Abstract

We present a theoretical model to describe the feature size produced by direct laser writing upon a photoresist relative to various experimental parameters. The model allows the number of parameters required for describing the linewidth to be reduced and shows how the description can be made in terms of the ratio of laser power to writing velocity. Both of the limiting cases of the truncation of the laser beam are analyzed; i.e., the case of a nontruncated (Gaussian) beam and the case of a strongly truncated beam (simplified with uniform illumination assumed). Experimental measurements are presented that are fitted to the model to permit its validity to be assessed and for a comparison of these two regimes, which are shown to be different.

© 2002 Optical Society of America

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References

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  1. D. Bäuerle, Laser Processing and Chemistry, 2nd ed. (Springer-Verlag, Berlin, 1996).
    [CrossRef]
  2. S. M. Metev, V. P. Veiko, Laser-Assisted Micro-technology, 2nd ed. (Springer-Verlag, Berlin, 1998).
    [CrossRef]
  3. H.-G. Rubahn, Laser Applications in Surface Science and Technology (Wiley, Chichester, UK, 1999).
  4. K. E. Wilson, C. T. Mueller, E. M. Garmire, “Laser writing of masks for integrated optical circuits,” IEEE Trans. Components Hybrids Manuf. Technol. CHMT-5, 202–204 (1982).
    [CrossRef]
  5. M. Haruna, S. Yoshida, H. Toda, H. Nishihara, “Laser-beam writing system for optical integrated circuits,” Appl. Opt. 26, 4587–4592 (1987).
    [CrossRef] [PubMed]
  6. M. G. Lad, G. M. Naik, A. Selvarajan, “Laser patterning system for integrated optics and storage applications,” Opt. Eng. 32, 725–729 (1993).
    [CrossRef]
  7. J. R. Salgueiro, J. F. Román, V. Moreno, “System for laser writing to lithograph masks for integrated optics,” Opt. Eng. 37, 1115–1123 (1998).
    [CrossRef]
  8. M. T. Gale, M. Rossi, J. Pedersen, H. Shütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
    [CrossRef]
  9. M. Haruna, M. Takahashi, K. Wakahayashi, H. Nishihara, “Laser beam lithographed micro-Fresnel lenses,” Appl. Opt. 29, 5120–5126 (1990).
    [CrossRef] [PubMed]
  10. U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
    [CrossRef]
  11. H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
    [CrossRef]
  12. P. C. Allen, P. Buck, “Resolution performance of a 0.60 NA, 364 nm laser direct writer,” in Optical/Laser Microlithography III,” V. Pol, ed., Proc. SPIE1264, 454–465 (1990).
    [CrossRef]
  13. W. Maurer, “Maskenschreiben mit Laser,” Verein Deutcher Ingenieure (Springer-VDI-Verlag, Düsseldorf, Germany) Berichte795, 115–135 (1989).
  14. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [CrossRef]
  15. M. Pluta, Advanced Light Microscopy (Polish Scientific, Warsaw, 1988), Vol. 1. Chap. 2.
  16. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 12.
  17. H. M. Haskal, “Laser recording with truncated Gaussian beams,” Appl. Opt. 18, 2143–2146 (1979).
    [CrossRef] [PubMed]
  18. P. Kuttner, “Image quality of optical systems for truncated Gaussian laser beams,” Opt. Eng. 25, 180–183 (1986).
    [CrossRef]
  19. C. A. Mack, “Absorption and exposure in positive photoresist,” Appl. Opt. 27, 4913–4919 (1988).
    [CrossRef] [PubMed]
  20. R. Dammel, Diazonaphthoquinone-Based Resists (SPIE, Bellingham, Wash., 1993), Chap. 2.
  21. W. M. Moreau, Semiconductor Lithography. Principles, Practices, and Materials (Plenum, New York, 1988), Chap. 13.
    [CrossRef]
  22. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK1966), Chap. 13.

