Abstract

The optical constants of electron-beam evaporated boron from 6.8 to 900eV were calculated through transmittance measurements of boron thin films deposited onto carbon-coated microgrids or LiF substrates in ultrahigh-vacuum conditions. In the low-energy part of the spectrum the measurements were performed in situ on freshly deposited samples, whereas in the high-energy range the samples were exposed to the atmosphere before the measurements. The extinction coefficient was calculated directly from the transmittance data, and a Kramers–Kronig analysis that combined the current data with data from the literature was performed to determine the dispersive part of the index of refraction. Finally, two different sum-rule tests were performed that indicated the good consistency of the data.

© 2007 Optical Society of America

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  1. M. Fernández-Perea, J. I. Larruquert, J. A. Aznárez, J. A. Méndez, L. Poletto, A. M. Malvezzi, A. Giglia, and S. Nannarone, "Determination of optical constants of scandium films in the 20-1000eV range," J. Opt. Soc. Am. A 23, 2880-2887 (2006).
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    [Crossref]
  7. E. Kierzek-Pecold, J. Kolodziejczak, A. Michalak, andI. Pracka, "Optical constants of β-rhombohedral boron in the region 1eV-6eV," Electron Technol. 3, 219-225 (1970).
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    [Crossref]
  9. S. Labov, S. Bowyer, and G. Steele, "Boron and silicon: filters for the extreme ultraviolet," Appl. Opt. 24, 576-578 (1985).
    [Crossref]
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    [Crossref]
  11. M. A. McKernan, "Magnetron sputter deposition of boron and boron carbide," Surf. Coat. Technol. 49, 411-415 (1991).
    [Crossref]
  12. P. A. Kearney, J. M. Slaughter, and C. M. Falco, "Boron-based multilayers for soft x-ray optics," Proc. SPIE 1547, 63-70 (1991).
    [Crossref]
  13. J. M. Slaughter, P. A. Kearney, and C. M. Falco, "Characterization of Pd-B, Ag-B and Si-B interfaces," Proc. SPIE 1547, 71-79 (1991).
    [Crossref]
  14. P. A. Kearney, J. M. Slaughter, and C. M. Falco, "Materials for multilayer x-ray optics at wavelengths below 100Å," Opt. Eng. 30, 1076-1080 (1991).
    [Crossref]
  15. M. F. Ravet, F. Bridou, A. Raynal, B. Pardo, J. P. Chavineau, and J. M. André, "B/Si multilayers for soft x-ray and extreme ultraviolet optics," J. Appl. Phys. 89, 1145-1150 (2001).
    [Crossref]
  16. M. Bavdaz, A. Peacock, R. den Hartog, A. Poelaert, and P. Underwood, "The performance of transmission filters for EUV and soft x-ray astronomy," Proc. SPIE 2808, 301-312 (1996).
    [Crossref]
  17. C. Montcalm, P. A. Kearney, J. M. Slaughter, B. T. Sullivan, M. Chaker, H. Pepin, and C. M. Falco, "Survey of Ti-, B-, and Y-based soft x-ray-extreme ultraviolet multilayer mirrors for the 2- to 12-nm wavelength region," Appl. Opt. 35, 5134-5147 (1996).
    [Crossref] [PubMed]
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    [Crossref]
  19. J. A. Aznárez, J. I. Larruquert, and J. A. Méndez, "Far-ultraviolet absolute reflectometer for optical constant determination of ultrahigh vacuum prepared thin films," Rev. Sci. Instrum. 67, 497-502 (1996).
    [Crossref]
  20. S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Oxford U. Press, 1948).
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    [Crossref]
  22. E. M. Gullikson, S. Mrowka, and B. B. Kaufmann, "Recent developments in EUV reflectometry at the Advanced Light Source," Proc. SPIE 4343, 363-373 (2001).
    [Crossref]
  23. E. Gullikson, "X-rays interactions with matter," http://www.cxro.lbl.gov/opticallowbarconstants/.
  24. R. Soufli, S. Bajt, and E. M. Gullikson, "Optical constants of beryllium from photoabsorption measurements for x-ray optics applications," Proc. SPIE 3767, 251-258 (1999).
    [Crossref]
  25. O. M. Moon, B.-C. Kang, S.-B. Lee, and J.-H. Boo, "Temperature effect on structural properties of boron oxide thin films deposited by MOCVD method," Thin Solid Films 464-465, 164-169 (2004).
    [Crossref]
  26. C. D. Wagner, L. E. Davis, M. V. Zeller, J. A. Taylor, R. H. Raymond, and L. H. Gale, "Empirical atomic sensitivity factors for quantitative analysis by electron spectroscopy for chemical analysis," Surf. Interface Anal. 3, 211-225 (1981).
    [Crossref]
  27. A tabulated form of the data is available on request at the following email address: larruquert@ifa.cetef.csic.es.
  28. E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, "Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: applications to aluminum," Phys. Rev. B 22, 1612-1628 (1980).
    [Crossref]

