Abstract

Optical monitoring is applied, in situ and in real time, to non-Newtonian, power law fluids in the spin coating process. An analytical exact solution is presented for thickness evolution that well fits to most measurement data. As result, typical rheological parameters are obtained for several CMC (carboximetilcelullose) concentrations and rotation speeds. Optical monitoring thus precisely indicates applicability of the model to power law fluids under spin coating.

© 2012 OSA

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References

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  1. P. H. Walker and J. G. Thompson, “Proceedings of the twenty-fifth annual meeting,” Am. Soc. Test. Mats. 22, 463–485 (1922).
  2. A. G. Emslie, F. T. Bonner, and L. G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29(5), 858–862 (1958).
    [CrossRef]
  3. B. D. Washo, “Rheology and modeling of the spin coating process,” IBM J. Res. Develop. 21(2), 190–198 (1977).
    [CrossRef]
  4. 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(6), 963–968 (1960).
    [CrossRef]
  5. S. A. Jenekhe and S. B. Schuldt, “Coating of non-Newtonian fluids on a flat rotating disk,” Ind. Eng. Chem. Fundam. 23(4), 432–436 (1984).
    [CrossRef]
  6. P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
    [CrossRef]
  7. P. L. G. Jardim, Laser and Film Optics Laboratory, Universidade Federal do Rio Grande do Sul, 9500 Bento Gonçalves Avenue, Porto Alegre, RS, Brasil. A. F. Michels, and F. Horowitz, are preparing a manuscript to be called “Spin coating process evolution and reproducibility for Power Law fluids.”
  8. A. F. Michels, T. Menegotto, and F. Horowitz, “Optically monitored dip coating as a contactless viscometry method for liquid films,” Appl. Opt. 44(6), 912–915 (2005).
    [CrossRef] [PubMed]
  9. A. F. Michels, T. Menegotto, H. P. Grieneisen, M. B. Susin, and F. Horowitz, “Double optical monitoring of dip coating with a time-varying refractive index,” Appl. Opt. 45(7), 1491–1494 (2006).
    [CrossRef] [PubMed]
  10. A. F. Michels, P. Lovato, and F. Horowitz, “Laser monitoring of non-Newtonian liquids during dip coating,” AIChE J. 55(12), 3052–3055 (2009).
    [CrossRef]
  11. F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, “Real-time optical monitoring of spin coating,” J. Phys. III France 3(11), 2059–2063 (1993).
    [CrossRef]
  12. F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, ““Optical monitoring of the sol-to gel transition in spinning silica films,” Sol-Gel Opt. III 2288, 67–70 (1994).
  13. F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
    [CrossRef]
  14. F. Horowitz, A. F. Michels, and E. M. Yeatman, “Optical viscometry of spinning sol coatings,” J. Sol-Gel Sci. Technol. 13(1/3), 707–712 (1998).
    [CrossRef]
  15. D. A. White and J. A. Tallmadge, “Theory of drag out of liquids on a flat plates,” Chem. Eng. Sci. 20(1), 33–37 (1965).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd, 1959).

2010 (1)

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[CrossRef]

2009 (1)

A. F. Michels, P. Lovato, and F. Horowitz, “Laser monitoring of non-Newtonian liquids during dip coating,” AIChE J. 55(12), 3052–3055 (2009).
[CrossRef]

2006 (1)

2005 (1)

1998 (1)

F. Horowitz, A. F. Michels, and E. M. Yeatman, “Optical viscometry of spinning sol coatings,” J. Sol-Gel Sci. Technol. 13(1/3), 707–712 (1998).
[CrossRef]

1997 (1)

F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
[CrossRef]

1994 (1)

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, ““Optical monitoring of the sol-to gel transition in spinning silica films,” Sol-Gel Opt. III 2288, 67–70 (1994).

