Can the optics get to 1-nm?
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Transcript of Can the optics get to 1-nm?
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Can the optics get to 1-nm?
Hanfei YanNSLS-II, Brookhaven National Laboratory
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• Multilayer-Laue-Lens (MLL) deposition • Al Macrander1
• Chian Liu1
• Ray Conley1
• MLL characterization and focusing measurement• Brian Stephenson2,3 • Hyon Chol Kang2,3
• Theoretical Modeling• Jörg Maser1,2
• Stefan Vogt1
Collaborators
1. Advanced Photon Source, Argonne National Laboratory2. Center for Nanoscale Materials, Argonne National Laboratory3. Materials Science Division, Argonne National Laboratory
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Outline
• What x-ray optics are capable of nanofocusing?
• What is multilayer Laue lens (MLL)?• Why MLL?• Can we really get to 1-nm focus by MLL?• What are the properties of MLL?• What are the fabrication challenges?
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Overview of x-ray focusing optics
• Reflective opticsWaveguide, capillary, K-B mirror w/o multilayerAchieved: ~25 nmHard limit: ~ 10 nm
• Refractive opticsCompound refractive lenses (CRLs): ~ 10 nmAdiabatically focusing lenses (AFLs): no hard limit, but has practical limit for
nanofocusingAchieved: ~50 nm
• Diffractive opticsFresnel zone plates (FZPs): fabrication limit Multilayer Laue Lenses (MLL’s): no hard limit, suitable for hard x-ray focusing
– Achieved line focus: ~16 nm– Promising for true nanometer focus– Chosen as candidate 1-nm optics for NSLS-II
• Kinoform lenses (Kenneth Evans-Lutterodt), multilayer mirrors
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1-D structure allows fabrication via thin film deposition techniques
• Almost limitless aspect ratio• very small zone width (1nm)
MLL’s are capable of achieving nanometer focus with high efficiency
Multilayer-Laue-Lens (MLL)
Lithography method: • >15 nm zone width
• <30 aspect ratio (w/rn)
Limited resolution and efficiency for hard x-ray focusing:
Au, w=300 nm, efficiency=15% @ 1 keV; 0.3% @ 30 keV H. C. Kang et al., Phys. Rev. Lett. 96, 127401
(2006).
http://www.xradia.com/Products/zoneplates.html
Fresnel Zone Plate
w
rn
Introduction to Multilayer Laue Lenses
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Full Wave Dynamical Diffraction Theory is Needed!
Zone plate law: 4/222 nfnrn
2
2
12 f
rrfr n
nn
Zone width:
Resolution limit: mrn /22.1
For the geometrical-optical theory be valid, the zone plate has to be “thin” so that the multiwave scattering (dynamical) effect can be ignored.
Geometrical-Optical theory:
2
2/
n
n
n rfrrw
Optimum thickness: (phase zone plate) n
w
2
w
rn/f
At optimum section depth, dynamical diffraction properties begin to dominate when the outmost zone width becomes smaller than ~ 10 nm!
http://www.xradia.com/Products/zoneplates.html
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A Takagi-Taupin Description of Dynamical Diffraction for Volume Diffractive Optics
• Diffraction from MLL’s is akin to that from strained single crystals.• Takagi-Taupin-similar equations can be derived for MLL’s.
x’x
Fresnel Zone Plate 1:1 Binary Bars
nth
1st
T
AB
z
,)](exp[)(0,
0MLL
hh
hh xix
)11/( 22 fxkfhh
0cos)()(20
lhlllhhh
hh EEr
ksE
ki
202
2
)(2)(kk
sk
ir hhhh
Central equations:
Pseudo Fourier series:
H. Yan, J. Maser, A. T. Macrander, Q. Shen, S. Vogt, B. Stephenson and H. C. Kang, Phys. Rev. B 76, 115438(2007)
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Focusing Properties of MLL
h
k0
kh
1
2
3
-1-2-3
Ewald sphere
Physical NA ≠ Effective NA!
