Abstract

Self-consistent optical constants of SiO2 and Ta2O5 films have been obtained for their relevance in optical coatings from the near ultraviolet to the near infrared spectral ranges, where they are transparent and have a high refractive index contrast. Particular attention has been paid to wavelengths close to and shorter than each material cutoff. The far and the extreme ultraviolet ranges are also covered here, where few (SiO2) or almost no optical constant data (Ta2O5) were available for films of these materials. This work is aimed at filling the lack of self-consistent sets of optical constants with data in a very broad spectral range, which can be widely applied in multilayer design for the everyday use of these materials in multilayer coatings. Oxide films were deposited by reactive electron-beam evaporation onto various sorts of substrates at 573 K. Transmittance, reflectance, and ellipsometry measurements were performed for each oxide in spectral intervals jointly covering from the extreme ultraviolet to the near infrared; starting with these measurements along with extrapolations, an iterative and double Kramers-Kronig analysis procedure has been followed to obtain a self-consistent set of optical constants per material. With the final data sets, we have satisfactorily reproduced the experimental measurements. Global data self-consistency was successfully evaluated through sum rules, and local consistency at each photon energy range was also evaluated through a novel sum-rule method which involves window functions.

© 2016 Optical Society of America

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References

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2016 (1)

L. V. Rodríguez-de Marcos, J. A. Méndez, and J. I. Larruquert, “Tuning sum rules with window functions for optical constant evaluation,” J. Opt. 18(7), 075606 (2016).
[Crossref]

2013 (4)

T. J. Bright, J. I. Watjen, Z. M. Zhang, C. Muratore, A. A. Voevodin, D. I. Koukis, D. B. Tanner, and D. J. Arenas, “Infrared optical properties of amorphous and nanocrystalline Ta2O5 thin films,” J. Appl. Phys. 114(8), 083515 (2013).
[Crossref]

J. I. Larruquert, L. V. Rodríguez-de Marcos, J. A. Méndez, P. J. Martin, and A. Bendavid, “High reflectance ta-C coatings in the extreme ultraviolet,” Opt. Express 21(23), 27537–27549 (2013).
[Crossref] [PubMed]

H. Liu, Y. Jiang, L. Wang, C. Jiang, Y. Ji, and D. Chen, “Study on optical anisotropy properties of SiO2 films with different thermal annealing temperatures,” Chin. Opt. Lett. 11, S10305 (2013).

G. A. Stanciu, M. Filipescu, V. Ion, E. Andronescu, and M. Dinescu, “Optical properties of tantalum oxide thin films obtained by laser deposition techniques,” U. P. B. Sci, Bull., Series B 75, 15–22 (2013).

2012 (5)

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

D.-X. Zhang, Y.-X. Zheng, Q.-Y. Cai, W. Lin, K.-N. Wu, P.-H. Mao, R.-J. Zhang, H.-B. Zhao, and L.-Y. Chen, “Thickness-dependence of optical constants for Ta2O5 ultrathin films,” Appl. Phys., A Mater. Sci. Process. 108(4), 975–979 (2012).
[Crossref]

P. S. Sharlandjiev and D. I. Nazarova, “Determination of optical functions of very thin tantalum pentoxide films on platinum substrate by genetic algorithm approach,” Opt. Quantum Electron. 44(14), 673–681 (2012).
[Crossref]

L. Gao, F. Lemarchand, and M. Lequime, “Exploitation of multiple incidences spectrometric measurements for thin film reverse engineering,” Opt. Express 20(14), 15734–15751 (2012).
[Crossref] [PubMed]

J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. T. Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012).
[Crossref] [PubMed]

2011 (1)

F. Bridou, M. Cuniot-Ponsard, J. M. Desvignes, A. Gottwald, U. Kroth, and M. Richter, “Polarizing and non-polarizing mirrors for the hydrogen Lyman-α radiation at 121.6 nm,” Appl. Phys., A Mater. Sci. Process. 102(3), 641–649 (2011).
[Crossref]

2010 (2)

Q.-Y. Cai, Y.-X. Zheng, P.-H. Mao, R.-J. Zhang, D.-X. Zhang, M.-H. Liu, and L.-Y. Chen, “Evolution of optical constants of silicon dioxide on silicon from ultrathin films to thick films,” J. Phys. D 43(44), 445302 (2010).
[Crossref]

S. Jakobs, M. Lappschies, U. Schallenberg, O. Stenzel, and S. Wilbrandt, “Characterization of metal-oxide thin films deposited by plasma-assisted reactive magnetron sputtering,” Chin. Opt. Lett. 8(S1), 73–77 (2010).
[Crossref]

2009 (1)

J. Zhou, D. Luo, Y. Li, and Z. Liu, “Properties of Ta2O5 thin films deposited by DC reactive magnetron sputtering,” Int. J. Mod. Phys. B 23(27), 5275–5282 (2009).
[Crossref]

2007 (1)

R. Chandrasekharan, S. Prakash, M. A. Shannon, and R. I. Masel, “Change in radiative optical properties of Ta2O5 thin films due to high-temperature heat treatment,” J. Heat Transfer 129(1), 27–36 (2007).
[Crossref]

2006 (3)

2005 (2)

S.-H. Woo, C. K. Hwangbo, Y. B. Son, I. C. Moon, G. M. Kang, and K.-S. Lee, “Optical properties of Ta2O5 thin films deposited by plasma ion-assisted deposition,” J. Korean Phys. Soc. 46, S187–S191 (2005).

