Abstract

We investigate the influence of the Mo-layer thickness on the EUV reflectance of Mo/Si mirrors with a set of unpolished and interface-polished Mo/Si/C multilayer mirrors. The Mo-layer thickness is varied in the range from 1.7 nm to 3.05 nm. We use a novel combination of specular and diffuse intensity measurements to determine the interface roughness throughout the multilayer stack and do not rely on scanning probe measurements at the surface only. The combination of EUV and X-ray reflectivity measurements and near-normal incidence EUV diffuse scattering allows to reconstruct the Mo layer thicknesses and to determine the interface roughness power spectral density. The data analysis is conducted by applying a matrix method for the specular reflection and the distorted-wave Born approximation for diffuse scattering. We introduce the Markov-chain Monte Carlo method into the field in order to determine the respective confidence intervals for all reconstructed parameters. We unambiguously detect a threshold thickness for Mo in both sample sets where the specular reflectance goes through a local minimum correlated with a distinct increase in diffuse scatter. We attribute that to the known appearance of an amorphous-to-crystallization transition at a certain thickness threshold which is altered in our sample system by the polishing.

© 2017 Optical Society of America

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2016 (1)

A. Haase, S. Bajt, P. Hönicke, V. Soltwisch, and F. Scholze, “Multiparameter characterization of subnanometre Cr/Sc multilayers based on complementary measurements,” J. Appl. Cryst. 49, 2161–2171 (2016).
[Crossref]

2014 (2)

2013 (1)

D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, “emcee: the MCMC Hammer,” Publications of the Astronomical Society of the Pacific 125, 306–312 (2013). ArXiv: 1202.3665.
[Crossref]

2010 (1)

J. Goodman and J. Weare, “Ensemble samplers with affine invariance,” Communications in Applied Mathematics and Computational Science 5, 65–80 (2010).
[Crossref]

2007 (2)

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
[Crossref]

S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “EUV reflectance and scattering of Mo/Si multilayers on differently polished substrates,” Opt. Express 15, 13997–14012 (2007).
[Crossref] [PubMed]

2003 (2)

S. Braun, T. Foltyn, H. Mai, M. Moss, and A. Leson, “Grenzflächen-optimierte Mo/Si Multischichten als Reflektoren für den EUV Spektralbereich,” Vakuum in Forschung und Praxis 15, 76–81 (2003).
[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]

2002 (2)

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[Crossref]

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 (2002).
[Crossref]

2001 (1)

S. Bajt, D. G. Stearns, and P. A. Kearney, “Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers,” J. Appl. Phys. 90, 1017–1025 (2001).
[Crossref]

2000 (3)

T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature 406, 1027–1031 (2000).
[Crossref] [PubMed]

D. S. Martínez-Galarce, A. B. C. Walker, D. B. Gore, C. C. Kankelborg, R. B. Hoover, T. W. Barbee, and P. F. X. Boerner, “High resolution imaging with multilayer telescopes: resolution performance of the MSSTA II telescopes,” Opt. Eng. 39, 1063–1079 (2000).
[Crossref]

M. Toyoda, Y. Shitani, M. Yanagihara, T. Ejima, M. Yamamoto, and M. Watanabe, “A soft-x-ray imaging microscope with a multilayer-coated Schwarzschild objective: imaging tests,” Jpn. J. Appl. Phys. 39, 1926–1929 (2000).
[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]

1995 (1)

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

1994 (3)

D. K. G. de Boer, A. J. G. Leenaers, and W. W. v. d. Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent X-ray fluorescence,” J. Phys. III France 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]

S. K. Sinha, “X-ray diffuse scattering as a probe for thin film and interface structure,” J. Phys. III France 4, 1543–1557 (1994).
[Crossref]

1993 (2)

V. Holý, J. Kuběna, 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]

1992 (1)

J. Verhoeven, L. Chunguang, E. J. Puik, M. J. van der Wiel, and T. P. Huijgen, “Ion beam modification of Mo?Si multilayer systems for X-ray reflection,” Appl. Surf. Sci. 55, 97–103 (1992).
[Crossref]

