Abstract

Ellipsometry is often used to determine the refractive index and/or the thickness of a polymer layer on a substrate. However, simultaneous determination of these parameters from a single-wavelength single-angle measurement is not always possible. The present study determines the sensitivity of the method to errors of measurement for the case of phase modulated ellipsometry and identifies conditions for decoupling film thickness and refractive index. For a specific range of film thickness, both the thickness and the refractive index can be determined from a single measurement with high precision. This optimal range of the film thickness is determined for organic thin films, and the analysis is tested on hydrogel-like polymer films in air and in water.

© 2006 Optical Society of America

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References

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  4. K. Vedam, "Spectroscopic ellipsometry: a historical overview," Thin Solid Films 313-314, 1-9 (1998).
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  6. J. Kattner and H. Hoffman, "Simultaneous determination of thicknesses and refractive indices of ultrathin films by multiple incidence medium ellipsometry," J. Phys. Chem. B 106, 9723-9729 (2002).
    [CrossRef]
  7. G. H. Bu-Abbud and N. M. Bashara, "Parameter correlation and precision in multiple-angle ellipsometry," Appl. Opt. 20, 3020-3026 (1981).
    [CrossRef] [PubMed]
  8. S. N. Jasperson and S. E. Schnatterly, "An improved method for high reflectivity ellipsometry based on a new polarization modulation technique," Rev. Sci. Instrum. 40, 761-767 (1969).
    [CrossRef]
  9. D. Beaglehole, "Etching of 50nm photoresist sample, 100 pts per second," Examples in Ellipsometry, http://www.beaglehole.com/examples/ex11.pdf.
  10. B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).
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    [CrossRef]
  12. T. C. Oakberg, "Modulated interference effects: Use of photoelastic modulators with lasers," Opt. Eng. (Bellingham) 34, 1545-1550 (1995).
    [CrossRef]
  13. F. A. Modine, G. E. Jellison, Jr., and G. R. Gruzalski, "Errors in ellipsometry measurements made with a photoelastic modulator," J. Opt. Soc. Am. 73, 892-900 (1983).
    [CrossRef]
  14. J. Lekner, Theory of Reflection (Martinus Nijhoff, 1987).
  15. D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 85th ed. (CRC Press, 2004).
  16. D. Beaglehole, Isoellipsometric-parameter curves for layers on silicon," J. Opt. Soc. Am. A 8, 311-313 (1991).
    [CrossRef]
  17. M. K. Smit and J. W. Verhoof, "Accuracy analysis in multiple angle of incidence ellipsometry," Thin Solid Films 189, 193-203 (1990).
    [CrossRef]
  18. S. A. Sukhishvili and S. Granick, "Layered, erasable polymer multilayers formed by hydrogen-bonded sequential self-assembly," Macromolecules 35, 301-310 (2002).
    [CrossRef]
  19. V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
    [CrossRef]

2003 (1)

V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
[CrossRef]

2002 (2)

S. A. Sukhishvili and S. Granick, "Layered, erasable polymer multilayers formed by hydrogen-bonded sequential self-assembly," Macromolecules 35, 301-310 (2002).
[CrossRef]

J. Kattner and H. Hoffman, "Simultaneous determination of thicknesses and refractive indices of ultrathin films by multiple incidence medium ellipsometry," J. Phys. Chem. B 106, 9723-9729 (2002).
[CrossRef]

1998 (1)

K. Vedam, "Spectroscopic ellipsometry: a historical overview," Thin Solid Films 313-314, 1-9 (1998).
[CrossRef]

1995 (1)

T. C. Oakberg, "Modulated interference effects: Use of photoelastic modulators with lasers," Opt. Eng. (Bellingham) 34, 1545-1550 (1995).
[CrossRef]

1991 (1)

1990 (1)

M. K. Smit and J. W. Verhoof, "Accuracy analysis in multiple angle of incidence ellipsometry," Thin Solid Films 189, 193-203 (1990).
[CrossRef]

1989 (1)

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase-modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

1987 (1)

1985 (1)

1983 (1)

1981 (1)

1980 (1)

D. Beaglehole, "Ellipsometric study of the surface of simple liquids," Physica B & C 100, 163-174 (1980).
[CrossRef]

1969 (1)

S. N. Jasperson and S. E. Schnatterly, "An improved method for high reflectivity ellipsometry based on a new polarization modulation technique," Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

Archer, O.

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase-modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

Bashara, N. M.

