Abstract

During the fabrication of multilayer-dielectric (MLD) thin-film-coated optics, such as the diffraction gratings used in OMEGA EP’s pulse compressors, acid piranha cleaning can lead to the formation of chemically induced delamination defects. We investigate the causes of these defects and describe a mechanism for the deformation and failure of the MLD coating in response to hydrogen peroxide in the cleaning solution. A fracture mechanics model is developed and used to calculate the crack path that maximizes the energy-release rate, which is found to be consistent with the characteristic fracture pattern observed in MLD coating delamination defects.

© 2013 Optical Society of America

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  1. M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
    [CrossRef]
  2. X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
    [CrossRef]
  3. J. Neauport, E. Lavastre, G. Razé, G. Dupuy, N. Bonod, M. Balas, G. de Villele, J. Flamand, S. Kaladgew, F. Desserouer, “Effect of electric field on laser induced damage threshold of multilayer dielectric gratings,” Opt. Express 15, 12508–12522 (2007).
    [CrossRef]
  4. Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
    [CrossRef]
  5. Y. Shan, H. He, C. Wei, S. Li, M. Zhou, D. Li, Y. Zhao, “Geometrical characteristics and damage morphology of nodules grown from artificial seeds in multilayer coating,” Appl. Opt. 49, 4290–4295 (2010).
    [CrossRef]
  6. J. F. DeFord, M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
    [CrossRef]
  7. M. D. Feit, L. W. Hrubesh, A. M. Rubenchik, J. N. Wong, “Scaling relations for laser damage initiation craters,” Proc. SPIE 4347, 316–323 (2001).
    [CrossRef]
  8. W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
    [CrossRef]
  9. H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
    [CrossRef]
  10. K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
    [CrossRef]
  11. H. A. Macleod, D. Richmond, “Moisture penetration patterns in thin films,” Thin Solid Films 37, 163–169 (1976).
    [CrossRef]
  12. H. K. Pulker, “Characterization of optical thin films,” Appl. Opt. 18, 1969–1977 (1979).
    [CrossRef]
  13. H. Howard, J. C. Lambropoulos, S. Jacobs, “Dependence of thermal stresses on substrate thickness during wet processing of large coated optics,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.3.
  14. B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
    [CrossRef]
  15. B. Ashe, C. Giacofei, G. Myhre, A. W. Schmid, “Optimizing a cleaning process for multilayer-dielectric-(MLD) diffraction grating,” Proc. SPIE 6720, 67200N (2007).
    [CrossRef]
  16. S. Chen, B. Sheng, X. Xu, S. Fu, “Wet-cleaning of contaminants on the surface of multilayer dielectric pulse compressor gratings by the piranha solution,” Proc. SPIE 7655, 765522 (2010).
    [CrossRef]
  17. H. M. Jensen, “Analysis of mode mixity in blister tests,” Int. J. Fract. 94, 79–88 (1998).
    [CrossRef]
  18. J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
    [CrossRef]
  19. MLD coating samples were dried with a filtered nitrogen gun because this standard technique avoids water spots and particle accumulation on the optic’s surface. Delicate, etched MLD grating samples would not be dried with nitrogen, however, because of the potential for pillar damage. Nitrogen drying is not expected to play a role in the defect formation mechanism; defect formation results were found to be similar on ambient-dried MLD grating samples and nitrogen-dried MLD coating samples.
  20. K. Mehrotra, H. P. Howard, S. D. Jacobs, J. C. Lambropoulos, “Mechanical characterization of ‘blister’ defects on optical oxide multilayers using nanoindentation,” in Nanocomposites, Nanostructures and Heterostructures of Correlated Oxide Systems, T. Endo, H. Nishikawa, N. Iwata, A. Bhattacharya, L. W. Martin, eds., Mat. Res. Soc. Symp. Proc. (Cambridge University, 2012), Vol. 1454, pp. 215–220.
  21. H. Leplan, B. Geenen, J. Y. Robic, Y. Pauleau, “Residual stresses in evaporated silicon dioxide thin films: correlation with deposition parameters and aging behavior,” J. Appl. Phys. 78, 962–968 (1995).
    [CrossRef]
  22. J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
    [CrossRef]
  23. J. F. Anzellotti, D. J. Smith, R. J. Sczupak, Z. R. Chrzan, “Stress and environmental shift characteristics of HfO2/SiO2 multilayer coatings,” Proc. SPIE 2966, 258–264 (1997).
    [CrossRef]
  24. J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.
  25. R. Thielsch, A. Gatto, N. Kaiser, “Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region,” Appl. Opt. 41, 3211–3217 (2002).
    [CrossRef]
  26. R. Thielsch, A. Gatto, J. Heber, 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, 86–93 (2002).
    [CrossRef]
  27. S. L. Dole, O. Hunter, C. J. Wooge, “Elastic properties of monoclinic hafnium oxide at room temperature,” J. Am. Ceram. Soc. 60, 488–490 (1977).
    [CrossRef]
  28. M. J. Bamber, K. E. Cooke, A. B. Mann, B. Derby, “Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation,” Thin Solid Films 398–399, 299–305 (2001).
    [CrossRef]
  29. Optical Glass Data Sheets, available online at http://www.schott.com/advanced_optics/us/abbe_datasheets/schott_datasheet_all_us.pdf , Schott, North America.
  30. M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface,” J. Appl. Mech. 56, 270–278 (1989).
    [CrossRef]
  31. J. Dundurs, “Discussion: ‘edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading’ (Bogy, D. B., 1968, ASME J. Appl. Mech., 35, pp. 460–466),” J. Appl. Mech. 36, 650–652 (1969).
    [CrossRef]
  32. J. W. Hutchinson, Z. Suo, “Mixed mode cracking in layered materials,” in Advances in Applied Mechanics, J. W. Hutchinson, T. Y. Wu, eds. (Academic, 1992), Vol. 29, pp. 163–191.
  33. M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface: tabulated solution coefficients,” Tech. Rep.  (Harvard University, Division of Applied Sciences, 1989).
  34. Z. Suo, J. W. Hutchinson, “Interface crack between two elastic layers,” Int. J. Fract. 43, 1–18 (1990).
    [CrossRef]
  35. M.-Y. He, J. W. Hutchinson, “Crack deflection at an interface between dissimilar elastic materials,” Int. J. Solids Struct. 25, 1053–1067 (1989).
    [CrossRef]