1991 (2)

T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

D. G. Stearns, R. S. Rosen, and S. P. Vernon, “Fabrication of high-reflectance Mo–Si multilayer mirrors by planar-magnetron sputtering,” J. Vac. Sci. Technol. A 9, 2662–2669 (1991).
[Crossref]

1990 (1)

1988 (1)

H. Nakajima, H. Fujimori, and M. Koiwa, “Interdiffusion and structural relaxation in Mo/Si multilayer films,” J. Appl. Phys. 63, 1046–1051 (1988).
[Crossref]

1987 (1)

A. K. Petford-Long, M. B. Stearns, C.-H. Chang, S. R. Nutt, D. G. Stearns, N. M. Ceglio, and A. M. Hawryluk, “High-resolution electron microscopy study of x-ray multilayer structures,” J. Appl. Phys. 61, 1422–1428 (1987).
[Crossref]

1985 (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. (Paris) 11, 113–125 (1976).
[Crossref]

1972 (1)

E. Spiller, “Low-loss reflection coatings using absorbing materials,” Appl. Phys. Lett. 20, 365–367 (1972).
[Crossref]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” Journal of the society for Industrial and Applied Mathematics 11, 431–441 (1963).
[Crossref]

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least square,” Quarterly Appl. Math. 2(2), 164–168 (1944).
[Crossref]

Alameda, J. B.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[Crossref]

Allen, M. J.

T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

Bajt, S.

A. Haase, S. Bajt, P. Hönicke, V. Soltwisch, and F. Scholze, “Multiparameter characterization of subnanometre Cr/Sc multilayers based on complementary measurements,” J. Appl. Cryst. 49, 2161–2171 (2016).
[Crossref]

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[Crossref]

S. Bajt, D. G. Stearns, and P. A. Kearney, “Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers,” J. Appl. Phys. 90, 1017–1025 (2001).
[Crossref]

Baker, P. C.

T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

Barbee, T. W.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[Crossref]

D. S. Martínez-Galarce, A. B. C. Walker, D. B. Gore, C. C. Kankelborg, R. B. Hoover, T. W. Barbee, and P. F. X. Boerner, “High resolution imaging with multilayer telescopes: resolution performance of the MSSTA II telescopes,” Opt. Eng. 39, 1063–1079 (2000).
[Crossref]

T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

T. W. Barbee, S. Mrowka, and M. C. Hettrick, “Molybdenum-silicon multilayer mirrors for the extreme ultraviolet,” Appl. Opt. 24, 883–886 (1985).
[Crossref] [PubMed]

Baumbach, T.

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

Bijkerk, F.

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]

Boerner, P. F. X.

D. S. Martínez-Galarce, A. B. C. Walker, D. B. Gore, C. C. Kankelborg, R. B. Hoover, T. W. Barbee, and P. F. X. Boerner, “High resolution imaging with multilayer telescopes: resolution performance of the MSSTA II telescopes,” Opt. Eng. 39, 1063–1079 (2000).
[Crossref]

Born, M.

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

Brandt, G.

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
[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]

Braun, S.

S. Braun, T. Foltyn, H. Mai, M. Moss, and A. Leson, “Grenzflächen-optimierte Mo/Si Multischichten als Reflektoren für den EUV Spektralbereich,” Vakuum in Forschung und Praxis 15, 76–81 (2003).
[Crossref]

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 (2002).
[Crossref]

Bürkmann, K.

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
[Crossref]

Ceglio, N. M.

A. K. Petford-Long, M. B. Stearns, C.-H. Chang, S. R. Nutt, D. G. Stearns, N. M. Ceglio, and A. M. Hawryluk, “High-resolution electron microscopy study of x-ray multilayer structures,” J. Appl. Phys. 61, 1422–1428 (1987).
[Crossref]

Chang, C.-H.

