Abstract

Fabrication of a thick analog profile with photoresist is a difficult task in photolithography. We demonstrate that a binary phase-grating photomask with an appropriate period and duty cycles is capable of manipulating the exposure illumination in an analog fashion and can be used for fabrication of the desired analog micro-optics profiles on the surface of a thick photoresist. By choosing the proper period and variation of duty cycle of the phase-grating mask, one can create the desired analog intensity of exposure illumination for an optical stepper. This allows the formation of a wide range of analog micro-optics profiles with an SPR 220-7 photoresist. The numerical convolution of the diffraction efficiency curve and resist exposure characteristics is used to predict the final resist profile and also to design the appropriate duty-cycle distribution for the binary phase grating. As a demonstration of this technology, we fabricated a variety of micro-optical elements, such as a positive lens, ring lens, prism, and vortex of 100200μm diameter, by using a phase-grating mask fabricated in a poly(methyl methacrylate) electron-beam resist.

© 2006 Optical Society of America

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  1. W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, "Simulation and experimental study of gray-tone lithography for the fabrication of arbitrary shaped surfaces," in Proceedings of the IEEE Workshop on Micro Electro Mechanical Systems 1994, MEMS '94 (Institute of Electrical and Electronics Engineers, 1994), pp. 205-210.
  2. W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
    [CrossRef]
  3. B. Morgan and C. M. Waits, "Development of deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching," IEEE J. Microelectromech. Syst. 13, 113-120 (2004).
    [CrossRef]
  4. C. M. Waits, R. Ghodssi, M. H. Ervin, and M. Dubey, "MEMS based gray-scale lithography," in Proceedings of the 2001 International Semiconductor Device Research Symposium, (Institute of Electrical and Electronics Engineers, 2001), pp. 182-185.
    [CrossRef]
  5. J. Shimada, O. Ohguchi, and R. Sawada, "Microlens fabricated by the planar process," J. Lightwave Technol. 9, 571-576 (1991).
    [CrossRef]
  6. E.-H. Park, M.-J. Kim, and Y.-S. Kwon, "Microlens for efficient coupling between LED and optical fiber," IEEE Photon. Technol. Lett. 11, 439-441 (1999).
    [CrossRef]
  7. C. David, B. Nohammer, and E. Ziegler, "Wavelength tunable diffractive transmission lenses for hard x-rays," Appl. Phys. Lett. 79, 1088-1090 (2001).
    [CrossRef]
  8. M. Pitchumani, H. Hockel, W. Mohammed, and E. G. Johnson, "Additive lithography for fabrication of diffractive optics," Appl. Opt. 41, 6176-6181 (2002).
    [CrossRef] [PubMed]
  9. M. Levinson, N. Viswanathan, and R. Simpson, "Improved resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron Devices ED-29, 1812-1846 (1982).
  10. A. K. Wong, Resolution Enhancement Techniques in Optical Lithography, Vol. TT47 of SPIE Tutorial Text Series (SPIE Press, 2001), Chaps. 2, 3, 5.
    [CrossRef]

2004 (1)

B. Morgan and C. M. Waits, "Development of deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching," IEEE J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

2002 (1)

2001 (1)

C. David, B. Nohammer, and E. Ziegler, "Wavelength tunable diffractive transmission lenses for hard x-rays," Appl. Phys. Lett. 79, 1088-1090 (2001).
[CrossRef]

1999 (1)

E.-H. Park, M.-J. Kim, and Y.-S. Kwon, "Microlens for efficient coupling between LED and optical fiber," IEEE Photon. Technol. Lett. 11, 439-441 (1999).
[CrossRef]

1996 (1)

W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
[CrossRef]

1991 (1)

J. Shimada, O. Ohguchi, and R. Sawada, "Microlens fabricated by the planar process," J. Lightwave Technol. 9, 571-576 (1991).
[CrossRef]

1982 (1)

M. Levinson, N. Viswanathan, and R. Simpson, "Improved resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron Devices ED-29, 1812-1846 (1982).

Daschner, W.

W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
[CrossRef]

David, C.

C. David, B. Nohammer, and E. Ziegler, "Wavelength tunable diffractive transmission lenses for hard x-rays," Appl. Phys. Lett. 79, 1088-1090 (2001).
[CrossRef]

Dubey, M.

C. M. Waits, R. Ghodssi, M. H. Ervin, and M. Dubey, "MEMS based gray-scale lithography," in Proceedings of the 2001 International Semiconductor Device Research Symposium, (Institute of Electrical and Electronics Engineers, 2001), pp. 182-185.
[CrossRef]

Ervin, M. H.

C. M. Waits, R. Ghodssi, M. H. Ervin, and M. Dubey, "MEMS based gray-scale lithography," in Proceedings of the 2001 International Semiconductor Device Research Symposium, (Institute of Electrical and Electronics Engineers, 2001), pp. 182-185.
[CrossRef]

Ghodssi, R.