2013 (1)

2012 (1)

2011 (2)

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[CrossRef]

Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
[CrossRef]

2010 (2)

S. Chen, B. Sheng, X. Xu, S. Fu, “Wet-cleaning of contaminants on the surface of multilayer dielectric pulse compressor gratings by the piranha solution,” Proc. SPIE 7655, 765522 (2010).
[CrossRef]

Y. Shan, H. He, C. Wei, S. Li, M. Zhou, D. Li, Y. Zhao, “Geometrical characteristics and damage morphology of nodules grown from artificial seeds in multilayer coating,” Appl. Opt. 49, 4290–4295 (2010).
[CrossRef]

2007 (4)

J. Neauport, E. Lavastre, G. Razé, G. Dupuy, N. Bonod, M. Balas, G. de Villele, J. Flamand, S. Kaladgew, F. Desserouer, “Effect of electric field on laser induced damage threshold of multilayer dielectric gratings,” Opt. Express 15, 12508–12522 (2007).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

B. Ashe, C. Giacofei, G. Myhre, A. W. Schmid, “Optimizing a cleaning process for multilayer-dielectric-(MLD) diffraction grating,” Proc. SPIE 6720, 67200N (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

2006 (1)

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

2005 (1)

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

2002 (2)

R. Thielsch, A. Gatto, J. Heber, 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, 86–93 (2002).
[CrossRef]

R. Thielsch, A. Gatto, N. Kaiser, “Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region,” Appl. Opt. 41, 3211–3217 (2002).
[CrossRef]

2001 (2)

M. J. Bamber, K. E. Cooke, A. B. Mann, B. Derby, “Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation,” Thin Solid Films 398–399, 299–305 (2001).
[CrossRef]

M. D. Feit, L. W. Hrubesh, A. M. Rubenchik, J. N. Wong, “Scaling relations for laser damage initiation craters,” Proc. SPIE 4347, 316–323 (2001).
[CrossRef]

2000 (1)

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

1998 (1)

H. M. Jensen, “Analysis of mode mixity in blister tests,” Int. J. Fract. 94, 79–88 (1998).
[CrossRef]

1997 (1)

J. F. Anzellotti, D. J. Smith, R. J. Sczupak, Z. R. Chrzan, “Stress and environmental shift characteristics of HfO2/SiO2 multilayer coatings,” Proc. SPIE 2966, 258–264 (1997).
[CrossRef]

1995 (1)

H. Leplan, B. Geenen, J. Y. Robic, Y. Pauleau, “Residual stresses in evaporated silicon dioxide thin films: correlation with deposition parameters and aging behavior,” J. Appl. Phys. 78, 962–968 (1995).
[CrossRef]

