X-ray reflectivity and Grazing Incidence Small Angle X-Ray - - PowerPoint PPT Presentation

X-ray reflectivity and Grazing Incidence Small Angle X-Ray Scattering

• G. Renaud,

CEA-Grenoble, France

Département de Recherche Fondamentale sur la Matière Condensée Service de Physique des Matériaux et des Microstructures And ESRF, BM32 beamline

grenaud@cea.fr

European School on Magnetism New Experimental Aproaches in Magnetism Constantza, Romania, Sept 7-16, 2005

Atomic structure, size, shape & organization

• non destructive - statistical information over mm scale
• depth sensitivity, from 20 Å up to several mm
• length scale probed : from a few Å to mm
• quantitative analysis
• following in-time: deposit

– annealing – gas adsorption

• in situ, in UHV, during growth (and sometimes in real time)
• no charge effects : insulating samples (single crystal oxide substrates)

X-ray

complementary to Near Field Microscopy

Growth conditions &

Morphology, temperature … of the substrate surface

Introduction

Nanoparticles, nanowires, thin films and multilayers… have

New physical properties (e.g. magnetic, but also electronic, catalytic or photonic)

i

k

f

k

X-Ray Scattering Explores Reciprocal Space

hkl i f

G k k q = − =

vector of the reciprocal space

substrate CTR

q// α (h2+k2)1/2 α 1/a// q┴ α 1/a┴

(000) (222) (002) (333) (331) (113) (111) (220)

Reciprocal Space of nanostructures deposited on a substrate

MORPHOLOGY at the nm – 100 nm scale

Specular reflectivity

GISAXS

r (z) z

d D

On-site M rod Relaxed M ∆q///q// ~ ∆a///a// ATOMIC STRUCTURE Of NANOPARTICLES

diffraction by adsorbate

a//

S

a//

A

d // a┴

A

a┴

S

Crystal Truncation Rods: interference with adsorbate ==> site, d interf. REGISTRY, i.e. location of adsorbate

• Structure, composition
• Epitaxial relashionships
• Relaxation

– Coherent – Incoherent (dislocations)

• Registry / substrate lattice
• Intermixing with substrate
• Substrate distortions
• ...

Grazing Incidence X-ray Scattering GIXS (or GID)

Structure @ atomic scale

• Shape (facets, equilibrium shape)
• Dimensions
• Size distributions
• Organization
• Growth mode
• Density profile
• Thin film thickness
• Interface roughness
• Buried layers
• ...

Grazing Incidence Small Angle X-ray Scattering (GISAXS)

and X-R Reflectivity (XRR)

Morphology @ nanometer scale

Crystalline properties

density profile

Morphology of nano islands

reflected beam

diffracted beam (GID)

Diffuse scattering (GISAXS)

STRUCTURE OF THIN LAYERS ON SUBSTRATE

α i/α c

d e p t h

< 1 0 n m 1

depth resolution 10nm-200nm

X-RAY M ETHODS AT GRAZING INCIDENCE

6

Nanostructures (nanoparticles, nanowires, thin films, multilayers …) & x-rays

n1 n2

n1<n2 Visible Light Reflectivity: n2 > 1

X-Ray Reflectivity: Principle

adapted M. Tolan Univ. Dortmund

n1 n2

X-Ray Reflectivity: n2 < 1 n1>n2

Reflection and refraction – Perfect surface

9 6 6 4 2

10 .. 10 4 10 .. 10 2

− − − −

≈ = ≈ = µ π λ β ρ π λ δ r

E0 Er Et

Dispersion Absorption Minus!!

∃ transmitted wave only if

c t

α α α ≥ ≤

i

i.e. , 1 ) cos(

If

,

i c

α α ≤

• Incident wave totally externally reflected.
• Transmitted wave exponentially damped with z.

t i

n α α cos cos =

Snell-Descartes law:

° ≈ × × = = 0.5 to 1 . 2 ρ λ π δ α r

c

c

α

critical angle for total external reflection of X-rays

Reflection and refraction: perfect surface

2

E E T

t

=

2

E E R

r

=

E0 Er Et

t i i t i t i t t i t i t i t i r

E E t E E r α α α α α α α α α α α α α α α + ≈ + = = + − ≈ + − = = 2 ) sin( ) cos( ) sin( 2 ) sin( ) sin(

• Fresnel equations:

Relationships between the amplitudes of incident, transmitted and reflected beam.

