Abstract

Optical lithography of thick film resist is an important approach to fabrication of continuous microstructures with large depth. However, factors of nonlinear distortion in the pattern transfer process should be taken into account, since these severely affect the profile quality of microstructures. In this work, nonlinear factors in thick film analog lithography are investigated. Combined with the simulated annealing algorithm (SAA), the transmission function of a mask is optimized in order to compensate for distortion in the pattern transfer. The coded gray-tone mask is adopted to realize the corresponding optical modulation based on the optimized transmission function. Simulation results are presented that show that the profile quality with compensation is obviously improved. This method clearly does promote the quality of the profile, but it does not lead to an increase in the difficulty of design and fabrication of the coded gray-tone mask.

©2008 Optical Society of America

Full Article  |  PDF Article
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References

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  1. X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
    [Crossref]
  2. G. Arthur and B. Martin, “Enhancing the development rate model in optical lithography simulation of ultra-thick films for applications such as MEMS and LIGA,” Proc. SPIE 4404, 209–220 (2001).
    [Crossref]
  3. J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
    [Crossref]
  4. W. X. Yu, X. C. Yuan, N. Q. Ngo, W. X. Que, W. C. Cheong, and V. Koudriachov, “Single-step fabrication of continuous surface relief micro-optical elements in hybrid sol-gel glass by laser direct writing,” Opt. Express 10, 443–448 (2002).
    [PubMed]
  5. A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
    [Crossref]
  6. Y. Fu and N. K. A. Bryan, “Investigation of diffractive optical element fabricated on diamond film by use of focused ion beam direct milling,” Opt. Eng. 42, 2214–2217 (2003).
    [Crossref]
  7. J. Paufler, S. Brunn, T. Körner, and F. Kühling, “Continuous image writer with improved critical dimension performance for high-accuracy maskless optical patterning,” Microelectron. Eng. 57, 31–40 (2001).
    [Crossref]
  8. S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).
  9. X. Dong, C. Du, S. Li, C. Wang, and Y. Fu, “Control approach for form accuracy of microlenses with continuous relief,” Opt. Express 13, 1353–1360 (2005).
    [Crossref] [PubMed]
  10. A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
    [Crossref]
  11. K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
    [Crossref]
  12. X. Xiao, J. Yang, J. Du, Y. Guo, and C. Du, “Simulation of optical lithography process for fabricating diffractive optics,” Proc. SPIE 4924, 221–227 (2002).
    [Crossref]
  13. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [Crossref] [PubMed]
  14. I. Karafyllidis, P. I. Hagouel, A. Thanailakis, and A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000).
    [Crossref]

2006 (1)

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

2005 (2)

X. Dong, C. Du, S. Li, C. Wang, and Y. Fu, “Control approach for form accuracy of microlenses with continuous relief,” Opt. Express 13, 1353–1360 (2005).
[Crossref] [PubMed]

X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
[Crossref]

2003 (1)

Y. Fu and N. K. A. Bryan, “Investigation of diffractive optical element fabricated on diamond film by use of focused ion beam direct milling,” Opt. Eng. 42, 2214–2217 (2003).
[Crossref]

2002 (2)

2001 (2)

G. Arthur and B. Martin, “Enhancing the development rate model in optical lithography simulation of ultra-thick films for applications such as MEMS and LIGA,” Proc. SPIE 4404, 209–220 (2001).
[Crossref]

J. Paufler, S. Brunn, T. Körner, and F. Kühling, “Continuous image writer with improved critical dimension performance for high-accuracy maskless optical patterning,” Microelectron. Eng. 57, 31–40 (2001).
[Crossref]

2000 (4)

I. Karafyllidis, P. I. Hagouel, A. Thanailakis, and A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000).
[Crossref]

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

1997 (1)

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[Crossref]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Arthur, G.

G. Arthur and B. Martin, “Enhancing the development rate model in optical lithography simulation of ultra-thick films for applications such as MEMS and LIGA,” Proc. SPIE 4404, 209–220 (2001).
[Crossref]

Audran, S.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Aumont, C.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Brunn, S.

J. Paufler, S. Brunn, T. Körner, and F. Kühling, “Continuous image writer with improved critical dimension performance for high-accuracy maskless optical patterning,” Microelectron. Eng. 57, 31–40 (2001).
[Crossref]

Bryan, N. K. A.