1993 (1)

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, “Real-time optical monitoring of spin coating,” J. Phys. III France 3(11), 2059–2063 (1993).
[CrossRef]

1984 (1)

S. A. Jenekhe and S. B. Schuldt, “Coating of non-Newtonian fluids on a flat rotating disk,” Ind. Eng. Chem. Fundam. 23(4), 432–436 (1984).
[CrossRef]

1977 (1)

B. D. Washo, “Rheology and modeling of the spin coating process,” IBM J. Res. Develop. 21(2), 190–198 (1977).
[CrossRef]

1965 (1)

D. A. White and J. A. Tallmadge, “Theory of drag out of liquids on a flat plates,” Chem. Eng. Sci. 20(1), 33–37 (1965).
[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(6), 963–968 (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(5), 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(6), 963–968 (1960).
[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(5), 858–862 (1958).
[CrossRef]

Conédéra, V.

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[CrossRef]

Dawnay, E.

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, ““Optical monitoring of the sol-to gel transition in spinning silica films,” Sol-Gel Opt. III 2288, 67–70 (1994).

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, “Real-time optical monitoring of spin coating,” J. Phys. III France 3(11), 2059–2063 (1993).
[CrossRef]

Dawnay, E. J. C.

F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
[CrossRef]

Doucet, J. B.

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[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(5), 858–862 (1958).
[CrossRef]

Fardad, A.

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, ““Optical monitoring of the sol-to gel transition in spinning silica films,” Sol-Gel Opt. III 2288, 67–70 (1994).

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, “Real-time optical monitoring of spin coating,” J. Phys. III France 3(11), 2059–2063 (1993).
[CrossRef]

Fardad, M. A.

F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
[CrossRef]

Green, M.

F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
[CrossRef]

Grieneisen, H. P.

Horowitz, F.

A. F. Michels, P. Lovato, and F. Horowitz, “Laser monitoring of non-Newtonian liquids during dip coating,” AIChE J. 55(12), 3052–3055 (2009).
[CrossRef]

A. F. Michels, T. Menegotto, H. P. Grieneisen, M. B. Susin, and F. Horowitz, “Double optical monitoring of dip coating with a time-varying refractive index,” Appl. Opt. 45(7), 1491–1494 (2006).
[CrossRef] [PubMed]

A. F. Michels, T. Menegotto, and F. Horowitz, “Optically monitored dip coating as a contactless viscometry method for liquid films,” Appl. Opt. 44(6), 912–915 (2005).
[CrossRef] [PubMed]

F. Horowitz, A. F. Michels, and E. M. Yeatman, “Optical viscometry of spinning sol coatings,” J. Sol-Gel Sci. Technol. 13(1/3), 707–712 (1998).
[CrossRef]

F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
[CrossRef]

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, ““Optical monitoring of the sol-to gel transition in spinning silica films,” Sol-Gel Opt. III 2288, 67–70 (1994).

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, “Real-time optical monitoring of spin coating,” J. Phys. III France 3(11), 2059–2063 (1993).
[CrossRef]

Jenekhe, S. A.

S. A. Jenekhe and S. B. Schuldt, “Coating of non-Newtonian fluids on a flat rotating disk,” Ind. Eng. Chem. Fundam. 23(4), 432–436 (1984).
[CrossRef]

Launay, J.

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[CrossRef]

Lovato, P.

A. F. Michels, P. Lovato, and F. Horowitz, “Laser monitoring of non-Newtonian liquids during dip coating,” AIChE J. 55(12), 3052–3055 (2009).
[CrossRef]

Mazenq, L.

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[CrossRef]

Menegotto, T.

Michels, A. F.

A. F. Michels, P. Lovato, and F. Horowitz, “Laser monitoring of non-Newtonian liquids during dip coating,” AIChE J. 55(12), 3052–3055 (2009).
[CrossRef]

A. F. Michels, T. Menegotto, H. P. Grieneisen, M. B. Susin, and F. Horowitz, “Double optical monitoring of dip coating with a time-varying refractive index,” Appl. Opt. 45(7), 1491–1494 (2006).
[CrossRef] [PubMed]

A. F. Michels, T. Menegotto, and F. Horowitz, “Optically monitored dip coating as a contactless viscometry method for liquid films,” Appl. Opt. 44(6), 912–915 (2005).
[CrossRef] [PubMed]

F. Horowitz, A. F. Michels, and E. M. Yeatman, “Optical viscometry of spinning sol coatings,” J. Sol-Gel Sci. Technol. 13(1/3), 707–712 (1998).
[CrossRef]

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(5), 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(6), 963–968 (1960).
[CrossRef]

Schuldt, S. B.