S. Kitova, S. Youroukov, Tz. Babeva, V. Denishev, and G. Danev, “Argon ion activated deposition of SiO2 films,” J. Optoelectron. Adv. Mater. 7, 2613–2618 (2005).

2004 (2)

St. Günster, H. Blaschke, D. Ristau, M. Danailov, M. Trovó, A. Gatto, N. Kaiser, F. Sarto, D. Flori, and F. Menchini, “Radiation resistance of single and multilayer coatings against synchrotron radiation,” Proc. SPIE 5250, 146–157 (2004).
[Crossref]

E. A. West, J. G. Porter, J. M. Davis, G. A. Gary, M. W. Noble, M. Lewis, and R. J. Thomas, “The Marshall Space Flight Center solar ultraviolet magnetograph,” Proc. SPIE 5488, 801 (2004).
[Crossref]

2002 (3)

P. Tripathi, G. S. Lodha, M. H. Modi, A. K. Sinha, K. J. S. Sawhney, and R. V. Nandedkar, “Optical constants of silicon and silicon dioxide using soft X-ray reflectance measurements,” Opt. Commun. 211(1-6), 215–223 (2002).
[Crossref]

R. Thielsch, A. Gatto, J. Heber, and N. Kaiser, “A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition,” Thin Solid Films 410(1-2), 86–93 (2002).
[Crossref]

B. von Blanckenhagen, D. Tonova, and J. Ullmann, “Application of the Tauc-Lorentz formulation to the interband absorption of optical coating materials,” Appl. Opt. 41(16), 3137–3141 (2002).
[Crossref] [PubMed]

2001 (1)

K. Postava, M. Aoyama, T. Yamaguchi, and H. Oda, “Spectroellipsometric characterization of materials for multilayer optics,” Appl. Surf. Sci. 175–176, 276–280 (2001).
[Crossref]

2000 (3)

E. Franke, C. L. Trimble, M. J. DeVries, J. A. Woollam, M. Schubert, and F. Frost, “Dielectric function of amorphous tantalum oxide from the far infrared to the deep ultraviolet spectral region measured by spectroscopic ellipsometry,” J. Appl. Phys. 88(9), 5166–5174 (2000).
[Crossref]

J.-Y. Zhang and I. W. Boyd, “Ultrathin high-quality tantalum pentoxide films grown by photoinduced chemical vapour deposition,” Appl. Phys. Lett. 77(22), 3574–3576 (2000).
[Crossref]

J.-Y. Zhang and I. W. Boyd, “Pulsed laser deposition of tantalum pentoxide film,” Appl. Phys., A Mater. Sci. Process. 70, 657–661 (2000).

1999 (2)

I. Porqueras, J. Marti, and E. Bertran, “Optical and electrical characterisation of Ta205 thin films for ionic conduction applications,” Thin Solid Films 343–344, 449–452 (1999).
[Crossref]

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. André, M. Idir, and Ph. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11(16), 3355–3370 (1999).
[Crossref]

1998 (1)

D. L. Windt, “IMD: Software for modeling the optical properties of multilayer films,” Comput. Phys. 12(4), 360–370 (1998), http://www.rxollc.com/idl/index.html .
[Crossref]

1997 (2)

J. D. Traylor Kruschwitz and W. T. Pawlewicz, “Optical and durability properties of infrared transmitting thin films,” Appl. Opt. 36(10), 2157–2159 (1997).
[Crossref] [PubMed]

F. E. Ghodsi, F. Z. Tepehan, and G. G. Tepehan, “Optical properties of Ta205 thin films deposited using the spin coating process,” Thin Solid Films 295(1-2), 11–15 (1997).
[Crossref]

1996 (2)

E. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 79, 63–66 (1996).
[Crossref]

K. Scherer, L. Nouvelot, P. Lacan, and R. Bosmans, “Optical and mechanical characterization of evaporated SiO(2) layers. Long-term evolution,” Appl. Opt. 35(25), 5067–5072 (1996).
[Crossref] [PubMed]

1995 (2)

K. Kukli, J. Aarik, A. Aidla, O. Kohana, T. Uustare, and W. Sammelselg, “Properties of tantalum oxide thin films grown by atomic layer deposition,” Thin Solid Films 260(2), 135–142 (1995).
[Crossref]

M. Cevro and G. Carter, “Ion-beam and dual-ion-beam sputter deposition of tantalum oxide films,” Opt. Eng. 34(2), 596–606 (1995).
[Crossref]

1993 (3)

1992 (1)

