Abstract

The far-UV reflectance of thin unoxidized aluminum films prepared and maintained in ultra-high-vacuum conditions was measured versus the angle of incidence, and the complex refractive index was obtained from those measurements on several wavelengths from 82.6 to 113.5 nm. Measurements were made on two perpendicular planes of incidence to deal with the unknown of the polarization state of the radiation beam. The surface roughness was characterized by atomic force microscopy. The refractive index is obtained for the first time, to our knowledge, from direct optical measurements in this spectral range. Current results match well the former values in the literature that were calculated through the Kramers–Kronig analysis by using in the above interval reflectances estimated from electron-energy-loss spectra and from optical measurements on surfaces of unstated roughness.

© 1995 Optical Society of America

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References

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  1. Lyman, Assessment Study (European Space Agency, Paris, 1985), vol. SCI(85) 4.
  2. G. Hass, W. R. Hunter, “Calculated reflectance of aluminum-overcoated iridium in the vacuum ultraviolet from 500 Å to 2000 Å,” Appl. Opt. 6, 2097–2100 (1967).
    [CrossRef] [PubMed]
  3. E. Shiles, T. Sasaki, M. Inokuti, 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]
  4. R. P. Madden, L. R. Canfield, G. Hass, “On the vacuum-ultraviolet reflectance of evaporated aluminum before and during oxidation,” J. Opt. Soc. Am. 53, 620–625 (1963).
    [CrossRef]
  5. A. N. Bunner, “Optical coating in space, final report,” Perkin-Elmer Engineering Report ER-591 (Perkin-Elmer Corporation, Space Science Division, Oct.1983), pp. 47, 156.
  6. R. C. Vehse, E. T. Arakawa, J. L. Stanford, “Normal-incidence reflectance of aluminum films in the wavelength region 800–2000 Å,” J. Opt. Soc. Am. 57, 551–552 (1967).
    [CrossRef] [PubMed]
  7. A. Daudé, S. Robin, “Appareillage permettant la détermination dans l’ultraviolet lointain des constantes optiques de couches évaporée sous ultra-vide,” Rev. Phys. Appl. 1, 120–122 (1966).
    [CrossRef]
  8. A. Daude, A. Savary, G. Jezequel, S. Robin, “Propriétés optiques de l’aluminium évaporé en ultravide entre 500 et 1400 Å,” C. R. Acad. Sci. B 269, 901–904 (1969).
  9. B. P. Feuerbacher, W. Steinmann, “Reflectance of evaporated aluminium films in the 1050–1600 Å region, and the influence of the surface plasmon,” Opt. Commun. 1, 81–85 (1969).
    [CrossRef]
  10. J. G. Endriz, W. E. Spicer, “Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
    [CrossRef]
  11. R. La Villa, H. Mendlowitz, “Optical constants of aluminum in vacuum ultraviolet,” Phys. Rev. Lett. 9, 149–150 (1962).
    [CrossRef]
  12. J. I. Larruquert, J. A. Méndez, J. A. Aznárez, “Far UV reflectance of UHV prepared Al films and its degradation after exposure to O2,” Appl. Opt. 33, 3518–3522 (1994).
    [CrossRef] [PubMed]
  13. J. I. Larruquert, Ph.D. dissertation (Universidad Autónoma de Madrid, Madrid, 1993).
  14. T. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” Natl. Stand. Ref. Data Ser. Natl. Bur. Stand.68 (U.S. Government Printing Office, Washington, D.C., 1980).
  15. J. S. Edmends, C. N. Maldé, S. J. B. Corrigan, “Measurements of the far ultraviolet reflectivity of evaporated aluminium films under exposure to O2, H2O, CO, and CO2,” Vacuum 40, 471–475 (1990).
    [CrossRef]
  16. E. Kretschmann, E. Kröger, “Reflection and transmission of light by a rough surface, including results for surface-plasmon effects,” J. Opt. Soc. Am. 65, 150–154 (1975).
    [CrossRef]
  17. R. Schiffer, “Reflectivity of a slightly rough surface,” Appl. Opt. 26, 704–712 (1987).
    [CrossRef] [PubMed]
  18. H. E. Bennett, J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961).
    [CrossRef]
  19. G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967); G. R. Valenzuela, “The effective reflection coefficients in forward scatter from a dielectric slightly rough surface,” Proc. IEEE 58, 1279 (1970).
    [CrossRef]
  20. G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surface,” Phys. Rev. B 15, 2371–2383 (1977).
    [CrossRef]
  21. P. Croce, “Sur l’effet des couches trés minces et des rugosités sur la réflexion, la transmission et la diffusion de la lumiére par un dioptre,” J. Opt. 8, 127–139 (1977).
    [CrossRef]
  22. A. Humbert, J. Hanus, “An ATR analysis of surface roughness induced by electron bombardment,” Surf. Sci. 129, 265–280 (1983).
    [CrossRef]
  23. W. L. Mochán, R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. II. Applications,” Phys. Rev. B 32, 4989–5001 (1985).
    [CrossRef]
  24. C. Efitmiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
    [CrossRef]
  25. J. J. Greffet, “Scattering of electromagnetic waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988).
    [CrossRef]
  26. P. Croce, “Complément à l’étude de l’effet des couches minces sur la réflexion, la transmission et la diffusion de la lumiére,” J. Opt. 9, 61–63 (1978).
    [CrossRef]
  27. T. T. Cole, F. Oppenheimer, “Polarization by reflection and some optical constants in the extreme ultraviolet,” Appl. Opt. 1, 709–710 (1962).
    [CrossRef]
  28. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten, 18-2 (Fachinformationszentrum Energie-Physik-Mathematik GmbH, Karlsruhe, Germany, 1981).

