Abstract

Transmittance measurements at normal incidence were carried out over the visible spectral range for metallic thin films deposited by electron beam evaporation on thick glass substrates. The presence of an inhomogeneous thin layer of Cu2O covering the deposited Cu films is required for a satisfactory model of the measurements taken from various samples with increasing thickness. A spectral projected gradient method is used to invert the transmission spectra from which the wavelength dependence of the effective dielectric function of the oxidized coating layer is obtained. Then an effective medium model is used to estimate the volume fraction of internal voids randomly distributed through the surface layer.

© 2004 Optical Society of America

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  21. E. G. Birgin, I. Chambouleyron, J. M. Martínez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comp. Phys. 151, 862–880 (1999).
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2003 (1)

W. E. Vargas, D. E. Azofeifa, N. Clark, “Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method,” Thin Solid Films 425, 1–8 (2003).
[CrossRef]

2002 (3)

2001 (5)

N. Hartmann, R. J. Madix, “Growth and ordering of Cu-O islands during oxygen adsorption on Cu(110) at 470 K,” Surf. Sci. 488, 107–122 (2001).
[CrossRef]

T. Babeva, S. Kitova, I. Konstantinov, “Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: selection of a combination of photometric quantities on the basis of error analysis,” Appl. Opt. 40, 2675–2681 (2001).
[CrossRef]

T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
[CrossRef]

V. Agarwal, J. E. Lugo, J. A. del Rio, “Reversible charging effects on optical properties of porous silicon,” Solid State Commun. 120, 21–24 (2001).
[CrossRef]

T. Babeva, S. Kitova, I. Konstantinov, “Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: criteria for precise and unambiguous determination of n, k, and d in a wide spectral range,” App. Opt. 40, 2682–2686 (2001).
[CrossRef]

2000 (2)

J. Rodríguez, M. Gómez, J. Ederth, G. A. Niklasson, C. G. Granqvist, “Thickness dependence of the optical properties of sputter deposited Ti oxide films,” Thin Solid Films 365, 119–125 (2000).
[CrossRef]

E. G. Birgin, J. M. Martinez, M. Raydan, “Nonmonotone spectral projected gradient methods on convex sets,” SIAM J. Optim. 10, 1196–1211 (2000).
[CrossRef]

1999 (2)

E. G. Birgin, I. Chambouleyron, J. M. Martínez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comp. Phys. 151, 862–880 (1999).
[CrossRef]

M. Veszelei, M. Strömme-Mattsson, L. Kullman, A. Azens, C. G. Granqvist, “Zr-Ce oxides as candidates for optically passive counter electrodes,” Solar Energy Mater. Solar Cells 56, 223–230 (1999).
[CrossRef]

1997 (5)

D. E. Azofeifa, N. Clark, A. Amador, A. Sáenz, “Determination of hydrogen absorption in Pd coated Al thin films,” Thin Solid Films 300, 295–298 (1997).
[CrossRef]

I. Chambouleyron, J. M. Martínez, A. C. Moretti, M. Mulato, “Retrieval of optical constants and thickness of thin films from transmission spectra,” Appl. Opt. 36, 8238–8247 (1997).
[CrossRef]

M. Raydan, “The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem,” SIAM J. Optim. 7, 26–33 (1997).
[CrossRef]

A. B. Djurisic, A. D. Rakic, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

E. N. Kotlikov, G. V. Tereshchenko, “Study of optical constants of films used for the synthesis of broad-band antireflection coatings,” Opt. Spectrosc. 82, 603–609 (1997).

1996 (1)

P. V. Adamson, “Differential reflection spectroscopy of surface layers on thick transparent substrates with normally incident light,” Opt. Spectrosc. 80, 459–468 (1996).