1993 (1)

J. F. DeFord, M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
[CrossRef]

1990 (1)

Z. Suo, J. W. Hutchinson, “Interface crack between two elastic layers,” Int. J. Fract. 43, 1–18 (1990).
[CrossRef]

1989 (2)

M.-Y. He, J. W. Hutchinson, “Crack deflection at an interface between dissimilar elastic materials,” Int. J. Solids Struct. 25, 1053–1067 (1989).
[CrossRef]

M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface,” J. Appl. Mech. 56, 270–278 (1989).
[CrossRef]

1979 (1)

1977 (1)

S. L. Dole, O. Hunter, C. J. Wooge, “Elastic properties of monoclinic hafnium oxide at room temperature,” J. Am. Ceram. Soc. 60, 488–490 (1977).
[CrossRef]

1976 (1)

H. A. Macleod, D. Richmond, “Moisture penetration patterns in thin films,” Thin Solid Films 37, 163–169 (1976).
[CrossRef]

1969 (1)

J. Dundurs, “Discussion: ‘edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading’ (Bogy, D. B., 1968, ASME J. Appl. Mech., 35, pp. 460–466),” J. Appl. Mech. 36, 650–652 (1969).
[CrossRef]

Aiello, A. F.

Alvisi, M.

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

Anzellotti, J. F.

J. F. Anzellotti, D. J. Smith, R. J. Sczupak, Z. R. Chrzan, “Stress and environmental shift characteristics of HfO2/SiO2 multilayer coatings,” Proc. SPIE 2966, 258–264 (1997).
[CrossRef]

Ashe, B.

B. Ashe, C. Giacofei, G. Myhre, A. W. Schmid, “Optimizing a cleaning process for multilayer-dielectric-(MLD) diffraction grating,” Proc. SPIE 6720, 67200N (2007).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

Balas, M.

Bamber, M. J.

M. J. Bamber, K. E. Cooke, A. B. Mann, B. Derby, “Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation,” Thin Solid Films 398–399, 299–305 (2001).
[CrossRef]

Bonod, N.

Chen, S.

S. Chen, B. Sheng, X. Xu, S. Fu, “Wet-cleaning of contaminants on the surface of multilayer dielectric pulse compressor gratings by the piranha solution,” Proc. SPIE 7655, 765522 (2010).
[CrossRef]

Cheng, X.

Chrzan, Z. R.

J. F. Anzellotti, D. J. Smith, R. J. Sczupak, Z. R. Chrzan, “Stress and environmental shift characteristics of HfO2/SiO2 multilayer coatings,” Proc. SPIE 2966, 258–264 (1997).
[CrossRef]

Cooke, K. E.

M. J. Bamber, K. E. Cooke, A. B. Mann, B. Derby, “Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation,” Thin Solid Films 398–399, 299–305 (2001).
[CrossRef]

Culakova, Z.

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

de Villele, G.

DeFord, J. F.

J. F. DeFord, M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
[CrossRef]

Derby, B.

M. J. Bamber, K. E. Cooke, A. B. Mann, B. Derby, “Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation,” Thin Solid Films 398–399, 299–305 (2001).
[CrossRef]

Desserouer, F.

Di Giulio, M.

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

Ding, T.

Dole, S. L.

S. L. Dole, O. Hunter, C. J. Wooge, “Elastic properties of monoclinic hafnium oxide at room temperature,” J. Am. Ceram. Soc. 60, 488–490 (1977).
[CrossRef]

Dressler, J. G.

Dundurs, J.

J. Dundurs, “Discussion: ‘edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading’ (Bogy, D. B., 1968, ASME J. Appl. Mech., 35, pp. 460–466),” J. Appl. Mech. 36, 650–652 (1969).
[CrossRef]

Dupuy, G.

Edwards, N. R.

Fan, Z.

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

Feit, M. D.

M. D. Feit, L. W. Hrubesh, A. M. Rubenchik, J. N. Wong, “Scaling relations for laser damage initiation craters,” Proc. SPIE 4347, 316–323 (2001).
[CrossRef]

Flamand, J.

Fu, S.

S. Chen, B. Sheng, X. Xu, S. Fu, “Wet-cleaning of contaminants on the surface of multilayer dielectric pulse compressor gratings by the piranha solution,” Proc. SPIE 7655, 765522 (2010).
[CrossRef]

Gatto, A.

