APPLIED PHYSICS LETTERS 92, 221114 共2008兲
Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens
Hyon Chol Kang,1,a兲 Hanfei Yan,1,b兲 Robert P. Winarski,1 Martin V. Holt,1 Jörg Maser,1,c兲
Chian Liu,2 Ray Conley,2 Stefan Vogt,2 Albert T. Macrander,2 and G. Brian Stephenson3
1
Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
3
Materials Science Division and Center for Nanoscale Materials, Argonne National Laboratory,
Argonne, Illinois 60439, USA
2
共Received 9 January 2008; accepted 1 April 2008; published online 6 June 2008兲
We report improved results for hard x-ray focusing using a multilayer Laue lens 共MLL兲. We have
measured a line focus of 16 nm width with an efficiency of 31% at a wavelength ␭ = 0.064 nm
共19.5 keV兲 using a partial MLL structure with an outermost zone width of 5 nm. The results are in
good agreement with the theoretically predicted performance. © 2008 American Institute of
Physics. 关DOI: 10.1063/1.2912503兴
The Rayleigh criterion gives the best possible 共i.e.,
diffraction-limited兲 spatial resolution for a focusing optic
with rectangular aperture as 0.5 ␭/NA, where NA is the numerical aperture. While hard x-rays have short wavelengths
␭, they refract and reflect only at very small angles, making
it difficult to produce an optic with large NA. The advent of
high-brilliance synchrotron x-ray sources has made focusing
to the diffraction limit feasible by providing sufficient flux of
coherent photons. Several approaches to hard x-ray focusing
are being pursued, and ever smaller focuses are being reported. Diffractive optics can conceptually reach a NA of 1.
Using Fresnel zone plates, a resolution of 30 nm has been
achieved at ␭ = 0.15 nm using the relatively weak third-order
diffraction.1 For reflecting optics, the maximum NA is set by
the critical angle for total external reflection, which gives the
best possible resolution of an ideal tapered capillary2 to be
10 nm. Experiments demonstrating a line focus of 25 nm at
␭ = 0.08 nm have recently been reported for an elliptically
figured mirror,3 which is at the diffraction limit for the largest NA practical with this approach. Use of a multilayer coating can in principle allow the NA of a mirror to be increased,
but such mirrors have yet to produce an improved focus.4,5
Refractive lenses also allow focusing to the nanometer scale,
with a smallest possible resolution of 2 nm having been calculated for a kinoform refractive lens design.6 Focusing to
47 nm with a compound refractive lens has been experimentally demonstrated7 at ␭ = 0.06 nm. A line focus with a width
of 26 nm was achieved with a planar waveguide at a photon
energy of 13.3 keV.8
Our approach is to use diffraction from a multilayer
structure illuminated in transmission geometry, called a
multilayer Laue lens 共MLL兲.9,10 The multilayer consists of a
sequence of bilayers deposited onto a substrate so that the
layer thicknesses increase progressively, giving interface positions xn related to focal length f by the zone plate law,11
x2n = n␭f. As illustrated in Fig. 1, the multilayer is sectioned
and illuminated through the cross section. The two halves of
the MLL can be tilted to satisfy the Bragg condition for the
outer, smallest layer spacings, giving an efficiency larger
than that of a conventional zone plate. The x-ray optical
arrangement for the MLL is akin to the Laue geometry in
crystal diffraction. It also operates in a diffraction regime
where dynamical diffraction effects inside the volume of the
optic are dominant. This enables the high NA required for
near-atomic-scale resolution x-ray optics.
While the structure of an MLL is similar to that of a zone
plate, its method of fabrication overcomes performance limitations imposed by conventional nanolithography. First,
zones with very small widths are required since the outermost zone width is approximately equal to the achievable
resolution. The deposition process used for the MLL permits
the controlled growth of layers thinner than 1 nm. Second, to
achieve high efficiency for hard x-rays, a zone depth of several microns is required. As the zone width becomes smaller,
this results in structures with very high aspect ratios. Such
structures are difficult to produce using lithography. Maximum aspect ratios of ⬃20 have been produced for
nanometer-width structures.1 For an MLL, on the other hand,
the aspect ratio is essentially limitless since any depth along
the optical axis can be fabricated. The aspect ratio for the
outermost zone of the MLL structure described below is
3000.