S. A. Jenekhe and S. B. Schuldt, “Coating of non-Newtonian fluids on a flat rotating disk,” Ind. Eng. Chem. Fundam. 23(4), 432–436 (1984).
[CrossRef]

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(6), 963–968 (1960).
[CrossRef]

Susin, M. B.

Tallmadge, J. A.

D. A. White and J. A. Tallmadge, “Theory of drag out of liquids on a flat plates,” Chem. Eng. Sci. 20(1), 33–37 (1965).
[CrossRef]

Temple-Boyer, P.

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[CrossRef]

Torbiéro, B.

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[CrossRef]

Washo, B. D.

B. D. Washo, “Rheology and modeling of the spin coating process,” IBM J. Res. Develop. 21(2), 190–198 (1977).
[CrossRef]

White, D. A.

D. A. White and J. A. Tallmadge, “Theory of drag out of liquids on a flat plates,” Chem. Eng. Sci. 20(1), 33–37 (1965).
[CrossRef]

Yeatman, E.

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, ““Optical monitoring of the sol-to gel transition in spinning silica films,” Sol-Gel Opt. III 2288, 67–70 (1994).

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, “Real-time optical monitoring of spin coating,” J. Phys. III France 3(11), 2059–2063 (1993).
[CrossRef]

Yeatman, E. M.

F. Horowitz, A. F. Michels, and E. M. Yeatman, “Optical viscometry of spinning sol coatings,” J. Sol-Gel Sci. Technol. 13(1/3), 707–712 (1998).
[CrossRef]

F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
[CrossRef]

AIChE J. (1)

A. F. Michels, P. Lovato, and F. Horowitz, “Laser monitoring of non-Newtonian liquids during dip coating,” AIChE J. 55(12), 3052–3055 (2009).
[CrossRef]

Appl. Opt. (2)

Chem. Eng. Sci. (1)

D. A. White and J. A. Tallmadge, “Theory of drag out of liquids on a flat plates,” Chem. Eng. Sci. 20(1), 33–37 (1965).
[CrossRef]

IBM J. Res. Develop. (1)

B. D. Washo, “Rheology and modeling of the spin coating process,” IBM J. Res. Develop. 21(2), 190–198 (1977).
[CrossRef]

Ind. Eng. Chem. Fundam. (1)

S. A. Jenekhe and S. B. Schuldt, “Coating of non-Newtonian fluids on a flat rotating disk,” Ind. Eng. Chem. Fundam. 23(4), 432–436 (1984).
[CrossRef]

J. Appl. Phys. (2)

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(6), 963–968 (1960).
[CrossRef]

A. G. Emslie, F. T. Bonner, and L. G. Peck, “Flow of a viscous liquid on a rotating disk,” J. Appl. Phys. 29(5), 858–862 (1958).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

F. Horowitz, E. J. C. Dawnay, M. A. Fardad, M. Green, and E. M. Yeatman, “Towards better control of sol-gel film processing for optical device applications,” J. Nonlinear Opt. Phys. Mater. 6(1), 1–18 (1997).
[CrossRef]

J. Phys. III France (1)

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, “Real-time optical monitoring of spin coating,” J. Phys. III France 3(11), 2059–2063 (1993).
[CrossRef]

J. Sol-Gel Sci. Technol. (1)

F. Horowitz, A. F. Michels, and E. M. Yeatman, “Optical viscometry of spinning sol coatings,” J. Sol-Gel Sci. Technol. 13(1/3), 707–712 (1998).
[CrossRef]

Microelectron. Eng. (1)

P. Temple-Boyer, L. Mazenq, J. B. Doucet, V. Conédéra, B. Torbiéro, and J. Launay, “Theoretical studies of the spin coating process for the deposition of polymer-based Maxwellian liquids,” Microelectron. Eng. 87(2), 163–166 (2010).
[CrossRef]

Sol-Gel Opt. III (1)

F. Horowitz, E. Yeatman, E. Dawnay, and A. Fardad, ““Optical monitoring of the sol-to gel transition in spinning silica films,” Sol-Gel Opt. III 2288, 67–70 (1994).

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd, 1959).

