Abstract

The basic properties in the extreme ultraviolet (EUV) of one-dimensional photonic crystals (Bragg reflectors) with incorporated superlattices are investigated by a numerical study using the multiple scattering method. The superlattice is realized in the “standard” Mo/Si system by periodically replacing certain Mo layers by Si layers. At 13.5 nm–the wavelength of interest for EUV lithography–the superlattice sharpens the reflection peak at normal incidence with only weak reduction of the peak value. Between normal incidence and total reflection at large angles, additional reflection peaks appear at certain angles where the reflection is zero for the “standard” Mo/Si system. By combining different superlattices and depth grading, the range of additional reflection peaks is extended towards all-angle reflection. The effect of interface imperfections is considered for the case of the interdiffusion of Mo and Si. The extension to other frequency ranges is addressed via band structure calculations.

© 2017 Optical Society of America

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References

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2017 (2)

Q. Huang, V. Medvedev, R. van de Kruijs, A. Yakshin, E. Louis, and F. Bijkerk, “Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics,” Appl. Phys. Rev. 4, 011104 (2017).

A. Haase, V. Soltwisch, S. Braun, C. Laubis, and F. Scholze, “Interface morphology of Mo/Si multilayer systems with varying Mo layer thickness studied by EUV diffuse scattering,” Opt. Express 25(13), 15441–15455 (2017).
[PubMed]

2015 (2)

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

D. L. Windt, “EUV multilayer coatings for solar imaging and spectroscopy,” Proc. SPIE,  9604, 96041 (2015).

2013 (2)

Z. V. Vardeny, “Optics of Photonic Quasicystals,” Nat. Photonics 7, 177–187 (2013).

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

2012 (2)

M. Fernández-Perea, R. Soufli, J. C. Robinson, L. Rodríguez-De Marcos, J. A. Méndez, J. I. Larruquert, and E. M. Gullikson, “Triple-wavelength, narrowband Mg/SiC multilayers with corrosion barriers and high peak reflectance in the 25-80 nm wavelength region,” Opt. Express 20(21), 24018–24029 (2012).
[PubMed]

R. Meisels, O. Glushko, and F. Kuchar, “Tuning the flow of light in semiconductor based photonic crystals by magnetic fields,” Photonics and Nanostructures – Fundamentals and Applications 10, 60– 68 (2012).

2010 (3)

2006 (3)

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, “Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies,” Opt. Express 14(15), 6766–6777 (2006).
[PubMed]

F. Kuchar, R. Meisels, P. Oberhumer, and R. Gajic, “Microwave Studies of Photonic Crystals,” Adv. Eng. Mater. 8, 1156–1161 (2006).

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Eng. 83, 703 (2006).

2003 (2)

S. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

S. A. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

2002 (1)

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

2001 (1)

Z. Wang and A. G. Michette, “Optimization of depth-graded multilayer designs for EUV and x-ray optics,” Proc. SPIE 4145, 243 (2001).

2000 (3)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[PubMed]

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Z. Wang and A. G. Michette, “Broadband multilayer mirrors for optimum use of soft x-ray source output,” J. Opt. A, Pure Appl. Opt. 2, 452 (2000).

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).

1995 (1)

V. G. Kohn, “On the Theory of Reflectivity by an X-Ray Multilayer Mirror,” Phys. Status Solidi 187, 61–70 (1995).

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[PubMed]

M. P. Bruijn, J. Verhoeven, and W. J. Bartels, “Improved resolution of multilayer x-ray coatings: a distributed Fabry-Perot etalon,” Opt. Eng. 26, 679–684 (1987).

Bartels, W. J.

M. P. Bruijn, J. Verhoeven, and W. J. Bartels, “Improved resolution of multilayer x-ray coatings: a distributed Fabry-Perot etalon,” Opt. Eng. 26, 679–684 (1987).

Benoit, N.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Eng. 83, 703 (2006).

Bernitzki, H.

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

Bijkerk, F.

Braun, S.

Brons, C.

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Bruijn, M. P.

M. P. Bruijn, J. Verhoeven, and W. J. Bartels, “Improved resolution of multilayer x-ray coatings: a distributed Fabry-Perot etalon,” Opt. Eng. 26, 679–684 (1987).

Butz, B.

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[PubMed]

Christensen, F. E.

