Abstract

In this paper, we present measurements of angle- and wavelength-resolved diffuse scattering of EUV radiation on a Mo/Si multilayer. Our sample is optimized for high reflectivity at 13.5 nm wavelength near-normal incidence. We present a rigorous theoretical analysis of the off-specular EUV scattering on the basis of the distorted-wave Born approximation. We prove that the determination of the interface roughness power spectral density (PSD) is only possible by considering geometry-dependent and dynamic contributions. The scattering from multilayer mirrors leads to an intrinsic enhancement in off-specular intensity independent of roughness properties. The thickness oscillations in the scattering intensity (Kiessig fringes) are found to cause additional dynamic enhancement in analogy to Bragg-like peaks for grazing incidence geometry. Considering these effects, the interface PSD is consistently determined.

© 2014 Optical Society of America

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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]
  19. E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
    [CrossRef]
  20. D. K. G. de Boer, A. J. G. Leenaers, and W. W. van den Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent x-ray fluorescence,” J. Phys. III 4, 1559–1564 (1994).
    [CrossRef]
  21. D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992).
    [CrossRef]
  22. E. M. Gullikson and D. G. Stearns, “Asymmetric extreme ultraviolet scattering from sputter-deposited multilayers,” Phys. Rev. B 59, 13273–13277 (1999).
    [CrossRef]
  23. H. Kiessig, “Interferenz von Röntgenstrahlen an dünnen Schichten,” Ann. Phys. 402, 769–788 (1931).
    [CrossRef]
  24. V. M. Kaganer, S. A. Stepanov, and R. Köhler, “Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces,” Phys. Rev. B 52, 16369–16372 (1995).
    [CrossRef]
  25. T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
    [CrossRef]
  26. P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
    [CrossRef]
  27. G. Palasantzas and J. Krim, “Effect of the form of the height–height correlation function on diffuse x-ray scattering from a self-affine surface,” Phys. Rev. B 48, 2873–2877 (1993).
    [CrossRef]

2014 (1)

2011 (1)

2009 (2)

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

2006 (1)

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Engin. 83, 703–706 (2006).
[CrossRef]

2003 (1)

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

2002 (1)

S. Braun, H. Mai, M. Moss, R. Scholz, and A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys. 41, 4074–4081 (2002).
[CrossRef]

2001 (1)

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

1999 (1)

E. M. Gullikson and D. G. Stearns, “Asymmetric extreme ultraviolet scattering from sputter-deposited multilayers,” Phys. Rev. B 59, 13273–13277 (1999).
[CrossRef]

1996 (2)

D. K. G. de Boer, “X-ray scattering and x-ray fluorescence from materials with rough interfaces,” Phys. Rev. B 53, 6048–6064 (1996).
[CrossRef]

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

1995 (2)

D. K. G. de Boer, “X-ray reflection and transmission by rough surfaces,” Phys. Rev. B 51, 5297–5305 (1995).
[CrossRef]

V. M. Kaganer, S. A. Stepanov, and R. Köhler, “Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces,” Phys. Rev. B 52, 16369–16372 (1995).
[CrossRef]

1994 (3)

D. K. G. de Boer, A. J. G. Leenaers, and W. W. van den Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent x-ray fluorescence,” J. Phys. III 4, 1559–1564 (1994).
[CrossRef]

V. Holý and T. Baumbach, “Nonspecular x-ray reflection from rough multilayers,” Phys. Rev. B 49, 10668–10676 (1994).
[CrossRef]

C. Amra, “Light scattering from multilayer optics. I. tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[CrossRef]

1993 (4)

C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef]

V. Holý, J. Kubuena, I. Ohlídal, K. Lischka, and W. Plotz, “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896–15903 (1993).
[CrossRef]

E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

G. Palasantzas and J. Krim, “Effect of the form of the height–height correlation function on diffuse x-ray scattering from a self-affine surface,” Phys. Rev. B 48, 2873–2877 (1993).
[CrossRef]

1992 (1)

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992).
[CrossRef]

1988 (1)

S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2297–2311 (1988).
[CrossRef]

1983 (1)

1980 (1)

1976 (1)

P. Croce and L. Névot, “étude des couches minces et des surfaces par réflexion rasante, spéculaire ou diffuse, de rayons x,” Rev. Phys. Appl. 11, 113–125 (1976).
[CrossRef]

1931 (1)

H. Kiessig, “Interferenz von Röntgenstrahlen an dünnen Schichten,” Ann. Phys. 402, 769–788 (1931).
[CrossRef]

Amra, C.