Beaglehole, D.

D. Beaglehole, Isoellipsometric-parameter curves for layers on silicon," J. Opt. Soc. Am. A 8, 311-313 (1991).
[CrossRef]

D. Beaglehole, "Ellipsometric study of the surface of simple liquids," Physica B & C 100, 163-174 (1980).
[CrossRef]

D. Beaglehole, "Etching of 50nm photoresist sample, 100 pts per second," Examples in Ellipsometry, http://www.beaglehole.com/examples/ex11.pdf.

Benferhat, R.

B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).

Bigan, E.

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase-modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, 1999).
[PubMed]

Bu-Abbud, G. H.

Dorf, M. C.

Drevillon, B.

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase-modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).

Gaillyová, Y.

Granick, S.

S. A. Sukhishvili and S. Granick, "Layered, erasable polymer multilayers formed by hydrogen-bonded sequential self-assembly," Macromolecules 35, 301-310 (2002).
[CrossRef]

Gruzalski, G. R.

Hoffman, H.

J. Kattner and H. Hoffman, "Simultaneous determination of thicknesses and refractive indices of ultrathin films by multiple incidence medium ellipsometry," J. Phys. Chem. B 106, 9723-9729 (2002).
[CrossRef]

Humlicek, J.

Jasperson, S. N.

S. N. Jasperson and S. E. Schnatterly, "An improved method for high reflectivity ellipsometry based on a new polarization modulation technique," Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

Jellison, G. E.

Josserand, Y.

B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).

Kattner, J.

J. Kattner and H. Hoffman, "Simultaneous determination of thicknesses and refractive indices of ultrathin films by multiple incidence medium ellipsometry," J. Phys. Chem. B 106, 9723-9729 (2002).
[CrossRef]

Kozlovskaya, V.

V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
[CrossRef]

Lekner, J.

Libera, M.

V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
[CrossRef]

Lide, D. R.

D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 85th ed. (CRC Press, 2004).

Modine, F. A.

Oakberg, T. C.

T. C. Oakberg, "Modulated interference effects: Use of photoelastic modulators with lasers," Opt. Eng. (Bellingham) 34, 1545-1550 (1995).
[CrossRef]

Ok, S.

V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
[CrossRef]

Parey, J. Y.

B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).

Schlayen, B.

B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).

Schmidt, E.

Schnatterly, S. E.

S. N. Jasperson and S. E. Schnatterly, "An improved method for high reflectivity ellipsometry based on a new polarization modulation technique," Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

Smit, M. K.

M. K. Smit and J. W. Verhoof, "Accuracy analysis in multiple angle of incidence ellipsometry," Thin Solid Films 189, 193-203 (1990).
[CrossRef]

Sousa, A.

V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
[CrossRef]

Stchakovsky, M.

B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).

Sukhishvili, S.

V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
[CrossRef]

Sukhishvili, S. A.

S. A. Sukhishvili and S. Granick, "Layered, erasable polymer multilayers formed by hydrogen-bonded sequential self-assembly," Macromolecules 35, 301-310 (2002).
[CrossRef]

Vedam, K.

K. Vedam, "Spectroscopic ellipsometry: a historical overview," Thin Solid Films 313-314, 1-9 (1998).
[CrossRef]

Verhoof, J. W.

M. K. Smit and J. W. Verhoof, "Accuracy analysis in multiple angle of incidence ellipsometry," Thin Solid Films 189, 193-203 (1990).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, 1999).
[PubMed]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Phys. Chem. B (1)

J. Kattner and H. Hoffman, "Simultaneous determination of thicknesses and refractive indices of ultrathin films by multiple incidence medium ellipsometry," J. Phys. Chem. B 106, 9723-9729 (2002).
[CrossRef]

Macromolecules (2)

S. A. Sukhishvili and S. Granick, "Layered, erasable polymer multilayers formed by hydrogen-bonded sequential self-assembly," Macromolecules 35, 301-310 (2002).
[CrossRef]

V. Kozlovskaya, S. Ok, A. Sousa, M. Libera, and S. Sukhishvili, "Hydrogen-bonded polymer capsules formed by layer-by-layer self-assembly," Macromolecules 36, 8590-8592 (2003).
[CrossRef]

Opt. Eng. (Bellingham) (1)

T. C. Oakberg, "Modulated interference effects: Use of photoelastic modulators with lasers," Opt. Eng. (Bellingham) 34, 1545-1550 (1995).
[CrossRef]

