X-Ray Microfocusing Optics

Barry Lai
X-Ray Science Division
Advanced Photon SourceOutline Introduction
 General considerations
 Reflective optics
Diffractive optics
Refractive optics
 Future prospects

Cheiron Summer School 20082

Introduction- Optics that focus x-rays to a spot size ≤ 10 micron

Reflective

Diffractive

Refractive

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When to use microfocusing optics:
 For x-ray microscopy– Most samples are heterogeneous, from micron down to nm scale Increased flux density– Gain ~ 106 is possible, hence higher sensitivity (signal/background) Enable smaller samples or new sample environment

Cheiron Summer School 20084

X-ray Microscopy

Lecture by I. McNulty on Oct. 3

ρ(x,y)

Direct imaging (radiography)*with magnification in visible light

Transmission microscope (TXM)
depends only on total flux, but not brilliance / coherence

Scanning microscope (SXM)
depends only on coherent flux, directly benefits
from reduced emittance

Coherent diffraction imaging*
Holography** May not require microfocusing
Cheiron Summer School 20085

Cross-sectional TEM of Strained-Si NMOSFET

popoly gatelyc
idepoly gaten2.
2Strained Si
Channel

m

te
a
g

o

e
x id

Si
ed l
n
i
ra e
S t annCh

Co silicide
Relaxed SiGe (15% [Ge]) Quality of epitaxial layers maintained during CMOS process steps
 Gate oxide with smooth interface formed by thermal oxidation

Ken Rim-IBM=> today’s manufacturer’s are already able to produce nm scale structures. To probe suchsmall structures meaningfully requires x-ray beam of the same order of magnitude.
Slide courtesy Cev Noyan, with modification
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Incident
x-raysMicrofocusing increases flux density
 Focusing increases the signal/background ratio For current probes with submicron

Detection Limit with 1 sec. Dwell Time

spot, attogram (10-18 gm) of materials

0.2 x 0.2 µm2 spot, E=10 keV

can be detected in fluorescence mode

zeptogram (10-21 gm) or a few atoms
is possible

Ti

Ca

10

Fe

V

5

10

Mn

Zn

Co
Cu

10

Attogram (10-18 gm)

 With a 5-nm probe, sensitivity of

Detection Limit (atoms)

10

100

K

6

4

2

4

6

8

10

Fluorescence Energy (keV)

Cheiron Summer School 20087

Microbeam for protein crystallography

Cheiron Summer School 20088

New High-Pressure Frontiers withhigher spatial resolution
 Diamond Anvil Cell uses focused microbeams at
high energy (>30 keV) to probe highest
pressure/temperature region
 High pressure: with better focused beams, canuse small anvil tips, and greatly extend theaccessible pressure from 350GPa ⇒ TPa– New areas for discovery of materials andphenomena High temperature: with smaller probes, can limit
the heating area to diffraction limit of laser, thus
extend max temperature from 6,000K to
12,400K
 Open up new opportunities for studies ofmaterials under core conditions (P,T)
 Improve ability to understand structures of Giant
Planets
Slide adapted from Steve Sutton (UoC) & David Mao (Carnegie Institute of Washington)
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General considerations
 Magnification
 Numerical Aperture Resolution
 Depth of Focus
 Chromatic aberration

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Geometrical Optics
1 1 1
+ =
p q f

 Thin-Lens Equation:fp Magnification:

M=

q

q
p

 Microfocusing optics produce a demagnified image of the source (M < 1).
Imaging optics produce a magnified image of the sample (M > 1).
 Some optics can work as both, others only for microfocusing (M < 1).

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Demagnification
 For synchrotron micro/nano-probes, M ~ 10-2 – 10-4
 If decreasing focal length becomes difficult, long beamlines (p) will help

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Numerical Aperture
1 ⎞⎛ N.A. = n sin θmax is a measure of the light gathering power ⎜ N.A. =
⎟
2
(
f
/#
)
⎝
⎠

r

θmax

N.A. ~rf

f

 Intimately related to the performance of the optics (focused flux, diffractionlimited resolution, depth of focus, etc.)