A. K. Petford-Long, M. B. Stearns, C.-H. Chang, S. R. Nutt, D. G. Stearns, N. M. Ceglio, and A. M. Hawryluk, “High-resolution electron microscopy study of x-ray multilayer structures,” J. Appl. Phys. 61, 1422–1428 (1987).
[Crossref]

Chuev, M. A.

Chunguang, L.

J. Verhoeven, L. Chunguang, E. J. Puik, M. J. van der Wiel, and T. P. Huijgen, “Ion beam modification of Mo?Si multilayer systems for X-ray reflection,” Appl. Surf. Sci. 55, 97–103 (1992).
[Crossref]

Clift, W. M.

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
[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. (Paris) 11, 113–125 (1976).
[Crossref]

de Boer, D. K. G.

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. v. d. Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent X-ray fluorescence,” J. Phys. III France 4, 1559–1564 (1994).
[Crossref]

DeForest, C. E.

T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

Duparré, A.

Eden, J.

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
[Crossref]

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D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, “emcee: the MCMC Hammer,” Publications of the Astronomical Society of the Pacific 125, 306–312 (2013). ArXiv: 1202.3665.
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Richter, M.

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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 (2002).
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A. Haase, S. Bajt, P. Hönicke, V. Soltwisch, and F. Scholze, “Multiparameter characterization of subnanometre Cr/Sc multilayers based on complementary measurements,” J. Appl. Cryst. 49, 2161–2171 (2016).
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A. Haase, V. Soltwisch, C. Laubis, and F. Scholze, “Role of dynamic effects in the characterization of multilayers by means of power spectral density,” Appl. Opt. 53, 3019–3027 (2014).
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G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
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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).
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A. Haase, V. Soltwisch, C. Laubis, and F. Scholze, “Role of dynamic effects in the characterization of multilayers by means of power spectral density,” Appl. Opt. 53, 3019–3027 (2014).
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E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
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S. Bajt, D. G. Stearns, and P. A. Kearney, “Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers,” J. Appl. Phys. 90, 1017–1025 (2001).
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D. G. Stearns, R. S. Rosen, and S. P. Vernon, “Fabrication of high-reflectance Mo–Si multilayer mirrors by planar-magnetron sputtering,” J. Vac. Sci. Technol. A 9, 2662–2669 (1991).
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A. K. Petford-Long, M. B. Stearns, C.-H. Chang, S. R. Nutt, D. G. Stearns, N. M. Ceglio, and A. M. Hawryluk, “High-resolution electron microscopy study of x-ray multilayer structures,” J. Appl. Phys. 61, 1422–1428 (1987).
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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]

Tünnermann, A.

Ulm, G.

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
[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]

van der Wiel, M. J.

J. Verhoeven, L. Chunguang, E. J. Puik, M. J. van der Wiel, and T. P. Huijgen, “Ion beam modification of Mo?Si multilayer systems for X-ray reflection,” Appl. Surf. Sci. 55, 97–103 (1992).
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Verhoeven, J.

J. Verhoeven, L. Chunguang, E. J. Puik, M. J. van der Wiel, and T. P. Huijgen, “Ion beam modification of Mo?Si multilayer systems for X-ray reflection,” Appl. Surf. Sci. 55, 97–103 (1992).
[Crossref]

Vernon, S. P.

D. G. Stearns, R. S. Rosen, and S. P. Vernon, “Fabrication of high-reflectance Mo–Si multilayer mirrors by planar-magnetron sputtering,” J. Vac. Sci. Technol. A 9, 2662–2669 (1991).
[Crossref]

Walker, A. B. C.

D. S. Martínez-Galarce, A. B. C. Walker, D. B. Gore, C. C. Kankelborg, R. B. Hoover, T. W. Barbee, and P. F. X. Boerner, “High resolution imaging with multilayer telescopes: resolution performance of the MSSTA II telescopes,” Opt. Eng. 39, 1063–1079 (2000).
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T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

Watanabe, M.