1994

1990

J. S. Edmends, C. N. Maldé, S. J. B. Corrigan, “Measurements of the far ultraviolet reflectivity of evaporated aluminium films under exposure to O2, H2O, CO, and CO2,” Vacuum 40, 471–475 (1990).
[CrossRef]

1988

J. J. Greffet, “Scattering of electromagnetic waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988).
[CrossRef]

1987

C. Efitmiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

R. Schiffer, “Reflectivity of a slightly rough surface,” Appl. Opt. 26, 704–712 (1987).
[CrossRef] [PubMed]

1985

W. L. Mochán, R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. II. Applications,” Phys. Rev. B 32, 4989–5001 (1985).
[CrossRef]

1983

A. Humbert, J. Hanus, “An ATR analysis of surface roughness induced by electron bombardment,” Surf. Sci. 129, 265–280 (1983).
[CrossRef]

1980

E. Shiles, T. Sasaki, M. Inokuti, 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]

1978

P. Croce, “Complément à l’étude de l’effet des couches minces sur la réflexion, la transmission et la diffusion de la lumiére,” J. Opt. 9, 61–63 (1978).
[CrossRef]

1977

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surface,” Phys. Rev. B 15, 2371–2383 (1977).
[CrossRef]

P. Croce, “Sur l’effet des couches trés minces et des rugosités sur la réflexion, la transmission et la diffusion de la lumiére par un dioptre,” J. Opt. 8, 127–139 (1977).
[CrossRef]

1975

1971

J. G. Endriz, W. E. Spicer, “Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

1969

A. Daude, A. Savary, G. Jezequel, S. Robin, “Propriétés optiques de l’aluminium évaporé en ultravide entre 500 et 1400 Å,” C. R. Acad. Sci. B 269, 901–904 (1969).

B. P. Feuerbacher, W. Steinmann, “Reflectance of evaporated aluminium films in the 1050–1600 Å region, and the influence of the surface plasmon,” Opt. Commun. 1, 81–85 (1969).
[CrossRef]

1967

G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967); G. R. Valenzuela, “The effective reflection coefficients in forward scatter from a dielectric slightly rough surface,” Proc. IEEE 58, 1279 (1970).
[CrossRef]

G. Hass, W. R. Hunter, “Calculated reflectance of aluminum-overcoated iridium in the vacuum ultraviolet from 500 Å to 2000 Å,” Appl. Opt. 6, 2097–2100 (1967).
[CrossRef] [PubMed]

R. C. Vehse, E. T. Arakawa, J. L. Stanford, “Normal-incidence reflectance of aluminum films in the wavelength region 800–2000 Å,” J. Opt. Soc. Am. 57, 551–552 (1967).
[CrossRef] [PubMed]

1966

A. Daudé, S. Robin, “Appareillage permettant la détermination dans l’ultraviolet lointain des constantes optiques de couches évaporée sous ultra-vide,” Rev. Phys. Appl. 1, 120–122 (1966).
[CrossRef]

1963

1962

R. La Villa, H. Mendlowitz, “Optical constants of aluminum in vacuum ultraviolet,” Phys. Rev. Lett. 9, 149–150 (1962).
[CrossRef]

T. T. Cole, F. Oppenheimer, “Polarization by reflection and some optical constants in the extreme ultraviolet,” Appl. Opt. 1, 709–710 (1962).
[CrossRef]

1961

Agarwal, G. S.