1995 (1)

A. D. Rakic, J. M. Elazar, A. B. Djurisic, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

1988 (1)

J. Barzilai, J. M. Borwein, “Two point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988).
[CrossRef]

1986 (2)

L. Grippo, F. Lampariello, S. Lucidi, “A nonmonotone line search technique for Newton’s method,” SIAM J. Numer. Anal. 23, 707–716 (1986).
[CrossRef]

P. J. Martin, “Ion-based methods for optical thin film deposition: a review,” J. Mater. Sci. 21, 1–25 (1986).
[CrossRef]

1984 (1)

G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
[CrossRef]

1983 (1)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

1972 (1)

A. R. Williams, J. F. Janak, V. L. Moruzzi, “One-electron analysis of optical data in copper,” Phys. Rev. Lett. 28, 671–675 (1972).
[CrossRef]

1970 (1)

C. Y. Fong, “Wavelength modulation spectrum of copper,” Phys. Rev. Lett. 25, 1486–1490 (1970).
[CrossRef]

1965 (2)

1939 (1)

1904 (1)

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Adamson, P. V.

P. V. Adamson, “Differential reflection spectroscopy of surface layers on thick transparent substrates with normally incident light,” Opt. Spectrosc. 80, 459–468 (1996).

Agarwal, V.

V. Agarwal, J. E. Lugo, J. A. del Rio, “Reversible charging effects on optical properties of porous silicon,” Solid State Commun. 120, 21–24 (2001).
[CrossRef]

Amador, A.

D. E. Azofeifa, N. Clark, A. Amador, A. Sáenz, “Determination of hydrogen absorption in Pd coated Al thin films,” Thin Solid Films 300, 295–298 (1997).
[CrossRef]

Anderson, J. C.

B. Lewis, J. C. Anderson, Nucleation and Growth of Thin Films (Academic, New York, 1978).

Araya-Pochet, J. A.

A. Ramírez-Porras, E. D. Avendaño-Soto, J. A. Araya-Pochet, “Design and characterization of a high vacuum metals deposition system based on electron beam evaporation,” in Surface Science and its Applications, Proceedings of the 9th Latin American Congress, O. de Melo, I. Hernández-Calderón, eds. (World Scientific, Singapore, 1999), pp. 420–422.

Athans, M.

M. Athans, M. L. Dertouzos, R. N. Spann, S. J. Mason, Systems, Networks, and Computations: Multivariable Methods (McGraw-Hill, New York, 1974).

Avendaño-Soto, E. D.

A. Ramírez-Porras, E. D. Avendaño-Soto, J. A. Araya-Pochet, “Design and characterization of a high vacuum metals deposition system based on electron beam evaporation,” in Surface Science and its Applications, Proceedings of the 9th Latin American Congress, O. de Melo, I. Hernández-Calderón, eds. (World Scientific, Singapore, 1999), pp. 420–422.

Azens, A.

M. Veszelei, M. Strömme-Mattsson, L. Kullman, A. Azens, C. G. Granqvist, “Zr-Ce oxides as candidates for optically passive counter electrodes,” Solar Energy Mater. Solar Cells 56, 223–230 (1999).
[CrossRef]

Azofeifa, D. E.

W. E. Vargas, D. E. Azofeifa, N. Clark, “Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method,” Thin Solid Films 425, 1–8 (2003).
[CrossRef]

D. E. Azofeifa, N. Clark, A. Amador, A. Sáenz, “Determination of hydrogen absorption in Pd coated Al thin films,” Thin Solid Films 300, 295–298 (1997).
[CrossRef]

Babeva, T.

Barrera, R. G.

Barzilai, J.

J. Barzilai, J. M. Borwein, “Two point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988).
[CrossRef]

Bennett, J. M.

Bennett, R. A.

T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
[CrossRef]

Birgin, E. G.

I. Chambouleyron, S. D. Ventura, E. G. Birgin, J. M. Martínez, “Optical constants and thickness determination of very thin amorphous semiconductor films,” J. Appl. Phys. 92, 3093–3102 (2002).
[CrossRef]

E. G. Birgin, J. M. Martinez, M. Raydan, “Nonmonotone spectral projected gradient methods on convex sets,” SIAM J. Optim. 10, 1196–1211 (2000).
[CrossRef]

E. G. Birgin, I. Chambouleyron, J. M. Martínez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comp. Phys. 151, 862–880 (1999).
[CrossRef]

Booty, M. J.

Borwein, J. M.

J. Barzilai, J. M. Borwein, “Two point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988).
[CrossRef]

Bowker, M.

T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
[CrossRef]

Cardona, M.

P. Yu, M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, Berlin, 1996).
[CrossRef]

Chambouleyron, I.