M. Toyoda, Y. Shitani, M. Yanagihara, T. Ejima, M. Yamamoto, and M. Watanabe, “A soft-x-ray imaging microscope with a multilayer-coated Schwarzschild objective: imaging tests,” Jpn. J. Appl. Phys. 39, 1926–1929 (2000).
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Weare, J.

J. Goodman and J. Weare, “Ensemble samplers with affine invariance,” Communications in Applied Mathematics and Computational Science 5, 65–80 (2010).
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T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

Willis, T. D.

T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
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M. Born and E. Wolf, Principles of optics (Cambridge University, 1965), 3rd ed.

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G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
[Crossref]

Yakunin, S. N.

Yamamoto, M.

M. Toyoda, Y. Shitani, M. Yanagihara, T. Ejima, M. Yamamoto, and M. Watanabe, “A soft-x-ray imaging microscope with a multilayer-coated Schwarzschild objective: imaging tests,” Jpn. J. Appl. Phys. 39, 1926–1929 (2000).
[Crossref]

Yanagihara, M.

M. Toyoda, Y. Shitani, M. Yanagihara, T. Ejima, M. Yamamoto, and M. Watanabe, “A soft-x-ray imaging microscope with a multilayer-coated Schwarzschild objective: imaging tests,” Jpn. J. Appl. Phys. 39, 1926–1929 (2000).
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Zwicker, A. P.

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J. Verhoeven, L. Chunguang, E. J. Puik, M. J. van der Wiel, and T. P. Huijgen, “Ion beam modification of Mo?Si multilayer systems for X-ray reflection,” Appl. Surf. Sci. 55, 97–103 (1992).
[Crossref]

Communications in Applied Mathematics and Computational Science (1)

J. Goodman and J. Weare, “Ensemble samplers with affine invariance,” Communications in Applied Mathematics and Computational Science 5, 65–80 (2010).
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A. Haase, S. Bajt, P. Hönicke, V. Soltwisch, and F. Scholze, “Multiparameter characterization of subnanometre Cr/Sc multilayers based on complementary measurements,” J. Appl. Cryst. 49, 2161–2171 (2016).
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E. Spiller, D. Stearns, and M. Krumrey, “Multilayer x-ray mirrors: interfacial roughness, scattering, and image quality,” J. Appl. Phys. 74, 107–118 (1993).
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S. Bajt, D. G. Stearns, and P. A. Kearney, “Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers,” J. Appl. Phys. 90, 1017–1025 (2001).
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A. K. Petford-Long, M. B. Stearns, C.-H. Chang, S. R. Nutt, D. G. Stearns, N. M. Ceglio, and A. M. Hawryluk, “High-resolution electron microscopy study of x-ray multilayer structures,” J. Appl. Phys. 61, 1422–1428 (1987).
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H. Nakajima, H. Fujimori, and M. Koiwa, “Interdiffusion and structural relaxation in Mo/Si multilayer films,” J. Appl. Phys. 63, 1046–1051 (1988).
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D. K. G. de Boer, A. J. G. Leenaers, and W. W. v. d. Hoogenhof, “Influence of roughness profile on reflectivity and angle-dependent X-ray fluorescence,” J. Phys. III France 4, 1559–1564 (1994).
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S. K. Sinha, “X-ray diffuse scattering as a probe for thin film and interface structure,” J. Phys. III France 4, 1543–1557 (1994).
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D. G. Stearns, R. S. Rosen, and S. P. Vernon, “Fabrication of high-reflectance Mo–Si multilayer mirrors by planar-magnetron sputtering,” J. Vac. Sci. Technol. A 9, 2662–2669 (1991).
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M. Toyoda, Y. Shitani, M. Yanagihara, T. Ejima, M. Yamamoto, and M. Watanabe, “A soft-x-ray imaging microscope with a multilayer-coated Schwarzschild objective: imaging tests,” Jpn. J. Appl. Phys. 39, 1926–1929 (2000).
[Crossref]

