Abstract

Sub-quarterwave multilayer coatings with more than two different materials are shown to provide a reflectance enhancement compared with the standard two-material multilayer coatings when reflectance is limited by material absorption. A remarkable reflectance enhancement is obtained when the materials in the multilayer are moderately absorbing. A simple rule based on the material optical constants is provided to select the most suitable materials for the multilayer and to arrange the materials in the correct sequence in order to obtain the highest possible reflectance. It is shown that sub-quarterwave multilayers generalize the concept of multilayers, of which the standard two-material multilayers are a particular case. Various examples illustrate the benefit of sub-quarterwave multilayer coatings for highest reflectance in the extreme ultraviolet. Applications for sub-quarterwave multilayer coatings are envisaged for astronomy in the extreme ultraviolet (EUV) and soft x rays and also for future EUV lithography.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2001 (3)

2000 (3)

1999 (1)

1997 (1)

1988 (1)

1986 (1)

J. B. Kortright, “Multilayer reflectors for the extreme ultraviolet spectral regions,” Nucl. Instrum. Methods Phys. Res. A 246, 344–347 (1986).
[CrossRef]

1984 (1)

1972 (1)

1970 (1)

Blumenstock, G. M.

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

Boher, P.

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft x-ray mirrors: theory and application,” in Advanced X-Ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

Braat, J. J. M.

Cox, J. T.

Ginter, M. L.

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

Grigoris, Marius

Hass, G.

Hennet, L.

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft x-ray mirrors: theory and application,” in Advanced X-Ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

Houdy, Ph.

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft x-ray mirrors: theory and application,” in Advanced X-Ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

Hunter, W. R.

Keski-Kuha, R. A. M.

J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the EUV for thin films of ion-beam-deposited SiC, Mo, Mg2Si, and InSb, and evaporated Cr,” Appl. Opt. 39, 2772–2781 (2000).
[CrossRef]

J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the extreme ultraviolet of thin films of ion-beam-deposited carbon,” Opt. Commun. 183, 437–443 (2000).
[CrossRef]

J. I. Larruquert, R. A. M. Keski-Kuha, “Multilayer coatings with high reflectance in the EUV spectral region from 50 to 121.6 nm,” Appl. Opt. 38, 1231–1236 (1999).
[CrossRef]

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

Keski-Kuha, Ritva A. M.

Knystautas, Émile J.

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten: Optical Properties of Metals (Fachinformationszentrum, Karlsruhe, Germany1981), Vol. 18, No. 1.

Kortright, J. B.

J. B. Kortright, D. L. Windt, “Amorphous silicon carbide coatings for extreme ultraviolet optics,” Appl. Opt. 27, 2841–2846 (1988).
[CrossRef] [PubMed]

J. B. Kortright, “Multilayer reflectors for the extreme ultraviolet spectral regions,” Nucl. Instrum. Methods Phys. Res. A 246, 344–347 (1986).
[CrossRef]

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten: Optical Properties of Metals (Fachinformationszentrum, Karlsruhe, Germany1981), Vol. 18, No. 1.

Larruquert, J. I.

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten: Optical Properties of Metals (Fachinformationszentrum, Karlsruhe, Germany1981), Vol. 18, No. 1.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1998), Vols. I–III.

Powell, C. J.

Ramsey, J. B.

Singh, M.

Spiller, E.

E. Spiller, Soft X-Ray Optics (SPIE–The International Society for Optical Engineering, Bellingham, Wash., 1994), p. 143.

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten: Optical Properties of Metals (Fachinformationszentrum, Karlsruhe, Germany1981), Vol. 18, No. 1.

Windt, D. L.

Appl. Opt. (6)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

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

J. B. Kortright, “Multilayer reflectors for the extreme ultraviolet spectral regions,” Nucl. Instrum. Methods Phys. Res. A 246, 344–347 (1986).
[CrossRef]

Opt. Commun. (1)

J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the extreme ultraviolet of thin films of ion-beam-deposited carbon,” Opt. Commun. 183, 437–443 (2000).
[CrossRef]

Other (6)

http://www-cxro.lbl.gov/optical_constants .

E. Spiller, Soft X-Ray Optics (SPIE–The International Society for Optical Engineering, Bellingham, Wash., 1994), p. 143.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1998), Vols. I–III.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten: Optical Properties of Metals (Fachinformationszentrum, Karlsruhe, Germany1981), Vol. 18, No. 1.

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft x-ray mirrors: theory and application,” in Advanced X-Ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Optical constants for various materials at 50.0 nm. Solid line, minimum polygon including all the materials. Dotted line, a secondary polygon not including LiF, Re, and W.

Fig. 2
Fig. 2

Layer thicknesses of a ten-period multilayer with seven materials: LiF, Re, Ir, BaF2, SrF2, InSb, and Al. The periods are numbered starting with the outermost period. The multilayer was optimized for the highest reflectance at 50.0 nm at normal incidence.

Fig. 3
Fig. 3

Intrinsic spectral bandwidth of ten-period, sub-quarterwave multilayers optimized for the highest reflectance at 50.0 nm at normal incidence. The optical constants of the different materials were set constant throughout the spectral region shown, equal to their value at 50.0 nm. In the figure, single letters represent materials as follows: L=LiF; R=Re; I=Ir; B=BaF2; S=SrF2; I=InSb; A=Al.

Fig. 4
Fig. 4

Reflectance as a function of the angle of incidence at 50.0 nm of ten-period, sub-quarterwave multilayers optimized for the highest reflectance at 50.0 nm. Radiation was assumed nonpolarized. See Fig. 3 caption for material definitions.

Fig. 5
Fig. 5

Optical constants for various materials at 30.4 nm. Solid line, minimum polygon including all the materials.

Fig. 6
Fig. 6

Layer thicknesses of a 25-period multilayer with ten materials: Al, Si, B, B4C, Os, Au, Mo, Hf, W, and Ge. The periods are numbered starting with the outermost period. The multilayer was optimized for the highest reflectance at 30.4 nm at normal incidence. The thickness of the following materials were shifted toward shorter or negative values to improve readability: Au (-3.5 nm), Hf (-3.0 nm), W (-2.5 nm), Ge (-2.0 nm), B4C (-1.5 nm), Mo (-1.0 nm), and Os (-0.5 nm).

Tables (2)

Tables Icon

Table 1 Calculated Normal Reflectance of Multilayers (Containing Ten Periods) Optimized for the Highest Reflectance at 50.0 nm at Normal Incidence

Tables Icon

Table 2 Calculated Normal Reflectance of Multilayers (Containing 25 Periods) Optimized for the Highest Reflectance at 30.4 nm at Normal Incidence

Equations (3)

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ImΔNiΔNi-1<0.
Imr01*(1-r012)N1ΔN1N1+N2>0,
ImΔN1ΔN0<0.

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