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage thresholds of dielectric UV/VUV-coatings deposited by conventional evaporation, IAD and lBS,” Proc. SPIE 1624, 221–235 (1992).
[Crossref]

1990 (1)

1989 (1)

K. Gürtler, K. Bange, W. Wagner, F. Rauch, and H. Hantsche, “Characterization of Ta2O5 layers by electron spectroscopy for chemical analysis Rutherford backscattering spectrometry, nuclear reaction analysis and optical methods,” Thin Solid Films 175, 185–189 (1989).
[Crossref]

1985 (1)

1982 (1)

F. Rubio, J. Denis, J. M. Albella, and J. M. Martínez-Duart, “Sputtered Ta2O5 antireflection coatings for silicon solar cells,” Thin Solid Films 90(4), 405–408 (1982).
[Crossref]

1980 (2)

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(4), 1612–1628 (1980).
[Crossref]

Z. Malacara-Hernandez and P. Baumeister, “Refractive index of a tantalum pentoxide film,” Appl. Opt. 19(11), 1737–1738 (1980).
[Crossref] [PubMed]

1979 (1)

Z. A. Weinberg, G. W. Rubloff, and E. Bassous, “Transmission, photoconductivity, and the experimental band gap of thermally grown Si02 films,” Phys. Rev. B 19(6), 3107–3117 (1979).
[Crossref]

1975 (1)

E. E. Khawaja and S. G. Tomlin, “The optical properties of thin films of tantalum pentoxide and zirconium dioxide,” Thin Solid Films 30(2), 361–369 (1975).
[Crossref]

1974 (1)

M. Altarelli and D. Y. Smith, “Superconvergence and sum rules for the optical constants: physical meaning, comparison with experiment, and generalization,” Phys. Rev. B 9(4), 1290–1298 (1974).
[Crossref]

1972 (1)

H. R. Philipp, “Influence of Oxide Layers on the Determination of the Optical Properties of Silicon,” J. Appl. Phys. 43(6), 2835–2839 (1972).
[Crossref]

1971 (1)

H. R. Philipp, “Optical properties of non-crystalline Si, SiO, SiOx and SiO2,” J. Phys. Chem. Solids 32(8), 1935–1945 (1971).
[Crossref]

Aarik, J.

K. Kukli, J. Aarik, A. Aidla, O. Kohana, T. Uustare, and W. Sammelselg, “Properties of tantalum oxide thin films grown by atomic layer deposition,” Thin Solid Films 260(2), 135–142 (1995).
[Crossref]

Aidla, A.

K. Kukli, J. Aarik, A. Aidla, O. Kohana, T. Uustare, and W. Sammelselg, “Properties of tantalum oxide thin films grown by atomic layer deposition,” Thin Solid Films 260(2), 135–142 (1995).
[Crossref]

Albella, J. M.

F. Rubio, J. Denis, J. M. Albella, and J. M. Martínez-Duart, “Sputtered Ta2O5 antireflection coatings for silicon solar cells,” Thin Solid Films 90(4), 405–408 (1982).
[Crossref]

Aleksandrova, A.

Al-Jumaily, G. A.

Altarelli, M.

M. Altarelli and D. Y. Smith, “Superconvergence and sum rules for the optical constants: physical meaning, comparison with experiment, and generalization,” Phys. Rev. B 9(4), 1290–1298 (1974).
[Crossref]

André, J.-M.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. André, M. Idir, and Ph. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11(16), 3355–3370 (1999).
[Crossref]

Andronescu, E.

G. A. Stanciu, M. Filipescu, V. Ion, E. Andronescu, and M. Dinescu, “Optical properties of tantalum oxide thin films obtained by laser deposition techniques,” U. P. B. Sci, Bull., Series B 75, 15–22 (2013).

Aoyama, M.

K. Postava, M. Aoyama, T. Yamaguchi, and H. Oda, “Spectroellipsometric characterization of materials for multilayer optics,” Appl. Surf. Sci. 175–176, 276–280 (2001).
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Arenas, D. J.

T. J. Bright, J. I. Watjen, Z. M. Zhang, C. Muratore, A. A. Voevodin, D. I. Koukis, D. B. Tanner, and D. J. Arenas, “Infrared optical properties of amorphous and nanocrystalline Ta2O5 thin films,” J. Appl. Phys. 114(8), 083515 (2013).
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Asghar, M. H.

M. H. Asghar, F. Placido, and S. Naseem, “Characterization of Ta2O5 thin films prepared by reactive evaporation,” Eur. Phys. J. Appl. Phys. 36(2), 119–124 (2006).
[Crossref]

Babeva, Tz.

S. Kitova, S. Youroukov, Tz. Babeva, V. Denishev, and G. Danev, “Argon ion activated deposition of SiO2 films,” J. Optoelectron. Adv. Mater. 7, 2613–2618 (2005).

Bange, K.