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Liouville’s Theorem Phase space density is conserved in a perfect optical system (η = 100%)

 Microfocusing optics inevitably will increase the angular spread Brightness is the radiated power per unit area per solid angle at the source
B=P
ΔA s ⋅ ΔΩ s

At the focus, available flux ~ B * δ2 * NA2 * η where δ is the spot size and η isthe efficiency of the optics, hence the importance of high brightness source
and large N.A. optics
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Diffraction from a Circular Aperture
Airy patternkaθ = 3.822
2π r= 3.822aλ z
λfr ≅ 0.61 λ = 0.61
a
NA
null

null

D. Attwood (LBNL)

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Rayleigh’s Criterion for Resolving Two Point Images<= Diffraction limited resolution
D. Attwood (LBNL)

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Resolution improves with smaller λ Malaria-infected red blood cell
X-ray microscopy

Visible light microscopy

C. Magowan, W. Meyer-Ilse, and J. Brown (LBNL)

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Depth of Focus
λ1.34δ 2=±
 DOF = ±2
λ2( NA )

 DOF determines the sample thickness in 2D imaging and the maximum
sample volume in 3D tomography. DOF increases with energy:

W. Yun (Xradia)

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Chromatic aberration
 Does focal length depends on λ?
– Reflective optics: achromatic, can focus white beam, higher flux
– Diffractive optics: f ~ E– Refractive optics: f ~ E2f(E+ΔE)f(E)Cheiron Summer School 200819

X-ray Microfocusing Optics
 Reflective optics
 Diffractive optics
 Refractive optics

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Reflective Optics
 Schwarzschild objective Wolter microscope Capillary optics
 Kirkpatrick-Baez mirrors

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Reflectivity of single and multi-layer

Single layer Total external reflection whenθ<θc (~ a few mrad):θ c = 2δ ∝ λ Z

n = 1 − δ + iβ
 Finite β/δ rounds the reflectivity
curve

Multilayers
 Large θ means shorter mirror or
larger acceptance Spectral bandwidth ~ a few %.
 Cannot focus white beam

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Schwarzschild Objective Near normal incidence with multilayer coating (126 eV)
 N.A. > 0.1
 Imaging microscope

F. Cerrina (UW-Madison), J. Underwood (LBNL)

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Wolter Type I Microscope Use 2 coaxial conical mirrors with hyperbolic and elliptical profile Imaging microscope Difficult to polish for the right figures and roughness

J.A. Jackson (LLNL)

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Glass capillary optics

holdercapillaryOne-bounce capillary

Multi-bounce condensing capillary Large working distance (cm) Easy to make with small opening(submicron) Compact: may fit into space too
small for K-B

 Short working distance (100 μm)

 Nearly 100% transmission

 Low transmission

 N.A. ~ 2-4 mrad (≤ 2θc)
 Difficult to make submicron spot
Cheiron Summer School 2008

D. Bilderback (Cornell)
25

Kirkpatrick-Baez mirrors pair
 A horizontal and a vertical mirror arranged
to have a common focus
 Achromatic: can focus pink beam (but notwith multilayer coating) Different focal lengths and demagnifications:can be used to produce ~ round focal spot Very popular for focusing in the 1-10 μm regime: relatively easy to make,longer mirrors can be used for higher flux
 For submicron focusing, mirrors with precise elliptical profile are required(figure error < 1 μrad)

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Elliptical x-ray mirrors
X

2b = 2 a2 (1+ e 2)

b

S

F

D

Z0

a

Z

s2

s1
X0

θ

φ φ θ

2a = s1 + s2

O
L
A. Macrander (APS)

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Methods used for making x-ray quality elliptical mirrors
 Bending– ALS– ESRF Differential deposition/profile
coating– APS (C. Liu)
7 µm
max

 Differential polishing– Osaka/Spring8– APS/Tinsley
G. Ice (ORNL)

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K-B mirrors are very popular for micron scale focusing At the APS, K-B microprobes with 100 and 200-mm long bent mirrors arecommon:– MR-CAT 10-ID
GSECARS microprobe(J. Kropf, K. Kemner)– GSECARS 13-ID-C(S. Sutton, M. Rivers)– BioCAT 18-ID(T. Irving, R. Barrea)– PNC/XOR 20-ID(S. Heald, D. Brewe) Monochromatic flux ~1011–1012 ph/sec

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KB mirror systems for nanofocusing
APS/ORNL 34-ID

