Abstract

A simulation of the profile of holographically recorded structures in photoresists is performed. In addition to its simplicity this simulation can be used to take into account the effects that arise from exposure, photosensitization, development, and resolution of positive photoresists. We analyzed the effects of isotropy of wet development, nonlinearity of the photoresist response curve, background light, and standing waves produced by reflection at the film–substrate interface by using this simulation, and the results agree with the experimentally recorded profiles.

© 1995 Optical Society of America

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References

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  1. R. A. Bartolini, “Characteristics of relief phase holograms recorded in photoresists,” Appl. Opt. 13, 129–139 (1974).
    [CrossRef] [PubMed]
  2. S. Austin, F. T. Stone, “Fabrication of thin periodic structures in photoresist: a model,” Appl. Opt. 15, 1071–1074 (1976).
    [CrossRef] [PubMed]
  3. R. R. Gerke, I. V. Golubenko, T. G. Dubrovina, G. M. Savitski, “Investigation of the reflection properties of holographic diffraction gratings with a symmetrical line profile,” Opt. Spectrosc. (USSR) 58, 808–810 (1986).
  4. K. Yokomori, “Dielectric surface-relief gratings with high diffraction efficiency,” Appl. Opt. 23, 2303–2310 (1984).
    [CrossRef] [PubMed]
  5. Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
    [CrossRef] [PubMed]
  6. P. Langois, R. Beaulieu, “Phase relief gratings with conic section profile used in the production of multiple beams,” Appl. Opt. 29, 3434–3439 (1990).
    [CrossRef] [PubMed]
  7. W. Stork, N. Streibl, H. Haidner, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
    [CrossRef] [PubMed]
  8. R. E. Jewett, P. I. Hagouel, T. Van Duzer, “Line-profile resist development simulation techniques,” Polym. Eng. Sci. 17, 381–384 (1977).
    [CrossRef]
  9. W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, M. O’Toole, “A general simulator for VLSI lithography and etching processes: Part I. Application to projection lithography,” IEEE Trans. Electron Devices ED-26, 717–722 (1979).
    [CrossRef]
  10. C. A. Mack, “Development of positive photoresists,” J. Electrochem. Soc. 134, 148–152 (1987).
    [CrossRef]
  11. F. H. Dill, W. Hornberger, P. S. Hauge, J. M. Shaw, “Characterization of positive photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
    [CrossRef]
  12. L. Mashev, S. Tonchev, “Formation of holographic diffraction gratings in photoresist,” Appl. Phys. A 26, 143–149 (1981)
    [CrossRef]
  13. AZ-1400 and AZ-1350 photoresists (Shipley, Newton, Mass., 1984).
  14. L. Cescato, J. Frejlich, “Real-time optical techniques for monitoring of etching process,” in Trends in Electrochemistry (Council of Scientific Research Integration/Research Trends, Sreekanteswaran, Trivandrum, India, 1992), 201–213.
  15. D. A. Kessler, J. Koplic, H. Levine, “Geometrical model of interface evolution. II. Numerical simulation,” Phys. Rev. A 30, 3163–3174 (1984).
    [CrossRef]
  16. S. Asaumi, H. Nakane, “Mechanism of photoresist resolution improvement by pre-exposure treatment,” J. Electrochem. Soc. 137, 2546–2549 (1990).
    [CrossRef]
  17. F. H. Dill, A. Neureuther, J. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices ED-22, 456–464 (1975).
    [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 157.
  19. R. G. Brandes, R. K. Curran, “Modulation transfer function,” Appl. Opt. 10, 2101–2103 (1971).
    [CrossRef] [PubMed]
  20. M. S. Sthel, C. R. A. de Lima, L. Cescato, “Photoresist resolution measurement during the exposure process,” Appl. Opt. 30, 5152–5156 (1991).
    [CrossRef] [PubMed]
  21. A. C. Livanos, A. Katzir, J. B. Shellan, A. Yariv, “Linearity and enhanced sensitivity of the Shipley AZ-1350B photoresist,” Appl. Opt. 16, 1633–1635 (1977).
    [CrossRef] [PubMed]
  22. L. Cescato, G. F. Mendes, J. Frejlich, “Stabilized holographic recording using the residual real-time effect in a positive photoresist,” Opt. Lett. 12, 982–983 (1987).
    [CrossRef] [PubMed]
  23. S. H. Zaidi, S. R. J. Brueck, “High aspect-ratio holographic photoresist gratings,” Appl. Opt. 27, 2999–3002 (1988).
    [CrossRef] [PubMed]
  24. W-T. Tsang, S. Wang, “Simultaneous exposure and development technique for making gratings on positive photoresist,” Appl. Phys. Lett. 24, 196–199 (1974).
    [CrossRef]