I. Chambouleyron, S. D. Ventura, E. G. Birgin, J. M. Martínez, “Optical constants and thickness determination of very thin amorphous semiconductor films,” J. Appl. Phys. 92, 3093–3102 (2002).
[CrossRef]

E. G. Birgin, I. Chambouleyron, J. M. Martínez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comp. Phys. 151, 862–880 (1999).
[CrossRef]

I. Chambouleyron, J. M. Martínez, A. C. Moretti, M. Mulato, “Retrieval of optical constants and thickness of thin films from transmission spectra,” Appl. Opt. 36, 8238–8247 (1997).
[CrossRef]

Clark, N.

W. E. Vargas, D. E. Azofeifa, N. Clark, “Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method,” Thin Solid Films 425, 1–8 (2003).
[CrossRef]

D. E. Azofeifa, N. Clark, A. Amador, A. Sáenz, “Determination of hydrogen absorption in Pd coated Al thin films,” Thin Solid Films 300, 295–298 (1997).
[CrossRef]

Cooper, B. R.

B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals. II,” Phys. Rev. 138, 494–507 (1965).
[CrossRef]

Curiel, F.

del Rio, J. A.

V. Agarwal, J. E. Lugo, J. A. del Rio, “Reversible charging effects on optical properties of porous silicon,” Solid State Commun. 120, 21–24 (2001).
[CrossRef]

Dertouzos, M. L.

M. Athans, M. L. Dertouzos, R. N. Spann, S. J. Mason, Systems, Networks, and Computations: Multivariable Methods (McGraw-Hill, New York, 1974).

Djurisic, A. B.

A. B. Djurisic, A. D. Rakic, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. D. Rakic, J. M. Elazar, A. B. Djurisic, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

Domen, K.

T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
[CrossRef]

Ederth, J.

J. Rodríguez, M. Gómez, J. Ederth, G. A. Niklasson, C. G. Granqvist, “Thickness dependence of the optical properties of sputter deposited Ti oxide films,” Thin Solid Films 365, 119–125 (2000).
[CrossRef]

Ehrenreich, H.

B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals. II,” Phys. Rev. 138, 494–507 (1965).
[CrossRef]

Elazar, J. M.

A. B. Djurisic, A. D. Rakic, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. D. Rakic, J. M. Elazar, A. B. Djurisic, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

Fong, C. Y.

C. Y. Fong, “Wavelength modulation spectrum of copper,” Phys. Rev. Lett. 25, 1486–1490 (1970).
[CrossRef]

Gómez, M.

J. Rodríguez, M. Gómez, J. Ederth, G. A. Niklasson, C. G. Granqvist, “Thickness dependence of the optical properties of sputter deposited Ti oxide films,” Thin Solid Films 365, 119–125 (2000).
[CrossRef]

Granqvist, C. G.

J. Rodríguez, M. Gómez, J. Ederth, G. A. Niklasson, C. G. Granqvist, “Thickness dependence of the optical properties of sputter deposited Ti oxide films,” Thin Solid Films 365, 119–125 (2000).
[CrossRef]

M. Veszelei, M. Strömme-Mattsson, L. Kullman, A. Azens, C. G. Granqvist, “Zr-Ce oxides as candidates for optically passive counter electrodes,” Solar Energy Mater. Solar Cells 56, 223–230 (1999).
[CrossRef]

G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
[CrossRef]

Grippo, L.

L. Grippo, F. Lampariello, S. Lucidi, “A nonmonotone line search technique for Newton’s method,” SIAM J. Numer. Anal. 23, 707–716 (1986).
[CrossRef]

Hartmann, N.

N. Hartmann, R. J. Madix, “Growth and ordering of Cu-O islands during oxygen adsorption on Cu(110) at 470 K,” Surf. Sci. 488, 107–122 (2001).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).

Janak, J. F.

A. R. Williams, J. F. Janak, V. L. Moruzzi, “One-electron analysis of optical data in copper,” Phys. Rev. Lett. 28, 671–675 (1972).
[CrossRef]

Kitova, S.

Konstantinov, I.

Kotlikov, E. N.

E. N. Kotlikov, G. V. Tereshchenko, “Study of optical constants of films used for the synthesis of broad-band antireflection coatings,” Opt. Spectrosc. 82, 603–609 (1997).