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Craig, W. W.

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[PubMed]

Dieker, C.

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

Feigl, T.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Eng. 83, 703 (2006).

S. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

S. A. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

Fernández-Perea, M.

Gajic, R.

Glushko, O.

R. Meisels, O. Glushko, and F. Kuchar, “Tuning the flow of light in semiconductor based photonic crystals by magnetic fields,” Photonics and Nanostructures – Fundamentals and Applications 10, 60– 68 (2012).

Gullikson, E. M.

Haase, A.

Harrison, F. A.

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[PubMed]

Hegeman, P.

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Hingerl, K.

Honkimaki, V.

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Huang, Q.

Q. Huang, V. Medvedev, R. van de Kruijs, A. Yakshin, E. Louis, and F. Bijkerk, “Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics,” Appl. Phys. Rev. 4, 011104 (2017).

Huskens, J.

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Jimenez-Garate, M. A.

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Kaiser, N.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Eng. 83, 703 (2006).

S. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

S. A. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

Kohn, V. G.

V. G. Kohn, “On the Theory of Reflectivity by an X-Ray Multilayer Mirror,” Phys. Status Solidi 187, 61–70 (1995).

Kozhevnikov, I.

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Kozhevnikov, I. V.

Krishnan, B.

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Kuchar, F.

R. Meisels, O. Glushko, and F. Kuchar, “Tuning the flow of light in semiconductor based photonic crystals by magnetic fields,” Photonics and Nanostructures – Fundamentals and Applications 10, 60– 68 (2012).

F. Kuchar, R. Meisels, P. Oberhumer, and R. Gajic, “Microwave Studies of Photonic Crystals,” Adv. Eng. Mater. 8, 1156–1161 (2006).

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, “Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies,” Opt. Express 14(15), 6766–6777 (2006).
[PubMed]

Kuhlmann, T.

S. A. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

S. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

Larruquert, J. I.

Laubis, C.

Laut, H.

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

Louis, E.

Mao, P. H.

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Mecke, K.

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

Medvedev, V.

Q. Huang, V. Medvedev, R. van de Kruijs, A. Yakshin, E. Louis, and F. Bijkerk, “Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics,” Appl. Phys. Rev. 4, 011104 (2017).

Meisels, R.

R. Meisels, O. Glushko, and F. Kuchar, “Tuning the flow of light in semiconductor based photonic crystals by magnetic fields,” Photonics and Nanostructures – Fundamentals and Applications 10, 60– 68 (2012).

F. Kuchar, R. Meisels, P. Oberhumer, and R. Gajic, “Microwave Studies of Photonic Crystals,” Adv. Eng. Mater. 8, 1156–1161 (2006).

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, “Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies,” Opt. Express 14(15), 6766–6777 (2006).
[PubMed]

Méndez, J. A.

Michette, A. G.

Z. Wang and A. G. Michette, “Optimization of depth-graded multilayer designs for EUV and x-ray optics,” Proc. SPIE 4145, 243 (2001).

Z. Wang and A. G. Michette, “Broadband multilayer mirrors for optimum use of soft x-ray source output,” J. Opt. A, Pure Appl. Opt. 2, 452 (2000).

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).

Montcalm, C.

I. V. Kozhevnikov and C. Montcalm, “Design of X-ray multilayer mirrors with maximal integral efficiency,” Nucl. Instrum. Methods Phys. Res. A 624, 192–202 (2010).

Oberhumer, P.

F. Kuchar, R. Meisels, P. Oberhumer, and R. Gajic, “Microwave Studies of Photonic Crystals,” Adv. Eng. Mater. 8, 1156–1161 (2006).

Robinson, J. C.

Rodríguez-De Marcos, L.

Scholze, F.

Schröder-Turk, G. E.

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[PubMed]

Soltwisch, V.

Soufli, R.

Spiecker, E.

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[PubMed]

van de Kruijs, R.

Q. Huang, V. Medvedev, R. van de Kruijs, A. Yakshin, E. Louis, and F. Bijkerk, “Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics,” Appl. Phys. Rev. 4, 011104 (2017).

van der Meer, R.

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Vardeny, Z. V.

Z. V. Vardeny, “Optics of Photonic Quasicystals,” Nat. Photonics 7, 177–187 (2013).

Verhoeven, J.

