Abstract

We present the final film thickness' expression of spin-coated photoresist on a spherical substrate. Firstly, some reasonable assumptions are put forward for a concise derivation process. Then, on the basis of the motion equation of spin-coated photoresist on a plane, considering the spherical surface shape, we put forward the motion equation of spin-coated photoresist on a spherical substrate. So two evolution equations of film thickness and radial position are derived, and the expression of initial film thickness evolution in a radial position is also gained. Finally, considering some effects of solvent volatilization, we gain the expression of final film thickness. The experiment result indicates that the expression is accurate.

© 2005 Optical Society of America

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References

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  1. J. H. Burge, D. S. Anderson, T. D. Milster, and C. L. Vernold, “Measurement of a convex secondary mirrorusing a holographic test plat,” in Proc. SPIE 2199, 193-198 (1994).
    [CrossRef]
  2. Yongjun XIE, Zhenwu LU, Fengyou LI, Jingli ZHAO, and Zhicheng WENG, “Lithographic fabrication of large diffractive optical elements on a concave lens surface,” Opt. Express 10, 1043-1047 (2002).
    [PubMed]
  3. S.B.G. O’Brien and L.W. Schwartz, “Theory and modeling of thin film flows,” Encyclopedia of Surface and Colloid Science, Marcel Dekker, New York, 5283-5297 (2002).
  4. T G Myers and J P F Charpin., “The effect of the coriolis force on axisymmetric rotating thin film flows,” Int.J. Non-linear Mech. 36, 629-635 (2001).
    [CrossRef]
  5. A. G. Emslie, F. T. Bonner, and L.G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29, 858-862 (1958).
    [CrossRef]
  6. A Acrivos, M J Shah, and E E. Petersen, “On the flow of a non-newtonian liquid on a rotating disk,” J. Appl. Phys. 31, 63-968 (1960).
    [CrossRef]
  7. D Meyerhofer, “Characteristics of resist films produced by spinning,” J. Appl. Phys. 49, 3993-3997 (1978).
    [CrossRef]
  8. YUE Hongda, PAN Longfa, and BIN Yuejing, et al, “Mechanics analysis in CD-R dye coating process,” in Proc. SPIE 4930, 253-257 (2002).
    [CrossRef]
  9. Peter C. Sukanek, “Spin Coating,” J. Imaging Technol. 11, 184-190(1985).

2002 (3)

Yongjun XIE, Zhenwu LU, Fengyou LI, Jingli ZHAO, and Zhicheng WENG, “Lithographic fabrication of large diffractive optical elements on a concave lens surface,” Opt. Express 10, 1043-1047 (2002).
[PubMed]

S.B.G. O’Brien and L.W. Schwartz, “Theory and modeling of thin film flows,” Encyclopedia of Surface and Colloid Science, Marcel Dekker, New York, 5283-5297 (2002).

YUE Hongda, PAN Longfa, and BIN Yuejing, et al, “Mechanics analysis in CD-R dye coating process,” in Proc. SPIE 4930, 253-257 (2002).
[CrossRef]

2001 (1)

T G Myers and J P F Charpin., “The effect of the coriolis force on axisymmetric rotating thin film flows,” Int.J. Non-linear Mech. 36, 629-635 (2001).
[CrossRef]

1994 (1)

J. H. Burge, D. S. Anderson, T. D. Milster, and C. L. Vernold, “Measurement of a convex secondary mirrorusing a holographic test plat,” in Proc. SPIE 2199, 193-198 (1994).
[CrossRef]

1985 (1)

Peter C. Sukanek, “Spin Coating,” J. Imaging Technol. 11, 184-190(1985).

1978 (1)

D Meyerhofer, “Characteristics of resist films produced by spinning,” J. Appl. Phys. 49, 3993-3997 (1978).
[CrossRef]

1960 (1)

A Acrivos, M J Shah, and E E. Petersen, “On the flow of a non-newtonian liquid on a rotating disk,” J. Appl. Phys. 31, 63-968 (1960).
[CrossRef]

1958 (1)

A. G. Emslie, F. T. Bonner, and L.G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29, 858-862 (1958).
[CrossRef]

Acrivos, A

A Acrivos, M J Shah, and E E. Petersen, “On the flow of a non-newtonian liquid on a rotating disk,” J. Appl. Phys. 31, 63-968 (1960).
[CrossRef]

Anderson, D. S.