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 (2002).
[Crossref]

Nature (1)

T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature 406, 1027–1031 (2000).
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Nucl. Instr. Meth. Phys. Res. B (1)

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld, “The Metrology Light Source – The new dedicated electron storage ring of PTB,” Nucl. Instr. Meth. Phys. Res. B 258, 445–452 (2007).
[Crossref]

Opt. Eng. (3)

D. S. Martínez-Galarce, A. B. C. Walker, D. B. Gore, C. C. Kankelborg, R. B. Hoover, T. W. Barbee, and P. F. X. Boerner, “High resolution imaging with multilayer telescopes: resolution performance of the MSSTA II telescopes,” Opt. Eng. 39, 1063–1079 (2000).
[Crossref]

T. W. Barbee, J. W. Weed, R. B. Hoover, M. J. Allen, J. F. Lindblom, R. H. O’Neal, C. C. Kankelborg, C. E. DeForest, E. S. Paris, A. B. C. Walker, T. D. Willis, E. S. Gluskin, P. A. Pianetta, and P. C. Baker, “Multi-spectral solar telescope array II: soft x-ray EUV reflectivity of the multilayer mirrors,” Opt. Eng. 30, 1067–1075 (1991).
[Crossref]

S. Bajt, J. B. Alameda, T. W. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. A. Spiller, “Improved reflectance and stability of Mo-Si multilayers,” Opt. Eng. 41, 1797–1804 (2002).
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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]

Publications of the Astronomical Society of the Pacific (1)

D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, “emcee: the MCMC Hammer,” Publications of the Astronomical Society of the Pacific 125, 306–312 (2013). ArXiv: 1202.3665.
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Vakuum in Forschung und Praxis (1)

S. Braun, T. Foltyn, H. Mai, M. Moss, and A. Leson, “Grenzflächen-optimierte Mo/Si Multischichten als Reflektoren für den EUV Spektralbereich,” Vakuum in Forschung und Praxis 15, 76–81 (2003).
[Crossref]

Other (3)

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

P. Mikul’ik, “X-ray reflectivity from planar and structured multilayers,” Ph.D. thesis, Thèse de l’Université Joseph Fourier (1997).

J. Kennedy, “Particle swarm optimization,” in “Encyclopedia of Machine Learning,” C. Sammut and G. I. Webb, eds. (SpringerUS, 2011), pp. 760–766.

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Figures (9)