Baumbach, T.

V. Holý and T. Baumbach, “Nonspecular x-ray reflection from rough multilayers,” Phys. Rev. B 49, 10668–10676 (1994).
[CrossRef]

Beckhoff, B.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Bennett, J. M.

Benoit, N.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Engin. 83, 703–706 (2006).
[CrossRef]

Blaschke, H.

Blume, H.

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Cambridge University, 1965).

Brandt, G.

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Braun, S.

S. Braun, H. Mai, M. Moss, R. Scholz, and A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys. 41, 4074–4081 (2002).
[CrossRef]

Bruel, L.

Cheng, X.

Chitu, L.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Croce, P.

P. Croce and L. Névot, “étude des couches minces et des surfaces par réflexion rasante, spéculaire ou diffuse, de rayons x,” Rev. Phys. Appl. 11, 113–125 (1976).
[CrossRef]

de Boer, D. K. G.

D. K. G. de Boer, “X-ray scattering and x-ray fluorescence from materials with rough interfaces,” Phys. Rev. B 53, 6048–6064 (1996).
[CrossRef]

D. K. G. de Boer, “X-ray reflection and transmission by rough surfaces,” Phys. Rev. B 51, 5297–5305 (1995).
[CrossRef]

D. K. G. de Boer, A. J. G. Leenaers, and W. W. van den Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent x-ray fluorescence,” J. Phys. III 4, 1559–1564 (1994).
[CrossRef]

Duparré, A.

Eden, J.

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

Elson, J. M.

Feigl, T.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Engin. 83, 703–706 (2006).
[CrossRef]

Fliegauf, R.

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Garoff, S.

S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2297–2311 (1988).
[CrossRef]

Gottwald, A.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Grèzes-Besset, C.

Gullikson, E. M.

E. M. Gullikson and D. G. Stearns, “Asymmetric extreme ultraviolet scattering from sputter-deposited multilayers,” Phys. Rev. B 59, 13273–13277 (1999).
[CrossRef]

Harada, T.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Heinzmann, U.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Herffurth, T.

Hinze, P.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Høghøj, P.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Holý, V.

V. Holý and T. Baumbach, “Nonspecular x-ray reflection from rough multilayers,” Phys. Rev. B 49, 10668–10676 (1994).
[CrossRef]

V. Holý, J. Kubuena, I. Ohlídal, K. Lischka, and W. Plotz, “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896–15903 (1993).
[CrossRef]

Jergel, M.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Kaganer, V. M.

V. M. Kaganer, S. A. Stepanov, and R. Köhler, “Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces,” Phys. Rev. B 52, 16369–16372 (1995).
[CrossRef]

Kaiser, N.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Engin. 83, 703–706 (2006).
[CrossRef]

Keckes, J.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Kiessig, H.

H. Kiessig, “Interferenz von Röntgenstrahlen an dünnen Schichten,” Ann. Phys. 402, 769–788 (1931).
[CrossRef]

Klein, R.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Köhler, R.

V. M. Kaganer, S. A. Stepanov, and R. Köhler, “Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces,” Phys. Rev. B 52, 16369–16372 (1995).
[CrossRef]

Krim, J.

G. Palasantzas and J. Krim, “Effect of the form of the height–height correlation function on diffuse x-ray scattering from a self-affine surface,” Phys. Rev. B 48, 2873–2877 (1993).
[CrossRef]

Krumrey, M.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

Kubuena, J.

V. Holý, J. Kubuena, I. Ohlídal, K. Lischka, and W. Plotz, “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896–15903 (1993).
[CrossRef]

Lauer, R.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Leenaers, A. J. G.

D. K. G. de Boer, A. J. G. Leenaers, and W. W. van den Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent x-ray fluorescence,” J. Phys. III 4, 1559–1564 (1994).
[CrossRef]

Leson, A.

S. Braun, H. Mai, M. Moss, R. Scholz, and A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys. 41, 4074–4081 (2002).
[CrossRef]

Lischka, K.

V. Holý, J. Kubuena, I. Ohlídal, K. Lischka, and W. Plotz, “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896–15903 (1993).
[CrossRef]

Lott, D.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Luby, S.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Mai, H.

S. Braun, H. Mai, M. Moss, R. Scholz, and A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys. 41, 4074–4081 (2002).
[CrossRef]

Maier, G.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Majkova, E.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Metzger, T. H.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Meyer, B.

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Moss, M.

S. Braun, H. Mai, M. Moss, R. Scholz, and A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys. 41, 4074–4081 (2002).
[CrossRef]

Müller, R.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

Névot, L.