 APS/ORNL collaboration KB optics– Poly/mono Beams 85 x 95 nm
 ESRF 45 nm
 Osaka/Spring-8 ~ 25 nm x30 nm
 Simple KB system diffraction limit~17 nmOsaka mirrors

G. Ice (ORNL)

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Diffractive Optics
 Fresnel zone plates (FZP) Multilayer Laue Lens (MLL)

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Fresnel zone plates: basic formulaf + rn22

nλ ⎞⎛= ⎜f + ⎟2 ⎠⎝2

rn ≈ nfλ2rn Δr = fλ# of zones =
NA =

r
2Δr

λ
2 Δr

D. Attwood (LBNL)

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Diffraction limited resolution

D. Attwood (LBNL)

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Depth of focus and spectral bandwidth

D. Attwood (LBNL)

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Higher orders and negative orders

D. Attwood (LBNL)

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Efficiency: Phase vs Amplitude Zone Plates Efficiency of an amplitude ZP with opaque zones ~ 10% Efficiency of a phase ZP with π-phase shift ~ 40%

Ni ZP, 0.5 keV

Diffraction Efficiency

30%

Au ZP, 8 keV
Au ZP, 20 keV

20%

10%

0%

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

thickness [um]Cheiron Summer School 200836

Fabrication of FZP
E-beamLithography

Pattern
Transfer

Electroplating

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Recent Hard X-ray Zone Plates
 Δr = 30 nm, 450 nm thick, AR = 15 (Academia Sinica) Δr = 24 nm, 300 nm thick, AR = 12.5 (Xradia)
 To achieve good efficiency, aspect ratio needs to be increased(e.g. needs 1.5 μm thick for optimal efficiency at 8 keV)

W. Yun (Xradia)

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Recent Images from TXM at 32-ID
Image of a Au test pattern at 8 keV

Modulation Transfer Function (MTF)

Δr=30 nmΔr=45 nmY-T. Chen et al., Nanotech. 19, 395302 (2008).
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Other means to increase the aspect ratio
Align and bond two ZPs within DOF

Use the first ZP as self-aligning mask

 Lateral alignment tolerance ~ Δr/3
(10 nm for 30-nm ZP)
 < 10 μm separation between the ZPs

 100 nm demonstrated
 Photoresist mechanical and stressissue

W. Yun (Xradia)

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Even with stacking, aspect ratio > 100 is
probably difficult to achieve withlithographic zone plates!

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Multilayer Laue Lens: novel approach for high aspect ratio
Varied d-spacing multilayers

Dicing ~ 1mm

Polishing ~ 5-25 μm

1D MLL2D MLLSi substrate Aspect ratio > 1000 (Δr = 5-10 nm,
10 μm thick) demonstrated

Sectioned graded-period multilayer

 Engineering challenge of aligning
and assembling 2 or 4 MLLs to
produce a single optics

A. Macrander (APS)

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SEM image of an MLL
WSi2/Si
12.4 μm

Δr~58 nmΔr~10 nmA. Macrander (APS)

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Best measured line focus of MLL
Fluorescence
Pt Lα,β,γdetector

X-raysMLL

5 nm wide
Pt layer

Flou. 17.6 nm
Scatt. 15.6 nm
Cal. 15.0 nm
Efficiency: 31%
Energy: 19.5 keV

H.C. Kang et al., APL 92, 221114 (2008)
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Thin vs Thick Zone Plate When aspect ratio increases, effects from dynamical diffraction vs kinematic
scattering need to be considered Zones should be inclined locally to satisfy Bragg condition
 Thin to thick transition: w = (2Δr)2/λ ~ DOF

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 For flat structure, local efficiency decreases at large r
 For tilted or ideal wedged structures, efficiency actually increases beyond
the thin phase ZP limit of 40%
 This effect is enhanced for high resolution (small Δr)(a) FlatM LL

flat(b)IdealM LL

ideal(wedged)(c)Tilted M LL

tiltedH.C. Kang et al., PRL 96, 127401 (2006)
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 Despite lower overall efficiency, both flat and tilted structure canachieve ~ 5 nm resolution(a) FlatM LL

flat(b)IdealM LL

ideal(wedged)(c)Tilted M LL

tiltedH.C. Kang et al., PRL 96, 127401 (2006)
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Refractive Optics
 Compound refractive lens (CRL)