2006 (1)

2004 (2)

2003 (1)

2001 (2)

E. M. Gullikson, S. Mrowka, and B. B. Kaufmann, "Recent developments in EUV reflectometry at the Advanced Light Source," Proc. SPIE 4343, 363-373 (2001).
[Crossref]

M. F. Ravet, F. Bridou, A. Raynal, B. Pardo, J. P. Chavineau, and J. M. André, "B/Si multilayers for soft x-ray and extreme ultraviolet optics," J. Appl. Phys. 89, 1145-1150 (2001).
[Crossref]

1999 (1)

R. Soufli, S. Bajt, and E. M. Gullikson, "Optical constants of beryllium from photoabsorption measurements for x-ray optics applications," Proc. SPIE 3767, 251-258 (1999).
[Crossref]

1998 (2)

J. H. Underwood and E. M. Gullikson, "High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50-1300eV energy region," J. Electron Spectrosc. Relat. Phenom. 92, 265-272 (1998).
[Crossref]

R. Soufli and E. Gullikson, "Absolute photoabsortion measurements of molybdenum in the range 60-930eV for optical constant determination," Appl. Opt. 37, 1713-1719 (1998).
[Crossref]

1996 (3)

C. Montcalm, P. A. Kearney, J. M. Slaughter, B. T. Sullivan, M. Chaker, H. Pepin, and C. M. Falco, "Survey of Ti-, B-, and Y-based soft x-ray-extreme ultraviolet multilayer mirrors for the 2- to 12-nm wavelength region," Appl. Opt. 35, 5134-5147 (1996).
[Crossref] [PubMed]

J. A. Aznárez, J. I. Larruquert, and J. A. Méndez, "Far-ultraviolet absolute reflectometer for optical constant determination of ultrahigh vacuum prepared thin films," Rev. Sci. Instrum. 67, 497-502 (1996).
[Crossref]

M. Bavdaz, A. Peacock, R. den Hartog, A. Poelaert, and P. Underwood, "The performance of transmission filters for EUV and soft x-ray astronomy," Proc. SPIE 2808, 301-312 (1996).
[Crossref]

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000eV, Z=1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[Crossref]

1991 (4)

M. A. McKernan, "Magnetron sputter deposition of boron and boron carbide," Surf. Coat. Technol. 49, 411-415 (1991).
[Crossref]

P. A. Kearney, J. M. Slaughter, and C. M. Falco, "Boron-based multilayers for soft x-ray optics," Proc. SPIE 1547, 63-70 (1991).
[Crossref]

J. M. Slaughter, P. A. Kearney, and C. M. Falco, "Characterization of Pd-B, Ag-B and Si-B interfaces," Proc. SPIE 1547, 71-79 (1991).
[Crossref]

P. A. Kearney, J. M. Slaughter, and C. M. Falco, "Materials for multilayer x-ray optics at wavelengths below 100Å," Opt. Eng. 30, 1076-1080 (1991).
[Crossref]

1990 (1)

D. M. Makowiecki, A. F. Jankowski, M. A. McKernan, and R. J. Foreman, "Magnetron sputtered boron films and Ti/B multilayer structures," J. Vac. Sci. Technol. A 8, 3910-3913 (1990).
[Crossref]

