Abstract

We present the fabrication and analysis of efficient and highly dispersive gratings for the x-ray and extreme ultraviolet (EUV) regime. We show that an asymmetric-cut multilayer structure can act as a near-perfect blazed grating. The precision and high line density are achieved by layer deposition of materials, which can be controlled to the angstrom level. We demonstrate this in the EUV regime with two structures made by cutting and polishing magnetron-sputtered multilayer mirrors of over 2000 bilayers thick, each with a period of 6.88 nm. These were cut at angles of 2.9° and 7.8° to the surface. Within the 3% bandwidth rocking curve of the multilayer, the angular dispersion of the diffracted wave was in agreement with the grating equation for elements with 7250 and 19,700 line pairs/mm, respectively. The dependence of the measured efficiency was in excellent agreement with a formulation of dynamical diffraction theory for multilayered structures. At a wavelength of 13.2 nm, the efficiency of the first-order diffraction was over 95% of the reflectivity of the uncut multilayer. We predict that such structures should also be effective at shorter x-ray wavelengths. Both the Laue (transmitting) and Bragg (reflecting) geometries are incorporated in our formalism, which is applied to the analysis of multilayer Laue lenses and focusing and dispersing Bragg optics.

© 2012 Optical Society of America

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  3. D. Hambach, G. Schneider, and E. M. Gullikson, “Efficient high-order diffraction of extreme-ultraviolet light and soft x-rays by nanostructured volume gratings,” Opt. Lett. 26, 1200–1202 (2001).
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  43. H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander, J. Maser, S. Bajt, and H. N. Chapman, “High-efficiency diffractive x-ray optics from sectioned multilayers,” Appl. Phys. Lett. 86, 151109 (2005).
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  44. H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander, and S. Vogt, “Nanometer linear focusing of hard x rays by a multilayer Laue lens,” Phys. Rev. Lett. 96, 127401 (2006).
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2010

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an ångstrom-wavelength free-electron laser,” Nat. Photon. 4, 641–647 (2010).
[CrossRef]

D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High-efficiency 5000  lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
[CrossRef]

2008

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92, 221114 (2008).
[CrossRef]

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Y. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[CrossRef]

2007

H. Yan, J. Maser, A. Macrander, Q. Shen, S. Vogt, G. B. Stephenson, and H. C. Kang, “Takagi-Taupin description of x-ray dynamical diffraction from diffractive optics with large numerical aperture,” Phys. Rev. B 76, 115438 (2007).
[CrossRef]

2006

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander, and S. Vogt, “Nanometer linear focusing of hard x rays by a multilayer Laue lens,” Phys. Rev. Lett. 96, 127401 (2006).
[CrossRef]

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73, 245331 (2006).
[CrossRef]

2005

S. Bajt and D. G. Stearns, “High temperature stability multilayers for extreme ultraviolet condenser optics,” Appl. Opt. 44, 7735–7743 (2005).
[CrossRef]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft x-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[CrossRef]

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander, J. Maser, S. Bajt, and H. N. Chapman, “High-efficiency diffractive x-ray optics from sectioned multilayers,” Appl. Phys. Lett. 86, 151109 (2005).
[CrossRef]

2003

X. Huang and M. Dudley, “A universal computation method for two-beam dynamical x-ray diffraction,” Acta Cryst. A 59, 163–167 (2003).
[CrossRef]

2002

H. Chapman and K. Nugent, “X-ray pulse compression using strained crystals,” Opt. Commun. 205, 351–359 (2002).
[CrossRef]

S. Bajt, J. Alameda, J. T. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. Spiller, “Improved reflectance and stability of Mo/Si mutilayers,” 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, 4074–4081 (2002).
[CrossRef]

2001

P. P. Naulleau, E. H. Anderson, E. M. Gullikson, and J. Bokor, “Fabrication of high-efficiency multilayer-coated binary blazed gratings in the EUV regime,” Opt. Commun. 200, 27–34(2001).
[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]

H. N. Chapman, A. K. Ray-Chaudhuri, D. A. Tichenor, W. C. Replogle, R. H. Stulen, G. D. Kubiak, P. D. Rockett, L. E. Klebanoff, D. O’Connell, A. H. Leung, K. L. Jefferson, J. B. Wronosky, J. S. Taylor, L. C. Hale, K. Blaedel, E. A. Spiller, G. E. Sommargren, J. A. Folta, D. W. Sweeney, E. M. Gullikson, P. Naulleau, K. A. Goldberg, J. Bokor, D. T. Attwood, U. Mickan, R. Hanzen, E. Panning, P.-Y. Yan, C. W. Gwyn, and S. H. Lee, “First lithographic results from the extreme ultraviolet Engineering Test Stand,” J. Vac. Sci. Technol. B 19, 2389–2395 (2001).
[CrossRef]