1991 (2)

1990 (2)

P. Langois, R. Beaulieu, “Phase relief gratings with conic section profile used in the production of multiple beams,” Appl. Opt. 29, 3434–3439 (1990).
[CrossRef] [PubMed]

S. Asaumi, H. Nakane, “Mechanism of photoresist resolution improvement by pre-exposure treatment,” J. Electrochem. Soc. 137, 2546–2549 (1990).
[CrossRef]

1988 (1)

1987 (3)

1986 (1)

R. R. Gerke, I. V. Golubenko, T. G. Dubrovina, G. M. Savitski, “Investigation of the reflection properties of holographic diffraction gratings with a symmetrical line profile,” Opt. Spectrosc. (USSR) 58, 808–810 (1986).

1984 (2)

K. Yokomori, “Dielectric surface-relief gratings with high diffraction efficiency,” Appl. Opt. 23, 2303–2310 (1984).
[CrossRef] [PubMed]

D. A. Kessler, J. Koplic, H. Levine, “Geometrical model of interface evolution. II. Numerical simulation,” Phys. Rev. A 30, 3163–3174 (1984).
[CrossRef]

1981 (1)

L. Mashev, S. Tonchev, “Formation of holographic diffraction gratings in photoresist,” Appl. Phys. A 26, 143–149 (1981)
[CrossRef]

1979 (1)

W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, M. O’Toole, “A general simulator for VLSI lithography and etching processes: Part I. Application to projection lithography,” IEEE Trans. Electron Devices ED-26, 717–722 (1979).
[CrossRef]

1977 (2)

R. E. Jewett, P. I. Hagouel, T. Van Duzer, “Line-profile resist development simulation techniques,” Polym. Eng. Sci. 17, 381–384 (1977).
[CrossRef]

A. C. Livanos, A. Katzir, J. B. Shellan, A. Yariv, “Linearity and enhanced sensitivity of the Shipley AZ-1350B photoresist,” Appl. Opt. 16, 1633–1635 (1977).
[CrossRef] [PubMed]

1976 (1)

1975 (2)

F. H. Dill, W. Hornberger, P. S. Hauge, J. M. Shaw, “Characterization of positive photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[CrossRef]

F. H. Dill, A. Neureuther, J. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices ED-22, 456–464 (1975).
[CrossRef]

1974 (2)

W-T. Tsang, S. Wang, “Simultaneous exposure and development technique for making gratings on positive photoresist,” Appl. Phys. Lett. 24, 196–199 (1974).
[CrossRef]

R. A. Bartolini, “Characteristics of relief phase holograms recorded in photoresists,” Appl. Opt. 13, 129–139 (1974).
[CrossRef] [PubMed]

1971 (1)

Asaumi, S.

S. Asaumi, H. Nakane, “Mechanism of photoresist resolution improvement by pre-exposure treatment,” J. Electrochem. Soc. 137, 2546–2549 (1990).
[CrossRef]

Austin, S.

Bartolini, R. A.

Beaulieu, R.

Brandes, R. G.

Brueck, S. R. J.

Cescato, L.

M. S. Sthel, C. R. A. de Lima, L. Cescato, “Photoresist resolution measurement during the exposure process,” Appl. Opt. 30, 5152–5156 (1991).
[CrossRef] [PubMed]

L. Cescato, G. F. Mendes, J. Frejlich, “Stabilized holographic recording using the residual real-time effect in a positive photoresist,” Opt. Lett. 12, 982–983 (1987).
[CrossRef] [PubMed]

L. Cescato, J. Frejlich, “Real-time optical techniques for monitoring of etching process,” in Trends in Electrochemistry (Council of Scientific Research Integration/Research Trends, Sreekanteswaran, Trivandrum, India, 1992), 201–213.

Curran, R. K.

de Lima, C. R. A.

Dill, F. H.