R. Thielsch, A. Gatto, J. Heber, 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, 86–93 (2002).
[CrossRef]

R. Thielsch, A. Gatto, N. Kaiser, “Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region,” Appl. Opt. 41, 3211–3217 (2002).
[CrossRef]

Geenen, B.

H. Leplan, B. Geenen, J. Y. Robic, Y. Pauleau, “Residual stresses in evaporated silicon dioxide thin films: correlation with deposition parameters and aging behavior,” J. Appl. Phys. 78, 962–968 (1995).
[CrossRef]

Giacofei, C.

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

B. Ashe, C. Giacofei, G. Myhre, A. W. Schmid, “Optimizing a cleaning process for multilayer-dielectric-(MLD) diffraction grating,” Proc. SPIE 6720, 67200N (2007).
[CrossRef]

Hand, R. D.

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

He, H.

He, H. B.

Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
[CrossRef]

He, M.-Y.

M.-Y. He, J. W. Hutchinson, “Crack deflection at an interface between dissimilar elastic materials,” Int. J. Solids Struct. 25, 1053–1067 (1989).
[CrossRef]

M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface,” J. Appl. Mech. 56, 270–278 (1989).
[CrossRef]

M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface: tabulated solution coefficients,” Tech. Rep.  (Harvard University, Division of Applied Sciences, 1989).

Heber, J.

R. Thielsch, A. Gatto, J. Heber, 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, 86–93 (2002).
[CrossRef]

Howard, H.

H. Howard, J. C. Lambropoulos, S. Jacobs, “Dependence of thermal stresses on substrate thickness during wet processing of large coated optics,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.3.

Howard, H. P.

H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
[CrossRef]

K. Mehrotra, H. P. Howard, S. D. Jacobs, J. C. Lambropoulos, “Mechanical characterization of ‘blister’ defects on optical oxide multilayers using nanoindentation,” in Nanocomposites, Nanostructures and Heterostructures of Correlated Oxide Systems, T. Endo, H. Nishikawa, N. Iwata, A. Bhattacharya, L. W. Martin, eds., Mat. Res. Soc. Symp. Proc. (Cambridge University, 2012), Vol. 1454, pp. 215–220.

Hrubesh, L. W.

M. D. Feit, L. W. Hrubesh, A. M. Rubenchik, J. N. Wong, “Scaling relations for laser damage initiation craters,” Proc. SPIE 4347, 316–323 (2001).
[CrossRef]

Huang, H.

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

Hunter, O.

S. L. Dole, O. Hunter, C. J. Wooge, “Elastic properties of monoclinic hafnium oxide at room temperature,” J. Am. Ceram. Soc. 60, 488–490 (1977).
[CrossRef]

Hutchinson, J. W.

Z. Suo, J. W. Hutchinson, “Interface crack between two elastic layers,” Int. J. Fract. 43, 1–18 (1990).
[CrossRef]

M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface,” J. Appl. Mech. 56, 270–278 (1989).
[CrossRef]

M.-Y. He, J. W. Hutchinson, “Crack deflection at an interface between dissimilar elastic materials,” Int. J. Solids Struct. 25, 1053–1067 (1989).
[CrossRef]

J. W. Hutchinson, Z. Suo, “Mixed mode cracking in layered materials,” in Advances in Applied Mechanics, J. W. Hutchinson, T. Y. Wu, eds. (Academic, 1992), Vol. 29, pp. 163–191.

M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface: tabulated solution coefficients,” Tech. Rep.  (Harvard University, Division of Applied Sciences, 1989).

Jacobs, S.

H. Howard, J. C. Lambropoulos, S. Jacobs, “Dependence of thermal stresses on substrate thickness during wet processing of large coated optics,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.3.

Jacobs, S. D.

H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
[CrossRef]

K. Mehrotra, H. P. Howard, S. D. Jacobs, J. C. Lambropoulos, “Mechanical characterization of ‘blister’ defects on optical oxide multilayers using nanoindentation,” in Nanocomposites, Nanostructures and Heterostructures of Correlated Oxide Systems, T. Endo, H. Nishikawa, N. Iwata, A. Bhattacharya, L. W. Martin, eds., Mat. Res. Soc. Symp. Proc. (Cambridge University, 2012), Vol. 1454, pp. 215–220.

Jensen, H. M.

H. M. Jensen, “Analysis of mode mixity in blister tests,” Int. J. Fract. 94, 79–88 (1998).
[CrossRef]

Jiao, H.

Kaiser, N.