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surface,” Phys. Rev. B 15, 2371–2383 (1977).
[CrossRef]

Arakawa, E. T.

Aznárez, J. A.

Barrera, R. G.

W. L. Mochán, R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. II. Applications,” Phys. Rev. B 32, 4989–5001 (1985).
[CrossRef]

Bennett, H. E.

Bunner, A. N.

A. N. Bunner, “Optical coating in space, final report,” Perkin-Elmer Engineering Report ER-591 (Perkin-Elmer Corporation, Space Science Division, Oct.1983), pp. 47, 156.

Canfield, L. R.

Cole, T. T.

Corliss, C. H.

T. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” Natl. Stand. Ref. Data Ser. Natl. Bur. Stand.68 (U.S. Government Printing Office, Washington, D.C., 1980).

Corrigan, S. J. B.

J. S. Edmends, C. N. Maldé, S. J. B. Corrigan, “Measurements of the far ultraviolet reflectivity of evaporated aluminium films under exposure to O2, H2O, CO, and CO2,” Vacuum 40, 471–475 (1990).
[CrossRef]

Croce, P.

P. Croce, “Complément à l’étude de l’effet des couches minces sur la réflexion, la transmission et la diffusion de la lumiére,” J. Opt. 9, 61–63 (1978).
[CrossRef]

P. Croce, “Sur l’effet des couches trés minces et des rugosités sur la réflexion, la transmission et la diffusion de la lumiére par un dioptre,” J. Opt. 8, 127–139 (1977).
[CrossRef]

Daude, A.

A. Daude, A. Savary, G. Jezequel, S. Robin, “Propriétés optiques de l’aluminium évaporé en ultravide entre 500 et 1400 Å,” C. R. Acad. Sci. B 269, 901–904 (1969).

Daudé, A.

A. Daudé, S. Robin, “Appareillage permettant la détermination dans l’ultraviolet lointain des constantes optiques de couches évaporée sous ultra-vide,” Rev. Phys. Appl. 1, 120–122 (1966).
[CrossRef]

Edmends, J. S.

J. S. Edmends, C. N. Maldé, S. J. B. Corrigan, “Measurements of the far ultraviolet reflectivity of evaporated aluminium films under exposure to O2, H2O, CO, and CO2,” Vacuum 40, 471–475 (1990).
[CrossRef]

Efitmiu, C.

C. Efitmiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

Endriz, J. G.

J. G. Endriz, W. E. Spicer, “Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

Feuerbacher, B. P.

B. P. Feuerbacher, W. Steinmann, “Reflectance of evaporated aluminium films in the 1050–1600 Å region, and the influence of the surface plasmon,” Opt. Commun. 1, 81–85 (1969).
[CrossRef]

Greffet, J. J.

J. J. Greffet, “Scattering of electromagnetic waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988).
[CrossRef]

Hanus, J.

A. Humbert, J. Hanus, “An ATR analysis of surface roughness induced by electron bombardment,” Surf. Sci. 129, 265–280 (1983).
[CrossRef]

Hass, G.

Humbert, A.

A. Humbert, J. Hanus, “An ATR analysis of surface roughness induced by electron bombardment,” Surf. Sci. 129, 265–280 (1983).
[CrossRef]

Hunter, W. R.

Inokuti, M.

E. Shiles, T. Sasaki, M. Inokuti, 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]

Jezequel, G.

A. Daude, A. Savary, G. Jezequel, S. Robin, “Propriétés optiques de l’aluminium évaporé en ultravide entre 500 et 1400 Å,” C. R. Acad. Sci. B 269, 901–904 (1969).

