Abstract

We present a procedure for the characterization and the linearization of the photoresist response to UV exposure for application to the gray-scale fabrication of diffractive optical elements. A simple and reliable model is presented as part of the characterization procedure. Application to the fabrication of surface-relief diffractive optical elements is presented, and theoretical predictions are shown to agree well with experiments.

© 2001 Optical Society of America

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References

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  1. G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).
  2. W. Dascher, P. Long, R. Stein, C. Wu, S. H. Lee, “Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single optical exposure with a gray-scale mask on high-energy beam-sensitive glass,” Appl. Opt. 36, 4675–4680 (1997).
    [CrossRef]
  3. M. R. Wang, H. Su, “Laser direct-write gray-level mask and one-step etching for diffractive microlens fabrication,” Appl. Opt. 37, 7568–7576 (1998).
    [CrossRef]
  4. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1989).
  5. G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1991).
  6. J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995).
    [CrossRef]
  7. D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
    [CrossRef]
  8. D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. FR22 of SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001), Chap. 5.
    [CrossRef]
  9. C. K. Wu, “High-energy beam-sensitive glasses,” U.S. patent5,285,517 (8February1994).
  10. C. Gimkiewicz, D. Hagedorn, J. Jahns, E. B. Kley, F. Thoma, “Fabrication of microprisms for planar optical interconnections by use of analog gray-scale lithography with high-energy beam-sensitive glass,” Appl. Opt. 38, 2986–2990 (1999).
    [CrossRef]
  11. T. J. Suleski, D. C. O’Shea, “Fidelity of postscript-generated masks for diffractive optics fabrication,” Appl. Opt. 34, 627–635 (1995).
    [CrossRef] [PubMed]
  12. T. J. Suleski, D. C. O’Shea, “Gray-scale masks for diffractive-optics fabrication,” Appl. Opt. 34, 7507–7517 (1995).
    [CrossRef] [PubMed]
  13. T. J. Suleski, B. Baggett, W. F. Delaney, C. Koehler, E. G. Johnson, “Fabrication of high-spatial-frequency gratings through computer-generated near-field holography,” Opt. Lett. 24, 602–604 (1999).
    [CrossRef]
  14. M. B. Stern, T. Rubico-Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
    [CrossRef]
  15. S. Murarka, M. Peckerar, Electronics Materials Science and Technology (Academic, New York, 1989).
  16. I. Brodie, J. J. Muray, The Physics of Micro/Nano-Fabrication (Plenum, New York, 1992).
    [CrossRef]
  17. L. E. Bogan, “Understanding the Novolak synthesis reaction,” in Advances in Resist Technology and Processing X, D. W. Hinsberg, ed., Proc. SPIE1925, 564–569 (1993).
    [CrossRef]
  18. V. N. Genkin, M. Y. Mylnikov, “Correlation between the sensitivity and the contrast of polymer resists for developing good and bad solvents,” in Advances in Resist Technology and Processing XI, O. Nalamascu, ed., Proc. SPIE2195, 751–753 (1994).
  19. R. D. Allen, R. K. Chen, P. M. Gallagher-Wetmore, “Performance properties of near-monodisperse Novolak resins,” in Advances in Resist Technology and Processing XII, R. D. Allen, ed., Proc. SPIE2438, 250–260 (1995).
    [CrossRef]
  20. K. Amaya, “Numerical analysis of high-resolution microlithography with thermoresist,” in Emerging Lithographic Technologies III, Y. Vladmirsky, ed., Proc. SPIE3676, 360–370 (1999).
    [CrossRef]
  21. G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
    [CrossRef]
  22. P. J. Paniez, G. Festes, J. P. E. Chollet, “Physical description of lithographic processes: correlation between bake conditions and photoresist contrast,” in Advances in Resist Technology and Processing IX, A. E. Novembre, ed., Proc. SPIE1672, 623–637 (1992).
    [CrossRef]
  23. W. E. Conley, G. E. Fuller, H. J. Levinson, L. W. Liebermann, H. M. Marchman, eds., Microlithography in Manufacturing Technology, Proc. SPIETTS5 (1996).
  24. C. R. Friedrich, A. Umeda, eds., Microlithography and Metrology in Micromaching III, Proc. SPIE3225 (1997).
  25. S. Inoue, T. Fujisawa, K. Izuha, “Effective exposure-dose measurement in optical microlithography,” in Metrology, Inspection, and Process Control for Microlithography XIV, N. T. Sullivan, ed., Proc. SPIE3998, 810–818 (2000).
    [CrossRef]
  26. B. Singh, ed., Metrology, Inspection, and Process Control for Microlithography XII, Proc. SPIE3332 (1998).
  27. S. A. Ekhorutomwen, S. P. Sawan, “Critical review on photoresists,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard, W. F. Frank, eds., Vol. CR63 of SPIE Critical Reviews Series (SPIE Press, Bellingham, Wash., 1996), pp. 214–238.

