Abstract

We study the evolution of the absorptance of amorphous metal oxide thin films when exposed to intense CW laser radiation measured using a photothermal microscope. The evolution of the absorptance is characterized by a nonexponential decay. Different models that incorporate linear and nonlinear absorption, free carrier absorption, and defect diffusion are used to fit the results, with constraints imposed on the fit parameters to scale with power and intensity. The model that best fits is that two types of interband defects are passivated independently, one by a one-photon process and the other one by a two-photon process.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. P. O’Reilly and J. Robertson, “Theory of defects in vitreous silicon dioxide,” Phys. Rev. B Condens. Matter 27(6), 3780–3795 (1983).
    [Crossref]
  2. A. S. Foster, F. Lopez Gejo, A. L. Shluger, and R. M. Nieminen, “Vacancy and interstitial defects in hafnia,” Phys. Rev. B Condens. Matter Mater. Phys. 65(17), 174117 (2002).
    [Crossref]
  3. A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
    [Crossref]
  4. P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
    [PubMed]
  5. C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
    [Crossref]
  6. C. R. Wolfe, M. R. Kozlowski, J. H. Campbell, F. Rainer, A. J. Morgan, and R. P. Gonzales, “Laser Conditioning of Optical Thin Films” NIST Special Publication 801, Laser Induced Damage in Optical Materials: 1989, p. 360–375 (1990)
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  8. E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
    [Crossref] [PubMed]
  9. E. A. Domené and O. E. Martínez, “Note: Focus error detection device for thermal expansion-recovery microscopy (ThERM),” Rev. Sci. Instrum. 84(1), 016104 (2013).
    [Crossref] [PubMed]
  10. O. E. Martínez, F. Balzarotti, and N. Mingolo, “Thermoreflectance and photodeflection combined for microscopic characterization of metallic surfaces,” Appl. Phys. B 90(1), 69–77 (2008).
    [Crossref]
  11. C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.
  12. S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).
  13. R. Kohlrausch, “Theorie des elektrischen rckstandes in der leidener asche,” Ann. Phys. 167(2), 179–214 (1854).
    [Crossref]
  14. R. A. B. Devine, “On the physical models of annealing of radiation induced defects in amorphous SiO2,” Nucl. Instrum. Methods Phys. Res. 46(1-4), 261–264 (1990).
    [Crossref]
  15. J. C. Phillips, “Microscopic aspects of Stretched Exponential Relaxation (SER) in homogeneous molecular and network glasses and polymers,” J. Non-Cryst. Solids 357(22-23), 3853–3865 (2011).
    [Crossref]
  16. J. C. Phillips, “Stretched exponential relaxation in molecular and electronic glasses,” Rep. Prog. Phys. 59(9), 1133–1207 (1996).
    [Crossref]
  17. J. C. Phillips, “Slow dynamics in glasses: A comparison between theory and experiment,” Phys. Rev. B 73(10), 104206 (2006).
  18. S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).
  19. F. V. Grigoriev, E. V. Katkova, A. V. Sulimov, V. B. Sulimov, and A. V. Tikhonravov, “Annealing of deposited SiO2 thin films: full atomistic simulation results,” Opt. Mater. Express 6(12), 3960 (2016).
    [Crossref]

2017 (1)

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (1)

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

2014 (2)

S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

2013 (2)

A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
[Crossref]

E. A. Domené and O. E. Martínez, “Note: Focus error detection device for thermal expansion-recovery microscopy (ThERM),” Rev. Sci. Instrum. 84(1), 016104 (2013).
[Crossref] [PubMed]

2011 (1)

J. C. Phillips, “Microscopic aspects of Stretched Exponential Relaxation (SER) in homogeneous molecular and network glasses and polymers,” J. Non-Cryst. Solids 357(22-23), 3853–3865 (2011).
[Crossref]

2008 (1)

O. E. Martínez, F. Balzarotti, and N. Mingolo, “Thermoreflectance and photodeflection combined for microscopic characterization of metallic surfaces,” Appl. Phys. B 90(1), 69–77 (2008).
[Crossref]

2006 (1)

J. C. Phillips, “Slow dynamics in glasses: A comparison between theory and experiment,” Phys. Rev. B 73(10), 104206 (2006).