F. H. Dill, W. Hornberger, P. S. Hauge, J. M. Shaw, “Characterization of positive photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[CrossRef]

F. H. Dill, A. Neureuther, J. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices ED-22, 456–464 (1975).
[CrossRef]

Dubrovina, T. G.

R. R. Gerke, I. V. Golubenko, T. G. Dubrovina, G. M. Savitski, “Investigation of the reflection properties of holographic diffraction gratings with a symmetrical line profile,” Opt. Spectrosc. (USSR) 58, 808–810 (1986).

Frejlich, J.

L. Cescato, G. F. Mendes, J. Frejlich, “Stabilized holographic recording using the residual real-time effect in a positive photoresist,” Opt. Lett. 12, 982–983 (1987).
[CrossRef] [PubMed]

L. Cescato, J. Frejlich, “Real-time optical techniques for monitoring of etching process,” in Trends in Electrochemistry (Council of Scientific Research Integration/Research Trends, Sreekanteswaran, Trivandrum, India, 1992), 201–213.

Gerke, R. R.

R. R. Gerke, I. V. Golubenko, T. G. Dubrovina, G. M. Savitski, “Investigation of the reflection properties of holographic diffraction gratings with a symmetrical line profile,” Opt. Spectrosc. (USSR) 58, 808–810 (1986).

Golubenko, I. V.

R. R. Gerke, I. V. Golubenko, T. G. Dubrovina, G. M. Savitski, “Investigation of the reflection properties of holographic diffraction gratings with a symmetrical line profile,” Opt. Spectrosc. (USSR) 58, 808–810 (1986).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 157.

Hagouel, P. I.

R. E. Jewett, P. I. Hagouel, T. Van Duzer, “Line-profile resist development simulation techniques,” Polym. Eng. Sci. 17, 381–384 (1977).
[CrossRef]

Haidner, H.

Hauge, P. S.

F. H. Dill, W. Hornberger, P. S. Hauge, J. M. Shaw, “Characterization of positive photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[CrossRef]

Hornberger, W.

F. H. Dill, W. Hornberger, P. S. Hauge, J. M. Shaw, “Characterization of positive photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[CrossRef]

Jewett, R. E.

R. E. Jewett, P. I. Hagouel, T. Van Duzer, “Line-profile resist development simulation techniques,” Polym. Eng. Sci. 17, 381–384 (1977).
[CrossRef]

Katzir, A.

Kessler, D. A.

D. A. Kessler, J. Koplic, H. Levine, “Geometrical model of interface evolution. II. Numerical simulation,” Phys. Rev. A 30, 3163–3174 (1984).
[CrossRef]

Kimura, Y.

Kipfer, P.

Koplic, J.

D. A. Kessler, J. Koplic, H. Levine, “Geometrical model of interface evolution. II. Numerical simulation,” Phys. Rev. A 30, 3163–3174 (1984).
[CrossRef]

Langois, P.

Levine, H.

D. A. Kessler, J. Koplic, H. Levine, “Geometrical model of interface evolution. II. Numerical simulation,” Phys. Rev. A 30, 3163–3174 (1984).
[CrossRef]

Livanos, A. C.

Mack, C. A.

C. A. Mack, “Development of positive photoresists,” J. Electrochem. Soc. 134, 148–152 (1987).
[CrossRef]

Mashev, L.

L. Mashev, S. Tonchev, “Formation of holographic diffraction gratings in photoresist,” Appl. Phys. A 26, 143–149 (1981)
[CrossRef]

Mendes, G. F.

Nakane, H.

S. Asaumi, H. Nakane, “Mechanism of photoresist resolution improvement by pre-exposure treatment,” J. Electrochem. Soc. 137, 2546–2549 (1990).
[CrossRef]

Nandgaonkar, S. N.

W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, M. O’Toole, “A general simulator for VLSI lithography and etching processes: Part I. Application to projection lithography,” IEEE Trans. Electron Devices ED-26, 717–722 (1979).
[CrossRef]

Neureuther, A.

F. H. Dill, A. Neureuther, J. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices ED-22, 456–464 (1975).
[CrossRef]

Neureuther, A. R.

W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, M. O’Toole, “A general simulator for VLSI lithography and etching processes: Part I. Application to projection lithography,” IEEE Trans. Electron Devices ED-26, 717–722 (1979).
[CrossRef]

Nishida, N.