1998 (1)

J. R. Salgueiro, J. F. Román, V. Moreno, “System for laser writing to lithograph masks for integrated optics,” Opt. Eng. 37, 1115–1123 (1998).
[CrossRef]

1997 (1)

H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
[CrossRef]

1994 (1)

M. T. Gale, M. Rossi, J. Pedersen, H. Shütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

1993 (2)

M. G. Lad, G. M. Naik, A. Selvarajan, “Laser patterning system for integrated optics and storage applications,” Opt. Eng. 32, 725–729 (1993).
[CrossRef]

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

1990 (1)

1988 (1)

1987 (1)

1986 (1)

P. Kuttner, “Image quality of optical systems for truncated Gaussian laser beams,” Opt. Eng. 25, 180–183 (1986).
[CrossRef]

1982 (1)

K. E. Wilson, C. T. Mueller, E. M. Garmire, “Laser writing of masks for integrated optical circuits,” IEEE Trans. Components Hybrids Manuf. Technol. CHMT-5, 202–204 (1982).
[CrossRef]

1979 (1)

Allen, P. C.

P. C. Allen, P. Buck, “Resolution performance of a 0.60 NA, 364 nm laser direct writer,” in Optical/Laser Microlithography III,” V. Pol, ed., Proc. SPIE1264, 454–465 (1990).
[CrossRef]

Bäuerle, D.

D. Bäuerle, Laser Processing and Chemistry, 2nd ed. (Springer-Verlag, Berlin, 1996).
[CrossRef]

Becker, H.

H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
[CrossRef]

Buck, P.

P. C. Allen, P. Buck, “Resolution performance of a 0.60 NA, 364 nm laser direct writer,” in Optical/Laser Microlithography III,” V. Pol, ed., Proc. SPIE1264, 454–465 (1990).
[CrossRef]

Caspary, R.

H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
[CrossRef]

Dammel, R.

R. Dammel, Diazonaphthoquinone-Based Resists (SPIE, Bellingham, Wash., 1993), Chap. 2.

Gale, M. T.

M. T. Gale, M. Rossi, J. Pedersen, H. Shütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Garmire, E. M.

K. E. Wilson, C. T. Mueller, E. M. Garmire, “Laser writing of masks for integrated optical circuits,” IEEE Trans. Components Hybrids Manuf. Technol. CHMT-5, 202–204 (1982).
[CrossRef]

Haruna, M.

Haskal, H. M.

Hunklinger, S.

H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
[CrossRef]

Krackhardt, U.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Kuttner, P.

P. Kuttner, “Image quality of optical systems for truncated Gaussian laser beams,” Opt. Eng. 25, 180–183 (1986).
[CrossRef]

Lad, M. G.

M. G. Lad, G. M. Naik, A. Selvarajan, “Laser patterning system for integrated optics and storage applications,” Opt. Eng. 32, 725–729 (1993).
[CrossRef]

Mack, C. A.

Maurer, W.

W. Maurer, “Maskenschreiben mit Laser,” Verein Deutcher Ingenieure (Springer-VDI-Verlag, Düsseldorf, Germany) Berichte795, 115–135 (1989).

Metev, S. M.

S. M. Metev, V. P. Veiko, Laser-Assisted Micro-technology, 2nd ed. (Springer-Verlag, Berlin, 1998).
[CrossRef]

Moreau, W. M.

W. M. Moreau, Semiconductor Lithography. Principles, Practices, and Materials (Plenum, New York, 1988), Chap. 13.
[CrossRef]

Moreno, V.

J. R. Salgueiro, J. F. Román, V. Moreno, “System for laser writing to lithograph masks for integrated optics,” Opt. Eng. 37, 1115–1123 (1998).
[CrossRef]

Mueller, C. T.

K. E. Wilson, C. T. Mueller, E. M. Garmire, “Laser writing of masks for integrated optical circuits,” IEEE Trans. Components Hybrids Manuf. Technol. CHMT-5, 202–204 (1982).
[CrossRef]

Naik, G. M.

M. G. Lad, G. M. Naik, A. Selvarajan, “Laser patterning system for integrated optics and storage applications,” Opt. Eng. 32, 725–729 (1993).
[CrossRef]

Nishihara, H.