R. Thielsch, A. Gatto, J. Heber, 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, 86–93 (2002).
[CrossRef]

R. Thielsch, A. Gatto, N. Kaiser, “Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region,” Appl. Opt. 41, 3211–3217 (2002).
[CrossRef]

Kaladgew, S.

Keck, J.

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

Kessler, T. J.

H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

Kong, W.

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

Kosc, T. Z.

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

Kozlov, A.

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

Kozlov, A. A.

Kozlowski, M. R.

J. F. DeFord, M. R. Kozlowski, “Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings,” Proc. SPIE 1848, 455–472 (1993).
[CrossRef]

Kupinski, P.

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

Lambropoulos, J. C.

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

H. Howard, J. C. Lambropoulos, S. Jacobs, “Dependence of thermal stresses on substrate thickness during wet processing of large coated optics,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.3.

K. Mehrotra, H. P. Howard, S. D. Jacobs, J. C. Lambropoulos, “Mechanical characterization of ‘blister’ defects on optical oxide multilayers using nanoindentation,” in Nanocomposites, Nanostructures and Heterostructures of Correlated Oxide Systems, T. Endo, H. Nishikawa, N. Iwata, A. Bhattacharya, L. W. Martin, eds., Mat. Res. Soc. Symp. Proc. (Cambridge University, 2012), Vol. 1454, pp. 215–220.

Lavastre, E.

Leplan, H.

H. Leplan, B. Geenen, J. Y. Robic, Y. Pauleau, “Residual stresses in evaporated silicon dioxide thin films: correlation with deposition parameters and aging behavior,” J. Appl. Phys. 78, 962–968 (1995).
[CrossRef]

Li, D.

Li, D. W.

Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
[CrossRef]

Li, S.

Li, X.

Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
[CrossRef]

Liu, S.

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

Lu, J.

Ma, B.

Macleod, H. A.

H. A. Macleod, D. Richmond, “Moisture penetration patterns in thin films,” Thin Solid Films 37, 163–169 (1976).
[CrossRef]

Mann, A. B.

M. J. Bamber, K. E. Cooke, A. B. Mann, B. Derby, “Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation,” Thin Solid Films 398–399, 299–305 (2001).
[CrossRef]

Manwaring, I. R. T.

Marrone, S. G.

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

Marshall, K. L.

H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

Mehrotra, K.

K. Mehrotra, H. P. Howard, S. D. Jacobs, J. C. Lambropoulos, “Mechanical characterization of ‘blister’ defects on optical oxide multilayers using nanoindentation,” in Nanocomposites, Nanostructures and Heterostructures of Correlated Oxide Systems, T. Endo, H. Nishikawa, N. Iwata, A. Bhattacharya, L. W. Martin, eds., Mat. Res. Soc. Symp. Proc. (Cambridge University, 2012), Vol. 1454, pp. 215–220.

Myhre, G.

B. Ashe, C. Giacofei, G. Myhre, A. W. Schmid, “Optimizing a cleaning process for multilayer-dielectric-(MLD) diffraction grating,” Proc. SPIE 6720, 67200N (2007).
[CrossRef]

Neauport, J.

Oliver, J. B.

H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

Papernov, S.

Pauleau, Y.

H. Leplan, B. Geenen, J. Y. Robic, Y. Pauleau, “Residual stresses in evaporated silicon dioxide thin films: correlation with deposition parameters and aging behavior,” J. Appl. Phys. 78, 962–968 (1995).
[CrossRef]

Perrone, M. R.

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

Protopapa, M. L.

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

Pulker, H. K.

Razé, G.

Richmond, D.

H. A. Macleod, D. Richmond, “Moisture penetration patterns in thin films,” Thin Solid Films 37, 163–169 (1976).
[CrossRef]

Rigatti, A. L.

H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

Robic, J. Y.

H. Leplan, B. Geenen, J. Y. Robic, Y. Pauleau, “Residual stresses in evaporated silicon dioxide thin films: correlation with deposition parameters and aging behavior,” J. Appl. Phys. 78, 962–968 (1995).
[CrossRef]

Roux, A. N.

Rubenchik, A. M.

M. D. Feit, L. W. Hrubesh, A. M. Rubenchik, J. N. Wong, “Scaling relations for laser damage initiation craters,” Proc. SPIE 4347, 316–323 (2001).
[CrossRef]

Schmid, A. W.