P. Croce and L. Névot, “étude des couches minces et des surfaces par réflexion rasante, spéculaire ou diffuse, de rayons x,” Rev. Phys. Appl. 11, 113–125 (1976).
[CrossRef]

Ohlídal, I.

V. Holý, J. Kubuena, I. Ohlídal, K. Lischka, and W. Plotz, “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896–15903 (1993).
[CrossRef]

Palasantzas, G.

G. Palasantzas and J. Krim, “Effect of the form of the height–height correlation function on diffuse x-ray scattering from a self-affine surface,” Phys. Rev. B 48, 2873–2877 (1993).
[CrossRef]

Peisl, J.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Plotz, W.

V. Holý, J. Kubuena, I. Ohlídal, K. Lischka, and W. Plotz, “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896–15903 (1993).
[CrossRef]

Rahn, J. P.

Richter, M.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

Roth, S.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Salditt, T.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Schärpf, O.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Scherr, H.

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

Scholz, F.

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

Scholz, R.

S. Braun, H. Mai, M. Moss, R. Scholz, and A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys. 41, 4074–4081 (2002).
[CrossRef]

Scholze, F.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Schröder, S.

Schwarz, U. D.

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Siffalovic, P.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Sinha, S. K.

S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2297–2311 (1988).
[CrossRef]

Sirota, E. B.

S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2297–2311 (1988).
[CrossRef]

Spiller, E.

E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

Stanley, H. B.

S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2297–2311 (1988).
[CrossRef]

Stearns, D.

E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

Stearns, D. G.

E. M. Gullikson and D. G. Stearns, “Asymmetric extreme ultraviolet scattering from sputter-deposited multilayers,” Phys. Rev. B 59, 13273–13277 (1999).
[CrossRef]

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992).
[CrossRef]

Stepanov, S. A.

V. M. Kaganer, S. A. Stepanov, and R. Köhler, “Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces,” Phys. Rev. B 52, 16369–16372 (1995).
[CrossRef]

Thornagel, R.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Timmann, A.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Trost, M.

Tsuru, T.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Tuemmler, J.

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Tummler, J.

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

Ulm, G.

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Unglaub, D.

van den Hoogenhof, W. W.

D. K. G. de Boer, A. J. G. Leenaers, and W. W. van den Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent x-ray fluorescence,” J. Phys. III 4, 1559–1564 (1994).
[CrossRef]

Vignaud, G.

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

Vogel, K.

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Weser, J.

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Cambridge University, 1965).

Yamamoto, M.

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Yulin, S.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Engin. 83, 703–706 (2006).
[CrossRef]

Zhang, J.

Ann. Phys. (1)

H. Kiessig, “Interferenz von Röntgenstrahlen an dünnen Schichten,” Ann. Phys. 402, 769–788 (1931).
[CrossRef]

Appl. Opt. (5)

J. Appl. Phys. (2)

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992).
[CrossRef]

E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. III (1)

D. K. G. de Boer, A. J. G. Leenaers, and W. W. van den Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent x-ray fluorescence,” J. Phys. III 4, 1559–1564 (1994).
[CrossRef]

Jpn. J. Appl. Phys. (1)

S. Braun, H. Mai, M. Moss, R. Scholz, and A. Leson, “Mo/Si multilayers with different barrier layers for applications as extreme ultraviolet mirrors,” Jpn. J. Appl. Phys. 41, 4074–4081 (2002).
[CrossRef]

Microelectron. Engin. (1)

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Engin. 83, 703–706 (2006).
[CrossRef]

Phys. Rev. B (9)

S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2297–2311 (1988).
[CrossRef]

D. K. G. de Boer, “X-ray scattering and x-ray fluorescence from materials with rough interfaces,” Phys. Rev. B 53, 6048–6064 (1996).
[CrossRef]

D. K. G. de Boer, “X-ray reflection and transmission by rough surfaces,” Phys. Rev. B 51, 5297–5305 (1995).
[CrossRef]

V. Holý and T. Baumbach, “Nonspecular x-ray reflection from rough multilayers,” Phys. Rev. B 49, 10668–10676 (1994).
[CrossRef]

V. Holý, J. Kubuena, I. Ohlídal, K. Lischka, and W. Plotz, “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896–15903 (1993).
[CrossRef]

E. M. Gullikson and D. G. Stearns, “Asymmetric extreme ultraviolet scattering from sputter-deposited multilayers,” Phys. Rev. B 59, 13273–13277 (1999).
[CrossRef]