Y. Fu and N. K. A. Bryan, “Investigation of diffractive optical element fabricated on diamond film by use of focused ion beam direct milling,” Opt. Eng. 42, 2214–2217 (2003).
[Crossref]

Cheong, W. C.

Cui, Z.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

Dong, X.

Du, C.

X. Dong, C. Du, S. Li, C. Wang, and Y. Fu, “Control approach for form accuracy of microlenses with continuous relief,” Opt. Express 13, 1353–1360 (2005).
[Crossref] [PubMed]

X. Xiao, J. Yang, J. Du, Y. Guo, and C. Du, “Simulation of optical lithography process for fabricating diffractive optics,” Proc. SPIE 4924, 221–227 (2002).
[Crossref]

Du, J.

X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
[Crossref]

X. Xiao, J. Yang, J. Du, Y. Guo, and C. Du, “Simulation of optical lithography process for fabricating diffractive optics,” Proc. SPIE 4924, 221–227 (2002).
[Crossref]

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

Fabrizio, E. D.

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

Faure, B.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Fellous, C.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Fu, Y.

X. Dong, C. Du, S. Li, C. Wang, and Y. Fu, “Control approach for form accuracy of microlenses with continuous relief,” Opt. Express 13, 1353–1360 (2005).
[Crossref] [PubMed]

Y. Fu and N. K. A. Bryan, “Investigation of diffractive optical element fabricated on diamond film by use of focused ion beam direct milling,” Opt. Eng. 42, 2214–2217 (2003).
[Crossref]

Gabrini, S.

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

Gao, F.

X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
[Crossref]

X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
[Crossref]

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

Gelatt, Jr., C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Gentili, M.

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

Gerardino, A.

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

Guo, Y.

X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
[Crossref]

X. Xiao, J. Yang, J. Du, Y. Guo, and C. Du, “Simulation of optical lithography process for fabricating diffractive optics,” Proc. SPIE 4924, 221–227 (2002).
[Crossref]

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

Hadziioannou, G.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Hagouel, P. I.

I. Karafyllidis, P. I. Hagouel, A. Thanailakis, and A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000).
[Crossref]

Herzig, H. P.

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

Jürss, M.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[Crossref]

Karafyllidis, I.

I. Karafyllidis, P. I. Hagouel, A. Thanailakis, and A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000).
[Crossref]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Kley, E. B.

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

Körner, T.

J. Paufler, S. Brunn, T. Körner, and F. Kühling, “Continuous image writer with improved critical dimension performance for high-accuracy maskless optical patterning,” Microelectron. Eng. 57, 31–40 (2001).
[Crossref]

Koudriachov, V.

Kühling, F.

J. Paufler, S. Brunn, T. Körner, and F. Kühling, “Continuous image writer with improved critical dimension performance for high-accuracy maskless optical patterning,” Microelectron. Eng. 57, 31–40 (2001).
[Crossref]

Li, S.

Liu, S.

X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
[Crossref]

Martin, B.

G. Arthur and B. Martin, “Enhancing the development rate model in optical lithography simulation of ultra-thick films for applications such as MEMS and LIGA,” Proc. SPIE 4404, 209–220 (2001).
[Crossref]

Melpignano, P.

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

Mortini, B.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Neureuther, A. R.

I. Karafyllidis, P. I. Hagouel, A. Thanailakis, and A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000).
[Crossref]

Ngo, N. Q.

Nottola, A.

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

Nussbaum, P.

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

Paufler, J.

J. Paufler, S. Brunn, T. Körner, and F. Kühling, “Continuous image writer with improved critical dimension performance for high-accuracy maskless optical patterning,” Microelectron. Eng. 57, 31–40 (2001).
[Crossref]

Philipoussis, I.

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

Que, W. X.

Quenzer, H. J.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[Crossref]

Regolini, J.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Reimer, K.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[Crossref]

Reynard, J. P.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Rossi, M.

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

Rotaris, G.

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

Sanchez, Y.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Schilling, A.

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

Schlatter, G.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Stauffer, L.

A. Schilling, P. Nussbaum, I. Philipoussis, H. P. Herzig, L. Stauffer, M. Rossi, and E. B. Kley, “Fabrication technologies for micro-optical elements with arbitrary surfaces,” Proc. SPIE 4179, 65–72 (2000).
[Crossref]

Su, J.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

Tang, X.

X. Tang, F. Gao, Y. Guo, J. Du, S. Liu, and F. Gao, “Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory,” Opt. Commun. 244, 123–130 (2005).
[Crossref]

Thanailakis, A.