2002 (1)

A. S. Foster, F. Lopez Gejo, A. L. Shluger, and R. M. Nieminen, “Vacancy and interstitial defects in hafnia,” Phys. Rev. B Condens. Matter Mater. Phys. 65(17), 174117 (2002).
[Crossref]

1996 (1)

J. C. Phillips, “Stretched exponential relaxation in molecular and electronic glasses,” Rep. Prog. Phys. 59(9), 1133–1207 (1996).
[Crossref]

1990 (1)

R. A. B. Devine, “On the physical models of annealing of radiation induced defects in amorphous SiO2,” Nucl. Instrum. Methods Phys. Res. 46(1-4), 261–264 (1990).
[Crossref]

1989 (1)

S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

1983 (1)

E. P. O’Reilly and J. Robertson, “Theory of defects in vitreous silicon dioxide,” Phys. Rev. B Condens. Matter 27(6), 3780–3795 (1983).
[Crossref]

1854 (1)

R. Kohlrausch, “Theorie des elektrischen rckstandes in der leidener asche,” Ann. Phys. 167(2), 179–214 (1854).
[Crossref]

Balzarotti, F.

O. E. Martínez, F. Balzarotti, and N. Mingolo, “Thermoreflectance and photodeflection combined for microscopic characterization of metallic surfaces,” Appl. Phys. B 90(1), 69–77 (2008).
[Crossref]

Braunlich, P.

S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Casper, R. T.

S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Day, T.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

Deng, J.

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

Devine, R. A. B.

R. A. B. Devine, “On the physical models of annealing of radiation induced defects in amorphous SiO2,” Nucl. Instrum. Methods Phys. Res. 46(1-4), 261–264 (1990).
[Crossref]

Domené, E. A.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

E. A. Domené and O. E. Martínez, “Note: Focus error detection device for thermal expansion-recovery microscopy (ThERM),” Rev. Sci. Instrum. 84(1), 016104 (2013).
[Crossref] [PubMed]

Emmert, L.

Emmert, L. A.

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Fan, H.

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

Fejer, M.

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Fejer, M. M.

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
[Crossref]

Foster, A. S.

A. S. Foster, F. Lopez Gejo, A. L. Shluger, and R. M. Nieminen, “Vacancy and interstitial defects in hafnia,” Phys. Rev. B Condens. Matter Mater. Phys. 65(17), 174117 (2002).
[Crossref]

Grigoriev, F. V.

Jankowska, E.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

Jones, S. C.

S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Katkova, E. V.

Kelly, P.

S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Kessler, T. J.

S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

Kohlrausch, R.

R. Kohlrausch, “Theorie des elektrischen rckstandes in der leidener asche,” Ann. Phys. 167(2), 179–214 (1854).
[Crossref]

Kozlov, A. A.

S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

Krous, E.

Krous, E. M.

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Langston, P.

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Langston, P. F.

Li, D.

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

Lopez Gejo, F.

A. S. Foster, F. Lopez Gejo, A. L. Shluger, and R. M. Nieminen, “Vacancy and interstitial defects in hafnia,” Phys. Rev. B Condens. Matter Mater. Phys. 65(17), 174117 (2002).
[Crossref]

Markosyan, A.

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Markosyan, A. S.

A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
[Crossref]

Marozas, B.

S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

Martínez, O. E.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

E. A. Domené and O. E. Martínez, “Note: Focus error detection device for thermal expansion-recovery microscopy (ThERM),” Rev. Sci. Instrum. 84(1), 016104 (2013).
[Crossref] [PubMed]

O. E. Martínez, F. Balzarotti, and N. Mingolo, “Thermoreflectance and photodeflection combined for microscopic characterization of metallic surfaces,” Appl. Phys. B 90(1), 69–77 (2008).
[Crossref]

Menoni, C.

A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
[Crossref]

Menoni, C. S.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Mingolo, N.