1985 (1)

1981 (1)

C. D. Wagner, L. E. Davis, M. V. Zeller, J. A. Taylor, R. H. Raymond, and L. H. Gale, "Empirical atomic sensitivity factors for quantitative analysis by electron spectroscopy for chemical analysis," Surf. Interface Anal. 3, 211-225 (1981).
[Crossref]

1980 (1)

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, "Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: applications to aluminum," Phys. Rev. B 22, 1612-1628 (1980).
[Crossref]

1975 (1)

N. Morita and A. Yamamoto, "Optical and electrical properties of boron," Jpn. J. Appl. Phys. 14, 825-831 (1975).
[Crossref]

1970 (1)

E. Kierzek-Pecold, J. Kolodziejczak, A. Michalak, andI. Pracka, "Optical constants of β-rhombohedral boron in the region 1eV-6eV," Electron Technol. 3, 219-225 (1970).

1958 (1)

W. G. Spitzer and W. Kaiser, "Optical properties of crystalline boron," Phys. Rev. Lett. 1, 230-232 (1958).
[Crossref]

1954 (1)

N. Morita, "Optical constants of boron in visible and near-infrared," J. Sci. Res. Inst. 48, 8-12 (1954).

Appl. Opt. (4)

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000eV, Z=1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[Crossref]

Electron Technol. (1)

E. Kierzek-Pecold, J. Kolodziejczak, A. Michalak, andI. Pracka, "Optical constants of β-rhombohedral boron in the region 1eV-6eV," Electron Technol. 3, 219-225 (1970).

J. Appl. Phys. (1)

M. F. Ravet, F. Bridou, A. Raynal, B. Pardo, J. P. Chavineau, and J. M. André, "B/Si multilayers for soft x-ray and extreme ultraviolet optics," J. Appl. Phys. 89, 1145-1150 (2001).
[Crossref]

J. Electron Spectrosc. Relat. Phenom. (1)

J. H. Underwood and E. M. Gullikson, "High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50-1300eV energy region," J. Electron Spectrosc. Relat. Phenom. 92, 265-272 (1998).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Sci. Res. Inst. (1)

N. Morita, "Optical constants of boron in visible and near-infrared," J. Sci. Res. Inst. 48, 8-12 (1954).

J. Vac. Sci. Technol. A (1)

D. M. Makowiecki, A. F. Jankowski, M. A. McKernan, and R. J. Foreman, "Magnetron sputtered boron films and Ti/B multilayer structures," J. Vac. Sci. Technol. A 8, 3910-3913 (1990).
[Crossref]

Jpn. J. Appl. Phys. (1)

N. Morita and A. Yamamoto, "Optical and electrical properties of boron," Jpn. J. Appl. Phys. 14, 825-831 (1975).
[Crossref]

Opt. Eng. (1)

P. A. Kearney, J. M. Slaughter, and C. M. Falco, "Materials for multilayer x-ray optics at wavelengths below 100Å," Opt. Eng. 30, 1076-1080 (1991).
[Crossref]

Phys. Rev. B (1)

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, "Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: applications to aluminum," Phys. Rev. B 22, 1612-1628 (1980).
[Crossref]

Phys. Rev. Lett. (1)

W. G. Spitzer and W. Kaiser, "Optical properties of crystalline boron," Phys. Rev. Lett. 1, 230-232 (1958).
[Crossref]

Proc. SPIE (5)

P. A. Kearney, J. M. Slaughter, and C. M. Falco, "Boron-based multilayers for soft x-ray optics," Proc. SPIE 1547, 63-70 (1991).
[Crossref]

J. M. Slaughter, P. A. Kearney, and C. M. Falco, "Characterization of Pd-B, Ag-B and Si-B interfaces," Proc. SPIE 1547, 71-79 (1991).
[Crossref]

E. M. Gullikson, S. Mrowka, and B. B. Kaufmann, "Recent developments in EUV reflectometry at the Advanced Light Source," Proc. SPIE 4343, 363-373 (2001).
[Crossref]