Amplitude Intensity

Reflection Transmission

Limiting and asymptotic values for Fresnel equations

δ α α δ δ α α δ α α α δ α α δ α α δ α α 2 .......... ...... 2 2 .......... ..... .......... 1 ) 2 2 1 1 ( ) 2 2 1 1 ( 2 2

2 2 2 2 2

>> − = << = + + + − ≈ − + − − =

i i i i i i i i i i i i i

for r for r r

δ α α α δ α δ α α δ α α α δ α α α δ α α α 2 ..... ......... .......... 1 2 2 2 ...... ...... 2 2 ) 2 2 1 1 ( 2 2 2

2 2

>> = ≈ < ≈ + ≈ + + ≈ − + =

i i i i i i i i i i i i i i i

for t for t t

0,00 0,05 0,10 0,15 0,20 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10

1/q

4

qc

qz=4π/λsin(αi)

Reflectivity

RF= r²

Qz = 4π/λ sin Θ1

1/Qz

4

Qc

0,00 0,05 0,10 0,15 0,20 1 2 3 4

T(qz)

2

qz=4π/λsin(αi)

T= t² Qz

2

Qz = 4π/λ sin Θ1

4 2 4 4

64 ) ( q q RF δ λ π =

Amplitude

Intensity

Reflection Transmission

Exact evaluation of Fresnel reflectivity

Absorption β also play a significant role

Total External Reflection Regime

Fresnel Reflectivity: RF(αi) with absorption

Qz

• 4 = (4π/λ sin αι)−4

Transmission Function with absorption TF= |t|2

Penetration Depth with absorption

Λ photoabsorption evanescent regime

{

[ ]

}

2 / 1 2 / 1 2 , 2 , 2 , , 1 , ,

4 ) 2 (sin ) sin 2 ( 2 1 2 / ) Im( β δ α α δ π λ + − + − = = =

− f i f i f i f i z t f i

l l k L

( )

1 −

ρ πr

The geometry of X-ray reflectivity

Transferred momentum:

Helmholtz equation

adapted from M. Tolan Univ. Dortmund

Formal solution:

Electron density profile X-ray reflectivity: main equation

Matrix formalism: Parrat iterations Parrat, 1954

adapted M. Tolan Univ. Dortmund

Reflectivity from multilayers

Multiple scattering (dynamical calculation)

Reflectivity used as an everyday laboratory tool to measure the thickness of layers deposited on a substrate

adapted from M. Tolan Univ. Dortmund

Reflectivity from layer on substrate. Ex: PS on Si

Rough interfaces: statistics

adapted M. Tolan Univ. Dortmund

Reflectivity by a rough surface : which roughness ?

Roughness in multilayers?

1/q

4

1/q4exp(-q2σ

2 )

Effect of interfacial roughness on reflectivity: single interface

Reflectivity very efficient to measure (small) (statistically averaged) roughness of surfaces or interfaces.

Roughness at several interfaces

Thin film with surface and interface roughness. Example: PS layer on Si, with roughness

Effects of surface and interface roughness very different σ1, σ2 and d can be determined independantly

Reflectivity calculation for arbitrary density profiles

Example of fit of reflectivity curve:

adapted M. Tolan Univ. Dortmund

Simplier aproach: Kinematical approximation

The « master » formula

′ ρ (z)= 1 2π σ exp(− z2 2σ

2 ) ⇒ R(q)= RF(q)exp −q 2σ 2

( )

Example: roughness

Kinematical versus dynamical calculation

Pb: Loss of the phase:

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1.0 0.8 0.6 0.4 0.2 0.0

1.0 0.8 0.6 0.4 0.2 0.0 60 40 20

• 20

Å

Different ways to solve the phase problem:

• Inclusion of pre-knowledge
• Anomalous reflectivity

R(qz) ρ(z)

?

|T.F.|2

Mat rices

Ex: Multilayers:

• Complex index profile

}xN

A B A B A B x N

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1.0 0.8 0.6 0.4 0.2 0.0

θ, q sinθΒ=λ/2d ∆θ=λ/2/Nd

X-ray reflectivity used to characterize the thickness, period and roughnesses of multilayers.

Rough surfaces diffuse scattering

q

qz qz qx

Lateral features of the roughness – Height-height correlations

Ex.: Roughness correlations in multilayers?

Conclusions on reflectivity

Specular reflectivity measures

• average density (mass and electron density)
• layer thicknesses
• interface roughness

Off-specular reflectivity probes

• Height-height correlations
• lateral order at nanometer-micrometer scale
• Refraction under grazing incidence

tuneable scattering depth

Why GISAXS ?