H. P. Howard, A. F. Aiello, J. G. Dressler, N. R. Edwards, T. J. Kessler, A. A. Kozlov, I. R. T. Manwaring, K. L. Marshall, J. B. Oliver, S. Papernov, A. L. Rigatti, A. N. Roux, A. W. Schmid, N. P. Slaney, C. C. Smith, B. N. Taylor, S. D. Jacobs, “Improving the performance of high-laser-damage-threshold, multilayer dielectric pulse-compression gratings through low-temperature chemical cleaning,” Appl. Opt. 52, 1682–1692 (2013).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, C. Smith, R. D. Hand, “Stress compensation in hafnia/silica optical coatings by inclusion of alumina layers,” Opt. Express 20, 16596–16610 (2012).
[CrossRef]

B. Ashe, C. Giacofei, G. Myhre, A. W. Schmid, “Optimizing a cleaning process for multilayer-dielectric-(MLD) diffraction grating,” Proc. SPIE 6720, 67200N (2007).
[CrossRef]

B. Ashe, K. L. Marshall, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, J. Keck, A. Kozlov, “Evaluation of cleaning methods for multilayer diffraction gratings,” Proc. SPIE 6403, 64030O (2007).
[CrossRef]

K. L. Marshall, Z. Culakova, B. Ashe, C. Giacofei, A. L. Rigatti, T. J. Kessler, A. W. Schmid, J. B. Oliver, A. Kozlov, “Vapor-phase-deposited organosilane coatings as ‘hardening’ agents for high-peak-power laser optics,” Proc. SPIE 6674, 667407 (2007).
[CrossRef]

J. B. Oliver, T. J. Kessler, H. Huang, J. Keck, A. L. Rigatti, A. W. Schmid, A. Kozlov, T. Z. Kosc, “Thin-film design for multilayer diffraction gratings,” Proc. SPIE 5991, 59911A (2005).
[CrossRef]

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

Sczupak, R. J.

J. F. Anzellotti, D. J. Smith, R. J. Sczupak, Z. R. Chrzan, “Stress and environmental shift characteristics of HfO2/SiO2 multilayer coatings,” Proc. SPIE 2966, 258–264 (1997).
[CrossRef]

Shan, Y.

Shan, Y. G.

Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
[CrossRef]

Shao, J.

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

Shen, J.

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

Shen, Z.

X. Cheng, Z. Shen, H. Jiao, J. Zhang, B. Ma, T. Ding, J. Lu, X. Wang, Z. Wang, “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50, C357–C363 (2011).
[CrossRef]

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

Sheng, B.

S. Chen, B. Sheng, X. Xu, S. Fu, “Wet-cleaning of contaminants on the surface of multilayer dielectric pulse compressor gratings by the piranha solution,” Proc. SPIE 7655, 765522 (2010).
[CrossRef]

Slaney, N. P.

Smith, C.

Smith, C. C.

Smith, D. J.

J. F. Anzellotti, D. J. Smith, R. J. Sczupak, Z. R. Chrzan, “Stress and environmental shift characteristics of HfO2/SiO2 multilayer coatings,” Proc. SPIE 2966, 258–264 (1997).
[CrossRef]

Suo, Z.

Z. Suo, J. W. Hutchinson, “Interface crack between two elastic layers,” Int. J. Fract. 43, 1–18 (1990).
[CrossRef]

J. W. Hutchinson, Z. Suo, “Mixed mode cracking in layered materials,” in Advances in Applied Mechanics, J. W. Hutchinson, T. Y. Wu, eds. (Academic, 1992), Vol. 29, pp. 163–191.

Taylor, B. N.

Thielsch, R.

R. Thielsch, A. Gatto, J. Heber, 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, 86–93 (2002).
[CrossRef]

R. Thielsch, A. Gatto, N. Kaiser, “Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region,” Appl. Opt. 41, 3211–3217 (2002).
[CrossRef]

Valentini, A.

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

Vasanelli, L.

M. Alvisi, M. Di Giulio, S. G. Marrone, M. R. Perrone, M. L. Protopapa, A. Valentini, L. Vasanelli, “HfO2 films with high laser damage threshold,” Thin Solid Films 358, 250–258 (2000).
[CrossRef]

Wang, X.

Wang, Y.

Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
[CrossRef]

Wang, Z.

Wei, C.

Wong, J. N.

M. D. Feit, L. W. Hrubesh, A. M. Rubenchik, J. N. Wong, “Scaling relations for laser damage initiation craters,” Proc. SPIE 4347, 316–323 (2001).
[CrossRef]

Wooge, C. J.