O. E. Martínez, F. Balzarotti, and N. Mingolo, “Thermoreflectance and photodeflection combined for microscopic characterization of metallic surfaces,” Appl. Phys. B 90(1), 69–77 (2008).
[Crossref]

Nguyen, D. N.

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Nieminen, R. M.

A. S. Foster, F. Lopez Gejo, A. L. Shluger, and R. M. Nieminen, “Vacancy and interstitial defects in hafnia,” Phys. Rev. B Condens. Matter Mater. Phys. 65(17), 174117 (2002).
[Crossref]

O’Reilly, E. P.

E. P. O’Reilly and J. Robertson, “Theory of defects in vitreous silicon dioxide,” Phys. Rev. B Condens. Matter 27(6), 3780–3795 (1983).
[Crossref]

Oliver, J. B.

S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

Papernov, S.

S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

Patel, D.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
[Crossref]

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Phillips, J. C.

J. C. Phillips, “Microscopic aspects of Stretched Exponential Relaxation (SER) in homogeneous molecular and network glasses and polymers,” J. Non-Cryst. Solids 357(22-23), 3853–3865 (2011).
[Crossref]

J. C. Phillips, “Slow dynamics in glasses: A comparison between theory and experiment,” Phys. Rev. B 73(10), 104206 (2006).

J. C. Phillips, “Stretched exponential relaxation in molecular and electronic glasses,” Rep. Prog. Phys. 59(9), 1133–1207 (1996).
[Crossref]

Qi, J.

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

Qiang, Y.

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

Reagan, B.

Robertson, J.

E. P. O’Reilly and J. Robertson, “Theory of defects in vitreous silicon dioxide,” Phys. Rev. B Condens. Matter 27(6), 3780–3795 (1983).
[Crossref]

Rocca, J. J.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

Route, R.

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
[Crossref]

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Rudolph, W.

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Schiltz, D.

E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

P. F. Langston, E. Krous, D. Schiltz, D. Patel, L. Emmert, A. Markosyan, B. Reagan, K. Wernsing, Y. Xu, Z. Sun, R. Route, M. M. Fejer, J. J. Rocca, W. Rudolph, and C. S. Menoni, “Point defects in Sc2O3 thin films by ion beam sputtering,” Appl. Opt. 53(4), A276–A280 (2014).
[PubMed]

Shen, X.-A.

S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Shluger, A. L.

A. S. Foster, F. Lopez Gejo, A. L. Shluger, and R. M. Nieminen, “Vacancy and interstitial defects in hafnia,” Phys. Rev. B Condens. Matter Mater. Phys. 65(17), 174117 (2002).
[Crossref]

Shvydky, A.

S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

Sulimov, A. V.

Sulimov, V. B.

Sun, Z.

Tikhonravov, A. V.

Tollerud, J.

C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

Wernsing, K.

Xu, C.

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

Xu, Y.

Yi, P.

C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

Ann. Phys. (1)

R. Kohlrausch, “Theorie des elektrischen rckstandes in der leidener asche,” Ann. Phys. 167(2), 179–214 (1854).
[Crossref]

Appl. Opt. (1)

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[Crossref]

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A. S. Markosyan, R. Route, M. M. Fejer, D. Patel, and C. Menoni, “Study of spontaneous and induced absorption in amorphous Ta2O5 and SiO2 dielectric thin films,” J. Appl. Phys. 113(13), 133104 (2013).
[Crossref]

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J. C. Phillips, “Microscopic aspects of Stretched Exponential Relaxation (SER) in homogeneous molecular and network glasses and polymers,” J. Non-Cryst. Solids 357(22-23), 3853–3865 (2011).
[Crossref]

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[Crossref]

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S. Papernov, A. A. Kozlov, J. B. Oliver, T. J. Kessler, A. Shvydky, and B. Marozas, “Near-ultraviolet absorption annealing in hafnium oxide thin films subjected to continuous-wave laser radiation,” Opt. Eng. 53(12), 122504 (2014).

S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen, and P. Kelly, “Recent progress on laser- induced modifications and intrinsic bulk damage of wide -gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Opt. Mater. Express (1)

Phys. Rev. B (1)

J. C. Phillips, “Slow dynamics in glasses: A comparison between theory and experiment,” Phys. Rev. B 73(10), 104206 (2006).