P. L. G. Jardim, Laser and Film Optics Laboratory, Universidade Federal do Rio Grande do Sul, 9500 Bento Gonçalves Avenue, Porto Alegre, RS, Brasil. A. F. Michels, and F. Horowitz, are preparing a manuscript to be called “Spin coating process evolution and reproducibility for Power Law fluids.”

P. H. Walker and J. G. Thompson, “Proceedings of the twenty-fifth annual meeting,” Am. Soc. Test. Mats. 22, 463–485 (1922).

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Figures (9)

Fig. 1
Fig. 1

Scheme of the spinner-interferometer coupled system, with a 5mW 660nm laser.

Fig. 2
Fig. 2

Reflectance profile for OP20 oil during spin coating, where the dashed lines indicate the four regions corresponding to distinct stages of the process.

Fig. 3
Fig. 3

Physical thickness variation for OP20 oil during spin coating.

Fig. 4
Fig. 4

Reflectance profile for 0.2% wt CMC at several rotation speeds, where the dashed lines indicate the four regions corresponding to distinct stages of the process.

Fig. 5
Fig. 5

Physical thickness variation for 0.2% wt CMC at several rotation speeds.

Fig. 6
Fig. 6

Physical thickness variation for 0.1% wt CMC at several rotation speeds.

Fig. 7
Fig. 7

Physical thickness variation for 0.5% wt CMC at several rotation speeds.

Fig. 8
Fig. 8

Reflectance profile for 0.1% wt, 0.2% wt and 0.5% wt CMC at a rotation speed of 5000 rpm, where the dashed lines indicate the four regions corresponding to distinct stages of the process.

Fig. 9
Fig. 9

Physical thickness variation for 0.1% wt, 0.2% wt and 0.5% wt CMC at a rotation speed of 5000 rpm.

Tables (6)

Tables Icon

Table 1 Density ρ and Refraction Index n for the OP 20 Oil and the Weight Concentrations in Water of CMC

Tables Icon

Table 2 Kinematic Viscosity (ν) and Initial Thickness in Steady State(h0) for OP20 Oil

Tables Icon

Table 3 Rheological Constants (K), Powers (s) and Initial Thicknesses in the Steady State (ho) for 0.2% wt CMC at Several Rotation Speeds

Tables Icon

Table 4 Rheological Constants (K), Powers (s) and Initial Thicknesses in Steady State (ho) for 0.1% wt CMC at Several Rotation Speeds

Tables Icon

Table 5 Rheological Constants (K), Powers (s) and Initial Thicknesses in Steady State (ho) for 0.5% wt CMC at Several Rotation Speeds

Tables Icon

Table 6 Rheological Constants (K), Powers (s) and Initial Thicknesses in the Steady State (ho) for 0.1% wt, 0.2% wt and 0.5% wt CMC at a Rotation Speed of 5000 rpm

Equations (10)

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

τ rz z =ρr ω 2 .
τ rz =K | v r z | s1 v r z ,
μ rz eff =K | v r z | s1 .
h t + (s+1) (2s+1) h 2s+1 s ( ρ ω 2 K ) 1 s r 1s s + ( ρ ω 2 K ) 1 s r 1 s h s+1 s h r =0,
h(r,t)= h 0 ( r r 0 ) (s1) (s+1) [ 1+ (3s+1) (2s+1) h 0 (s+1) s r 0 (1s) s ( ρ ω 2 K ) 1 s t ] s (s+1) .
h(t)= h 0 [ 1+ 4 3 ( ω 2 ν ) h 0 2 t ] 1 2 .
2β= 4π λ 0 n 1 h.
R= ( n 0 2 + n 1 2 )( n 1 2 + n 2 2 )4 n 0 n 1 2 n 2 +( n 0 2 n 1 2 )( n 1 2 n 2 2 )cos2β+ζ ( n 0 2 + n 1 2 )( n 1 2 + n 2 2 )+4 n 0 n 1 2 n 2 +( n 0 2 n 1 2 )( n 1 2 n 2 2 )cos2β+ζ .
ζ=( n 0 2 n 1 2 )( 2 n 1 n 2 κ 2 sin2β n 2 2 κ 2 2 cos2β )+( n 0 2 + n 1 2 ) n 2 2 κ 2 2 .
Δh n 1 =m λ o 4 ,form=1,2,....

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