can the optics get to 1-nm?

1 BROOKHAVEN SCIENCE ASSOCIATES

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.