Here, we report fabrication and characterization of a partial MLL structure with a 5 nm outermost zone width and
1588 zones, as shown in Fig. 2. The alternating WSi2 and Si
layers correspond to zones n = 66 through 1653 of a structure
a兲
Present address: Advanced Photonics Research Institute, Gwangju Institute
of Science and Technology, Gwangju 500-712, Republic of Korea.
b兲
Present address: National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973.
c兲
Author to whom correspondence should be addressed. Electronic mail:
[email protected].
FIG. 1. Schematic of complete MLL made of two halves obtained from
cross sections of a multilayer coating on a substrate.
0003-6951/2008/92共22兲/221114/3/$23.00
92, 221114-1
© 2008 American Institute of Physics
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221114-2
Kang et al.
Appl. Phys. Lett. 92, 221114 共2008兲
FIG. 2. 共Color兲 Scanning electron microscope image of the multilayer with magnified insets showing the individual layers at both ends and in the center. As
illustrated by the color, the layers forming the zones vary in thickness from 5 to 25 nm according to the zone plate law for a focal length of 2.6 mm at ␭
= 0.064 nm, with 1588 alternating WSi2 and Si layers for a total thickness of 13.25 ␮m.
with ␭f = 1.653⫻ 10−13 m2, comprising the outer 13.25 ␮m
of the full 16.53 ␮m radius. The optical depth used, 15 ␮m,
was chosen to optimize diffraction efficiency at ␭ near
0.06 nm.
The fabrication process for an ideal MLL must result in
many accurately placed layers that diffract in phase at the
focus. The first step is the sputter deposition of a variablelayer-thickness multilayer. The outermost zone, i.e., the thinnest layer, is the first layer deposited. This lessens the impact
of any buildup in layer thickness errors during the deposition
process. Successful deposition of the multilayer, as shown in
Fig. 2, was accomplished following a development study to
eliminate growth-related defects.10 The choice of materials
system is key in lessening the build up of interface roughness. An x-ray reflectivity study done in situ during the
growth of a WSi2 / Si multilayer revealed that although the Si
layers noticeably roughen, the WSi2 layers cancel the added
roughness.12 The rate of deposition is also very important,
since otherwise the time to accomplish the entire growth
becomes excessive. We have found that both WSi2 and Si
can be quite rapidly sputtered. The time taken to grow the
13.25-␮m-thick multilayer in Fig. 2 was 36 h. The accumulation of stress is also a concern since excessive stress can
cause delamination. We have found that there is a compensation of compressive stresses in Si layers by tensile stresses
in WSi2 layers, with very little net accumulation.13 Subsequent to growth, the multilayer is sectioned and thinned to
the requisite optical depth to form the halves of the MLL. A
series of steps similar to that for making cross-section transmission electron microscopy samples has been found to be
successful in making sections of sufficient perfection.14
The synchrotron x-ray measurements reported here were
performed at the Center for Nanoscale Materials beamline
26ID of the Advanced Photon Source. Supporting measurements were also carried out at beamlines 12BM and 8ID.
The x-ray source was defined by upstream slits to produce a
coherence length of 14 ␮m in the horizontal 共focusing兲 direction at the position of the MLL. Using a double-bounce
diamond 共111兲 monochromator, an x-ray energy of 19.5 keV
共␭ = 0.064 nm兲 was selected. High precision slits in front of
the MLL allowed illumination of all or part of the structure,
with incident intensity monitored by an ion chamber. A
50 ␮m vertical length of the MLL was illuminated. The
MLL was mounted on a vertical axis goniometer to allow
characterization as a function of incidence angle. Focal width
measurements were performed using a Pt analyzer of cross
section 5 nm⫻ 5 ␮m produced by sectioning a 5-nm-thick
Pt film. The analyzer was mounted on a gimbal to allow
alignment parallel to the line focus of the MLL and adjustment of the plane of the Pt film with respect to the focused
beam direction. We measured the intensity of both fluorescence and scattering from the analyzer as it was scanned
through the focus using an encoded nanostage with 2 nm
reproducibility. An energy-dispersive detector monitored the
sum of the Pt L␣ and L␤ fluorescence lines. X rays scattered
from the analyzer were monitored using a scintillation
counter in the far field positioned at an angle of 0.435° from
the incident beam direction.