K. Gürtler, K. Bange, W. Wagner, F. Rauch, and H. Hantsche, “Characterization of Ta2O5 layers by electron spectroscopy for chemical analysis Rutherford backscattering spectrometry, nuclear reaction analysis and optical methods,” Thin Solid Films 175, 185–189 (1989).
[Crossref]

Barchewitz, R.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. André, M. Idir, and Ph. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11(16), 3355–3370 (1999).
[Crossref]

Bassous, E.

Z. A. Weinberg, G. W. Rubloff, and E. Bassous, “Transmission, photoconductivity, and the experimental band gap of thermally grown Si02 films,” Phys. Rev. B 19(6), 3107–3117 (1979).
[Crossref]

Baumeister, P.

Bendavid, A.

Bertran, E.

I. Porqueras, J. Marti, and E. Bertran, “Optical and electrical characterisation of Ta205 thin films for ionic conduction applications,” Thin Solid Films 343–344, 449–452 (1999).
[Crossref]

Blaschke, H.

St. Günster, H. Blaschke, D. Ristau, M. Danailov, M. Trovó, A. Gatto, N. Kaiser, F. Sarto, D. Flori, and F. Menchini, “Radiation resistance of single and multilayer coatings against synchrotron radiation,” Proc. SPIE 5250, 146–157 (2004).
[Crossref]

Blessing, C.

E. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 79, 63–66 (1996).
[Crossref]

Bosmans, R.

Boyd, I. W.

J.-Y. Zhang and I. W. Boyd, “Ultrathin high-quality tantalum pentoxide films grown by photoinduced chemical vapour deposition,” Appl. Phys. Lett. 77(22), 3574–3576 (2000).
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J.-Y. Zhang and I. W. Boyd, “Pulsed laser deposition of tantalum pentoxide film,” Appl. Phys., A Mater. Sci. Process. 70, 657–661 (2000).

Bridou, F.

F. Bridou, M. Cuniot-Ponsard, J. M. Desvignes, A. Gottwald, U. Kroth, and M. Richter, “Polarizing and non-polarizing mirrors for the hydrogen Lyman-α radiation at 121.6 nm,” Appl. Phys., A Mater. Sci. Process. 102(3), 641–649 (2011).
[Crossref]

Bright, T. J.

T. J. Bright, J. I. Watjen, Z. M. Zhang, C. Muratore, A. A. Voevodin, D. I. Koukis, D. B. Tanner, and D. J. Arenas, “Infrared optical properties of amorphous and nanocrystalline Ta2O5 thin films,” J. Appl. Phys. 114(8), 083515 (2013).
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Cai, Q.-Y.

D.-X. Zhang, Y.-X. Zheng, Q.-Y. Cai, W. Lin, K.-N. Wu, P.-H. Mao, R.-J. Zhang, H.-B. Zhao, and L.-Y. Chen, “Thickness-dependence of optical constants for Ta2O5 ultrathin films,” Appl. Phys., A Mater. Sci. Process. 108(4), 975–979 (2012).
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Q.-Y. Cai, Y.-X. Zheng, P.-H. Mao, R.-J. Zhang, D.-X. Zhang, M.-H. Liu, and L.-Y. Chen, “Evolution of optical constants of silicon dioxide on silicon from ultrathin films to thick films,” J. Phys. D 43(44), 445302 (2010).
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Carter, G.

M. Cevro and G. Carter, “Ion-beam and dual-ion-beam sputter deposition of tantalum oxide films,” Opt. Eng. 34(2), 596–606 (1995).
[Crossref]

Cevro, M.

M. Cevro and G. Carter, “Ion-beam and dual-ion-beam sputter deposition of tantalum oxide films,” Opt. Eng. 34(2), 596–606 (1995).
[Crossref]

Chandrasekharan, R.

R. Chandrasekharan, S. Prakash, M. A. Shannon, and R. I. Masel, “Change in radiative optical properties of Ta2O5 thin films due to high-temperature heat treatment,” J. Heat Transfer 129(1), 27–36 (2007).
[Crossref]

Chashnikova, M.

Chen, D.

H. Liu, Y. Jiang, L. Wang, C. Jiang, Y. Ji, and D. Chen, “Study on optical anisotropy properties of SiO2 films with different thermal annealing temperatures,” Chin. Opt. Lett. 11, S10305 (2013).

Chen, L.-Y.

D.-X. Zhang, Y.-X. Zheng, Q.-Y. Cai, W. Lin, K.-N. Wu, P.-H. Mao, R.-J. Zhang, H.-B. Zhao, and L.-Y. Chen, “Thickness-dependence of optical constants for Ta2O5 ultrathin films,” Appl. Phys., A Mater. Sci. Process. 108(4), 975–979 (2012).
[Crossref]

Q.-Y. Cai, Y.-X. Zheng, P.-H. Mao, R.-J. Zhang, D.-X. Zhang, M.-H. Liu, and L.-Y. Chen, “Evolution of optical constants of silicon dioxide on silicon from ultrathin films to thick films,” J. Phys. D 43(44), 445302 (2010).
[Crossref]

Cheng, X.

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

Chun-Xian, T.