E. M. Gullikson, S. Mrowka, and B. B. Kaufmann, “Recent developments in EUV reflectometry at the Advanced Light Source,” Proc. SPIE 4343, 363–373 (2001).
[CrossRef]

D. Hambach, G. Schneider, and E. M. Gullikson, “Efficient high-order diffraction of extreme-ultraviolet light and soft x-rays by nanostructured volume gratings,” Opt. Lett. 26, 1200–1202 (2001).
[CrossRef]

2000

C. Pellegrini, “High power femtosecond pulses from an x-ray SASE-FEL,” Nucl. Instrum. Meth. Phys. Res. A 445, 124–127 (2000).
[CrossRef]

1999

S. Bajt, R. D. Behymer, P. B. Mirkarimi, C. Montcalm, M. A. Wall, M. Wedowski, and J. A. Folta, “Experimental investigation of beryllium-based multilayer coatings for extreme ultraviolet lithography,” Proc. SPIE 3767, 259–270 (1999).
[CrossRef]

1998

D. L. Windt, “IMD–software for modeling the optical properties of multilayer films,” Comput. Phys. 12, 360–370 (1998).
[CrossRef]

1997

L. De Caro and L. Tapfer, “Generalized Laue dynamical theory for x-ray reflectivity at low and high incidence angles on ideal crystals of finite size,” Phys. Rev. B 55, 105–112 (1997).
[CrossRef]

G. Schneider, “Zone plates with high efficiency in high orders of diffraction described by dynamical theory,” Appl. Phys. Lett. 71, 2242–2244 (1997).
[CrossRef]

V. F. Sears, “Dynamical diffraction in periodic multilayers,” Acta Cryst. A 53, 649–662 (1997).
[CrossRef]

1995

S. Brauer, G. B. Stephenson, and M. Sutton, “Perfect crystals in the asymmetric Bragg geometry as optical elements for coherent x-ray beams,” J. Synchrotron Rad. 2, 163–173 (1995).
[CrossRef]

J. Kirz, C. Jacobsen, and M. Howells, “Soft x-ray microscopes and their biological applications,” Q. Rev. Biophys. 28, 33–130 (1995).
[CrossRef]

1994

V. Levashov, E. Zubarev, A. Fedorenko, V. Kondratenko, O. Poltseva, S. Yulin, I. Struk, and A. Vinogradov, “High throughput and resolution compact spectrograph for the 124–250 Å range based on MoSi2-Si sliced multilayer grating,” Opt. Commun. 109, 1–4 (1994).
[CrossRef]

1993

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000  eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

V. E. Levashov and A. V. Vinogradov, “Resonance diffraction efficiency enhancement in sliced multilayers,” Appl. Opt. 32, 1130–1135 (1993).
[CrossRef]

1992

M. Sánchez del Río and F. Cerrina, “Asymmetrically cut crystals for synchrotron radiation monochromators,” Rev. Sci. Instrum. 63, 936–940 (1992).
[CrossRef]

J. Maser and G. Schmahl, “Coupled wave description of the diffraction by zone plates with high aspect ratios,” Opt. Commun. 89, 355–362 (1992).
[CrossRef]

1990

D. G. Stearns, M. B. Stearns, Y. Cheng, J. H. Stith, and N. M. Ceglio, “Thermally induced structural modification of Mo-Si multilayers,” J. Appl. Phys. 67, 2415–2427 (1990).
[CrossRef]

1989

D. G. Stearns, “The scattering of x rays from nonideal multilayer structures,” J. Appl. Phys. 65, 491–506 (1989).
[CrossRef]

T. W. Barbee, “Combined microstructure x-ray optics,” Rev. Sci. Instrum. 60, 1588–1595 (1989).
[CrossRef]

J. C. Rife, W. R. Hunter, J. Troy, W. Barbee, and R. G. Cruddace, “Multilayer-coated blazed grating performance in the soft x-ray region,” Appl. Opt. 28, 2984–2986 (1989).
[CrossRef]

1988

V. V. Aristov, A. I. Erko, and V. V. Martynov, “Principles of Bragg–Fresnel multilayer optics,” Rev. Phys. Appl. 23, 1623–1630 (1988).
[CrossRef]

1986

V. V. Aristov, A. A. Snigirev, Yu. A. Basov, and A. Yu. Nikulin, “X-ray Bragg optics,” AIP Conf. Proc. 147, 253–259 (1986).
[CrossRef]

1980

D. Rudolph and G. Schmahl, “High power zone plates for a soft x-ray microscope,” Ann. N.Y. Acad. Sci. 342, 94–104(1980).
[CrossRef]

1972

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

1964

B. W. Batterman and H. Cole, “Dynamical diffraction of x rays by perfect crystals,” Rev. Mod. Phys. 36, 681–717 (1964).
[CrossRef]

Ahn, M.

