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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.
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Keywords:
- optical lithography /
- source model /
- Sigmoid function /
- off-axis illumination
[1] Schellenberg F M 2005 Opt. Rev. 12 83
[2] Cao P F, Cheng L, Zhang X P 2008 Acta. Phys. Sin. 57 6946 (in Chinese) [曹鹏飞、程 琳、张晓萍 2008 57 6946]
[3] Li H H, Chen J, Wang Q K 2010 Chin. Phys. B 19 114203
[4] Perin G, Sezginer A, Zach F X 2006 J. Microlith. Microfab. Microsyst. 5 023006
[5] Zhang S L, Zheng Q 1985 Acta. Phys. Sin. 34 439 (in Chinese) [庄松林、郑 权 1985 34 439]
[6] Zhang S L, Chen X Z 1979 Acta. Phys. Sin. 28 657 (in Chinese) [庄松林、陈祥祯 1979 28 657]
[7] Liu W, Liu S Y, Zhou T T, Wang L J 2009 Opt. Express 17 19278
[8] Liu W, Liu S Y, Shi T L, Tang Z R 2010 Opt. Express 18 20096
[9] Yamazoe K 2010 Appl. Opt. 49 3909
[10] Ma X, Arce G R 2008 Opt. Express 16 20126
[11] Bodendorf C, Schlief R E, Ziebold R 2004 Proc. SPIE 5377 1130
[12] Barrett T C 2000 Proc. SPIE 4000 804
[13] Phillips M C, Slonaker S D, Treadway C, Darby Greg 2005 Proc. SPIE 5754 1562
[14] Guo L P, Wang X Z, Hang H J 2006 Chin. Opt. Lett. 4 237
[15] Granik Y 2004 Proc. SPIE 5524 217
[16] Renwick S P, Nishinaga H, Kita N 2006 Proc. SPIE 6154 61540O
[17] Flagello D G, Geh B, Socha R, Liu P, Cao Y, Stas R, Natt O, Zimmermann J 2008 Proc. SPIE 6924 69241U
[18] Laan H van der, Dierichs M, Greevenbroek H van, McCoo E, Stoffels F, Pongers R, Willekers R 2001 Proc. SPIE 4346 394
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[1] Schellenberg F M 2005 Opt. Rev. 12 83
[2] Cao P F, Cheng L, Zhang X P 2008 Acta. Phys. Sin. 57 6946 (in Chinese) [曹鹏飞、程 琳、张晓萍 2008 57 6946]
[3] Li H H, Chen J, Wang Q K 2010 Chin. Phys. B 19 114203
[4] Perin G, Sezginer A, Zach F X 2006 J. Microlith. Microfab. Microsyst. 5 023006
[5] Zhang S L, Zheng Q 1985 Acta. Phys. Sin. 34 439 (in Chinese) [庄松林、郑 权 1985 34 439]
[6] Zhang S L, Chen X Z 1979 Acta. Phys. Sin. 28 657 (in Chinese) [庄松林、陈祥祯 1979 28 657]
[7] Liu W, Liu S Y, Zhou T T, Wang L J 2009 Opt. Express 17 19278
[8] Liu W, Liu S Y, Shi T L, Tang Z R 2010 Opt. Express 18 20096
[9] Yamazoe K 2010 Appl. Opt. 49 3909
[10] Ma X, Arce G R 2008 Opt. Express 16 20126
[11] Bodendorf C, Schlief R E, Ziebold R 2004 Proc. SPIE 5377 1130
[12] Barrett T C 2000 Proc. SPIE 4000 804
[13] Phillips M C, Slonaker S D, Treadway C, Darby Greg 2005 Proc. SPIE 5754 1562
[14] Guo L P, Wang X Z, Hang H J 2006 Chin. Opt. Lett. 4 237
[15] Granik Y 2004 Proc. SPIE 5524 217
[16] Renwick S P, Nishinaga H, Kita N 2006 Proc. SPIE 6154 61540O
[17] Flagello D G, Geh B, Socha R, Liu P, Cao Y, Stas R, Natt O, Zimmermann J 2008 Proc. SPIE 6924 69241U
[18] Laan H van der, Dierichs M, Greevenbroek H van, McCoo E, Stoffels F, Pongers R, Willekers R 2001 Proc. SPIE 4346 394
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