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten, 18-2 (Fachinformationszentrum Energie-Physik-Mathematik GmbH, Karlsruhe, Germany, 1981).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten, 18-2 (Fachinformationszentrum Energie-Physik-Mathematik GmbH, Karlsruhe, Germany, 1981).

Kretschmann, E.

Kröger, E.

La Villa, R.

R. La Villa, H. Mendlowitz, “Optical constants of aluminum in vacuum ultraviolet,” Phys. Rev. Lett. 9, 149–150 (1962).
[CrossRef]

Larruquert, J. I.

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten, 18-2 (Fachinformationszentrum Energie-Physik-Mathematik GmbH, Karlsruhe, Germany, 1981).

Madden, R. P.

Maldé, C. N.

J. S. Edmends, C. N. Maldé, S. J. B. Corrigan, “Measurements of the far ultraviolet reflectivity of evaporated aluminium films under exposure to O2, H2O, CO, and CO2,” Vacuum 40, 471–475 (1990).
[CrossRef]

Martin, G. A.

T. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” Natl. Stand. Ref. Data Ser. Natl. Bur. Stand.68 (U.S. Government Printing Office, Washington, D.C., 1980).

Méndez, J. A.

Mendlowitz, H.

R. La Villa, H. Mendlowitz, “Optical constants of aluminum in vacuum ultraviolet,” Phys. Rev. Lett. 9, 149–150 (1962).
[CrossRef]

Mochán, W. L.

W. L. Mochán, R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. II. Applications,” Phys. Rev. B 32, 4989–5001 (1985).
[CrossRef]

Oppenheimer, F.

Porteus, J. O.

Reader, T.

T. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” Natl. Stand. Ref. Data Ser. Natl. Bur. Stand.68 (U.S. Government Printing Office, Washington, D.C., 1980).

Robin, S.

A. Daude, A. Savary, G. Jezequel, S. Robin, “Propriétés optiques de l’aluminium évaporé en ultravide entre 500 et 1400 Å,” C. R. Acad. Sci. B 269, 901–904 (1969).

A. Daudé, S. Robin, “Appareillage permettant la détermination dans l’ultraviolet lointain des constantes optiques de couches évaporée sous ultra-vide,” Rev. Phys. Appl. 1, 120–122 (1966).
[CrossRef]

Sasaki, T.

E. Shiles, T. Sasaki, M. Inokuti, 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]

Savary, A.

A. Daude, A. Savary, G. Jezequel, S. Robin, “Propriétés optiques de l’aluminium évaporé en ultravide entre 500 et 1400 Å,” C. R. Acad. Sci. B 269, 901–904 (1969).

Schiffer, R.

Shiles, E.

E. Shiles, T. Sasaki, M. Inokuti, 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]

Smith, D. Y.

E. Shiles, T. Sasaki, M. Inokuti, 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]

Spicer, W. E.

J. G. Endriz, W. E. Spicer, “Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

Stanford, J. L.

Steinmann, W.

B. P. Feuerbacher, W. Steinmann, “Reflectance of evaporated aluminium films in the 1050–1600 Å region, and the influence of the surface plasmon,” Opt. Commun. 1, 81–85 (1969).
[CrossRef]

Valenzuela, G. R.

G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967); G. R. Valenzuela, “The effective reflection coefficients in forward scatter from a dielectric slightly rough surface,” Proc. IEEE 58, 1279 (1970).
[CrossRef]

Vehse, R. C.

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten, 18-2 (Fachinformationszentrum Energie-Physik-Mathematik GmbH, Karlsruhe, Germany, 1981).

Welland, G. V.

C. Efitmiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

Wiese, W. L.

T. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” Natl. Stand. Ref. Data Ser. Natl. Bur. Stand.68 (U.S. Government Printing Office, Washington, D.C., 1980).

Appl. Opt.

C. R. Acad. Sci. B

A. Daude, A. Savary, G. Jezequel, S. Robin, “Propriétés optiques de l’aluminium évaporé en ultravide entre 500 et 1400 Å,” C. R. Acad. Sci. B 269, 901–904 (1969).

IEEE Trans. Antennas Propag.