G. Palasantzas and J. Krim, “Effect of the form of the height–height correlation function on diffuse x-ray scattering from a self-affine surface,” Phys. Rev. B 48, 2873–2877 (1993).
[CrossRef]

V. M. Kaganer, S. A. Stepanov, and R. Köhler, “Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces,” Phys. Rev. B 52, 16369–16372 (1995).
[CrossRef]

T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, P. Høghøj, O. Schärpf, P. Hinze, and R. Lauer, “Interfacial roughness and related growth mechanisms in sputtered W/Si multilayers,” Phys. Rev. B 54, 5860–5872 (1996).
[CrossRef]

phys. status solidi (b) (1)

B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey, R. Müller, M. Richter, F. Scholze, R. Thornagel, and G. Ulm, “A quarter-century of metrology using synchrotron radiation by PTB in Berlin,” phys. status solidi (b) 246, 1415–1434 (2009).

Proc. SPIE (2)

F. Scholze, B. Beckhoff, G. Brandt, R. Fliegauf, A. Gottwald, R. Klein, B. Meyer, U. D. Schwarz, R. Thornagel, J. Tuemmler, K. Vogel, J. Weser, and G. Ulm, “High-accuracy EUV metrology of PTB using synchrotron radiation,” Proc. SPIE 4344, 402 (2001).
[CrossRef]

J. Tummler, H. Blume, G. Brandt, J. Eden, B. Meyer, H. Scherr, F. Scholz, F. Scholze, and G. Ulm, “Characterization of the PTB EUV reflectometry facility for large EUVL optical components,” Proc. SPIE 5037, 265–273 (2003).
[CrossRef]

Rev. Phys. Appl. (1)

P. Croce and L. Névot, “étude des couches minces et des surfaces par réflexion rasante, spéculaire ou diffuse, de rayons x,” Rev. Phys. Appl. 11, 113–125 (1976).
[CrossRef]

Vacuum (1)

P. Siffalovic, E. Majkova, L. Chitu, M. Jergel, S. Luby, J. Keckes, G. Maier, A. Timmann, S. Roth, T. Tsuru, T. Harada, M. Yamamoto, and U. Heinzmann, “Characterization of Mo/Si soft x-ray multilayer mirrors by grazing-incidence small-angle x-ray scattering,” Vacuum 84, 19–25 (2009).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Cambridge University, 1965).

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Figures (9)

Fig. 1.
Fig. 1.

Coplanar measurement geometries. By keeping the opening angle Δ Θ between incident and exit beam and the detector fixed, respectively, a rocking scan can be performed by changing the sample angle ω . In a detector scan, the sample angle ω is kept fixed and defines the angle of incidence while the detector is moved along Θ .

Fig. 2.
Fig. 2.

Schematic positions in reciprocal space in dependence on the measurement geometry. The dashed path represents a rocking scan with the angle ω . The solid line shows the movement in q space when changing the detector angle Θ at a fixed angle of incidence. By tuning the wavelength at each angular position, the q z direction becomes accessible as indicated by the dotted arrows.

Fig. 3.
Fig. 3.

(a) Measured intensity map of a detector scan of a Mo/Si multilayer mirror at an angle of incidence α i = 6.75 ° . (b) Measured intensity maps of the identical sample obtained through rocking scans at an opening angle between detector and incident beam of Δ Θ = 13.5 ° and (c)  Δ Θ = 30 ° . The area close to the specular axis was excluded from this dataset due to its strong intensity compared with the diffuse scattering shown here. The access to the negative q x axis in (a) is limited due clipping of the incoming beam with the detector.

Fig. 4.
Fig. 4.

Averaged diffuse scattering intensity along q x in the interval q z = ( 0.930 ± 0.003 ) nm 1 corresponding to the resonance of the multilayer. The data shown are two rocking scan and one detector scan geometries (see text for details).

Fig. 5.
Fig. 5.

Scattering intensity along q z for q x = 0.05 nm 1 for the dynamic and semi-kinematic calculations for a rocking scan at Δ Θ = 30 ° in comparison to the measured data.

Fig. 6.
Fig. 6.

Scattering intensity distribution at q z = 0.93 nm 1 . The solid line shows the result of the dynamic calculation for a rocking scan with an opening angle of Δ Θ = 30 ° . The dashed line represents the calculation applying the semi-kinematic approximation, ignoring any multiple reflections within the multilayer. The dashed vertical lines are the limits of the main Bragg peak, while the red solid vertical lines show the position of dynamic contributions of the Kiessig fringes close to the main maximum. Each Kiessig fringe marked in the inset appears for the corresponding positive and negative q x value. The strong intensity at q x 0.1 nm 1 results from the overlap of the dynamic maxima of two different Kiessig fringes (see text).