O’Toole, M.

W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, M. O’Toole, “A general simulator for VLSI lithography and etching processes: Part I. Application to projection lithography,” IEEE Trans. Electron Devices ED-26, 717–722 (1979).
[CrossRef]

Ohta, Y.

Oldham, W. G.

W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, M. O’Toole, “A general simulator for VLSI lithography and etching processes: Part I. Application to projection lithography,” IEEE Trans. Electron Devices ED-26, 717–722 (1979).
[CrossRef]

Ono, Y.

Savitski, G. M.

R. R. Gerke, I. V. Golubenko, T. G. Dubrovina, G. M. Savitski, “Investigation of the reflection properties of holographic diffraction gratings with a symmetrical line profile,” Opt. Spectrosc. (USSR) 58, 808–810 (1986).

Shaw, J. M.

F. H. Dill, W. Hornberger, P. S. Hauge, J. M. Shaw, “Characterization of positive photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[CrossRef]

Shellan, J. B.

Sthel, M. S.

Stone, F. T.

Stork, W.

Streibl, N.

Tonchev, S.

L. Mashev, S. Tonchev, “Formation of holographic diffraction gratings in photoresist,” Appl. Phys. A 26, 143–149 (1981)
[CrossRef]

Tsang, W-T.

W-T. Tsang, S. Wang, “Simultaneous exposure and development technique for making gratings on positive photoresist,” Appl. Phys. Lett. 24, 196–199 (1974).
[CrossRef]

Tuttle, J.

F. H. Dill, A. Neureuther, J. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices ED-22, 456–464 (1975).
[CrossRef]

Van Duzer, T.

R. E. Jewett, P. I. Hagouel, T. Van Duzer, “Line-profile resist development simulation techniques,” Polym. Eng. Sci. 17, 381–384 (1977).
[CrossRef]

Walker, E. J.

F. H. Dill, A. Neureuther, J. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices ED-22, 456–464 (1975).
[CrossRef]

Wang, S.

W-T. Tsang, S. Wang, “Simultaneous exposure and development technique for making gratings on positive photoresist,” Appl. Phys. Lett. 24, 196–199 (1974).
[CrossRef]

Yariv, A.

Yokomori, K.

Zaidi, S. H.

Appl. Opt. (9)

Appl. Phys. A (1)

L. Mashev, S. Tonchev, “Formation of holographic diffraction gratings in photoresist,” Appl. Phys. A 26, 143–149 (1981)
[CrossRef]

Appl. Phys. Lett. (1)

W-T. Tsang, S. Wang, “Simultaneous exposure and development technique for making gratings on positive photoresist,” Appl. Phys. Lett. 24, 196–199 (1974).
[CrossRef]

IEEE Trans. Electron Devices (3)

F. H. Dill, A. Neureuther, J. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices ED-22, 456–464 (1975).
[CrossRef]

W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, M. O’Toole, “A general simulator for VLSI lithography and etching processes: Part I. Application to projection lithography,” IEEE Trans. Electron Devices ED-26, 717–722 (1979).
[CrossRef]

F. H. Dill, W. Hornberger, P. S. Hauge, J. M. Shaw, “Characterization of positive photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[CrossRef]

J. Electrochem. Soc. (2)

C. A. Mack, “Development of positive photoresists,” J. Electrochem. Soc. 134, 148–152 (1987).
[CrossRef]

S. Asaumi, H. Nakane, “Mechanism of photoresist resolution improvement by pre-exposure treatment,” J. Electrochem. Soc. 137, 2546–2549 (1990).
[CrossRef]

Opt. Lett. (2)

Opt. Spectrosc. (USSR) (1)

R. R. Gerke, I. V. Golubenko, T. G. Dubrovina, G. M. Savitski, “Investigation of the reflection properties of holographic diffraction gratings with a symmetrical line profile,” Opt. Spectrosc. (USSR) 58, 808–810 (1986).

Phys. Rev. A (1)

D. A. Kessler, J. Koplic, H. Levine, “Geometrical model of interface evolution. II. Numerical simulation,” Phys. Rev. A 30, 3163–3174 (1984).
[CrossRef]

Polym. Eng. Sci. (1)

R. E. Jewett, P. I. Hagouel, T. Van Duzer, “Line-profile resist development simulation techniques,” Polym. Eng. Sci. 17, 381–384 (1977).
[CrossRef]

Other (3)

AZ-1400 and AZ-1350 photoresists (Shipley, Newton, Mass., 1984).