1999

1998

1997

1995

1994

M. B. Stern, T. Rubico-Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

Allen, R. D.

R. D. Allen, R. K. Chen, P. M. Gallagher-Wetmore, “Performance properties of near-monodisperse Novolak resins,” in Advances in Resist Technology and Processing XII, R. D. Allen, ed., Proc. SPIE2438, 250–260 (1995).
[CrossRef]

Amaya, K.

K. Amaya, “Numerical analysis of high-resolution microlithography with thermoresist,” in Emerging Lithographic Technologies III, Y. Vladmirsky, ed., Proc. SPIE3676, 360–370 (1999).
[CrossRef]

Baggett, B.

Bogan, L. E.

L. E. Bogan, “Understanding the Novolak synthesis reaction,” in Advances in Resist Technology and Processing X, D. W. Hinsberg, ed., Proc. SPIE1925, 564–569 (1993).
[CrossRef]

Brodie, I.

I. Brodie, J. J. Muray, The Physics of Micro/Nano-Fabrication (Plenum, New York, 1992).
[CrossRef]

Burns, S. D.

G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
[CrossRef]

Chen, R. K.

R. D. Allen, R. K. Chen, P. M. Gallagher-Wetmore, “Performance properties of near-monodisperse Novolak resins,” in Advances in Resist Technology and Processing XII, R. D. Allen, ed., Proc. SPIE2438, 250–260 (1995).
[CrossRef]

Chollet, J. P. E.

P. J. Paniez, G. Festes, J. P. E. Chollet, “Physical description of lithographic processes: correlation between bake conditions and photoresist contrast,” in Advances in Resist Technology and Processing IX, A. E. Novembre, ed., Proc. SPIE1672, 623–637 (1992).
[CrossRef]

Collins, J. P.

Dascher, W.

Delaney, W. F.

Ekhorutomwen, S. A.

S. A. Ekhorutomwen, S. P. Sawan, “Critical review on photoresists,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard, W. F. Frank, eds., Vol. CR63 of SPIE Critical Reviews Series (SPIE Press, Bellingham, Wash., 1996), pp. 214–238.

Festes, G.

P. J. Paniez, G. Festes, J. P. E. Chollet, “Physical description of lithographic processes: correlation between bake conditions and photoresist contrast,” in Advances in Resist Technology and Processing IX, A. E. Novembre, ed., Proc. SPIE1672, 623–637 (1992).
[CrossRef]

Flanagin, L. W.

G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
[CrossRef]

Fujisawa, T.

S. Inoue, T. Fujisawa, K. Izuha, “Effective exposure-dose measurement in optical microlithography,” in Metrology, Inspection, and Process Control for Microlithography XIV, N. T. Sullivan, ed., Proc. SPIE3998, 810–818 (2000).
[CrossRef]

Gallagher-Wetmore, P. M.

R. D. Allen, R. K. Chen, P. M. Gallagher-Wetmore, “Performance properties of near-monodisperse Novolak resins,” in Advances in Resist Technology and Processing XII, R. D. Allen, ed., Proc. SPIE2438, 250–260 (1995).
[CrossRef]

Genkin, V. N.