Kullman, L.

M. Veszelei, M. Strömme-Mattsson, L. Kullman, A. Azens, C. G. Granqvist, “Zr-Ce oxides as candidates for optically passive counter electrodes,” Solar Energy Mater. Solar Cells 56, 223–230 (1999).
[CrossRef]

Lampariello, F.

L. Grippo, F. Lampariello, S. Lucidi, “A nonmonotone line search technique for Newton’s method,” SIAM J. Numer. Anal. 23, 707–716 (1986).
[CrossRef]

Lewis, B.

B. Lewis, J. C. Anderson, Nucleation and Growth of Thin Films (Academic, New York, 1978).

Liddell, H. M.

H. M. Liddell, Computer-Aided Techniques for the Design of Multilayer Filters (Adam Hilger, Bristol, 1981).

Lucidi, S.

L. Grippo, F. Lampariello, S. Lucidi, “A nonmonotone line search technique for Newton’s method,” SIAM J. Numer. Anal. 23, 707–716 (1986).
[CrossRef]

Lugo, J. E.

V. Agarwal, J. E. Lugo, J. A. del Rio, “Reversible charging effects on optical properties of porous silicon,” Solid State Commun. 120, 21–24 (2001).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, London, 1969).

Madix, R. J.

N. Hartmann, R. J. Madix, “Growth and ordering of Cu-O islands during oxygen adsorption on Cu(110) at 470 K,” Surf. Sci. 488, 107–122 (2001).
[CrossRef]

Martin, P. J.

P. J. Martin, “Ion-based methods for optical thin film deposition: a review,” J. Mater. Sci. 21, 1–25 (1986).
[CrossRef]

Martinez, J. M.

E. G. Birgin, J. M. Martinez, M. Raydan, “Nonmonotone spectral projected gradient methods on convex sets,” SIAM J. Optim. 10, 1196–1211 (2000).
[CrossRef]

Martínez, J. M.

I. Chambouleyron, S. D. Ventura, E. G. Birgin, J. M. Martínez, “Optical constants and thickness determination of very thin amorphous semiconductor films,” J. Appl. Phys. 92, 3093–3102 (2002).
[CrossRef]

E. G. Birgin, I. Chambouleyron, J. M. Martínez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comp. Phys. 151, 862–880 (1999).
[CrossRef]

I. Chambouleyron, J. M. Martínez, A. C. Moretti, M. Mulato, “Retrieval of optical constants and thickness of thin films from transmission spectra,” Appl. Opt. 36, 8238–8247 (1997).
[CrossRef]

Mason, S. J.

M. Athans, M. L. Dertouzos, R. N. Spann, S. J. Mason, Systems, Networks, and Computations: Multivariable Methods (McGraw-Hill, New York, 1974).

Matsumoto, T.

T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
[CrossRef]

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Mednikarov, B.

Moretti, A. C.

Moruzzi, V. L.

A. R. Williams, J. F. Janak, V. L. Moruzzi, “One-electron analysis of optical data in copper,” Phys. Rev. Lett. 28, 671–675 (1972).
[CrossRef]

Mulato, M.

Niklasson, G. A.

J. Rodríguez, M. Gómez, J. Ederth, G. A. Niklasson, C. G. Granqvist, “Thickness dependence of the optical properties of sputter deposited Ti oxide films,” Thin Solid Films 365, 119–125 (2000).
[CrossRef]

G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
[CrossRef]

Rakic, A. D.

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A. Ramírez-Porras, E. D. Avendaño-Soto, J. A. Araya-Pochet, “Design and characterization of a high vacuum metals deposition system based on electron beam evaporation,” in Surface Science and its Applications, Proceedings of the 9th Latin American Congress, O. de Melo, I. Hernández-Calderón, eds. (World Scientific, Singapore, 1999), pp. 420–422.

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E. G. Birgin, J. M. Martinez, M. Raydan, “Nonmonotone spectral projected gradient methods on convex sets,” SIAM J. Optim. 10, 1196–1211 (2000).
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C. G. Ribbing, A. Roos, “Copper oxides (Cu2O, CuO),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1991), pp. 875–882.

Rodríguez, J.

