Abstract

We demonstrate a technique for determining optical constants of materials in the extreme UV from the ratio of p-polarized to s-polarized reflectance. The measurements are based on laser-generated high-order harmonics, which have easily rotatable linear polarization but that are prone to brightness fluctuations and systematic drifts during measurement. Rather than measure the absolute reflectance, we extract the optical constants of a material from the ratio of p-polarized to s-polarized reflectance at multiple incident angles. This has the advantage of dividing out long-term fluctuations and possible systematic errors. We show that the reflectance ratio is as sensitive as the absolute reflectance to material optical properties.

© 2009 Optical Society of America

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  1. B. Kjornrattanawanich, R. Soufli, S. Bajt, D. L. Windt, and J. F. Seely, Proc. SPIE 5538, 17 (2004).
    [CrossRef]
  2. R. Soufli, A. L. Aquila, F. Salmassi, M. Fernández-Perea, and E. M. Gullikson, Appl. Opt. 47, 4633 (2008).
    [CrossRef] [PubMed]
  3. D. Garoli, F. Frassetto, G. Monaco, P. Nicolosi, M. G. Pelizzo, F. Rigato, V. Rigato, A. Giglia, and S. Nannarone, Appl. Opt. 45, 5642 (2006).
    [CrossRef] [PubMed]
  4. R. Soufli and E. Gullikson, Appl. Opt. 36, 5499 (1997).
    [CrossRef] [PubMed]
  5. J. B. Kortright and D. L. Windt, Appl. Opt. 27, 2841 (1988).
    [CrossRef] [PubMed]
  6. N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
    [CrossRef] [PubMed]
  7. D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
    [CrossRef]
  8. R. F. Miller and A. J. Taylor, J. Phys. D 4, 1419 (1971).
    [CrossRef]
  9. R. F. Miller, L. S. Julien, and A. J. Taylor, J. Phys. F 4, 2338 (1974).
    [CrossRef]
  10. H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
    [CrossRef]
  11. D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
    [CrossRef]
  12. In this measurement, our samples typically become contaminated with a thin layer of hydrocarbons during transfer from the deposition chamber to the measurement chamber. Our algorithm also had to determine the constants for the contaminant layer (the thickness of the contaminant having been characterized by a separate ellipsometry measurement) to extract the constants for the SiO2 layer. We used the optical constants of carbon for this first layer when determining the constants for SiO2. Conversely, we obtained the optical constants of carbon when the constants for SiO2 were used for the layer beneath the contaminant. In the future, we plan to do in situ deposition and measurement (an advantage for our instrument) for which sample contamination should be less of an issue.
  13. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).
  14. A. Vasicek, Optics of Thin Films (North-Holland, 1960).
  15. B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993).
    [CrossRef]

2008 (2)

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

R. Soufli, A. L. Aquila, F. Salmassi, M. Fernández-Perea, and E. M. Gullikson, Appl. Opt. 47, 4633 (2008).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

B. Kjornrattanawanich, R. Soufli, S. Bajt, D. L. Windt, and J. F. Seely, Proc. SPIE 5538, 17 (2004).
[CrossRef]

1998 (1)

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

1997 (1)

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

1988 (1)

1974 (1)

R. F. Miller, L. S. Julien, and A. J. Taylor, J. Phys. F 4, 2338 (1974).
[CrossRef]

1971 (1)

R. F. Miller and A. J. Taylor, J. Phys. D 4, 1419 (1971).
[CrossRef]

1959 (1)

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

1952 (1)

D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
[CrossRef]

Allred, D. D.

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Aquila, A. L.

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
[CrossRef]

Bajt, S.

B. Kjornrattanawanich, R. Soufli, S. Bajt, D. L. Windt, and J. F. Seely, Proc. SPIE 5538, 17 (2004).
[CrossRef]

Brimhall, N.

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

Dorr, M.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Drescher, M.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Fernández-Perea, M.

Frassetto, F.

Garoli, D.

Giglia, A.

Gullikson, E.

Gullikson, E. M.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Heinzmann, U.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

Herrick, N.

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Julien, L. S.

R. F. Miller, L. S. Julien, and A. J. Taylor, J. Phys. F 4, 2338 (1974).
[CrossRef]

Kjornrattanawanich, B.

B. Kjornrattanawanich, R. Soufli, S. Bajt, D. L. Windt, and J. F. Seely, Proc. SPIE 5538, 17 (2004).
[CrossRef]

Kleineberg, U.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Kortright, J. B.

Ludwig, J.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Miller, R. F.

R. F. Miller, L. S. Julien, and A. J. Taylor, J. Phys. F 4, 2338 (1974).
[CrossRef]

R. F. Miller and A. J. Taylor, J. Phys. D 4, 1419 (1971).
[CrossRef]

Monaco, G.