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Refraction & Absorption
Refraction of hard x-rays in matter is weak

• strong curvature of lens surfaces• stacking of many lenses behind each other
Absorption of x-rays in lenses reduces the efficiency• lenses must be made of low Z material (Be, B, C, Al, ...)• lenses should be made as thin as possible
Refractive index n smaller than 1:• focusing lens must be concave
C. Schroer (Tech Univ Dresden)

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Parabolic Refractive X-Ray Lenses
single lensstack of lenses:
compound refractive lens (CRL)

variable number of lenses: N = 10 ... 300
parabolic profile:

No spherical aberration
imaging optic
C. Schroer (Tech Univ Dresden)

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Parabolic Refractive X-Ray Lenses

Aachen University
APL 74, 3924 (1999)
C. Schroer (Tech Univ Dresden)Imaging with Magnification
Lens used as
objective in
x-ray microscope

image distancenumerical aperture

C. Schroer (Tech Univ Dresden)

Undistorted (Magnified) Image
Parabolic profile of lenses is crucial to good image quality
parameters:• E = 12keV• N = 91 (Be)• f = 495mm,• m = 10xsimulation:
spherical lens

25µm
Ni-mesh (2000mesh)C. Schroer (Tech Univ Dresden)Full-Field Imaging: Resolution
line profile

expected resolution: 84nm

deconvolve
film granularity

resolution of Optic: 105nm ± 30nm
C. Schroer (Tech Univ Dresden)

1-Dimensional Nanofocusing Lenses (NFLs)strong lenscurvature:nanolens

R = 1µm - 5µm

N = 35 - 140

op
a
tic
la
xis

singlelens

100 µmlens made of Si by e-beam lithography and deep reactive ion etching!

APL 82, 1485 (2003)
C. Schroer (Tech Univ Dresden)

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Fabrication of Si Nanofocusing Lenses

500 μmOver 1200 lens arrays
Over 100000 structureshigh accuracy, reproducibility

100 μm
C. Schroer (Tech Univ Dresden)

Crossed Nanofocusing Lenses
Setup at the European
Synchrotron Radiation
Facility (ESRF)

aperture defining pinhole

samplevertically focusinglenshorizontally focusing
lens

10mm
C. Schroer (Tech Univ Dresden)

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Focusing with NFLs
horizontal focus: 47nm
Si lens: E = 21keV, L1 = 47m
f = 10.7mm

source:
ID13 low-β invac. undulator
source size: 150 x 60µm2
vertical focus: 55nm
f = 19.4mm

demagnification:~ 2400 x 4400
flux: 1.7 ·108ph/s
APL 87, 124103 (2005)
C. Schroer (Tech Univ Dresden)

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Effective Aperture and Diffraction Limit
Diffraction limit:

N = 100l ≥ 0.084
R = 0.5 - 50µm
bounded byBest materials: high density and low Z
C. Schroer (Tech Univ Dresden)

Summary: best resolution achieved currently
 K-B mirrors : 25 x 30 nm
H. Mimura et al., APL 90, 051903 (2007);
S. Matsuyama et al., RSI 77, 103102(2006).
 FZP: 29 nm
Y-T. Chen et al., Nanotech. 19, 395302 (2008).
 MLL: 17 nm line focus
H.C. Kang et al., APL 92, 221114 (2008).
 CRL: 47 x 55 nm
C. G. Schroer et al, APL 87, 124103 (2005).
 Waveguides: 25 X 47 nm
A. Jarre et al., PRL 94, 074801 (2005).

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Summary: other considerations

K-B mirror

FZP/MLL

Refractive Lens

Resolution

25 x 30 nm

29/17 nm

47 x 55 nm

Flux density gain

> 500,000> 500,000

10,000Chromatic
aberration

Achromatic

1/λ

1/λ2

Coherence
preservation

Fair

Good

Acceptable

Easy to use

Require effort

Good

Fair

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Future Prospects

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Resolution had improved dramatically

C. Jacobsen (Stony Brook)

Where is the limit? 1 nm? 1 Å?