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

Cuniot-Ponsard, M.

F. Bridou, M. Cuniot-Ponsard, J. M. Desvignes, A. Gottwald, U. Kroth, and M. Richter, “Polarizing and non-polarizing mirrors for the hydrogen Lyman-α radiation at 121.6 nm,” Appl. Phys., A Mater. Sci. Process. 102(3), 641–649 (2011).
[Crossref]

Danailov, M.

S. Günster, D. Ristau, A. Gatto, N. Kaiser, M. Trovó, and M. Danailov, “Storage ring free-electron lasing at 176 nm--dielectric mirror development for vacuum ultraviolet free-electron lasers,” Appl. Opt. 45(23), 5866–5870 (2006).
[Crossref] [PubMed]

St. Günster, H. Blaschke, D. Ristau, M. Danailov, M. Trovó, A. Gatto, N. Kaiser, F. Sarto, D. Flori, and F. Menchini, “Radiation resistance of single and multilayer coatings against synchrotron radiation,” Proc. SPIE 5250, 146–157 (2004).
[Crossref]

Danev, G.

S. Kitova, S. Youroukov, Tz. Babeva, V. Denishev, and G. Danev, “Argon ion activated deposition of SiO2 films,” J. Optoelectron. Adv. Mater. 7, 2613–2618 (2005).

Davis, J. M.

E. A. West, J. G. Porter, J. M. Davis, G. A. Gary, M. W. Noble, M. Lewis, and R. J. Thomas, “The Marshall Space Flight Center solar ultraviolet magnetograph,” Proc. SPIE 5488, 801 (2004).
[Crossref]

Da-Wei, L.

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

Demiryont, H.

Denis, J.

F. Rubio, J. Denis, J. M. Albella, and J. M. Martínez-Duart, “Sputtered Ta2O5 antireflection coatings for silicon solar cells,” Thin Solid Films 90(4), 405–408 (1982).
[Crossref]

Denishev, V.

S. Kitova, S. Youroukov, Tz. Babeva, V. Denishev, and G. Danev, “Argon ion activated deposition of SiO2 films,” J. Optoelectron. Adv. Mater. 7, 2613–2618 (2005).

Desvignes, J. M.

F. Bridou, M. Cuniot-Ponsard, J. M. Desvignes, A. Gottwald, U. Kroth, and M. Richter, “Polarizing and non-polarizing mirrors for the hydrogen Lyman-α radiation at 121.6 nm,” Appl. Phys., A Mater. Sci. Process. 102(3), 641–649 (2011).
[Crossref]

DeVries, M. J.

E. Franke, C. L. Trimble, M. J. DeVries, J. A. Woollam, M. Schubert, and F. Frost, “Dielectric function of amorphous tantalum oxide from the far infrared to the deep ultraviolet spectral region measured by spectroscopic ellipsometry,” J. Appl. Phys. 88(9), 5166–5174 (2000).
[Crossref]

Dinescu, M.

G. A. Stanciu, M. Filipescu, V. Ion, E. Andronescu, and M. Dinescu, “Optical properties of tantalum oxide thin films obtained by laser deposition techniques,” U. P. B. Sci, Bull., Series B 75, 15–22 (2013).

Dobrowolski, J. A.

Edlou, S. M.

Fedosenko, O.

Filatova, E.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. André, M. Idir, and Ph. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11(16), 3355–3370 (1999).
[Crossref]

E. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 79, 63–66 (1996).
[Crossref]

Filipescu, M.

G. A. Stanciu, M. Filipescu, V. Ion, E. Andronescu, and M. Dinescu, “Optical properties of tantalum oxide thin films obtained by laser deposition techniques,” U. P. B. Sci, Bull., Series B 75, 15–22 (2013).

Flores, Y.

Flori, D.

St. Günster, H. Blaschke, D. Ristau, M. Danailov, M. Trovó, A. Gatto, N. Kaiser, F. Sarto, D. Flori, and F. Menchini, “Radiation resistance of single and multilayer coatings against synchrotron radiation,” Proc. SPIE 5250, 146–157 (2004).
[Crossref]

Franke, E.

E. Franke, C. L. Trimble, M. J. DeVries, J. A. Woollam, M. Schubert, and F. Frost, “Dielectric function of amorphous tantalum oxide from the far infrared to the deep ultraviolet spectral region measured by spectroscopic ellipsometry,” J. Appl. Phys. 88(9), 5166–5174 (2000).
[Crossref]

Friedrich, J.

E. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 79, 63–66 (1996).
[Crossref]

Frost, F.

E. Franke, C. L. Trimble, M. J. DeVries, J. A. Woollam, M. Schubert, and F. Frost, “Dielectric function of amorphous tantalum oxide from the far infrared to the deep ultraviolet spectral region measured by spectroscopic ellipsometry,” J. Appl. Phys. 88(9), 5166–5174 (2000).
[Crossref]

Gao, L.

Gary, G. A.