I. Karafyllidis, P. I. Hagouel, A. Thanailakis, and A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000).
[Crossref]

Tiron, R.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Wagner, B.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997).
[Crossref]

Wang, C.

Xiao, X.

X. Xiao, J. Yang, J. Du, Y. Guo, and C. Du, “Simulation of optical lithography process for fabricating diffractive optics,” Proc. SPIE 4924, 221–227 (2002).
[Crossref]

Yang, J.

X. Xiao, J. Yang, J. Du, Y. Guo, and C. Du, “Simulation of optical lithography process for fabricating diffractive optics,” Proc. SPIE 4924, 221–227 (2002).
[Crossref]

Yao, J.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

Yu, W. X.

Yuan, X. C.

Zhang, Y.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

Zinck, C.

S. Audran, B. Faure, B. Mortini, C. Aumont, R. Tiron, C. Zinck, Y. Sanchez, C. Fellous, J. Regolini, J. P. Reynard, G. Schlatter, and G. Hadziioannou, “Study of dynamical formation and shape of microlenses formed by the reflow method,” Proc. SPIE 6153, 61534D1–61534D10 (2006).

IEEE Trans. Semicond. Manuf. (1)

I. Karafyllidis, P. I. Hagouel, A. Thanailakis, and A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000).
[Crossref]

Microelectron. Eng. (3)

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531–534 (2000).
[Crossref]

A. Nottola, A. Gerardino, M. Gentili, E. D. Fabrizio, S. Gabrini, P. Melpignano, and G. Rotaris “Fabrication of semi-continuous profile diffractive optical elements for beam shaping by electron beam lithography,” Microelectron. Eng. 53, 325–328 (2000).
[Crossref]

J. Paufler, S. Brunn, T. Körner, and F. Kühling, “Continuous image writer with improved critical dimension performance for high-accuracy maskless optical patterning,” Microelectron. Eng. 57, 31–40 (2001).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of exposure.
Fig. 2.
Fig. 2. Flowchart for solving the optimized transmission function.
Fig. 3.
Fig. 3. The designed microlens with aspheric convex surface.
Fig. 4.
Fig. 4. Coded gray-tone mask for aspheric shape (a) without optimization of the transmission function and (b) with optimization for the transmission function (right side is close-up view for the left side).
Fig. 5.
Fig. 5. Comparison between the designed (bold line) and simulation results (slim line) of cross-section profile of aspheric microlens; (a) and (c) are in the long axis and (b) and (d) are in the short axis direction. Upper and lower graphs denote results without and with compensation for transfer distortion, respectively.
Fig. 6.
Fig. 6. Simulation results of 3-D relief surface (a) without and (b) with compensation for distortion of transfer pattern.

Tables (1)

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Table 1. The resist AZ P4620 parameters and process parameters used for simulation.

Equations (12)

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U ( x , y , d ) = 1 { [ t ( x , y ) ] · H ( ξ , η ) } ,
H ( ξ , η ) = { exp ( jkd 1 λ 2 ( ξ 2 + η 2 ) ) ξ 2 + η 2 λ 2 exp ( kd λ 2 ( ξ 2 + η 2 ) 1 ) ξ 2 + η 2 > λ 2 ,
U in ( x , y , z , t ) = S { U ( x , y , d ) , z , t } ,
I ( x , y , z , t ) = c i I i ( x , y , z , t ) ,
Dose ( x , y , z ) = I ( x , y , z , t ) dt ,
m ( x , y , z ) = M 0 exp ( C × Dose ( x , y , z ) ) ,
R ( x , y , z ) = R max ( a + 1 ) [ 1 m ( x , y , z ) ] n a + [ 1 m ( x , y , z ) ] n + R min , a = n + 1 n 1 ( 1 m th ) n ,
t 0 ( x , y ) = 1 f ( x , y ) max ( f ( x , y ) ) ,
Δ ( x , y ) = f 0 ( x , y ) f ( x , y ) .
t ( x , y ) = t 0 ( x , y ) + c 0 + c 1 Δ ( x , y ) + c 2 Δ 2 ( x , y ) [ t 0 ( x , y ) + c 0 + c 1 Δ ( x , y ) + c 2 Δ 2 ( x , y ) ] max ,
V ( r 0 ) = f ( x , y ) f ( x , y ) dxdy f ( x , y ) dxdy ,
Δ V = V ( r 0 + δ r ) V ( r 0 ) .

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