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Reflective Optics: Focal size ultimately limited by θc
Diffraction limit
0.0016 δ(nm) ~ 100λC(Å)/Δθ(mrad)

0.00140.00120.001

 Δθ ~ 0.85θc standard KB mirror

17 nm

0.00080.00060.00040.0002
0

-8

-4 10

 θc ~ proportional to λ
δ ~ 17 nm- Pt 50% reflectivity
δ ~ 14 nm- Pt 10% reflectivity

-8

-2 10

0

-8

2 10

-8

4 10

K-B Nanofocusing Mirrors

Focus

Incident X-Rays

G. Ice (ORNL)

Cheiron Summer School 200864

Reflective optics: radical approaches needed for sub 10 nm
 Multilayers → 4-5 nm– ESRF/Osaka– Limited bandpass - ideal for undulator harmonic Coaxial/multiple reflections → 3-4 nm

 Combination of both →→ 1 nm?
G. Ice (ORNL)

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MLL: Presently Feasible Outermost Zone Width(0.75 nm layer width has been demonstrated: Y. Chu et al., RSI 73, 1485 (2002) )Calculated for:Wedged zones
Outermost zone width: 0.75 nm;
Energy: 19.5 keV
Efficiency: 50%
Radius: 40 microns

Lateral gradient mask on
sputtering target: wedge MLL

H.C. Kang , H. Yan, et al., submitted
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MLL: when Δr ~ single atomic layer
Each zone is tilted progressively to satisfy the local Bragg condition,
resulting in a wedged shape.
Outermost zone width : 0.25 nm(b) 1.22
1
Δx (nm)Normalized Intensity

1.0
0.8

0.34 nm
0.6

0
-1
-2
-100

-50

0

50

100

Δ z (nm)

0.4
0.2
0.0
-1

0

1

2

3

4

Δ x (nm)

H. Yan et al., PRB 76, 115438 (2007).

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Ultimately parabolically curved interfaces are needed

Outermost zone width: 0.25 nm
1.2

2
1Δx (nm)Normalized Intensity

0.9

0.21 nm

0
-1

0.6

-2
-50

-25

0

Δz (nm)

25

50

0.3

0.0
-1

0

1

2

3

Δx (nm)H. Yan et al., PRB 76, 115438 (2007).

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Refractive Lens: Adiabatically Focusing Lens (AFL)
Current limitation:geometry of lens limits
refractive power per unit
length for given aperture:adiabatically focusing lens (AFL)

Solution:adjust R0 to fit theconverging beam
as it is focused
PRL 94, 054802 (2005)
C. Schroer (Tech Univ Dresden)

Example AFL
contracting wave field inside lensDiamond lens:
low atomic number Z and high density ρ
N = 1166 individual lenses
entrance aperture: 18.9µm
exit aperture: 100nm
f = 2.3mm

diffraction limit: 4.7nm
compare to NFL:same aperture
diffraction limit: 14.2nm
C. Schroer (Tech Univ Dresden)

AFLs Made of Siliconentrance aperture: 2R0i = 20µm
exit aperture: 2R0f = 1µm
energy: 10 - 20keV in 500eV steps

properties:
f = 2.7mm
dt = 12.6nm
as horizontal lens in x-ray
nanoprobe (e. g. ID13 ESRF):
L1 = 47m, source size:
150µm
horizontal focus: 15.3nm(17400 x reduction)

C. Schroer (Tech Univ Dresden)

(Lensless) Coherent Diffraction Imaging
Î Coherent diffraction imaging ismuch like crystallography but
applied to noncrystalline materials
Î Lateral resolution can in principle
approach λ, not limited by N.A. ofavailable optics. Long depth offocus.
Î Requires a fully coherent x-ray
beam

Miao et al. (1999)

Analogous to crystallography

Cheiron Summer School 200872

Conclusions
 Microfocusing optics is an vibrant field with many parallel developments:– Reflective optics– Diffractive optics– Refractive optics
 Resolution had improved dramatically over the last two decades. 30-50 nm
are currently available.
 Future spot size of a few nm is physically possible, but requires great
engineering effort. There may be sufficient sensitivity and resolution to
detect single atoms?
 However, microprobes of all length scale are required for most scientificstudies. It is likely that 10 nm – 10 μm will remain the primary workhorse.

Cheiron Summer School 200873