J. H. Burge, D. S. Anderson, T. D. Milster, and C. L. Vernold, “Measurement of a convex secondary mirrorusing a holographic test plat,” in Proc. SPIE 2199, 193-198 (1994).
[CrossRef]

Bonner, F. T.

A. G. Emslie, F. T. Bonner, and L.G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29, 858-862 (1958).
[CrossRef]

Burge, J. H.

J. H. Burge, D. S. Anderson, T. D. Milster, and C. L. Vernold, “Measurement of a convex secondary mirrorusing a holographic test plat,” in Proc. SPIE 2199, 193-198 (1994).
[CrossRef]

Charpin, J P F

T G Myers and J P F Charpin., “The effect of the coriolis force on axisymmetric rotating thin film flows,” Int.J. Non-linear Mech. 36, 629-635 (2001).
[CrossRef]

Emslie, A. G.

A. G. Emslie, F. T. Bonner, and L.G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29, 858-862 (1958).
[CrossRef]

Hongda, YUE

YUE Hongda, PAN Longfa, and BIN Yuejing, et al, “Mechanics analysis in CD-R dye coating process,” in Proc. SPIE 4930, 253-257 (2002).
[CrossRef]

LI, Fengyou

Longfa, PAN

YUE Hongda, PAN Longfa, and BIN Yuejing, et al, “Mechanics analysis in CD-R dye coating process,” in Proc. SPIE 4930, 253-257 (2002).
[CrossRef]

LU, Zhenwu

Meyerhofer, D

D Meyerhofer, “Characteristics of resist films produced by spinning,” J. Appl. Phys. 49, 3993-3997 (1978).
[CrossRef]

Milster, T. D.

J. H. Burge, D. S. Anderson, T. D. Milster, and C. L. Vernold, “Measurement of a convex secondary mirrorusing a holographic test plat,” in Proc. SPIE 2199, 193-198 (1994).
[CrossRef]

Myers, T G

T G Myers and J P F Charpin., “The effect of the coriolis force on axisymmetric rotating thin film flows,” Int.J. Non-linear Mech. 36, 629-635 (2001).
[CrossRef]

O’Brien, S.B.G.

S.B.G. O’Brien and L.W. Schwartz, “Theory and modeling of thin film flows,” Encyclopedia of Surface and Colloid Science, Marcel Dekker, New York, 5283-5297 (2002).

Peck, L.G.

A. G. Emslie, F. T. Bonner, and L.G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29, 858-862 (1958).
[CrossRef]

Petersen, E E.

A Acrivos, M J Shah, and E E. Petersen, “On the flow of a non-newtonian liquid on a rotating disk,” J. Appl. Phys. 31, 63-968 (1960).
[CrossRef]

Schwartz, L.W.

S.B.G. O’Brien and L.W. Schwartz, “Theory and modeling of thin film flows,” Encyclopedia of Surface and Colloid Science, Marcel Dekker, New York, 5283-5297 (2002).

Shah, M J

A Acrivos, M J Shah, and E E. Petersen, “On the flow of a non-newtonian liquid on a rotating disk,” J. Appl. Phys. 31, 63-968 (1960).
[CrossRef]

Sukanek, Peter C.

Peter C. Sukanek, “Spin Coating,” J. Imaging Technol. 11, 184-190(1985).

Vernold, C. L.