G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967); G. R. Valenzuela, “The effective reflection coefficients in forward scatter from a dielectric slightly rough surface,” Proc. IEEE 58, 1279 (1970).
[CrossRef]

C. Efitmiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

J. Opt.

P. Croce, “Sur l’effet des couches trés minces et des rugosités sur la réflexion, la transmission et la diffusion de la lumiére par un dioptre,” J. Opt. 8, 127–139 (1977).
[CrossRef]

P. Croce, “Complément à l’étude de l’effet des couches minces sur la réflexion, la transmission et la diffusion de la lumiére,” J. Opt. 9, 61–63 (1978).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

B. P. Feuerbacher, W. Steinmann, “Reflectance of evaporated aluminium films in the 1050–1600 Å region, and the influence of the surface plasmon,” Opt. Commun. 1, 81–85 (1969).
[CrossRef]

Phys. Rev. B

J. G. Endriz, W. E. Spicer, “Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

E. Shiles, T. Sasaki, M. Inokuti, 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]

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surface,” Phys. Rev. B 15, 2371–2383 (1977).
[CrossRef]

J. J. Greffet, “Scattering of electromagnetic waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988).
[CrossRef]

W. L. Mochán, R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. II. Applications,” Phys. Rev. B 32, 4989–5001 (1985).
[CrossRef]

Phys. Rev. Lett.

R. La Villa, H. Mendlowitz, “Optical constants of aluminum in vacuum ultraviolet,” Phys. Rev. Lett. 9, 149–150 (1962).
[CrossRef]

Rev. Phys. Appl.

A. Daudé, S. Robin, “Appareillage permettant la détermination dans l’ultraviolet lointain des constantes optiques de couches évaporée sous ultra-vide,” Rev. Phys. Appl. 1, 120–122 (1966).
[CrossRef]

Surf. Sci.

A. Humbert, J. Hanus, “An ATR analysis of surface roughness induced by electron bombardment,” Surf. Sci. 129, 265–280 (1983).
[CrossRef]

Vacuum

J. S. Edmends, C. N. Maldé, S. J. B. Corrigan, “Measurements of the far ultraviolet reflectivity of evaporated aluminium films under exposure to O2, H2O, CO, and CO2,” Vacuum 40, 471–475 (1990).
[CrossRef]

Other

A. N. Bunner, “Optical coating in space, final report,” Perkin-Elmer Engineering Report ER-591 (Perkin-Elmer Corporation, Space Science Division, Oct.1983), pp. 47, 156.

J. I. Larruquert, Ph.D. dissertation (Universidad Autónoma de Madrid, Madrid, 1993).

T. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” Natl. Stand. Ref. Data Ser. Natl. Bur. Stand.68 (U.S. Government Printing Office, Washington, D.C., 1980).

Lyman, Assessment Study (European Space Agency, Paris, 1985), vol. SCI(85) 4.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten, 18-2 (Fachinformationszentrum Energie-Physik-Mathematik GmbH, Karlsruhe, Germany, 1981).

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Figures (4)

Fig. 1
Fig. 1

Scheme of the optical components of the experimental equipment: C, capillary; L, lamp; MC, monochromator; G, diffraction grating; ENS, entrance slit; EXS, exit slit; CC, chopper chamber; CB, chopper blade; S, aperture stop; DR, deposition and reflectometer chamber; C1, C2, and C3, channel electron multipliers; MP, sample manipulator; SH, sample holder; P1, P2, P3, small conductance pipes. The diffraction grating introduces an undetermined partially vertically polarized beam.

Fig. 2
Fig. 2

Measured power-spectral-density functions of aluminum and glass rough surfaces.

Fig. 3
Fig. 3

Aluminium complex refractive index. Current results: ●, real part; ×, imaginary part; solid curves, data in the literature.28

Fig. 4
Fig. 4

Normal reflectance of an ideally smooth aluminium film: ×, values obtained from present refractive indices; solid curve, values obtained from refractive indices in the literature.28

Tables (8)

Tables Icon

Table 1 Unoxidized Aluminum Reflectance Measurements at 82.6 nm

Tables Icon

Table 2 Unoxidized Aluminum Reflectance Measurements at 83.5 nm

Tables Icon

Table 3 Unoxidized Aluminum Reflectance Measurements at 86.8 nm

Tables Icon

Table 4 Unoxidized Aluminum Reflectance Measurements at 92.0 nm

Tables Icon

Table 5 Unoxidized Aluminum Reflectance Measurements at 96.4 nm

Tables Icon

Table 6 Unoxidized Aluminum Reflectance Measurements at 104.8 nm

Tables Icon

Table 7 Unoxidized Aluminum Reflectance Measurements at 113.5 nm

Tables Icon

Table 8 Optical Constants and Calculated Normal Reflectance of Unoxidized Aluminum