M. P. Bruijn, J. Verhoeven, and W. J. Bartels, “Improved resolution of multilayer x-ray coatings: a distributed Fabry-Perot etalon,” Opt. Eng. 26, 679–684 (1987).

Vratzov, B.

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Wang, Z.

Z. Wang and A. G. Michette, “Optimization of depth-graded multilayer designs for EUV and x-ray optics,” Proc. SPIE 4145, 243 (2001).

Z. Wang and A. G. Michette, “Broadband multilayer mirrors for optimum use of soft x-ray source output,” J. Opt. A, Pure Appl. Opt. 2, 452 (2000).

Windt, D. L.

D. L. Windt, “EUV multilayer coatings for solar imaging and spectroscopy,” Proc. SPIE,  9604, 96041 (2015).

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Winter, B.

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[PubMed]

Yakshin, A.

Q. Huang, V. Medvedev, R. van de Kruijs, A. Yakshin, E. Louis, and F. Bijkerk, “Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics,” Appl. Phys. Rev. 4, 011104 (2017).

Yakshin, A. E.

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).

Yulin, S.

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Eng. 83, 703 (2006).

S. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

Yulin, S. A.

S. A. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

Ziegler, J. M.

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Zoethout, E.

Adv. Eng. Mater. (1)

F. Kuchar, R. Meisels, P. Oberhumer, and R. Gajic, “Microwave Studies of Photonic Crystals,” Adv. Eng. Mater. 8, 1156–1161 (2006).

AIP Adv. (1)

R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, and B. Vratzov, “Single order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Adv. 3, 012103 (2013).

Appl. Phys. Rev. (1)

Q. Huang, V. Medvedev, R. van de Kruijs, A. Yakshin, E. Louis, and F. Bijkerk, “Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics,” Appl. Phys. Rev. 4, 011104 (2017).

Comput. Phys. Commun. (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).

J. Opt. A, Pure Appl. Opt. (1)

Z. Wang and A. G. Michette, “Broadband multilayer mirrors for optimum use of soft x-ray source output,” J. Opt. A, Pure Appl. Opt. 2, 452 (2000).

Microelectron. Eng. (1)

T. Feigl, S. Yulin, N. Benoit, and N. Kaiser, “EUV multilayer optics,” Microelectron. Eng. 83, 703 (2006).

Nat. Photonics (1)

Z. V. Vardeny, “Optics of Photonic Quasicystals,” Nat. Photonics 7, 177–187 (2013).

Nature (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[PubMed]

Nucl. Instrum. Methods Phys. Res. A (1)

I. V. Kozhevnikov and C. Montcalm, “Design of X-ray multilayer mirrors with maximal integral efficiency,” Nucl. Instrum. Methods Phys. Res. A 624, 192–202 (2010).

Nuclear Instrum. Methods Phys. Res. Section A (1)

F. E. Christensen, W. W. Craig, D. L. Windt, M. A. Jimenez-Garate, F. A. Harrison, P. H. Mao, J. M. Ziegler, and V. Honkimaki, “Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes,” Nuclear Instrum. Methods Phys. Res. Section A 451, 572–581 (2000).

Opt. Eng. (1)

M. P. Bruijn, J. Verhoeven, and W. J. Bartels, “Improved resolution of multilayer x-ray coatings: a distributed Fabry-Perot etalon,” Opt. Eng. 26, 679–684 (1987).

Opt. Express (5)

Photonics and Nanostructures – Fundamentals and Applications (1)

R. Meisels, O. Glushko, and F. Kuchar, “Tuning the flow of light in semiconductor based photonic crystals by magnetic fields,” Photonics and Nanostructures – Fundamentals and Applications 10, 60– 68 (2012).

Phys. Rev. Lett. (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[PubMed]

Phys. Status Solidi (1)

V. G. Kohn, “On the Theory of Reflectivity by an X-Ray Multilayer Mirror,” Phys. Status Solidi 187, 61–70 (1995).

Proc. Natl. Acad. Sci. U.S.A. (1)

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi,” Proc. Natl. Acad. Sci. U.S.A. 112(42), 12911–12916 (2015).
[PubMed]

Proc. SPIE (5)

D. L. Windt, “EUV multilayer coatings for solar imaging and spectroscopy,” Proc. SPIE,  9604, 96041 (2015).

Z. Wang and A. G. Michette, “Optimization of depth-graded multilayer designs for EUV and x-ray optics,” Proc. SPIE 4145, 243 (2001).