S. L. Dole, O. Hunter, C. J. Wooge, “Elastic properties of monoclinic hafnium oxide at room temperature,” J. Am. Ceram. Soc. 60, 488–490 (1977).
[CrossRef]

Xu, X.

S. Chen, B. Sheng, X. Xu, S. Fu, “Wet-cleaning of contaminants on the surface of multilayer dielectric pulse compressor gratings by the piranha solution,” Proc. SPIE 7655, 765522 (2010).
[CrossRef]

Yao, J.

W. Kong, S. Liu, J. Shen, Z. Shen, J. Shao, Z. Fan, J. Yao, “Study on LIDT of MDGs for different fabrication processes,” Microelectron. Eng. 83, 1426–1429 (2006).
[CrossRef]

Zhang, J.

Zhao, Y.

Zhao, Y. A.

Y. G. Shan, H. B. He, Y. Wang, X. Li, D. W. Li, Y. A. Zhao, “Electrical field enhancement and laser damage growth in high-reflective coatings at 1064 nm,” Opt. Commun. 284, 625–629 (2011).
[CrossRef]

Zhou, M.

Appl. Opt. (5)

Int. J. Fract. (2)

Z. Suo, J. W. Hutchinson, “Interface crack between two elastic layers,” Int. J. Fract. 43, 1–18 (1990).
[CrossRef]

H. M. Jensen, “Analysis of mode mixity in blister tests,” Int. J. Fract. 94, 79–88 (1998).
[CrossRef]

Int. J. Solids Struct. (1)

M.-Y. He, J. W. Hutchinson, “Crack deflection at an interface between dissimilar elastic materials,” Int. J. Solids Struct. 25, 1053–1067 (1989).
[CrossRef]

J. Am. Ceram. Soc. (1)

S. L. Dole, O. Hunter, C. J. Wooge, “Elastic properties of monoclinic hafnium oxide at room temperature,” J. Am. Ceram. Soc. 60, 488–490 (1977).
[CrossRef]

J. Appl. Mech. (2)

M.-Y. He, J. W. Hutchinson, “Kinking of a crack out of an interface,” J. Appl. Mech. 56, 270–278 (1989).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Optical Glass Data Sheets, available online at http://www.schott.com/advanced_optics/us/abbe_datasheets/schott_datasheet_all_us.pdf , Schott, North America.

J. B. Oliver, P. Kupinski, A. L. Rigatti, A. W. Schmid, J. C. Lambropoulos, S. Papernov, A. Kozlov, R. D. Hand, “Modification of stresses in evaporated hafnia coatings for use in vacuum,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper WD6.

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MLD coating samples were dried with a filtered nitrogen gun because this standard technique avoids water spots and particle accumulation on the optic’s surface. Delicate, etched MLD grating samples would not be dried with nitrogen, however, because of the potential for pillar damage. Nitrogen drying is not expected to play a role in the defect formation mechanism; defect formation results were found to be similar on ambient-dried MLD grating samples and nitrogen-dried MLD coating samples.

K. Mehrotra, H. P. Howard, S. D. Jacobs, J. C. Lambropoulos, “Mechanical characterization of ‘blister’ defects on optical oxide multilayers using nanoindentation,” in Nanocomposites, Nanostructures and Heterostructures of Correlated Oxide Systems, T. Endo, H. Nishikawa, N. Iwata, A. Bhattacharya, L. W. Martin, eds., Mat. Res. Soc. Symp. Proc. (Cambridge University, 2012), Vol. 1454, pp. 215–220.

H. Howard, J. C. Lambropoulos, S. Jacobs, “Dependence of thermal stresses on substrate thickness during wet processing of large coated optics,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.3.

Supplementary Material (1)

» Media 1: MOV (1309 KB)     

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Figures (13)

Fig. 1.
Fig. 1.

Nomarski micrographs of representative delamination defects. (a) and (b) Defects associated with nodules. (c) A defect associated with a piece of surface debris. (d) and (e) Defects that formed along scratches. (f) A defect that was not observed with any apparent surface feature. Defects were generated by submerging the samples in 21 piranha, with the following temperature treatments: (a) and (b) 90°C soak for 2 h with 30 min heating and cooling ramps; (c) sample submerged at 70°C and cooled to room temperature over 2 h; (d) and (e) sample submerged at 90°C and cooled over 30 min; and (f) sample submerged at 70°C and cooled over 30 min.

Fig. 2.
Fig. 2.