E. A. West, J. G. Porter, J. M. Davis, G. A. Gary, M. W. Noble, M. Lewis, and R. J. Thomas, “The Marshall Space Flight Center solar ultraviolet magnetograph,” Proc. SPIE 5488, 801 (2004).
[Crossref]

Gatto, A.

S. Günster, D. Ristau, A. Gatto, N. Kaiser, M. Trovó, and M. Danailov, “Storage ring free-electron lasing at 176 nm--dielectric mirror development for vacuum ultraviolet free-electron lasers,” Appl. Opt. 45(23), 5866–5870 (2006).
[Crossref] [PubMed]

St. Günster, H. Blaschke, D. Ristau, M. Danailov, M. Trovó, A. Gatto, N. Kaiser, F. Sarto, D. Flori, and F. Menchini, “Radiation resistance of single and multilayer coatings against synchrotron radiation,” Proc. SPIE 5250, 146–157 (2004).
[Crossref]

R. Thielsch, A. Gatto, J. Heber, and N. Kaiser, “A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition,” Thin Solid Films 410(1-2), 86–93 (2002).
[Crossref]

Geib, K.

Ghodsi, F. E.

F. E. Ghodsi, F. Z. Tepehan, and G. G. Tepehan, “Optical properties of Ta205 thin films deposited using the spin coating process,” Thin Solid Films 295(1-2), 11–15 (1997).
[Crossref]

Gottwald, A.

F. Bridou, M. Cuniot-Ponsard, J. M. Desvignes, A. Gottwald, U. Kroth, and M. Richter, “Polarizing and non-polarizing mirrors for the hydrogen Lyman-α radiation at 121.6 nm,” Appl. Phys., A Mater. Sci. Process. 102(3), 641–649 (2011).
[Crossref]

Gruska, B.

Günster, S.

Günster, St.

St. Günster, H. Blaschke, D. Ristau, M. Danailov, M. Trovó, A. Gatto, N. Kaiser, F. Sarto, D. Flori, and F. Menchini, “Radiation resistance of single and multilayer coatings against synchrotron radiation,” Proc. SPIE 5250, 146–157 (2004).
[Crossref]

Gürtler, K.

K. Gürtler, K. Bange, W. Wagner, F. Rauch, and H. Hantsche, “Characterization of Ta2O5 layers by electron spectroscopy for chemical analysis Rutherford backscattering spectrometry, nuclear reaction analysis and optical methods,” Thin Solid Films 175, 185–189 (1989).
[Crossref]

Hantsche, H.

K. Gürtler, K. Bange, W. Wagner, F. Rauch, and H. Hantsche, “Characterization of Ta2O5 layers by electron spectroscopy for chemical analysis Rutherford backscattering spectrometry, nuclear reaction analysis and optical methods,” Thin Solid Films 175, 185–189 (1989).
[Crossref]

Hao, M.

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

Heber, J.

R. Thielsch, A. Gatto, J. Heber, and N. Kaiser, “A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition,” Thin Solid Films 410(1-2), 86–93 (2002).
[Crossref]

Hofmann, T.

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage thresholds of dielectric UV/VUV-coatings deposited by conventional evaporation, IAD and lBS,” Proc. SPIE 1624, 221–235 (1992).
[Crossref]

Hwangbo, C. K.

S.-H. Woo, C. K. Hwangbo, Y. B. Son, I. C. Moon, G. M. Kang, and K.-S. Lee, “Optical properties of Ta2O5 thin films deposited by plasma ion-assisted deposition,” J. Korean Phys. Soc. 46, S187–S191 (2005).

Idir, M.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. André, M. Idir, and Ph. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11(16), 3355–3370 (1999).
[Crossref]

Ikonen, E.

Inokuti, M.

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(4), 1612–1628 (1980).
[Crossref]

Ion, V.

G. A. Stanciu, M. Filipescu, V. Ion, E. Andronescu, and M. Dinescu, “Optical properties of tantalum oxide thin films obtained by laser deposition techniques,” U. P. B. Sci, Bull., Series B 75, 15–22 (2013).

Jakobs, S.

S. Jakobs, M. Lappschies, U. Schallenberg, O. Stenzel, and S. Wilbrandt, “Characterization of metal-oxide thin films deposited by plasma-assisted reactive magnetron sputtering,” Chin. Opt. Lett. 8(S1), 73–77 (2010).
[Crossref]

Ji, Y.

H. Liu, Y. Jiang, L. Wang, C. Jiang, Y. Ji, and D. Chen, “Study on optical anisotropy properties of SiO2 films with different thermal annealing temperatures,” Chin. Opt. Lett. 11, S10305 (2013).

Jiang, C.

H. Liu, Y. Jiang, L. Wang, C. Jiang, Y. Ji, and D. Chen, “Study on optical anisotropy properties of SiO2 films with different thermal annealing temperatures,” Chin. Opt. Lett. 11, S10305 (2013).

Jiang, Y.

H. Liu, Y. Jiang, L. Wang, C. Jiang, Y. Ji, and D. Chen, “Study on optical anisotropy properties of SiO2 films with different thermal annealing temperatures,” Chin. Opt. Lett. 11, S10305 (2013).