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[Crossref]

Phys. Rev. B Condens. Matter Mater. Phys. (1)

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[Crossref]

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[Crossref]

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E. A. Domené, D. Schiltz, D. Patel, T. Day, E. Jankowska, O. E. Martínez, J. J. Rocca, and C. S. Menoni, “Thin film absorption characterization by focus error thermal lensing,” Rev. Sci. Instrum. 88(12), 123104 (2017).
[Crossref] [PubMed]

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C. Xu, D. Li, H. Fan, J. Deng, J. Qi, P. Yi, and Y. Qiang, “Effect of different post-treatment methods on optical properties, absorption and nanosecond laser-induced damage threshold of Ta2O5 films,” Thin Solid Films 580, 12–20 (2015).
[Crossref]

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C. S. Menoni, E. M. Krous, D. Patel, P. Langston, J. Tollerud, D. N. Nguyen, L. A. Emmert, A. Markosyan, R. Route, M. Fejer, and W. Rudolph, “Advances in ion beam sputtered Sc2O3 for optical interference coatings,” Proc. SPIE7842, 784202.

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Figures (11)

Fig. 1
Fig. 1 Schematics of the photothermal microscope. M1 and M2: 1064nm-mirrors. M3 and M4: HeNe-mirrors. LF: long pass filter (cutoff 750nm). SF: short pass filter (cuttof 850nm). f0 collimator lens (pump beam). Ob: objective lens (fOb = 10mm). BS1: beam splitter (R: 90% probe reflectivity). BS2: beam splitter (R: 50% probe reflectivity) TL: tube lens (fTL = 200mm, focuses the probe beam onto the back focal plane of the objective). LC: cylindrical lenses (f = 75mm). Dz, Z0 and δ0: distances of the focus measurement system. XYZ: Micrometric translation stage. ND: neutral filters. LED: Lighting. CAM: Camera. 4Q: Four-Quadrant detector.
Fig. 2
Fig. 2 Calibration of the FE signal against the absorption loss of the samples measured by Photothermal Common Path Interferometry (PCI).
Fig. 3
Fig. 3 (a) Absorptance map for a SiO2 film deposited on a fused silica substrate. The dashed lines delimit the initial sweep of 40μm by 40μm. (b) Average absorptance over 22 pixels as a function of time. The pixel size is 4 μm. The change in absorptance due to laser annealing is 0.5 ppm.
Fig. 4
Fig. 4 Absorptance decay for the six cases of Table 2 as a function of time showing that the annealing process is characterized by an apparent fast process in the first minute followed by a slower process of tens of minutes.
Fig. 5
Fig. 5 Schematics of a typical band diagram of an oxide showing the different mechanisms used to analyze the absorptance recovery. (1) One photon absorption from a shalow state. (2) Two photon absorption from a deeper shallow state. (3) Free electron intraband absorption in the conduction band. (4) n photon absorption from a deep trap state. (5) Decay to a deep trap state. Not indicated are defect annihilation by temperature or collision. In the case of Sc2O3 the bandgap is 5.7eV.
Fig. 6
Fig. 6 Fit with the expression for stretched exponential relaxation using Kohlrausch’s expression (Eq. (18)).
Fig. 7
Fig. 7 Fit for measurement A1 with 1, 2, 3, 4 and 10 photon processes. a) Full measurement. b) Zoom out of the short time evolution.
Fig. 8
Fig. 8 Fit of the absorptance decay for sample A1 for one type of defect with an excitation process that includes a combination of one and two photons absorbed. The fit is not adequate for short times.
Fig. 9
Fig. 9 a) Two types of defects that anneal each by a one photon mechanism: (M_1 + 1). b) Two type of defects that anneal one by a one photon process and the other one by a two photon process (M_1 + 2). c) Two type of defects that anneal each by a two photon process (M_2 + 2)
Fig. 10
Fig. 10 Rate coefficients as a function of the pump power for the two defects, one and one photon annealing mechanism (M_1 + 1). a) k1 = beam area*b1 for the fast one photon contribution and linear fit (dashed lines indicate the confidence bounds from the linear fit). b) k2 = (beam area)*b2 for the slow one photon contribution and linear fit (dashed lines indicate the confidence bounds from the linear fit).
Fig. 11
Fig. 11 Rate coefficients as a function of the pump power for the two defects, one and two photon annealing mechanism (M_1 + 2). a) k1 = beam area*b1 for the one photon contribution and linear fit (dashed lines indicate the confidence bounds from the linear fit). b) k2 = (beam area)2*b2 for the two photon contribution and linear fit (dashed lines indicate the confidence bounds from the linear fit).