Figure 3 shows the focusing performance obtained from
a single section of the multilayer of Fig. 2 at ␭ = 0.064 nm.
This represents 40% of a complete linear MLL. Results are
an average of 29 scans taken in alternating directions to cancel effects of drift. The observed size of the focus was
17.6 nm full width at half maximum 共FWHM兲 for the fluorescence signal and 15.6 nm FWHM for the scattering signal. The difference is likely due to the better resolution of the
analyzer in the case of the scattering measurement.
The efficiency of focusing of the MLL was measured by
two methods. The far-field diffraction pattern of the MLL
with the analyzer removed shows a distinct region corresponding to the first diffraction order from the zone structure.
By integrating the signal from the first-order diffraction region and normalizing it to the zero-order integrated intensity
with the MLL removed, we obtain an efficiency of 31% at
the experimentally determined optimum MLL tilt angle of
0.10°. We also measured the efficiency by monitoring the
intensity of the zero-order beam as the MLL was scanned
through the incident beam. We compared two tilt angles, one
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221114-3
Appl. Phys. Lett. 92, 221114 共2008兲
Kang et al.
nanoscience,20 and as a key objective for making full use of
the continuing investments in major x-ray source facilities.21
The unique properties of MLL structures may make it possible to fulfill the longstanding goal of near-atomic-scale imaging with x-rays.
Note added in proof: After submission of the manuscript,
a spatial resolution of less than 40 nm at a photon energy of
8 keV has been reported by Y. Chu et al., Appl. Phys. Lett.
92, 103119 共2008兲.
FIG. 3. 共Color兲 Intensity distribution in the focal plane at ␭ = 0.064 nm from
a 15-␮m-deep section of the multilayer of Fig. 2 at a tilt of 0.10° measured
using fluorescence and scattering from a 5 nm Pt analyzer scanned through
the line focus. Also shown is the calculated result for this structure, with
intensity scaled according to the measured and calculated integrated efficiencies. The widths are 17.6, 15.6, and 15.0 nm FWHM for the fluorescence measurements, scattering measurements, and calculation; the measured and calculated efficiencies are 31% and 30%, respectively. The inset
shows the isophote pattern near the focus, where coordinates z and x are
parallel and transverse to the incident beam.
共0.10°兲 at the optimum for first-order diffraction, and one
共5.00°兲 well away from the optimum. We observe intensity
decreases to 42% and 73%, respectively. The difference of
31% corresponds to extinction of the direct beam due to
diffraction into the focus, which agrees well with the direct
measurement of the first-order efficiency.
We have developed a method15 for calculating MLL focusing performance based on the Takagi–Taupin formalism
of dynamical diffraction from strained crystals.16 This
method is accurate even at NA values near unity, unlike our
previous approach.9,17 Other calculation methods based on
parabolic wave equations are limited to smaller values of NA
due to the paraxial approximation.18,19 The calculated intensity distribution around the focal plane for the partial MLL
structure is shown with the measurement in Fig. 3. The calculated FWHM of 15 nm and efficiency of 30% are in good
agreement with the measurements, which include some
broadening from vibrations, finite analyzer width, and finite
source size. The good agreement between the measured and
calculated performance supports the use of the calculations
to predict the behavior and guide the development of future
MLL structures. In particular, we anticipate15 that the “tilted”
geometry used here will allow focusing to 5 nm, while more
ideal geometries will allow focusing to below 1 nm.
The impact of an optic that focuses hard x-rays to 5 nm
and below is expected to be large for many areas of science.
This has been identified as a critical analysis tool for
Fabrication of MLL structures was carried out at Argonne using facilities of the Advanced Photon Source, Center for Nanoscale Materials, and Electron Microscopy Center. X-ray characterization was performed at APS beamlines
26ID, 12BM, and 8ID. This work was supported under Contract No. DE-AC-02-06CH11357 between UChicago Argonne, LLC and the Department of Energy.
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