Fig. 7.
Fig. 7.

Enhancement factor due to the specific properties of multilayer reflectivity for three different measurement geometries. The simulations shown here were normalized with respect to the diffuse contribution to the specular reflectivity at q x = 0 .

Fig. 8.
Fig. 8.

Diffuse scattering intensity corrected for the multilayer enhancement factor considering a tilt angle of β = 1 ° according to Eq. (22). The black solid line corresponds to a PSD with ξ = 5.6 nm , H = 1.0 , and σ = 0.2 nm and a vertical correlation length of ξ ( q x ) = 7.5 / q x 2 nm 1 .

Fig. 9.
Fig. 9.

Measured (a) and simulated (b) reciprocal space maps for a rocking scan at an opening angle of Δ Θ = 30 ° with the roughness parameters determined in Section 4.C.

Equations (23)

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q x = 2 π λ ( sin ( Θ ) sin ( α i ) ) ,
q z = 2 π λ ( cos ( Θ ) + cos ( α i ) ) ,
( Δ + K 2 ) | E ( r ) = V ( r ) | E ( r )
r ( j ) = r id ( j ) exp ( 2 k z ( j ) k z ( j + 1 ) σ j 2 ) ,
t ( j ) = t id ( j ) exp ( ( k z ( j ) k z ( j + 1 ) ) 2 σ j 2 / 2 ) ,
( d σ d Ω ) diffuse = Cov ( E id , 1 | V r | E id , 2 ) ,
( d σ d Ω ) diffuse semi-kinematic = A π 2 λ 4 j = 1 N i = 1 N ( ( n j 2 n j + 1 2 ) * ( n i 2 n i + 1 2 ) × T j ( 1 ) * T j ( 2 ) * T i ( 1 ) T i ( 2 ) S i j ( q x ) ) ,
E t ( j ) ( z ) = T j e i k z ( j ) z ,
E r ( j ) ( z ) = R j e i k z ( j ) z
S i j ( q⃗ ; q z ( j ) , q z ( i ) ) = exp [ ( ( q z ( j ) * ) 2 σ j 2 + ( q z ( i ) ) 2 σ i 2 ) / 2 ] q z ( j ) * q z ( i ) d 2 X⃗ ( exp [ q z ( j ) * q z ( i ) C i j ( X⃗ ) ] 1 ) exp ( i q⃗ · X⃗ ) ,
exp [ ( ( q z ( j ) * ) 2 σ j 2 + ( q z ( i ) ) 2 σ i 2 ) / 2 ] q z ( j ) * q z ( i ) 1 q z ( j ) * q z ( i )
S i j ( q⃗ ) d 2 X⃗ C i j ( X⃗ ) exp ( i q⃗ · X⃗ ) .
S i j ( q x ) = c i j ( q x ) C max ( i , j ) ( q x ) .
C ˜ i ( X⃗ ) = P i ξ H i | X⃗ | H i K H i ( | X⃗ | / ξ ) .
P i = σ i 2 ξ H i 1 2 H i 1 Γ ( 1 + H i ) / H i .
C ( q x ) = 4 π H σ 2 ξ 2 ( 1 + | q x | 2 ξ 2 ) 1 + H .
w ( f ) t = 4 π 2 v f 2 w ( f ) + η ( f ) t ,
w i ( f ) = c ( f ; δ d ) w i 1 ( f ) + η ( f ) ,
c ( f , d n ) = exp ( 4 π 2 f 2 v d n ) = exp ( q x 2 v d n )
c i j ( q x ) = exp ( n = min ( i , j ) max ( i , j ) 1 d n / ξ ( q x ) ) .
q ¯ z = q z q x tan β .
S i j ¯ ( q x ) = exp ( i q x tan β ( z i z j ) ) S i j ( q x ) ,
( d σ d Ω ) diffuse dynamic = [ A π 2 λ 4 j = 1 N i = 1 N ( n j 2 n j + 1 2 ) * ( n i 2 n i + 1 2 ) ( ( T j ( 1 ) + R j ( 1 ) ) * ( T j ( 2 ) + R j ( 2 ) ) * × ( T i ( 1 ) + R i ( 1 ) ) ( T i ( 2 ) + R i ( 2 ) ) ) c i j ] C ( q x ) ,

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