Tables (7)

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Table 1 Data for the different sets of measurements.

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Table 2 Parameters obtained for the fit using Kohlrausch’s expression (Eq. (18)). The values in the parenthesis are the confidence interval (95%).

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Table 3 Multiphoton process. Parameter 1/τ0, n: number of photons simultaneously absorbed. In parenthesis the 95% confidence interval.

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Table 4 Fitted parameters for the one and two photon annealing model for a single defect. In parenthesis the 95% confidence interval. Fitted function: Eq. (19)

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Table 5 Rate parameters for a two defects one photon annealing (M_1 + 1). In parenthesis the 95% confidence interval. Fit with Eq. (20)

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Table 6 Rate parameters for a two defects one and two photon annealing (M_1 + 2). In parenthesis the 95% confidence interval. Fit with Eq. (21)

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Table 7 Rate parameters for a two defects with two photon annealing (M_2 + 2). In parenthesis the 95% confidence interval. Fit with Eq. (22)

Equations (22)

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  d n film dT l film d n substrate dT μ  
μ= D πf = σ probe f pump = D π σ probe 2 1.7KHz
FE| f pump = [ (C1+C3)-(C2+C4) ]| f pump C1+C2+C3+C4 1 <P pump > = Signal Amplitude (V) <P pump (W)> Signal Sum (V)
c( t )=c(0)exp( ( t τ ) β )  
 β= d d+2  
  C(x,y,t) C 0 (x,y) =exp( t τ ) 
  1 τ =a I n ( x,y )=a I 0 n exp(( n ρ 2 2 ))= 1 τ 0 exp(( n ρ 2 2 )) 
 S exp( ( ρ 2 2 ) )exp( t τ )ρdρdφ 
 g=exp( ( ρ 2 2 ) ) 
  t ' = t τ  0  
S 0 1 exp(( g n t´))dg= Γ( 1 n )Γ( 1 n ,t' ) n t 1/n  
S (1exp(t')) t´  
S π erf( t´ ) 2 t´  
  1 τ = a 1 I 0 exp(( ρ 2 2 ))+ a 2 I 0 2 exp(( 2 ρ 2 2 )) 
 S 0 1 exp[(t( b 1 g+ b 2 g 2 ))]dg= π exp( c 1 2 t 4 )[ erf( t ( c 1 +2 c 2 ) 2 )erf( c 1 t 2 ) ] 2 c 2 t  
α=a( N 0 N )+bN=[ a 1+σIτ + b 1+ 1 σIτ ] N 0 (a+bσIτ) N 0  
 αI=a N 0 I+bσ N 0 τ I 2  
f( t )=aexp( ( t τ ) β )+c 
 S=a π exp( c 1 2 t 4 )[ erf( t ( c 1 +2 c 2 ) 2 )erf( c 1 t 2 ) ] 2 c 2 t +c 
 Sfit= a 1 (1exp( b 1 t)) ( b 1 t) + a 2 (1exp( b 2 t)) ( b 2 t) +c 
 Sfit= a 1 (1exp( b 1 t)) ( b 1 t)  +   a 2 Γ(0.5)Γ(0.5, b 2 t) sqrt( b 2 t) +c
 Sfit= a 1 Γ(0.5)Γ(0.5, b 1 t) sqrt( b 1 t)  +   a 2 Γ(0.5)Γ(0.5, b 2 t) sqrt( b 2 t) +c 

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