Ji-Fei, W.

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

Ji-Nan, N.

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

Jiong-Tian, L.

X. Cheng, Y. Shuai, W. Ji-Fei, N. Ji-Nan, M. Hao, Q. Ying-Huai, L. Jiong-Tian, L. Da-Wei, and T. Chun-Xian, “Effect of oxygen vacancy on the band gap and nanosecond laser-induced damage threshold of Ta2O5 films,” Chin. Phys. Lett. 29(8), 084207 (2012).
[Crossref]

Kaiser, N.

S. Günster, D. Ristau, A. Gatto, N. Kaiser, M. Trovó, and M. Danailov, “Storage ring free-electron lasing at 176 nm--dielectric mirror development for vacuum ultraviolet free-electron lasers,” Appl. Opt. 45(23), 5866–5870 (2006).
[Crossref] [PubMed]

St. Günster, H. Blaschke, D. Ristau, M. Danailov, M. Trovó, A. Gatto, N. Kaiser, F. Sarto, D. Flori, and F. Menchini, “Radiation resistance of single and multilayer coatings against synchrotron radiation,” Proc. SPIE 5250, 146–157 (2004).
[Crossref]

R. Thielsch, A. Gatto, J. Heber, and N. Kaiser, “A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition,” Thin Solid Films 410(1-2), 86–93 (2002).
[Crossref]

Kang, G. M.

S.-H. Woo, C. K. Hwangbo, Y. B. Son, I. C. Moon, G. M. Kang, and K.-S. Lee, “Optical properties of Ta2O5 thin films deposited by plasma ion-assisted deposition,” J. Korean Phys. Soc. 46, S187–S191 (2005).

Kessler, H.

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage thresholds of dielectric UV/VUV-coatings deposited by conventional evaporation, IAD and lBS,” Proc. SPIE 1624, 221–235 (1992).
[Crossref]

Khawaja, E. E.

E. E. Khawaja and S. G. Tomlin, “The optical properties of thin films of tantalum pentoxide and zirconium dioxide,” Thin Solid Films 30(2), 361–369 (1975).
[Crossref]

Kischkat, J.

Kitova, S.

S. Kitova, S. Youroukov, Tz. Babeva, V. Denishev, and G. Danev, “Argon ion activated deposition of SiO2 films,” J. Optoelectron. Adv. Mater. 7, 2613–2618 (2005).

Klinkmüller, M.

Kohana, O.

K. Kukli, J. Aarik, A. Aidla, O. Kohana, T. Uustare, and W. Sammelselg, “Properties of tantalum oxide thin films grown by atomic layer deposition,” Thin Solid Films 260(2), 135–142 (1995).
[Crossref]

Kolbe, J.

J. Kolbe, H. Kessler, T. Hofmann, F. Meyer, H. Schink, and D. Ristau, “Optical properties and damage thresholds of dielectric UV/VUV-coatings deposited by conventional evaporation, IAD and lBS,” Proc. SPIE 1624, 221–235 (1992).
[Crossref]

Koukis, D. I.

T. J. Bright, J. I. Watjen, Z. M. Zhang, C. Muratore, A. A. Voevodin, D. I. Koukis, D. B. Tanner, and D. J. Arenas, “Infrared optical properties of amorphous and nanocrystalline Ta2O5 thin films,” J. Appl. Phys. 114(8), 083515 (2013).
[Crossref]

Kroth, U.

F. Bridou, M. Cuniot-Ponsard, J. M. Desvignes, A. Gottwald, U. Kroth, and M. Richter, “Polarizing and non-polarizing mirrors for the hydrogen Lyman-α radiation at 121.6 nm,” Appl. Phys., A Mater. Sci. Process. 102(3), 641–649 (2011).
[Crossref]

Kukli, K.

K. Kukli, J. Aarik, A. Aidla, O. Kohana, T. Uustare, and W. Sammelselg, “Properties of tantalum oxide thin films grown by atomic layer deposition,” Thin Solid Films 260(2), 135–142 (1995).
[Crossref]

Lacan, P.

Lamminpää, A.

Lappschies, M.

S. Jakobs, M. Lappschies, U. Schallenberg, O. Stenzel, and S. Wilbrandt, “Characterization of metal-oxide thin films deposited by plasma-assisted reactive magnetron sputtering,” Chin. Opt. Lett. 8(S1), 73–77 (2010).
[Crossref]

Larruquert, J. I.

L. V. Rodríguez-de Marcos, J. A. Méndez, and J. I. Larruquert, “Tuning sum rules with window functions for optical constant evaluation,” J. Opt. 18(7), 075606 (2016).
[Crossref]

J. I. Larruquert, L. V. Rodríguez-de Marcos, J. A. Méndez, P. J. Martin, and A. Bendavid, “High reflectance ta-C coatings in the extreme ultraviolet,” Opt. Express 21(23), 27537–27549 (2013).
[Crossref] [PubMed]

Lee, K.-S.