C. M. Waits, R. Ghodssi, M. H. Ervin, and M. Dubey, "MEMS based gray-scale lithography," in Proceedings of the 2001 International Semiconductor Device Research Symposium, (Institute of Electrical and Electronics Engineers, 2001), pp. 182-185.
[CrossRef]

Henke, W.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, "Simulation and experimental study of gray-tone lithography for the fabrication of arbitrary shaped surfaces," in Proceedings of the IEEE Workshop on Micro Electro Mechanical Systems 1994, MEMS '94 (Institute of Electrical and Electronics Engineers, 1994), pp. 205-210.

Hockel, H.

Hoppe, W.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, "Simulation and experimental study of gray-tone lithography for the fabrication of arbitrary shaped surfaces," in Proceedings of the IEEE Workshop on Micro Electro Mechanical Systems 1994, MEMS '94 (Institute of Electrical and Electronics Engineers, 1994), pp. 205-210.

Johnson, E. G.

Kim, M.-J.

E.-H. Park, M.-J. Kim, and Y.-S. Kwon, "Microlens for efficient coupling between LED and optical fiber," IEEE Photon. Technol. Lett. 11, 439-441 (1999).
[CrossRef]

Kwon, Y.-S.

E.-H. Park, M.-J. Kim, and Y.-S. Kwon, "Microlens for efficient coupling between LED and optical fiber," IEEE Photon. Technol. Lett. 11, 439-441 (1999).
[CrossRef]

Lee, S. H.

W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
[CrossRef]

Levinson, M.

M. Levinson, N. Viswanathan, and R. Simpson, "Improved resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron Devices ED-29, 1812-1846 (1982).

Long, P.

W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
[CrossRef]

Mohammed, W.

Morgan, B.

B. Morgan and C. M. Waits, "Development of deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching," IEEE J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

Nohammer, B.

C. David, B. Nohammer, and E. Ziegler, "Wavelength tunable diffractive transmission lenses for hard x-rays," Appl. Phys. Lett. 79, 1088-1090 (2001).
[CrossRef]

Ohguchi, O.

J. Shimada, O. Ohguchi, and R. Sawada, "Microlens fabricated by the planar process," J. Lightwave Technol. 9, 571-576 (1991).
[CrossRef]

Park, E.-H.

E.-H. Park, M.-J. Kim, and Y.-S. Kwon, "Microlens for efficient coupling between LED and optical fiber," IEEE Photon. Technol. Lett. 11, 439-441 (1999).
[CrossRef]

Pitchumani, M.

Quenzer, H. J.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, "Simulation and experimental study of gray-tone lithography for the fabrication of arbitrary shaped surfaces," in Proceedings of the IEEE Workshop on Micro Electro Mechanical Systems 1994, MEMS '94 (Institute of Electrical and Electronics Engineers, 1994), pp. 205-210.

Sawada, R.

J. Shimada, O. Ohguchi, and R. Sawada, "Microlens fabricated by the planar process," J. Lightwave Technol. 9, 571-576 (1991).
[CrossRef]

Shimada, J.

J. Shimada, O. Ohguchi, and R. Sawada, "Microlens fabricated by the planar process," J. Lightwave Technol. 9, 571-576 (1991).
[CrossRef]

Simpson, R.

M. Levinson, N. Viswanathan, and R. Simpson, "Improved resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron Devices ED-29, 1812-1846 (1982).

Staudt-Fischbach, P.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, "Simulation and experimental study of gray-tone lithography for the fabrication of arbitrary shaped surfaces," in Proceedings of the IEEE Workshop on Micro Electro Mechanical Systems 1994, MEMS '94 (Institute of Electrical and Electronics Engineers, 1994), pp. 205-210.

Stein, R.

W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
[CrossRef]

Viswanathan, N.

M. Levinson, N. Viswanathan, and R. Simpson, "Improved resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron Devices ED-29, 1812-1846 (1982).

Wagner, B.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, "Simulation and experimental study of gray-tone lithography for the fabrication of arbitrary shaped surfaces," in Proceedings of the IEEE Workshop on Micro Electro Mechanical Systems 1994, MEMS '94 (Institute of Electrical and Electronics Engineers, 1994), pp. 205-210.

Waits, C. M.

B. Morgan and C. M. Waits, "Development of deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching," IEEE J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

C. M. Waits, R. Ghodssi, M. H. Ervin, and M. Dubey, "MEMS based gray-scale lithography," in Proceedings of the 2001 International Semiconductor Device Research Symposium, (Institute of Electrical and Electronics Engineers, 2001), pp. 182-185.
[CrossRef]

Wong, A. K.

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography, Vol. TT47 of SPIE Tutorial Text Series (SPIE Press, 2001), Chaps. 2, 3, 5.
[CrossRef]

Wu, C.

W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
[CrossRef]

Ziegler, E.