Akre, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an ångstrom-wavelength free-electron laser,” Nat. Photon. 4, 641–647 (2010).
[CrossRef]

Alameda, J.

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

Anderson, E. H.

D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High-efficiency 5000  lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
[CrossRef]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft x-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[CrossRef]

P. P. Naulleau, E. H. Anderson, E. M. Gullikson, and J. Bokor, “Fabrication of high-efficiency multilayer-coated binary blazed gratings in the EUV regime,” Opt. Commun. 200, 27–34(2001).
[CrossRef]

Aristov, V. V.

V. V. Aristov, A. I. Erko, and V. V. Martynov, “Principles of Bragg–Fresnel multilayer optics,” Rev. Phys. Appl. 23, 1623–1630 (1988).
[CrossRef]

V. V. Aristov, A. A. Snigirev, Yu. A. Basov, and A. Yu. Nikulin, “X-ray Bragg optics,” AIP Conf. Proc. 147, 253–259 (1986).
[CrossRef]

A. I. Erko, V. V. Aristov, and B. Vidal, Diffraction X-Ray Optics (IOP, 1996).

Arthur, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an ångstrom-wavelength free-electron laser,” Nat. Photon. 4, 641–647 (2010).
[CrossRef]

J. Arthur, “LCLS design study report,” Internal Technical Report 521, SLAC (Stanford University, 1998).

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft x-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

A multilayer is cut at an angle Φ=π/2ϕ (right). The reflection from the asymmetric-cut multilayer film (center) is identical to reflection from an ideal multilayer-coated blazed grating (left) [5] because the multilayer structure is the same in both cases. The incident wave is in the direction s0 and the reflected wave is in the direction sm. The sense of the angles and the direction of the trace of the surfaces s is defined by 0<θB=(s,s0)<π/2, and so the angles α=(n,s0), β=(n,sm), ϕ=(n,s) are all negative in this diagram. A beam of width Win exits with width Wout.

Fig. 2.
Fig. 2.

a, Reflectivity at a wavelength of 13.4 nm for σ polarization of a symmetric Mo-Si EUV multilayer (b=1, d=7.5nm), as calculated by Eq. (17) with θ=θB+Δθ (solid line) and as calculated by the IMD program [20] for a multilayer with sharp interfaces (dashed line). b, σ-polarization reflectivity of the same Mo-Si structure with an asymmetric-cut angle ϕ varying from 70° (highest peak reflectivity) to 140° (lowest peak reflectivity), in 10° steps. The Bragg angle of 63.6° is indicated in panels a and b.

Fig. 3.
Fig. 3.

a, Measured reflectivity of the cut multilayer with Φ=7.8°, θ=80°, α=2.2°, β=162.2° (solid line) and the uncut multilayer (dashed line). The dotted line shows the calculated reflectivity of the uncut multilayer, obtained by fitting a four-layer model of the periodic structure. The wavelength satisfying the Bragg condition, Eq. (3), is indicated, and the insert depicts the experimental geometry. b, Measured reflectivity of the same Φ=7.8° cut multilayer at a fixed wavelength of 13.2 nm, as a function of detector angle, 2θ, for an incidence angle of α=2.2°. An equivalent grating with a period D=d/cosϕ=50.7nm would have a second-order diffraction peak at 2θ=143.8° [as per Eq. (1)].

Fig. 4.
Fig. 4.

AFM height maps of the cut regions for a, the Φ=2.9° cut and b, the Φ=7.8° cut. The scale bar is 1 μm, and the range of the color scale is 20 nm from lowest height (black) to highest (white). These correspond to blazed gratings of 7250 and 19,700 line pairs/mm, respectively. The grating efficiency is essentially insensitive to surface imperfections because x-ray diffraction is a volume effect.

Fig. 5.
Fig. 5.

a, Reflectivity of the Φ=7.8° cut mirror at a Bragg angle of 30.39°, b=1.49, as a function of detector angle 2θ and wavelength λ. The incidence angle was α=53.0°. Positions of the peak reflectivity at each wavelength are displayed with diamonds, and the line is a fit of the grating equation, Eq. (1), to these peaks. b, Reflectivity, integrated over 2θ, from a dataset similar to that shown in panel a is displayed with diamonds The solid line is a calculation from Eq. (17), scaled by a factor 0.53, and the dashed line is a calculation for the symmetric reflection using the IMD program and applying the same scaling factor.