V. N. Genkin, M. Y. Mylnikov, “Correlation between the sensitivity and the contrast of polymer resists for developing good and bad solvents,” in Advances in Resist Technology and Processing XI, O. Nalamascu, ed., Proc. SPIE2195, 751–753 (1994).

Gimkiewicz, C.

Hagedorn, D.

Inoue, S.

S. Inoue, T. Fujisawa, K. Izuha, “Effective exposure-dose measurement in optical microlithography,” in Metrology, Inspection, and Process Control for Microlithography XIV, N. T. Sullivan, ed., Proc. SPIE3998, 810–818 (2000).
[CrossRef]

Izuha, K.

S. Inoue, T. Fujisawa, K. Izuha, “Effective exposure-dose measurement in optical microlithography,” in Metrology, Inspection, and Process Control for Microlithography XIV, N. T. Sullivan, ed., Proc. SPIE3998, 810–818 (2000).
[CrossRef]

Jahns, J.

Johnson, E. G.

Kley, E. B.

Koehler, C.

Lee, S. H.

Long, P.

Mait, J. N.

Mirotznik, M. S.

D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
[CrossRef]

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. FR22 of SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001), Chap. 5.
[CrossRef]

Murarka, S.

S. Murarka, M. Peckerar, Electronics Materials Science and Technology (Academic, New York, 1989).

Muray, J. J.

I. Brodie, J. J. Muray, The Physics of Micro/Nano-Fabrication (Plenum, New York, 1992).
[CrossRef]

Mylnikov, M. Y.

V. N. Genkin, M. Y. Mylnikov, “Correlation between the sensitivity and the contrast of polymer resists for developing good and bad solvents,” in Advances in Resist Technology and Processing XI, O. Nalamascu, ed., Proc. SPIE2195, 751–753 (1994).

O’Shea, D. C.

Paniez, P. J.

P. J. Paniez, G. Festes, J. P. E. Chollet, “Physical description of lithographic processes: correlation between bake conditions and photoresist contrast,” in Advances in Resist Technology and Processing IX, A. E. Novembre, ed., Proc. SPIE1672, 623–637 (1992).
[CrossRef]

Peckerar, M.

S. Murarka, M. Peckerar, Electronics Materials Science and Technology (Academic, New York, 1989).

Prather, D. W.

D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
[CrossRef]

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. FR22 of SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001), Chap. 5.
[CrossRef]

Rubico-Jay, T.

M. B. Stern, T. Rubico-Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

Sawan, S. P.

S. A. Ekhorutomwen, S. P. Sawan, “Critical review on photoresists,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard, W. F. Frank, eds., Vol. CR63 of SPIE Critical Reviews Series (SPIE Press, Bellingham, Wash., 1996), pp. 214–238.

Schmid, G. M.

G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
[CrossRef]

Shi, S.

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. FR22 of SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001), Chap. 5.
[CrossRef]

Singh, V. K.

G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
[CrossRef]

Stein, R.

Stern, M. B.

M. B. Stern, T. Rubico-Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

Stewart, M. D.

G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
[CrossRef]

Su, H.

Suleski, T. J.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1989).

G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1991).

Thoma, F.

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).

Wang, M. R.

Willson, G. C.

G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
[CrossRef]

Wu, C.

Wu, C. K.

C. K. Wu, “High-energy beam-sensitive glasses,” U.S. patent5,285,517 (8February1994).

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

M. B. Stern, T. Rubico-Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33, 3547–3551 (1994).
[CrossRef]

Opt. Lett.

Other

S. Murarka, M. Peckerar, Electronics Materials Science and Technology (Academic, New York, 1989).

I. Brodie, J. J. Muray, The Physics of Micro/Nano-Fabrication (Plenum, New York, 1992).
[CrossRef]

L. E. Bogan, “Understanding the Novolak synthesis reaction,” in Advances in Resist Technology and Processing X, D. W. Hinsberg, ed., Proc. SPIE1925, 564–569 (1993).
[CrossRef]

V. N. Genkin, M. Y. Mylnikov, “Correlation between the sensitivity and the contrast of polymer resists for developing good and bad solvents,” in Advances in Resist Technology and Processing XI, O. Nalamascu, ed., Proc. SPIE2195, 751–753 (1994).