Scanning electron microscope (SEM) images showing (a) a delamination defect observed from a bird’s eye view, showing its surface structure; (b) a high-magnification, cross-sectional view of a defect bisected by focused-ion-beam (FIB) milling, showing the crack path through MLD layers near the surface. The angle ω shows how the crack kink angles were measured for the fracture mechanics analysis; and (c) a larger view of the FIB-milled defect’s cross section.

Fig. 3.
Fig. 3.

Series of 75μm×75μm frames captured from a Nomarski microscope video (Media 1) of an individual delamination defect’s formation approximately 45 min after a 2 h submersion in 21 piranha at 90°C. The defect’s development is shown (a) 0 s, (b) 2.0 s, (c) 2.6 s, (d) 2.7 s, (e) 3.0 s, (f) 6.0 s, (g) 11.0 s, and (h) 20.0 s after it began to form.

Fig. 4.
Fig. 4.

Nomarski micrographs of a 160μm×140μm region containing the defect seen in Fig. 3. Images were captured (a) 45 min, (b) 60 min, (c) 61 min, (d) 100 min, (e) 48 h, and (f) 6 months after the sample was removed from the piranha solution.

Fig. 5.
Fig. 5.

Schematic illustrating the hypothesized delamination defect formation mechanism: (a) undisturbed MLD coating, (b) initial pressure development in coating and deformation, (c) kinked fracture at edge of pressurized blister, and finally (d) propagation of the crack to MLD surface. Light bands represent hafnia layers in the coating, while dark bands represent silica layers.

Fig. 6.
Fig. 6.

Nomarski micrographs of two delamination defects with schematics showing hypothesized cross-sectional geometries. (a) Defect initiated between the second and third MLD layer pairs, with arc-shaped cracks. (b) Substrate-initiated defect with fracture through all 14 layer pairs. Fracture in the bottom few layers occurred as circular cracks at the blister’s perimeter, while cracks in upper layers were arc-shaped.

Fig. 7.
Fig. 7.

SEM images showing cross sections of single-layer oxide films used in nanoindentation experiments. (a) A 160 nm layer of hafnia. (b) A 180 nm layer of silica. There was no visible interface between the substrate and the amorphous silica film.

Fig. 8.
Fig. 8.

Schematic of a pressurized blister in an MLD film with a residual film stress.

Fig. 9.
Fig. 9.

Measurement of blister diameter.

Fig. 10.
Fig. 10.

Dependence of blister deformations on internal blister pressure for intrinsic coating stresses of zero (dashed curves) and 150 MPa (solid curves). Inset plot shows a larger view of the pc=3MPa curves.

Fig. 11.
Fig. 11.

Geometry of kinked crack.

Fig. 12.
Fig. 12.

Relationship between energy-release rate ratio G/G0 and kink angle for several mode mixity angles for the BK7/MLD coating material combination.

Fig. 13.
Fig. 13.

Energy-release-rate ratio versus kink angle for two problem length scales: fracture involving the full MLD coating and fracture involving only the first MLD layer. The blue band shows the broad range of energetically preferred kink angles between ω=45° and 60°.

Tables (3)

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Table 1. ANOVA Results for the Delamination Defect Screening Experiment

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Table 2. Material Properties Used in the Fracture Mechanics Analysis

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Table 3. Values for the Dundurs Parameters α, β, and Bimaterial Modulus ε

Equations (10)

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μMLDupper=μhafVhaf+μsilVsil,BMLDupper=BhafVhaf+BsilVsil,
1μMLDlower=Vhafμhaf+Vsilμsil,1BMLDlower=VhafBhaf+VsilBsil,
ν=3B2μ6B+2μ,E=2μ(1+ν).
112(1ν2)ρddρ[1ρddρ(ρξ)]φ¯ξ+pcR42Eh4ρ2=σR2Eh4ξ,ρddρ[1ρddρ(ρφ¯)]+12ξ2=0,ξ(ρ)=dw¯dρ,φ¯(ρ)=RφEh3,φ=dΦdr,
ρ2ξ+ρξ(Sρ+1)ξ=Pρ3,
ξ(ρ)=P8(ρ3ρ)
w¯(ρ)=ξdρ=P32(ρ42ρ2+1).
GG0=|c|2+|d|2+2Re[cdexp(2iψ¯)]q2,q=1β21+α2,ψ¯=ψ+εln(a/h),
α=μ1(1ν2)μ2(1ν1)μ1(1ν2)+μ2(1ν1),β=12[μ1(12ν2)μ2(12ν1)μ1(1ν2)+μ2(1ν1)],ε=12πln(1β1+β),
p0=16E3(1ν2)(hR)4.

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