Nannarone, S.

Nickles, P.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Nicolosi, P.

Peatross, J.

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Pelizzo, M. G.

Philipp, H. R.

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

Rigato, F.

Rigato, V.

Salmassi, F.

Sandner, W.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Schlegel, T.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Schulze, D.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Seely, J. F.

B. Kjornrattanawanich, R. Soufli, S. Bajt, D. L. Windt, and J. F. Seely, Proc. SPIE 5538, 17 (2004).
[CrossRef]

Sommerer, G.

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Soufli, R.

Taft, E. A.

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

Taylor, A. J.

R. F. Miller, L. S. Julien, and A. J. Taylor, J. Phys. F 4, 2338 (1974).
[CrossRef]

R. F. Miller and A. J. Taylor, J. Phys. D 4, 1419 (1971).
[CrossRef]

Turley, R. S.

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Turner, M.

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Vasicek, A.

A. Vasicek, Optics of Thin Films (North-Holland, 1960).

Ware, M.

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Windt, D. L.

B. Kjornrattanawanich, R. Soufli, S. Bajt, D. L. Windt, and J. F. Seely, Proc. SPIE 5538, 17 (2004).
[CrossRef]

J. B. Kortright and D. L. Windt, Appl. Opt. 27, 2841 (1988).
[CrossRef] [PubMed]

Appl. Opt. (4)

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

J. Phys. D (1)

R. F. Miller and A. J. Taylor, J. Phys. D 4, 1419 (1971).
[CrossRef]

J. Phys. F (1)

R. F. Miller, L. S. Julien, and A. J. Taylor, J. Phys. F 4, 2338 (1974).
[CrossRef]

Phys. Rev. (1)

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

Phys. Rev. A (1)

D. Schulze, M. Dorr, G. Sommerer, J. Ludwig, P. Nickles, T. Schlegel, W. Sandner, M. Drescher, U. Kleineberg, and U. Heinzmann, Phys. Rev. A 57, 3003 (1998).
[CrossRef]

Proc. Phys. Soc. London Sect. B (1)

D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
[CrossRef]

Proc. SPIE (1)

B. Kjornrattanawanich, R. Soufli, S. Bajt, D. L. Windt, and J. F. Seely, Proc. SPIE 5538, 17 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

N. Brimhall, M. Turner, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, and J. Peatross, Rev. Sci. Instrum. 79, 103108 (2008).
[CrossRef] [PubMed]

Other (3)

In this measurement, our samples typically become contaminated with a thin layer of hydrocarbons during transfer from the deposition chamber to the measurement chamber. Our algorithm also had to determine the constants for the contaminant layer (the thickness of the contaminant having been characterized by a separate ellipsometry measurement) to extract the constants for the SiO2 layer. We used the optical constants of carbon for this first layer when determining the constants for SiO2. Conversely, we obtained the optical constants of carbon when the constants for SiO2 were used for the layer beneath the contaminant. In the future, we plan to do in situ deposition and measurement (an advantage for our instrument) for which sample contamination should be less of an issue.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

A. Vasicek, Optics of Thin Films (North-Holland, 1960).

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Figures (2)

Fig. 1
Fig. 1

Measured and calculated s- and p-polarized absolute reflectances and the ratio of p-polarized to s-polarized reflectance from a silica sample at a wavelength of 29.6 nm. The error bars represent the average relative residual for each measured data set.

Fig. 2
Fig. 2

Calculated plots of s-polarized absolute reflectance and the ratio of p-polarized to s-polarized reflectance from a single 1-nm-thick layer of SiO 2 on Si. Solid curves show the accepted values of n = 0.911 and κ = 0.085 . Dashed curves show the extent of the change when (a) n is varied by ±0.05 with κ held fixed, and (b) κ is varied by ±0.05 with n held fixed.

Equations (6)

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

[ a 11 s a 12 s a 21 s a 22 s ] = 1 2 N 0   sin   θ 0 [ N 0   cos   θ 0 1 N 0   cos   θ 0 1 ]
× j = 1 k [ sin   β j i   cos   β j / ( N j   sin   θ j ) i N j sin   θ j   cos   β j sin   θ j ]
× [ 1 0 N k + 1   sin   θ k + 1 0 ] .
[ a 11 p a 12 p a 21 p a 22 p ] = 1 2 N 0   sin   θ 0 [ N 0 sin   θ 0 N 0 sin   θ 0 ]
× j = 1 k [ sin   β j i   cos   β j   sin   θ j / N j i N j   cos   β j / sin   θ j sin   θ j ]
× [ sin   θ k + 1 0 N k + 1 0 ] ,

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