Fig. 1
Fig. 1 Model of the multilayer stack including the substrate and the capping layers. The periodic part is enclosed between the dashed lines with four layers in each period repeated 49 times. The capping period does not include a compound layer but has a natural SiO2 layer and a carbon-like layer accounting for contamination on the top surface.
Fig. 2
Fig. 2 Schematic measurement geometry for the EUV reflectance and diffuse scattering measurements. The detector is kept at a fixed position ΔΘ for all experiments. In the case of the specular reflectance measurement, the detector is positioned in such that αi = αf for a sample rocking angle of ω = 0. For the diffuse scattering experiment, the sample rocking angle ω is varied such that the diffusely scattered radiation hits the detector (see text).
Fig. 3
Fig. 3 a) Reflectivity curves for the unpolished samples across the wavelength at a fixed angle of incidence of αi = 15° from the surface normal. The nine samples differ by the nominal Mo layer thickness indicated at the bottom axis. b) Reflectivity curves of the ten polished samples measured under the same conditions as for the first sample set.
Fig. 4
Fig. 4 a) Fitted Mo thickness values for both sample sets resulting from the MCMC analysis (see text). The nominal Mo layer thickness is shown in comparison in good agreement with the obtained thicknesses. b) Fitted total period thickness D for both sample sets. For both sample sets, clear jumps can be observed at approx. dMo ≈ 2.0 nm and dMo ≈ 2.4 nm, respectively. The marked (circle) samples were measured and analyzed with respect to the diffuse scattering.
Fig. 5
Fig. 5 Peak reflectance values for each unpolished (a) and polished (b) sample obtained from the measurements shown in Fig. 3 in comparison to the maximum theoretical reflectance for a respective optimal multilayer stack without roughness and interdiffusion (blue solid line in (a) and (b)). The dashed lines indicate the expected reflectance for a realistic multilayer system including interdiffusion and roughness for both sample sets. A significant deviation (reflectance dip) can be observed in both sets for different molybdenum layer thicknesses and two data points in each set (see main text).
Fig. 6
Fig. 6 Measured diffuse scattering distributions in reciprocal space representation shown on linear false-color scale. The selected unpolished samples are shown in a) with increasing Mo layer thickness dMo. The selected samples for the polished set are shown in b) also in order of increasing Mo thickness dMo. The samples with strongest scattering are shown in larger detail in Fig. 8.
Fig. 7
Fig. 7 a) Diffuse scattering map for the unpolished sample with strongest total scattering intensity measured at the same orientation as in Fig. 6. b) Corresponding reciprocal space map for the same sample but irradiated from a different angle by rotating the sample by 90° around the surface normal. Clear differences in the tilt angle of the Bragg sheet can be observed associated with the vertical roughness correlation direction (see main text).
Fig. 8
Fig. 8 Direct comparison of the measured reciprocal space maps with the DWBA calculation resulting from the parameters obtained with the MCMC optimization procedure (see text). a) shows the maps of the unpolished sample with strongest diffuse scattering. Similarly, b) shows the maps of the polished sample at the respective presumed crystallization threshold with strongest scattering.
Fig. 9
Fig. 9 a) Root mean square roughness results from the analysis of the diffuse scattering for the two sample sets in comparison to the σ-factor obtained in the specular reflectivity analysis (indicated through their confidence intervals as shaded area). In each set, an increase of roughness is observed at the crystallization threshold. For comparison, the max peak reflectance (cf. Fig. 3(c)) for each sample set is shown in b). The increase in roughness clearly correlates with a significant dip in the peak reflectance as indicated by the dashed vertical lines.

Tables (3)

Tables Icon

Table 1 Multilayer parametrization and parameter limits

Tables Icon

Table 2 Parameters of the DWBA analysis with parameter limits

Tables Icon

Table 3 Results for the DWBA model parameters

Equations (14)

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r ( j ) = r i d ( j ) exp ( 2 k z ( j ) k z ( j + 1 ) σ 2 ) , t ( j ) = t i d ( j ) exp ( ( k z ( j ) k z ( j + 1 )   2 σ 2 / 2 ) ,
r i d ( j ) = k z ( j ) k z ( j + 1 ) k z ( j ) + k z ( j + 1 ) , t i d ( j ) = 2 k z ( j ) k z ( j ) + k z ( j + 1 ) .
k z ( j ) = ( n ( j ) k v a c ) 2 k x 2
(   E R E 0 ) = j M j (   0 E T ) .
M j = 1 t ( j ) ( 1 r ( j ) r ( j ) 1 ) ( e i k z ( j + 1 ) d j 1 1 e i k z ( j + 1 ) d j ) ,
R = | E R / E 0 | 2 , T = | E T / E 0 | 2 .
E t ( j ) ( z ) = T j e i k z ( j ) z ,
E r ( j ) ( z ) = R j e i k z ( j ) z ,
( d σ d Ω ) = [ π 2 λ 4 cos α i 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 ) ) ) exp ( i q tan β ( z i z j ) ) c i j ] C ( q ) ,
c i j ( q ) = exp ( n = min ( i , j ) max ( i , j ) 1 d n / ξ ( q ) ) ,
C ( q ) = 4 π H σ r 2 ξ 2 ( 1 + | q | 2 ξ 2 ) 1 + H ,
χ ˜ = 1 m p [ m ( I m model I m means ) 2 σ ˜ m 2 ] ,
χ 2 = χ ˜ EUV 2 + χ ˜ XRR 2 ,
χ 2 = χ ˜ diff 2 .

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