Pedersen, J.

M. T. Gale, M. Rossi, J. Pedersen, H. Shütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Pluta, M.

M. Pluta, Advanced Light Microscopy (Polish Scientific, Warsaw, 1988), Vol. 1. Chap. 2.

Román, J. F.

J. R. Salgueiro, J. F. Román, V. Moreno, “System for laser writing to lithograph masks for integrated optics,” Opt. Eng. 37, 1115–1123 (1998).
[CrossRef]

Rossi, M.

M. T. Gale, M. Rossi, J. Pedersen, H. Shütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Rubahn, H.-G.

H.-G. Rubahn, Laser Applications in Surface Science and Technology (Wiley, Chichester, UK, 1999).

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Salgueiro, J. R.

J. R. Salgueiro, J. F. Román, V. Moreno, “System for laser writing to lithograph masks for integrated optics,” Opt. Eng. 37, 1115–1123 (1998).
[CrossRef]

Schickfus, M. V.

H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
[CrossRef]

Schrader, M.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Schwider, J.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Selvarajan, A.

M. G. Lad, G. M. Naik, A. Selvarajan, “Laser patterning system for integrated optics and storage applications,” Opt. Eng. 32, 725–729 (1993).
[CrossRef]

Shütz, H.

M. T. Gale, M. Rossi, J. Pedersen, H. Shütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 12.

Streibl, N.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Takahashi, M.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Toda, H.

Toepfer, C.

H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
[CrossRef]

Veiko, V. P.

S. M. Metev, V. P. Veiko, Laser-Assisted Micro-technology, 2nd ed. (Springer-Verlag, Berlin, 1998).
[CrossRef]

Wakahayashi, K.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK1966), Chap. 13.

Wilson, K. E.

K. E. Wilson, C. T. Mueller, E. M. Garmire, “Laser writing of masks for integrated optical circuits,” IEEE Trans. Components Hybrids Manuf. Technol. CHMT-5, 202–204 (1982).
[CrossRef]

Yoshida, S.

Appl. Opt. (4)

IEEE Trans. Components Hybrids Manuf. Technol. (1)

K. E. Wilson, C. T. Mueller, E. M. Garmire, “Laser writing of masks for integrated optical circuits,” IEEE Trans. Components Hybrids Manuf. Technol. CHMT-5, 202–204 (1982).
[CrossRef]

J. Mod. Opt. (1)

H. Becker, R. Caspary, C. Toepfer, M. V. Schickfus, S. Hunklinger, “Low-cost direct writing lithography system for the sub-micron range,” J. Mod. Opt. 44, 1715–1723 (1997).
[CrossRef]

Opt. Eng. (5)

M. G. Lad, G. M. Naik, A. Selvarajan, “Laser patterning system for integrated optics and storage applications,” Opt. Eng. 32, 725–729 (1993).
[CrossRef]

J. R. Salgueiro, J. F. Román, V. Moreno, “System for laser writing to lithograph masks for integrated optics,” Opt. Eng. 37, 1115–1123 (1998).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, H. Shütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

P. Kuttner, “Image quality of optical systems for truncated Gaussian laser beams,” Opt. Eng. 25, 180–183 (1986).
[CrossRef]

Other (11)

R. Dammel, Diazonaphthoquinone-Based Resists (SPIE, Bellingham, Wash., 1993), Chap. 2.

W. M. Moreau, Semiconductor Lithography. Principles, Practices, and Materials (Plenum, New York, 1988), Chap. 13.
[CrossRef]

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK1966), Chap. 13.

P. C. Allen, P. Buck, “Resolution performance of a 0.60 NA, 364 nm laser direct writer,” in Optical/Laser Microlithography III,” V. Pol, ed., Proc. SPIE1264, 454–465 (1990).
[CrossRef]

W. Maurer, “Maskenschreiben mit Laser,” Verein Deutcher Ingenieure (Springer-VDI-Verlag, Düsseldorf, Germany) Berichte795, 115–135 (1989).

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

M. Pluta, Advanced Light Microscopy (Polish Scientific, Warsaw, 1988), Vol. 1. Chap. 2.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 12.