Physica B & C (1)

D. Beaglehole, "Ellipsometric study of the surface of simple liquids," Physica B & C 100, 163-174 (1980).
[CrossRef]

Rev. Sci. Instrum. (2)

S. N. Jasperson and S. E. Schnatterly, "An improved method for high reflectivity ellipsometry based on a new polarization modulation technique," Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

O. Archer, E. Bigan, and B. Drevillon, "Improvements of phase-modulated ellipsometry," Rev. Sci. Instrum. 60, 65-77 (1989).
[CrossRef]

Thin Solid Films (2)

M. K. Smit and J. W. Verhoof, "Accuracy analysis in multiple angle of incidence ellipsometry," Thin Solid Films 189, 193-203 (1990).
[CrossRef]

K. Vedam, "Spectroscopic ellipsometry: a historical overview," Thin Solid Films 313-314, 1-9 (1998).
[CrossRef]

Other (5)

D. Beaglehole, "Etching of 50nm photoresist sample, 100 pts per second," Examples in Ellipsometry, http://www.beaglehole.com/examples/ex11.pdf.

B. Drevillon, J. Y. Parey, M. Stchakovsky, R. Benferhat, Y. Josserand, and B. Schlayen, "Design of a new in situ spectroscopic phase modulated ellipsometer," in Multichamber and in-situ Processing of Electronic Material, R.S.Freund, ed., Proc. SPIE 1188, 174-184 (1989).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, 1999).
[PubMed]

J. Lekner, Theory of Reflection (Martinus Nijhoff, 1987).

D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 85th ed. (CRC Press, 2004).

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Figures (7)

Fig. 1
Fig. 1

Phase-modulated ellipsometer setup.

Fig. 2
Fig. 2

Dependence of ellipsometric parameters X and Y on the film thickness d for different values of film refractive index n in the range from 1.4 to 1.6. The substrate is silicon ( n = 3.877 , k = 0.016 ) with 20 Å layer of silicon oxide ( n = 1.465 ) on the top. Ambient media is air ( n = 1.0 ) , the angle of incidence is 70°, and the incident light wavelength is 632.8 nm .

Fig. 3
Fig. 3

Y d as a measure of the sensitivity of the PME to the film thickness change for an incident angle in the range from 40° to 80°. Film refractive index n = 1.55 . The substrate is the same as in Fig. 2.

Fig. 4
Fig. 4

X n as a measure of the sensitivity of the PME to refractive index change for film thickness in the range 1000 Å 1700 Å . The incident angle is 70°. The substrate is the same as in Fig. 2.

Fig. 5
Fig. 5

Fitting results for a 800 Å layer with refractive index n = 1.5 , measured with 0.02 precision for both X and Y values. The angle of incidence is 70°, and the substrate is the same as in Fig. 2.

Fig. 6
Fig. 6

Discrepancy of fitting for a 1250 Å layer with refractive index n = 1.55 for an angle of incidence in the range from 55° to 75°. The substrate is the same as in Fig. 2.

Fig. 7
Fig. 7

Thickness and the refractive index of PMMA hydrogel film in water ( n = 1.333 ) for pH values in the range from 5.0 to 5.9. The angle of incidence is 60°, the light wavelength is 632.8 nm . The substrate is the same as in Table 1.

Tables (1)

Tables Icon

Table 1 Measurement Results for a Dry Hydrogel Film a

Equations (8)

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

X = 2 Re ( ρ ) 1 + ρ 2 , Y = 2 Im ( ρ ) 1 + ρ 2
δ ( t ) = A sin ( ω t ) ,
I = I 0 ± X sin [ δ ( t ) ] ± Y cos [ δ ( t ) ] ,
X = 2 Re ( ρ ) 1 + ρ 2 = sin ( 2 Ψ ) cos ( Δ ) ,
Y = 2 Im ( ρ ) 1 + ρ 2 = sin ( 2 Ψ ) sin ( Δ ) .
sin [ A sin ( ω t ) ] = 2 J 1 ( A ) sin ( ω t ) + 2 J 3 ( A ) sin ( 3 ω t ) + ,
cos [ A sin ( ω t ) ] = J 0 ( A ) + 2 J 2 ( A ) cos ( 2 ω t ) + 2 J 4 ( A ) cos ( 4 ω t ) +
X = I ω 2 J 1 ( A ) I 0 , Y = I 2 ω 2 J 2 ( A ) I 0 .

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