J. Rodríguez, M. Gómez, J. Ederth, G. A. Niklasson, C. G. Granqvist, “Thickness dependence of the optical properties of sputter deposited Ti oxide films,” Thin Solid Films 365, 119–125 (2000).
[CrossRef]

Roos, A.

C. G. Ribbing, A. Roos, “Copper oxides (Cu2O, CuO),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1991), pp. 875–882.

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D. E. Azofeifa, N. Clark, A. Amador, A. Sáenz, “Determination of hydrogen absorption in Pd coated Al thin films,” Thin Solid Films 300, 295–298 (1997).
[CrossRef]

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T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
[CrossRef]

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M. Veszelei, M. Strömme-Mattsson, L. Kullman, A. Azens, C. G. Granqvist, “Zr-Ce oxides as candidates for optically passive counter electrodes,” Solar Energy Mater. Solar Cells 56, 223–230 (1999).
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M. Veszelei, M. Strömme-Mattsson, L. Kullman, A. Azens, C. G. Granqvist, “Zr-Ce oxides as candidates for optically passive counter electrodes,” Solar Energy Mater. Solar Cells 56, 223–230 (1999).
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T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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I. Chambouleyron, S. D. Ventura, E. G. Birgin, J. M. Martínez, “Optical constants and thickness determination of very thin amorphous semiconductor films,” J. Appl. Phys. 92, 3093–3102 (2002).
[CrossRef]

G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
[CrossRef]

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E. G. Birgin, I. Chambouleyron, J. M. Martínez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comp. Phys. 151, 862–880 (1999).
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[CrossRef]

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P. V. Adamson, “Differential reflection spectroscopy of surface layers on thick transparent substrates with normally incident light,” Opt. Spectrosc. 80, 459–468 (1996).

E. N. Kotlikov, G. V. Tereshchenko, “Study of optical constants of films used for the synthesis of broad-band antireflection coatings,” Opt. Spectrosc. 82, 603–609 (1997).

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J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

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B. R. Cooper, H. Ehrenreich, “Optical properties of noble metals. II,” Phys. Rev. 138, 494–507 (1965).
[CrossRef]

Phys. Rev. E (2)

A. D. Rakic, J. M. Elazar, A. B. Djurisic, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

A. B. Djurisic, A. D. Rakic, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

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C. Y. Fong, “Wavelength modulation spectrum of copper,” Phys. Rev. Lett. 25, 1486–1490 (1970).
[CrossRef]

A. R. Williams, J. F. Janak, V. L. Moruzzi, “One-electron analysis of optical data in copper,” Phys. Rev. Lett. 28, 671–675 (1972).
[CrossRef]

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L. Grippo, F. Lampariello, S. Lucidi, “A nonmonotone line search technique for Newton’s method,” SIAM J. Numer. Anal. 23, 707–716 (1986).
[CrossRef]

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E. G. Birgin, J. M. Martinez, M. Raydan, “Nonmonotone spectral projected gradient methods on convex sets,” SIAM J. Optim. 10, 1196–1211 (2000).
[CrossRef]

M. Raydan, “The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem,” SIAM J. Optim. 7, 26–33 (1997).
[CrossRef]

Solar Energy Mater. Solar Cells (1)

M. Veszelei, M. Strömme-Mattsson, L. Kullman, A. Azens, C. G. Granqvist, “Zr-Ce oxides as candidates for optically passive counter electrodes,” Solar Energy Mater. Solar Cells 56, 223–230 (1999).
[CrossRef]

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V. Agarwal, J. E. Lugo, J. A. del Rio, “Reversible charging effects on optical properties of porous silicon,” Solid State Commun. 120, 21–24 (2001).
[CrossRef]

Surf. Sci. (2)

T. Matsumoto, R. A. Bennett, P. Stone, T. Yamada, K. Domen, M. Bowker, “Scanning tunneling microscopy studies of oxygen adsorption on Cu(111),” Surf. Sci. 471, 225–245 (2001).
[CrossRef]

N. Hartmann, R. J. Madix, “Growth and ordering of Cu-O islands during oxygen adsorption on Cu(110) at 470 K,” Surf. Sci. 488, 107–122 (2001).
[CrossRef]

Thin Solid Films (3)

J. Rodríguez, M. Gómez, J. Ederth, G. A. Niklasson, C. G. Granqvist, “Thickness dependence of the optical properties of sputter deposited Ti oxide films,” Thin Solid Films 365, 119–125 (2000).
[CrossRef]

W. E. Vargas, D. E. Azofeifa, N. Clark, “Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method,” Thin Solid Films 425, 1–8 (2003).
[CrossRef]

D. E. Azofeifa, N. Clark, A. Amador, A. Sáenz, “Determination of hydrogen absorption in Pd coated Al thin films,” Thin Solid Films 300, 295–298 (1997).
[CrossRef]

Other (8)

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, London, 1969).