S.-H. Woo, C. K. Hwangbo, Y. B. Son, I. C. Moon, G. M. Kang, and K.-S. Lee, “Optical properties of Ta2O5 thin films deposited by plasma ion-assisted deposition,” J. Korean Phys. Soc. 46, S187–S191 (2005).

Lemarchand, F.

Lequime, M.

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http://henke.lbl.gov/optical_constants/ .

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables 2005” (version 2.1) [Online] Available: http://physics.nist.gov/ffast (2006, May 29). National Institute of Standards and Technology, Gaithersburg, MD; originally published as C. T. Chantler, J. Phys. Chem. Ref. Data 29 (2000) 597; and C. T. Chantler, J. Phys. Chem. Ref. Data 24, 71 (1995).

Downloaded from the following web of Physical Reference Data, Physics Laboratory at NIST: http://physics.nist.gov/PhysRefData/FFast/Text/cover.html

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Figures (8)

Fig. 1
Fig. 1 Comparison between the experimental measurements and calculations with SiO2 optical constants obtained in this subsection. a: transmittance (normalized to the transmittance of the bare MgF2 substrate) of a 56-nm thick film on a MgF2 substrate. b: reflectance of a 125-nm thick film on a Si substrate. Wavelength is in log scale.
Fig. 2
Fig. 2 Ellipsometry measurements at 77° on a 56-nm thick SiO2 film (a) and at 76° on a 125-nm thick SiO2 film (b) deposited on Si wafers, along with the fits performed with a single Lorentz oscillator and calculations with optical constants obtained in this subsection.
Fig. 3
Fig. 3 SiO2 optical constants (a: linear axis; b: log-axis) versus wavelength in log axis.
Fig. 4
Fig. 4 Comparison between the experimental measurements and calculations with Ta2O5 optical constants obtained in this subsection. a: transmittance (normalized to the transmittance of the bare MgF2 substrate) of a 53-nm thick film on a MgF2 substrate. b: reflectance of a 53-nm thick film on a glass substrate. Wavelength is in log scale.
Fig. 5
Fig. 5 Ellipsometry measurements at 63° on a 53-nm thick Ta2O5 film deposited on a Si wafer, along with the fit performed with 3 Lorentz oscillators and calculations with the optical constants obtained in this subsection.
Fig. 6
Fig. 6 Ta2O5 optical constants (a: linear axis; b: log-axis) versus wavelength in log axis.
Fig. 7
Fig. 7 ζ versus the central energy Ew for sum rules represented through Eqs. (12) to (16) calculated with H2 window function and with the optical constants of SiO2 (a) and of Ta2O5 (b). The five inertial-like sum rules are identified in the legend by the power of photon energy in the integral. Window function parameters at each Ew are given by: Ew = (E1E2)0.5, E2/E1 = 3, c1(2) = E1(2)/10.
Fig. 8
Fig. 8 neff versus the central energy Ew for sum rule represented through Eq. (18) calculated with H1 window function and with the optical constants of SiO2 (left axis) and of Ta2O5 (right axis). Window function parameters at each Ew are given by: Ew = (E1E2)0.5, E2/E1 = 3, c = E1/5.

Tables (1)

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Table 1 Scheme of the procedure and data sources for the iterative KK analysis.

Equations (18)

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φ( E )= E π P 0 ln[ R( E' ) ] E ' 2 E 2 dE'
n(E)1= 2 π P 0 E'k( E' ) E ' 2 E 2 dE'
r= (n+ik)1 (n+ik)+1
n+ik= 1+r 1r
T fs T s =exp( 4πkz λ )
n eff = 4 ε 0 m πN e 2 2 0 E'k(E')dE'
0 [ n(E)1 ]dE=0
ζ= 0 [ n(E)1 ]dE 0 | n(E)1 |dE
H 1 ( E )= 1 π [ L( E; E 2 ,c )L( E; E 1 ,c ) ]
H 2 ( E )= 1 π [ L( E; E 2 , c 2 )+L( E; E 1 , c 1 )2L( E; E 1 E 2 , c 1 + c 2 2 ) ]
L( E; E j ,c )ln( E j 2 E 2 icE ) j = 1,2
0 E ' 2 Re{ H 2 ( E' )[ N( E' )1 ] }dE'=0
0 E ' 1 Im{ H 2 ( E' )[ N( E' )1 ] }dE'=0
0 Re{ H 2 ( E' )[ N( E' )1 ] }dE'=0
0 E'Im{ H 2 ( E' )[ N( E' )1 ] }dE'=0
0 E ' 2 Re{ H 2 ( E' )[ N( E' )1 ] }dE'=0
0 E ' 3 Im{ H 1 ( E' )[ N( E' )1 ] }dE'= 2 ω p 2 4 ( E 1 2 E 2 2 )
n eff = 4 ε 0 m N e 2 2 ( E 1 2 E 2 2 ) 0 E ' 3 Im{ H 1 ( E' )[ N( E' )1 ] }dE'

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