R. D. Allen, R. K. Chen, P. M. Gallagher-Wetmore, “Performance properties of near-monodisperse Novolak resins,” in Advances in Resist Technology and Processing XII, R. D. Allen, ed., Proc. SPIE2438, 250–260 (1995).
[CrossRef]

K. Amaya, “Numerical analysis of high-resolution microlithography with thermoresist,” in Emerging Lithographic Technologies III, Y. Vladmirsky, ed., Proc. SPIE3676, 360–370 (1999).
[CrossRef]

G. M. Schmid, V. K. Singh, L. W. Flanagin, M. D. Stewart, S. D. Burns, G. C. Willson, “Recent advances in molecular level lithography simulation,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 675–685 (2000).
[CrossRef]

P. J. Paniez, G. Festes, J. P. E. Chollet, “Physical description of lithographic processes: correlation between bake conditions and photoresist contrast,” in Advances in Resist Technology and Processing IX, A. E. Novembre, ed., Proc. SPIE1672, 623–637 (1992).
[CrossRef]

W. E. Conley, G. E. Fuller, H. J. Levinson, L. W. Liebermann, H. M. Marchman, eds., Microlithography in Manufacturing Technology, Proc. SPIETTS5 (1996).

C. R. Friedrich, A. Umeda, eds., Microlithography and Metrology in Micromaching III, Proc. SPIE3225 (1997).

S. Inoue, T. Fujisawa, K. Izuha, “Effective exposure-dose measurement in optical microlithography,” in Metrology, Inspection, and Process Control for Microlithography XIV, N. T. Sullivan, ed., Proc. SPIE3998, 810–818 (2000).
[CrossRef]

B. Singh, ed., Metrology, Inspection, and Process Control for Microlithography XII, Proc. SPIE3332 (1998).

S. A. Ekhorutomwen, S. P. Sawan, “Critical review on photoresists,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard, W. F. Frank, eds., Vol. CR63 of SPIE Critical Reviews Series (SPIE Press, Bellingham, Wash., 1996), pp. 214–238.

G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1989).

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1991).

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. FR22 of SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001), Chap. 5.
[CrossRef]

C. K. Wu, “High-energy beam-sensitive glasses,” U.S. patent5,285,517 (8February1994).

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Figures (4)

Fig. 1
Fig. 1

Solubility plotted versus the transmittance for the photoresist samples. Solubility was inferred from the profile depth after development, and values are normalized with respect to the percentage of remaining photoresist. The asterisks represent experimental measurements; the solid curve represents our model for an 8-s exposure time and κ = 0.9053; the dashed curve fits the model for a 16-s exposure time and κ = 1.8106; the dotted curve corresponds to a 24-s exposure and κ = 2.7159 [Eq. (7)].

Fig. 2
Fig. 2

Solubility plotted versus the OD for the photoresist samples. All definitions, parameters, and representations are as for Fig. 1.

Fig. 3
Fig. 3

Values of the discrete transmittance (asterisks) and the OD (diamonds) plotted for the gray-scale mask. The mask has eight gray levels distributed linearly across a wide range of ODs.

Fig. 4
Fig. 4

Test-pattern profiles for the three photoresist samples. The vertical lines in the graphs of the average profiles represent step boundaries; the asterisks mark the average height of a step. Samples were exposed and developed, respectively, for (a) 8 s and 14 s, (b) 16 s and 7 s, (c) 24 s and 5.5 s.

Tables (1)

Tables Icon

Table 1 Photoresist Fabrication-Process Recipes Used to Obtain the Experimental Results Shown in Fig. 4a

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

St=0=S0=0,  Ct=0=C0=1.
ΔSt=μCtIΔt.
Ct+St=1.
St=1-exp-μIt.
S=1-exp-μI0Tt0.
solubility=DSS+DC1-S=DC+DS-DCS.
S=1-exp-κT.

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