=0 =1.1 mrad
=2.1 mrad =3.2 mrad
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Focus profile as a function of tilting angle
WSi2/Si, 19.5 keV, outermost zone width of 5 nm, half structure.
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Trade-off between efficiency and effective NA
• Geometrical theory becomes valid when the lens is thin enough and does not diffract “dynamically”.
• In geometrical theory, physical NA = effective NA
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50
1
2
3
4
5
6
7
=0 Tilted
Inte
gral
Widt
h (n
m)
Section depth w (m)
Diffraction Limit
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
=0 Tilted
Tota
l Effic
iency
(%)
Section depth w (m)
Example: MLL with flat zones and outmost zone width of 1 nm
Focal size Total EfficiencyE=19.5 keV
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Can we achieve high efficiency and large effective NA simultaneously?
• Bragg condition needs to be satisfied.• Each zone is tilted progressively to satisfy the local Bragg
condition, resulting in a wedged shape.
2
2
12)(fx
xfxxd n
fxm
xdm
2)(2sin
First order, m=1, all zones shrink homogeneously by a factor,
fzza
21)(
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Wedged MLL
Wedged MLL, 0.75 nm outmost zone width, WSi2/Si, energy at 19.5 keV, FWHM=0.7 nm, total efficiency=50% .
The wedged structure is an approximation to the ideal structure, but it is enough for 1-nm focusing.
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Properties of 1-nm MLL optics
510/1/ NEENarrow energy bandwidth:
Short work distance: 2~3 mm, limited by the deposition techniques (accuracy and growth time)
More suitable for hard x-rays focusing (easier to fabricate)For wedged MLL’s, only within a small range around an optimum energy, which is determined from the tiling angle of the wedged structure, can its full physical NA be utilized.
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For a MLL with flat zones,
fnxn 2
as long as f=const. the zone plate law is satisfied. However for a wedged MLL its focal length is determined by the shrinkage factor in order to satisfy the Bragg condition,
fzza
21)(
As a result, only at a specific energy the performance of a wedged MLL is optimized.
Optimum Operating Energy for Wedged MLL’s
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Initial wedged structure
14 16 18 20 22 24 26 28 30 320
2
4
6
8
10
Exp. Tan.
Effe
ctive
radiu
s r (
m)
Position z (mm)
slope=-1.210-3
R. Conley/APS
f=2.64 mm, =0.151 Å
Optimum energy: 82.1 keV. Within ±10% of the optimum energy the focal spot is not broadened.
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Challenges
• Build-up stress• High quality thin films (defects, roughness,
interface diffusion and uniformity)• Fast growth rate (~100 µm)• Long-term machine stability to ensure nanometer
accuracy during deposition (~days)• Deposition techniques for wedged structures• Slicing and polishing techniques• Engineering challenges of assembling two MLL’s
for point focusing
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Growth Error
Actual zone profile
Calculated intensity isophote pattern
Comparison
H. Yan, H. C. kang, J. Maser et al., Nuclear Inst. and Methods in Physics Research, A 582, 126-128(2007)
Optical axis
Diffraction Limit: 30 nmMeasured size: 50 nm
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Current state-of-the-art MLL
40% of full structure, 5 nm outermost zone width
5 nm thick, 5 m wide Pt nano-layer
Pt La,,g
MLL
Fluorescence detector
X-rays
Far-field detector
Line focus measurement
H. C. Kang, H. Yan, J. Maser et al., to appear in Appl. Phys. Letts
FWHM=16 nm
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Conclusions
• No hard theoretical limit prevents hard x-rays from being focused to 1-nm by MLL method.
• To achieve 1-nm focus with high efficiency, wedged MLL’s are required.
• There are significant technical challenges on 1-nm MLL fabrication.
• With the R&D effort, we believe that 1-nm spatial resolution is achievable.