H. M. Liddell, Computer-Aided Techniques for the Design of Multilayer Filters (Adam Hilger, Bristol, 1981).

B. Lewis, J. C. Anderson, Nucleation and Growth of Thin Films (Academic, New York, 1978).

P. Yu, M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, Berlin, 1996).
[CrossRef]

A. Ramírez-Porras, E. D. Avendaño-Soto, J. A. Araya-Pochet, “Design and characterization of a high vacuum metals deposition system based on electron beam evaporation,” in Surface Science and its Applications, Proceedings of the 9th Latin American Congress, O. de Melo, I. Hernández-Calderón, eds. (World Scientific, Singapore, 1999), pp. 420–422.

M. Athans, M. L. Dertouzos, R. N. Spann, S. J. Mason, Systems, Networks, and Computations: Multivariable Methods (McGraw-Hill, New York, 1974).

C. G. Ribbing, A. Roos, “Copper oxides (Cu2O, CuO),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1991), pp. 875–882.

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Figures (4)

Fig. 1
Fig. 1

Optimization of the thickness values h of the Cu2O layer on Cu films, as obtained from application of the spectral projected gradient method. Solid curve, power fit displayed for visual aid.

Fig. 2
Fig. 2

Visible spectral dependence of (a) the measured and retrieved transmittance, (b) the input (circles) and the retrieved (solid curve) Cu2O and Cu refractive indices, and (c) the Cu2O and Cu extinction coefficients for a 153-Å-thick Cu film covered with a 18.2-Å-thick layer of Cu2O. The dashed curve in (a) corresponds to the transmittance of a 171.2-Å-thick film with no surface oxidation. The inset depicts the calculated reflectance and absorptance spectra of this 171.2-Å-thick Cu film.

Fig. 3
Fig. 3

Visible transmittance spectra of Cu2O-coated Cu films on glass substrates whose thickness has been indicated in Table 1, according to the number labels shown. The solid curves correspond to the fitted spectra from application of the spectral projected gradient method, and the dots correspond to some of the measured transmittance values.

Fig. 4
Fig. 4

Energy dependence of the parameter (αh ν)2/3 [in units of (eV/cm)2/3], where α is the effective absorption coefficient calculated from the extinction coefficient of the Cu2O surface layer, obtained from application of the spectral projected gradient method.

Tables (1)

Tables Icon

Table 1 Optimized Values for the Thickness h of Inhomogeneous Thin Cu2O Layers on Cu Filmsa

Equations (15)

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

F=i=1M |Texpλi-Tni, ki, h, Ni, Ki, H, λi|2,
Zi=ni,i=1, 2,, Mki,i=M+1, M+2,, 2MNi,i=2M+1, 2M+2,, 3MKi,i=3M+1, 3M+2,, 4MH,i=4M+1.
Tbn, k, h, N, K, H, λ=AXB-CX+DX2,
A=64n2+k2N2+K2Y,
B=n+12+k2B1-B2,
B1=n+N2+k+K2N+12+K2,
B2=n-N2+k-K2N-12+K2Y2,
C=2C1-C2cos ϕ-2C3+C4sin ϕ,
C1=n2+k2-1n2+k2-N2-K2N+12+K2-Y2N-12+K2,
C2=4kkN-KnN+12+K2+Y2N-12+K2,
C3=2n2+k2-1kN-KnN+12+K2+Y2N-12+K2,
C4=2kn2+k2-N2-K2N+12+K2-Y2N-12+K2,
D=n-12+k2D1-D2,
D1=N+12+K2n-N2+k-K2,
D2=N-12+K2n+N2+k+K2Y2,

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