Fig. 6.
Fig. 6.

Geometry of a pulse compressor in Bragg geometry for the case that b<1. Ray paths are indicated by dashed lines. The circular arrows labeled “positive” show the direction of positive angles for the two reflections.

Fig. 7.
Fig. 7.

Geometry of a pulse compressor in Laue geometry, b>0. Ray paths are indicated by dashed lines. The circular arrows labeled “positive” show the direction of positive angles for the two reflections.

Fig. 8.
Fig. 8.

Four sliced multilayer elements arranged to compress pulses and correct for the beam shear. The geometry shown here has 1<b<0.

Fig. 9.
Fig. 9.

The calculated efficiency of the reflected and transmitted beams from a cut W/SiC multilayer slab of thickness t in the symmetric Laue geometry (e.g., the local zone-plate efficiency), with b=+1 for a wavelength of λ=0.5nm. The multilayer period is d=2nm, and the reflectivity is optimized at Γ=0.22.

Tables (3)

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Table 1. Geometries of Some Reflections Possible for the d = 6.88 nm Multilayer with Cut Angles of 2.9° and 7.8°

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Table 2. Parameters of Pulse Compressorsa

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Table 3. Reflectivities of Various Sliced Multilayers in the Symmetric Laue Geometry (b = 1)

Equations (47)

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nλ=D(sinαsinβ),
=2Dcosϕsinθ,
mλ=2dsinθB,
π2<α<π2+2θB,
π22θB<β<π2,
π2θB<ϕ<π2+θB.
b=n·s0n·sm=γ0γm=cosαcosβ,
|b|=WinWout
βα=b.
b=cos(ϕ+θB)cos(ϕθB).
ϕ=±cos1[±(1+b)sinθB1+b22bcos2θB].
ϕ=cos1[(1+b)sinθB1+b22bcos2θB]=cos1[m(1+b)λ2(b1)2d2+m2λ2b],
ϕ=cos1[(1+b)sinθB1+b22bcos2θB],b<0,
ϕ=cos1[(1+b)sinθB1+b22bcos2θB],0<b<1,
ϕ=cos1[(1+b)sinθB1+b22bcos2θB],b>1.
βλ=1λ(1+b)tanθB.
RB=|χmχm¯||ϵ1ϵ2|2|η(ϵ1ϵ2)+η21(ϵ1+ϵ2)|2,
η=(ΔθΔθs)/δs
Δθs=χ0(11/b)2sin2θB,
δs=Cχmχm¯|b|sin2θB,
Λ0=λ|γm|δssin2θB.
Δθ=Δλ/λtanθB=mΔλ2d2m2λ2.
Δλs/λ=χ0(11/b)4sin2θB,
Δλw/λ=Cχmχm¯|b|sin2θB.
RL=|χmχm¯|exp[μ02(1γ0+1γm)t]|ϵ1ϵ2|24|1+η2|,
TL=exp[μ02(1γ0+1γm)t]|η(ϵ1ϵ2)+1+η2(ϵ1+ϵ2)|24|1+η2|,
χm=1Vχ(r)exp(iqm·r)dr,
=1dχ(z)exp(2πimz/d)dz,
χ(z)2(δ(z)+iβ(z)).
δ(z)={δ1,0<zΓd,δ2,Γd<zd,
χ0=2(δ¯+iβ¯),
χmχm¯=2(δ1δ2+i(β1β2))sin(mπΓ)mπ,
|χmχm¯|=1.
δ(z)=δ2+12(δ1δ2)[Erf(zσ1)Erf(zΓdσ2)],
χmχm¯2(δ1δ2+i(β1β2))sin(mπΓ)mπexp(m2π2(σ12+σ22)d2),
R=RBexp{(4πσs(n1)cosα/λ)2},
sinβ=λcosϕd+sinα.
λ(x)=λ0(1γcx/Lp),
xc(λ)=x0+Lp(λλ0)/λ(1/γc),
Δxc(Δλ)=Lp(Δλλ)/γc.
Lβ=Hcos2β.
Δxc=ΔL(sinαsinβ).
Δxc=2ΔλλHcos2β(1+b)tanθBcosϕsinθB.
Δxc=(n1·n2)ΔλλHcosβ(1+b)2tanθB.
Δy=(H/cosβ)sin2θB.
S=ΔLcosβ2=ΔLcosα,=Δxcb1+bcotθB.
b=1+r2/f2.

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