Statistical information Lateral and vertical correlation shape as seen by x-rays: input for diffraction experiments Information about buried objects GISAXS AFM / STM Local information Detailed shape

Example : 20 Å Ag/MgO(001) 500K

αi

(001) (001)

(111) (111)

[110] [110]

d d

Anisotropic islands: truncated square pyramids with (111) facets

(111) (111)

1/D 1/D 1/d 1/d

(001) (001) (111) (111)

[100] [100]

d d

1/h 1/h

h h

1/h 1/h

Grazing Incidence Small Angle X-ray Scattering (GISAXS)

d D h

ω

αi αf

2θ

qx qz qy

Principle

2D image around direct beam: Fourier transform of objects

Standard 3D growth (Volmer-Weber)

Morphology

• Shape
• Sizes
• Size distributions
• Particle-particle

pair correlation function

Off-specular reflectivity: Probed length scales?

q= kf - ki Specular direction: αf = αi : qz = 4π/λ( sin αi) = 2π/d qx=(2π/λ)(cos αf –cos αi) qz=(2π/λ) (sin αf + sin αi)

qz qx

αi <0 αf <0

ki kf kf q

qz qx αi αf ≠ αi

Lengthscales d: lateral and vertical λ=1.54Å αi = 0.5o

dx= 2π/ qx, max ≤ λ / (cos αf –1) ≈ 10 000 Å dz = 2π/ qz, ≈ 20 Å for αf = αi

Small angles of incidence and exit: plane of incidence

αi αf 2θ GISXAS or how to measure nm lateral lengthscales qx

• qy

qz Plane of incidence

Q= kf - ki qx=(2π/λ)(cos αf cos 2θ –cos αi) qy=(2π/λ) (cosαf sin 2θ) qz=(2π/λ) (sin αf + sin αi)

Lengthscales d: lateral λ=1.54Å 2θ = 2o αf=0.5o

dy= 2π/ qy ≤ λ / (cos αf sin2θ) ≈ 44 Å !!! Out-of plane scattering suited for nanostructure investigations “No” limitation in 2θ : d from 100nm to 0.1nm

I q q F S q ( , ) ( )

// // ⊥ ≈

×

2

( )

r d e r g q S

r iq S 2 //

//

1 ) ( 1 ) (

−

∫

− + = ρ

Interference function: FT of pair correlation function

×

Form factor : a kind of shape FT with refraction effects

) , , (

// f i DWBA

k k q F

α α α

• Pyramid
• Cylinder
• Troncated

sphere

• Tetraedron
• Cubooctaedron

Quantitative analysis of GISAXS

IsGISAXS program :

http://www.esrf.fr/computing/scientific/joint_projects/IsGISAXS/

• R. Lazzari, J. Appl. Cryst. 35, 406 (2002)
• F. Leroy, R. Lazzari and G. Renaud, Acta. Cryst. A 60, 565, (2004)

Analyse quantitative du signal GISAXS

) ( ) (

// 2

q S F q I = r

kf

z + ki z

R(αi) kf

z- ki z

• kf

z- ki z

R(αf)

• kf

z+ ki z

R(αi) R(αf)

Forme, taille et orientation

• pyramide
• cylindre
• sphère

tronquée + distributions

Facteur de forme = ) (

//

q S

TF Fonction de corrélation de

paires Arrangement spatial

• réseau
• modèle de désordre

(paracristal...) distance moyenne + distribution de distances

Fonction d’interférence

IsGISAXS program : http://www.esrf.fr/computing/scientific/joint_projects/IsGISAXS/

• R. Lazzari, J. Appl. Cryst. 35, 406 (2002)
• F. Leroy, R. Lazzari and G. Renaud,
• Acta. Cryst. A 60, 565, (2004)

0.0001 0.001 0.01 0.1 1

I(q//)

• 3
• 2
• 1

1 2 3

q//D/2π

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

S(q//)

STM pictures

Goodman et al.

40nm

[001] [110]

Growth of Au on TiO2(110)

12 Å flashed annealed @ 800K

Experiment

αf

• 3.25°

3.25°

2θ

3.25° Simulation

R = 2.9 nm sR(log normal) = 1.2 H= 4.9 nm sH(gaussian) = 0.1 r=9.1 1011 part/cm2; qc=132° FITS: Truncated spheres

10

1

10

2

10

3

10

4

Intensity (a.u.)

45 40 35 30 25 20 15 10 5

sin(2θ) x 10

3

2.5 2.0 1.5 1.0 0.5

qy (nm

• 1)

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Interference function

80 60 40 20

Probability x 103

5.0 4.0 3.0 2.0 1.0 0.0

Radius (nm)

Parallel cut

10

1

10

2

10

3

10

4

Intensity (a.u.)