L. Cescato, J. Frejlich, “Real-time optical techniques for monitoring of etching process,” in Trends in Electrochemistry (Council of Scientific Research Integration/Research Trends, Sreekanteswaran, Trivandrum, India, 1992), 201–213.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 157.

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Figures (10)

Fig. 1
Fig. 1

Schema of the interfering waves on photoresist film showing the incident and reflected beams.

Fig. 2
Fig. 2

V X E experimental curves for the AZ-1350J photoresist developed at different dilutions of NaOH in deionized water (solid curves) and for the AZ-1400 photoresist developed at different dilutions of AZ-351 developer (dashed curves). Both developers were kept at a room temperature of approximately 23 °C. The films were homogeneously exposed to the line λ = 0.4579 μm of an Ar laser. Taking into account the changes in the development rate along the z direction, the values were averaged along the 1-μm thickness of the films.

Fig. 3
Fig. 3

Schema of the resist–developer interface with vector n perpendicular to the interface at each point r and time t.

Fig. 4
Fig. 4

Schema of numerical computing of the surface. Note that surface points are created or eliminated as necessary.

Fig. 5
Fig. 5

MTF of a spatial frequency filter, which we assumed to be a simple function that decays linearly with the period from Λ2 to Λ1.

Fig. 6
Fig. 6

Example of the application of the MTF filter in a resulting surface relief with (dashed curve) and without (solid curve) a filter.

Fig. 7
Fig. 7

Evolution of the computed profiles with the development time for photoresist films on glass substrates exposed to an interference pattern of 0.8-μm period at λ = 0.4579 in three different conditions: (a) strong nonlinear V X E condition, (b) linear V X E curve, (c) linear V X E curve with a light background. The V X E curves assumed in each case are shown on the right-hand side for each case. The energy that corresponds to the exposed interference pattern is indicated in the V X E curves and was the same for the three cases. The profiles are equally spaced by the same developing time for each case.

Fig. 8
Fig. 8

SEM photos of the cross section of deep relief gratings of 0.8-μm period, recorded in a photoresist film on glass substrates with exposure energies of (a) 150 mJ/cm2 and (b) 200 mJ/cm2.

Fig. 9
Fig. 9

Evolution of computed profile gratings of 1.6-μm period exposed at λ = 0.4579 μm in photoresist films over Si substrates for three different conditions: (a) strong nonlinear V X E condition, (b) linear V X E curve, (c) linear V X E curve with a light background.

Fig. 10
Fig. 10

SEM photograph of the cross section of a holographic grating of 1.6-μm period recorded on a Si substrate.

Equations (12)

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I ( x , z ) = | E 1 exp [ i ( k 1 · r ) ] + E 2 exp [ i ( k 2 · r ) ] + E 1 exp { i [ k 2 · ( d r ) ] } + E 2 exp { i [ k 1 · ( d r ) ] } | 2 ,
E 1 = E 1 · y ˆ , E 1 r = E 1 r · y ˆ , E 2 = E 2 · y ˆ , E 2 r = E 2 r · y ˆ ,
k 1 = 2 π / λ 0 [ n ( cos θ x ˆ + sin θ z ˆ ) + i k z ˆ / cos θ ] ,
k 2 = 2 π / λ 0 [ n ( cos θ x ˆ + sin θ z ˆ ) + i k z ˆ / cos θ ] ,
r = x x ˆ + z z ˆ
m ( x , z ) = exp [ C I ( x , z ) Δ t ] ,
V ( x , z ) = V max ( a + 1 ) [ 1 m ( x , z ) ] n a + [ 1 m ( x , z ) ] n + V min ,
a = ( n + 1 ) ( n 1 ) ( 1 m th ) n ,
z ( x , t ) = z ( x , t 0 ) 0 t V ( x , z ) d t .
r t = V ( r ) n ˆ ,
n ˆ = sin ( φ ) x ˆ + cos ( φ ) z ˆ ,
r ( t + Δ t ) = r ( t ) V [ r ( t ) ] · Δ t ( sin φ x ˆ + cos φ z ˆ ) ,

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