R. Soufli, S. Bajt, and E. M. Gullikson, "Optical constants of beryllium from photoabsorption measurements for x-ray optics applications," Proc. SPIE 3767, 251-258 (1999).
[Crossref]

M. Bavdaz, A. Peacock, R. den Hartog, A. Poelaert, and P. Underwood, "The performance of transmission filters for EUV and soft x-ray astronomy," Proc. SPIE 2808, 301-312 (1996).
[Crossref]

Rev. Sci. Instrum. (1)

J. A. Aznárez, J. I. Larruquert, and J. A. Méndez, "Far-ultraviolet absolute reflectometer for optical constant determination of ultrahigh vacuum prepared thin films," Rev. Sci. Instrum. 67, 497-502 (1996).
[Crossref]

Surf. Coat. Technol. (1)

M. A. McKernan, "Magnetron sputter deposition of boron and boron carbide," Surf. Coat. Technol. 49, 411-415 (1991).
[Crossref]

Surf. Interface Anal. (1)

C. D. Wagner, L. E. Davis, M. V. Zeller, J. A. Taylor, R. H. Raymond, and L. H. Gale, "Empirical atomic sensitivity factors for quantitative analysis by electron spectroscopy for chemical analysis," Surf. Interface Anal. 3, 211-225 (1981).
[Crossref]

Thin Solid Films (1)

O. M. Moon, B.-C. Kang, S.-B. Lee, and J.-H. Boo, "Temperature effect on structural properties of boron oxide thin films deposited by MOCVD method," Thin Solid Films 464-465, 164-169 (2004).
[Crossref]

Other (3)

E. Gullikson, "X-rays interactions with matter," http://www.cxro.lbl.gov/opticallowbarconstants/.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Oxford U. Press, 1948).

A tabulated form of the data is available on request at the following email address: larruquert@ifa.cetef.csic.es.

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Figures (8)

Fig. 1
Fig. 1

Transmittance of substrates used in different spectral ranges as a function of the photon energy on log scale.

Fig. 2
Fig. 2

(a) Transmittance of B films of different thickness measured in situ divided by the transmittance of the substrate (log scale), versus photon energy. The thickness of each film is indicated. Squares, films deposited onto LiF substrates; crosses, films on C-grid substrates. (b) Transmittance of the three B films of different thickness measured ex situ divided by the transmittance of the substrate, versus photon energy (log scale). The transmittance of the 100 nm -thick film was taken from [9] and is displayed for comparison.

Fig. 3
Fig. 3

Transmittance ratio T f s T s (log scale) versus thickness at different photon energies. The corresponding fits are shown as dash lines.

Fig. 4
Fig. 4

Log-log plot of the extinction coefficient of B obtained from the transmittance measurements. Data calculated from [18] with ρ = 2.1 g cm 3 are also plotted for comparison. The region around the B K edge is presented in detail in the inset.

Fig. 5
Fig. 5

Log-log plot of the extinction coefficient data set used for the KK analysis.

Fig. 6
Fig. 6

Dispersive part of the refractive index versus photon energy in the low-energy part of the studied range.

Fig. 7
Fig. 7

Log-log plot of the index of refraction unit decrement δ = 1 n versus photon energy in the high-energy part of the studied range.

Fig. 8
Fig. 8

Effective number of electrons contributing to the extinction coefficient versus photon energy.

Tables (2)

Tables Icon

Table 1 Coefficients of Quadratic Fits of n and k versus Photon Energy Corresponding to 6.8 23.1 eV

Tables Icon

Table 2 Coefficients of Fits ln ( Y ) = A ln ( X ) + B for Y = δ , k and X = E Corresponding to the Indicated Intervals

Equations (4)

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

ln ( T f s T s ) A + ( 4 π k λ ) d ,
n ( E ) 1 = 2 π P 0 E k ( E ) E 2 E 2 d E ,
n eff ( E ) = 4 ε 0 m π N at e 2 h 2 0 E E k ( E ) d E ,
ζ = 0 [ n ( E ) 1 ] d E 0 n ( E ) 1 d E .

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