T. Kuhlmann, S. A. Yulin, T. Feigl, N. Kaiser, H. Bernitzki, and H. Laut, “Ion beam sputter deposition of low-defect EUV mask blanks on 6-in. LTEM substrates in a real production environment,” Proc. SPIE 4688, 509 (2002).

S. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

S. A. Yulin, T. Kuhlmann, T. Feigl, and N. Kaiser, “Spectral reflectance tuning of EUV mirrors for metrology applications,” Proc. SPIE 5037, 286 (2003).

Other (6)

https://www.classe.cornell.edu/~dms79/refl/XR-Roughness.html

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

http://henke.lbl.gov/optical_constants/multi2.html

J. I. Larruquert, A. G. Minette, Ch. Morawe, Ch. Borel, and B. V. Vidal, in A. Erko, M. Idir, T. Krist, and A. G. Michette, eds., Modern Developments in X-Ray and Neutron Optics, Springer Series in Optical Sciences (Springer, 2008), Ch. 25.

V. Bakshi, ed., EUV Lithography (Wiley, 2009).

H. T. Grahn, ed., Semiconductor Superlattices (World Scientific, 1995).

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Figures (7)

Fig. 1
Fig. 1 Contour plot of the reflectance R at normal incidence in the complex permittivity plane for values representative for the EUV. R values are calculated for a PhC with double layers consisting of an element with permittivity ε and silicon. A few 1D PhCs (element/Si) are indicated. The total number of double layers is 40. The period of the PhC is 6.9 nm. The thickness of the silicon layer is 60% of the period. The “standard” PhC with Mo/Si layers has the highest reflectance (0.74).
Fig. 2
Fig. 2 Example of a 1D PhC with superlattice where every 4th layer of Mo is replaced by Si (“superlattice-4”). The period of the superlattice is four times the lattice constant of the basic structure, i.e. in the “standard” PhC 4x6.9 nm = 27.6 nm
Fig. 3
Fig. 3 Reflectance at normal incidence of superlattice-2 (a), −3 (b), −4 (c), −5 (d) and of the PhC without superlattice (e). The number of double layers is 80, 60, 53, 50 and 40, respectively. This way the number of Mo/Si interfaces is constant (40).
Fig. 4
Fig. 4 Contour plot of the reflectance vs. wavelength and angle of incidence. From top to bottom: superlattice-3, −4 and −5. Positive (negative) angle: s (p) polarization. Dashed curves: positions of Bragg reflections according to Eq. (1). Solid curve: critical angle of total reflection according to Eq. (2). Details see text.
Fig. 5
Fig. 5 Reflectance as a function of angle of incidence for superlattice-4 (middle) and 5 (bottom) at 13.5 nm. For comparison the reflectance for the “standard” PhC is shown (top). Positive (negative) angle: s (p) polarization. The dotted-blue and yellow curves for superlattice-5 are for an interdiffusion layer with σ = 0.07 and 0.35 nm, respectively. Details in the text.
Fig. 6
Fig. 6 Reflectance as a function of angle of incidence for combined superlattices-4 and 5 without (top) and with depth grading (bottom) at 13.5 nm. Positive (negative) angle: s (p) polarization. Details of the grading see text.
Fig. 7
Fig. 7 Band structure (reduced frequency a/λ vs. wavevector kz) of the basic structure (dashed) and superlattice-4 (solid) for kx = 0. The lowest gap of the basic structure is at kz = π/a, the lowest mini-gap of superlattice-4 at kz = π/4a. The mini-gaps are indicated by red arrows.

Tables (2)

Tables Icon

Table 1 Peak values and full widths at half maximum (FWHM) of the reflectance peaks at normal incidence (2nd and 3rd column). Angles of strong reflectance R near 13.5 nm (4th column): bold angles indicate additional reflection peaks due to the superlattices (details in Figs. 4 and 5).

Tables Icon

Table 2 Comparison of peak reflectance and peak width of superlattice PhCs and standard PhCs for normal incidence at 13.5 nm. Details see text.

Equations (2)

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sin( α )= n 2 ( λ peak ) k sl λ peak 2 Λ sl .
sin α crit =n(λ).

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