C. David, B. Nohammer, and E. Ziegler, "Wavelength tunable diffractive transmission lenses for hard x-rays," Appl. Phys. Lett. 79, 1088-1090 (2001).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. David, B. Nohammer, and E. Ziegler, "Wavelength tunable diffractive transmission lenses for hard x-rays," Appl. Phys. Lett. 79, 1088-1090 (2001).
[CrossRef]

IEEE J. Microelectromech. Syst. (1)

B. Morgan and C. M. Waits, "Development of deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching," IEEE J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E.-H. Park, M.-J. Kim, and Y.-S. Kwon, "Microlens for efficient coupling between LED and optical fiber," IEEE Photon. Technol. Lett. 11, 439-441 (1999).
[CrossRef]

IEEE Trans. Electron Devices (1)

M. Levinson, N. Viswanathan, and R. Simpson, "Improved resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron Devices ED-29, 1812-1846 (1982).

J. Lightwave Technol. (1)

J. Shimada, O. Ohguchi, and R. Sawada, "Microlens fabricated by the planar process," J. Lightwave Technol. 9, 571-576 (1991).
[CrossRef]

Proc. SPIE (1)

W. Daschner, R. Stein, P. Long, C. Wu, and S. H. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) gray-level mask," in Diffractive and Holographic Optics Technology III, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2689, 153-155 (1996).
[CrossRef]

Other (3)

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, "Simulation and experimental study of gray-tone lithography for the fabrication of arbitrary shaped surfaces," in Proceedings of the IEEE Workshop on Micro Electro Mechanical Systems 1994, MEMS '94 (Institute of Electrical and Electronics Engineers, 1994), pp. 205-210.

C. M. Waits, R. Ghodssi, M. H. Ervin, and M. Dubey, "MEMS based gray-scale lithography," in Proceedings of the 2001 International Semiconductor Device Research Symposium, (Institute of Electrical and Electronics Engineers, 2001), pp. 182-185.
[CrossRef]

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography, Vol. TT47 of SPIE Tutorial Text Series (SPIE Press, 2001), Chaps. 2, 3, 5.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Two different types of photomask for analog-resist-profile formation: (a) halftone mask and (b) binary phase-grating mask. a, size of the pixel; Λ, pixel pitch.

Fig. 2
Fig. 2

Zeroth-order diffraction efficiency versus duty-cycle curve for a 2D binary phase grating.

Fig. 3
Fig. 3

Developed thickness of the SPR 220-7 resist versus exposure time in the stepper.

Fig. 4
Fig. 4

Remaining thickness versus duty cycle obtained by numerical convolution of the resist characterization curve with a zeroth-order efficiency curve of a binary 2D phase grating for 0.6 s of bias and 2.6 s of exposure time.

Fig. 5
Fig. 5

Intensity-transmittance and duty-cycle profiles of the phase-grating mask for (a) the 100 μm microprism and (b) the V-groove.

Fig. 6
Fig. 6

One-dimensional target resist profile (solid curve) and developed resist profile (dotted curve) of the microprism resulting from the numerical convolution of the exposure curve of the SPR 220 and the designed duty-cycle map: (a) from the intensity-transmittance-based phase-grating mask and (b) from the resist-profile-based phase-grating mask.

Fig. 7
Fig. 7

Microscope image of the phase-grating mask fabricated on the PMMA e-beam resist by using the e-beam direct-writing technique.

Fig. 8
Fig. 8

Two-dimensional Zygo profiles of fabricated analog elements on the SPR 220 resist: (a) microprism and (b) V-groove.

Fig. 9
Fig. 9

Comparison of the numerically predicted 1D microprism profile (solid curve) and the fabricated 1D microprism profile (dotted curve): (a) microprism and (b) V-groove.

Fig. 10
Fig. 10

Two-dimensional Zygo profiles of fabricated analog-vortex elements on the SPR 220 resist: (a) vortex with charge number equal to one and (b) vortex with charge number equal to three.

Fig. 11
Fig. 11

Measured angular-vortex height profile: (a) upper curve is from the analog vortex with 0.6 s of bias time and (b) lower curve is from the analog vortex with 0.8 s of bias time.

Equations (12)

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G ( f , g ) = H ( f , g ) F T [ g o ( x , y ) ] ,
g i ( x , y ) = F T - 1 [ G ( f , g ) ] .
p c = λ ( 1 + σ ) NA .
I = 1 A pixel / A pitch .
F = w 2 = a 2 / Λ 2 .
t ( x , y ) = [ 2 rect ( x a / 2 a , y a / 2 a ) 1 ] 1 Λ 2 comb ( x Λ , y Λ ) .
D E ( w ) = 1 4 w 2 + 4 w 4 .
D ( w ) = I 0 [ t b + D E ( w ) × t ] .
W ( x , y ) = { [ 1 I ( x , y ) ] / 2 } 1 / 2 .
D ( h ) = a 0 + a 1 h + a 2 h 2 + a 3 h 3 + a 4 h 4 + a 5 h 5 + a 6 h 6 .
I ( x , y ) = [ D ( x , y ) / I 0 t b ] / t e .
d ( x , y ) = d 0 [ tan 1 ( m y / x ) + π ] / ( 2 π ) .

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