D. Bäuerle, Laser Processing and Chemistry, 2nd ed. (Springer-Verlag, Berlin, 1996).
[CrossRef]

S. M. Metev, V. P. Veiko, Laser-Assisted Micro-technology, 2nd ed. (Springer-Verlag, Berlin, 1998).
[CrossRef]

H.-G. Rubahn, Laser Applications in Surface Science and Technology (Wiley, Chichester, UK, 1999).

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Figures (7)

Fig. 1
Fig. 1

Irradiance distribution of the focal spot for several values of truncation relation γ. The aperture radius is fixed at a value of a = 2.5 mm, corresponding to that for a conventional microscope 60× objective (=2.9 mm; NA, 0.85), and the laser beam radius was properly established for each curve to produce the truncation relation. Dashed curve, uniform illumination. The wavelength was set at 457.9 nm (Ar+ laser).

Fig. 2
Fig. 2

Schematic of the laser spot profile (Gaussian profile) and the line drawn on the photoresist film, together with the reference system used.

Fig. 3
Fig. 3

Plot of Φ(z) = H 1(z)/z 2 function (continuous curve) together with that which describes its asymptotic behavior, 2/(πz 2) (dashed curve). Inset, the region containing the secondary maxima plotted on a different scale for clarity.

Fig. 4
Fig. 4

Line traced with a 20× objective and Ω properly set to transfer the structure generated by the first secondary maximum of function Φ, patterned as an opening in a chromium mask by wet etching after development of the photoresist.

Fig. 5
Fig. 5

Linewidth versus parameter Ω for the two limiting cases of a nontruncated (γ ≪ 1) laser beam (Gaussian spot profile) and a strongly truncated (γ ≫ 1) beam (uniform illumination), together with the respective fits to the corresponding theoretical functions. A 20× microscope objective (f = 8.3 mm; NA, 0.40) was used.

Fig. 6
Fig. 6

Linewidth versus parameter Ω in this case the inverse of parameter Ω-1 can perform the fit to function Φ: Ω-1 = a 1Φ[a 2(L - a 0)]} for two microscope objectives, 20× (f = 8.3 mm; NA, 0.40) and 60× (f = 2.9 mm; NA, 0.85). In addition to the fit to the Φ function the fit to its asymptotic form, Ω-1 = a 1/(L - a 0)2, is also plotted.

Fig. 7
Fig. 7

Linewidth versus laser power for several values of writing speed and fits to the theoretical function in the broad-line regime.

Tables (1)

Tables Icon

Table 1 Parameters of the Fit of Linewidth Relative to Laser Power and Parameter κ b

Equations (21)

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γ=wa=wfNA.
Igρ=2Pπwg2exp-2ρ2wg2,
2wg=4λfπ2w=1.27λf2w.
Iaρ=Pα24π2J1αραρ2,
α=2πaλf=2πNAλ,
2wa=5.15α=1.64λf2a.
Dζ=-+ I(ρ)dt=2v0+ Iη2+ζ2dη,
Dg(ζ)=4Pπvwg2exp-2ζ2wg20+exp-2η2wg2dη=2πPwgvexp-2ζ2wg2.
Lg=2ζ0=wg2 log2πPD0wgv1/2.
Ω=Pv,
κg=2π1wgD0,
Lg=wg2 logκgΩ1/2.
Daζ=2Pα2πv0+J12αη2+ζ2α2η2+ζ2dη.
0+Jν2t2+z2t2+z2ν t2ν-2dt= Γν-1/22zν+1π Hν2z,
Daζ=4αPπv Φ2αζ,
La=2ζ0=1α Φ-11κaΩ=wa2.57 Φ-11κaΩ,
κa=4απD01-exp(-2/γ2) =3.28waD01-exp(-2/γ2),
1κaΩ=ΦαLa.
Φz  2πz2.
Lb=2κaπα2 Ω1/2=κbΩ,
κb=2π21-exp-2/γ2αD01/2= 0.56wa1-exp-2/γ2D01/2.

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