Equations (20)

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

z D = h 2 [ exp ( i k · r ) + exp ( - i k · r ) ] .
k ours = 2 π k Croce X 1 i j x i j X 1 i i x i x 1 i x i 0 = 2 π λ ,
h 2 4 + - f ( k ) 1 4 π 2 Ω g ( k ) d k t f ( k ) h 2 σ ,
Ω d k g ( k ) = 4 π 2 σ 2 .
g ( k ) g ( k ) .
r s p = r p s = t s p = t p s = 0.
r s = r s 0 [ 1 - 2 k 1 n k 2 n σ 2 + k 1 n ( k 2 2 - k 1 2 ) 1 2 π 2 × 0 d k t 0 2 π d Λ k t g ( k ) × ( cos 2 Λ k 1 n + k 2 n + k 1 n k 2 n sin 2 Λ k 2 n k 1 2 + k 1 n k 2 2 ) ] ,
t s = t s 0 [ 1 - ( k 1 n - k 2 n ) σ 2 2 + ( k 1 n - k 2 n ) ( k 2 2 - k 1 2 ) 1 4 π 2 × 0 d k t 0 2 π d Λ k t g ( k ) × ( cos 2 Λ k 1 n + k 2 n + k 1 n k 2 n sin 2 Λ k 2 n k 1 2 + k 1 n k 2 2 ) ] ,
r p = r p 0 { 1 - 2 k 1 n k 2 n σ 2 + k 1 n ( k 2 2 - k 1 2 ) k 1 n 2 k 2 n 2 - k t 4 1 4 π 2 × 0 d k t 0 2 π d Λ k t g ( k ) × [ ( k 2 n k 1 n cos Λ + k t k t ) ( k 2 n k 2 n k 1 cos Λ - k t k t k 2 2 ) k 2 n k 1 2 + k 1 n k 2 2 + k 2 n 2 k 1 2 sin 2 Λ k 1 n + k 2 n ] } ,
t p = t p 0 { 1 + ( k 1 n - k 2 n ) 2 σ 2 2 + ( k 1 n - k 2 n ) ( k 2 2 - k 1 2 ) k 1 n k 2 n + k t 2 1 4 π 2 × 0 d k t 0 2 π d Λ k t g ( k ) × [ ( k 2 n k 1 n cos Λ + k t k t ) ( k 1 n k 2 n cos Λ + k t k t ) k 2 n k 1 2 + k 1 n k 2 2 + k 1 n k 2 n sin 2 Λ k 1 n + k 2 n ] } ,
r = r 12 + t 12 t 21 r 23 exp ( - 2 i β ) 1 - r 12 r 23 exp ( - 2 i β ) ,
β = k 2 n x = k 0 x ( n 2 2 - n 1 2 sin 2 θ 1 ) 1 / 2 ,
R s = r s 2 ,             R p = r p 2 .
p = I p - I s I p + I s ,
R = 1 + p 2 R p + 1 - p 2 R s .
{ I θ ( i ) π ( j ) / I 78 ° π ( j ) ,     i = 1 to n - 1 ,     j = 1 , 2 ; I inc π ( j ) / I 78 ° π ( j ) }
{ R θ ( i ) π ( j ) / R 78 ° π ( j ) ,     i = 1 to n - 1 ,     j = 1 , 2 ; 1 / R 78 ° π ( j ) } ,
{ R θ ( i ) π ( j ) / R 78 ° π ( j ) ,     i = 1 to n ,     j = 1 , 2 }
s I 2 = i = 1 , n j = 1 , 2 { R θ ( i ) π ( j ) R 78 ° π ( j ) - R [ θ ( i ) ; n 1 , k 1 , p l ( j ) ] R [ 78 ° ; n l , k l , p l ( j ) ] } 2 ,
1 R 78 ° π ( j ) - 1 R [ 78 ° ; n l , k l , p l ( j ) ] .

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