipticity, etc. The proposed analytical model provides both simulation condition and theoretical basis for the resolution enhancement technique and the related research fields, thus has important applications.