J. H. Burge, D. S. Anderson, T. D. Milster, and C. L. Vernold, “Measurement of a convex secondary mirrorusing a holographic test plat,” in Proc. SPIE 2199, 193-198 (1994).
[CrossRef]

WENG, Zhicheng

XIE, Yongjun

Yuejing, BIN

YUE Hongda, PAN Longfa, and BIN Yuejing, et al, “Mechanics analysis in CD-R dye coating process,” in Proc. SPIE 4930, 253-257 (2002).
[CrossRef]

ZHAO, Jingli

Encyclopedia of Surface and Colloid Science, Marcel Dekker, New York (1)

S.B.G. O’Brien and L.W. Schwartz, “Theory and modeling of thin film flows,” Encyclopedia of Surface and Colloid Science, Marcel Dekker, New York, 5283-5297 (2002).

in Proc. SPIE (2)

J. H. Burge, D. S. Anderson, T. D. Milster, and C. L. Vernold, “Measurement of a convex secondary mirrorusing a holographic test plat,” in Proc. SPIE 2199, 193-198 (1994).
[CrossRef]

YUE Hongda, PAN Longfa, and BIN Yuejing, et al, “Mechanics analysis in CD-R dye coating process,” in Proc. SPIE 4930, 253-257 (2002).
[CrossRef]

Int.J. Non-linear Mech. (1)

T G Myers and J P F Charpin., “The effect of the coriolis force on axisymmetric rotating thin film flows,” Int.J. Non-linear Mech. 36, 629-635 (2001).
[CrossRef]

J. Appl. Phys. (3)

A. G. Emslie, F. T. Bonner, and L.G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29, 858-862 (1958).
[CrossRef]

A Acrivos, M J Shah, and E E. Petersen, “On the flow of a non-newtonian liquid on a rotating disk,” J. Appl. Phys. 31, 63-968 (1960).
[CrossRef]

D Meyerhofer, “Characteristics of resist films produced by spinning,” J. Appl. Phys. 49, 3993-3997 (1978).
[CrossRef]

J. Imaging Technol. (1)

Peter C. Sukanek, “Spin Coating,” J. Imaging Technol. 11, 184-190(1985).

Opt. Express (1)

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Figures (2)

Fig. 1.
Fig. 1.

The force diagram of infinitesimal fluid

Fig. 2.
Fig. 2.

Final photoresist thickness on a concave spherical substrate with a spherical radius of 20mm, the angular velocity of 2000rpm. C o =0.015 , g ≈ 0 , μ/ρ ∙ C √ω = ve = 0.03 m 2/s 2.

Equations (25)

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μ 2 u z 2 = ρ ω 2 r
sin θ = r R
μ 2 u z 2 = ρ ω 2 r cos θ g sin θ
u ( r , z , t ) = 0 .
u z ( r , z , t ) = 0
u = r μR ( 1 2 z 2 + hz ) ( ρ ω 2 R 2 r 2 g )
h t + 1 r r ( r 0 h udz ) = 0
( 2 g 2 ρ ω 2 R 2 r 2 + ρ ω 2 r 2 R 2 r 2 ) h 3 3 μR = h t + r h 2 ( ρ ω 2 R 2 r 2 g ) μR h r
dh dt = h t + h r dr dt
dh dt = ( 2 g 2 ρ ω 2 R 2 r 2 + ρ ω 2 r 2 R 2 r 2 ) h 3 3 μR
dr dt = r h 2 μR ρ ω 2 R 2 r 2 g )
h = h 0 [ 1 + ( 2 ρ ω 2 R 2 r 2 2 g ρ ω 2 r 2 R 2 r 2 ) 2 h 0 2 t 3 μR ] 1 2
ρ ω 2 r cos θ g sin θ
r R 2 g 2 ρ 2 ω 4
0 < r R 2 g 2 ρ 2 ω 4
h = h 0 ( 1 4 g h 0 2 t 3 μR ) 1 2
h = h 0 [ 1 + 4 ρ ω 2 h 0 2 t 3 μ ] 1 2
c ( t ) = S ( S + L )
h = S + L
dS dt = c ( 2 ρ ω 2 R 2 r 2 2 g ρ ω 2 r 2 R 2 r 2 ) h 3 3 μR
dL dt = ( 1 c ) ( 2 ρ ω 2 R 2 r 2 2 g ρ ω 2 r 2 R 2 r 2 ) h 3 3 μR e
h f = S f
μ = μ solvent + μ solids c γ
e = C ω
h f = S f = c 0 h 1 3 = c 0 [ 3 μR C ω ( 1 c 0 ) ( 2 ρ ω 2 R 2 r 2 ρ ω 2 r 2 R 2 r 2 2 g ) ] 1 3

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