70 60 50 40 30 20 10

sin(α f) x 10

3

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

qz (nm

• 1)

Perpendicular cut

H/d = cte = 0.62

• Equilibrium

island shape

To be compared with TEM : β = 0.95 J/m2

Adhesion energy from GISAXS: β=1.12 J/m2 Wulff’s construction

Equilibrium shape of particles. Ex: 1.5nm Pd/MgO @ 650 K

Θ=54.7°

0.3 nm

3 30

d h D

Size (nm)

Thickness (nm)

0.56 0.64

h/d

(B)

GISAXS → Equilibrium shape, in situ, non destructively during growth

• C. Revenant, F. Lazzari, F. Leroy, G. Renaud, C.R. Henry, PRB 69 (2004)
• G. Renaud, et al., Science 300, 1416 (2003).

Fit with truncated octaedron 2θ ∼ Q//

αf ~ Q⊥

Θ=54.7°

D=22±0.2nm d=11.4 ±0.4nm - σFWHM=6nm h=6.2 ±0.4nm - σFWHM=0.8nm h(001)/d=0.46 h/d=0.62 ±0.2

d

(100) (111)

h100

• Exp. ω= [110]
• Exp. ω= [100]

Simulation

Self-organized growth : systems

25nm

• B. Voigtländer et al.
• Phys. Rev. B 44 (1991)

10354

Co dots on Au(111)

Surface reconstruction 3 main types of surface structuration

10nm

Co wires on Pt(997)

• P. Gambardella et al.

Nature 416 (2002) 301

Vicinal surface Dislocation Network

Fe islands on a bilayer of Cu/Pt(111)

• H. Brune et al.

Nature 394 (1998) 451 20nm

• Self-organized growth of

cobalt islands on a –Au(677) kinked surface

STM image (S. Rohart (GPS, Paris))

12nm

[211]

1 2 n m

X α ω

q// q┴

3D Measurements of reciprocal space by GISAXS

ω+4° The kinked Au(677) surface ω-10° ω-9° ω-8° ω-7° ω-6° ω-5° ω-4° ω-3° ω-2° ω-1° ω+0° ω+1° ω+2° ω+3° ω+4° ω+6° ω+7° ω+8° ω+9° ω+10° ω+11° ω+12° ω+13° ω+14°

Scattering rods from steps 20 nm Reconstruction period ~ 8 nm Ordered kinks

qx (nm-1)

• 2

2

3,8 4,8

qy (nm-1) Intensity (log)

Map of reciprocal space at q┴=0 (11) (12) (10)(20)

Steps

(02) (01)

π/2 - ε

Kinks q// q┴

ω+0°

Scattering rods from steps

Modelisation of a kinked Au(677) surface

z y x

O Dkinks

k h

Dstep L

h k

Elementary object

( ) ( ) ( ) ( )⎭

⎬ ⎫ ⎩ ⎨ ⎧ × − × + ℜ × ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − + ℜ × ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = L D e L D e e D e D e e q q q k q h q q I

marche h iq marche h iq cran k iq cran k iq z y x x z

z z x x

1 1 1 1 2 sin 2 sin 4 ) (

2

r

Paracrystal : step edge Paracrystal : distance between steps Shape and size of kinks

Principle : Paracrystal

Kinks position

Dstep = 3.42 ± 0.23 nm

Steps

Dkink = 8.04 ± 0.62 nm Determined by the reconstruction k = 0.7 ± 0.35 nm

Kinks size

Monoatomic kinks Packed by 3±1.5

L = 0 ± 0.3 nm

GISAXS data and fits

102 10

(11L) rods: crossed

10 20 30

5 0,2

20 40

0,00 3,65 ,30

0,1

102 103 10

(01L) rods: kinks

10

1

10

2

10

3

5

10 10

1

10

2

q// (nm-1)

q┴ (nm-1)

1 10 102 103

Intensité (photons)

(10L) rods: steps

5

q┴(nm-1)

2

Data Fits

10

1

10

2

10

3

10

1

10

2

10

3

∆q// (nm-1) 5 0,5

Intensité (photons)

Co growth at room temperature

z y x

• L

L D H Top view Side view

Model Shape and size

U V Top view k

y x

• k/2

Position 0.5ML 100 nm STM image

• S. Rohart (Au(788) surface )
• in between kinks
• at the step edge

Island position

• anisotropic growth

Shape and size

• bilayer islands

Self-organized growth : Systems

25nm

• B. Voigtländer et al.
• Phys. Rev. B 44 (1991)

10354

Co dots on Au(111)

Surface reconstruction

10nm

Co wires on Pt(997)

• P. Gambardella et al.

Nature 416 (2002) 301

Vicinal surface 3 main surface structuration Dislocation Network

Fe islands on a bilayer of Cu/Pt(111)

• H. Brune et al.

Nature 394 (1998) 451 20nm

Co Ag MgO

Co dots on a dislocation network buried at the Ag/MgO(001) interface

• Self-organized growth of

cobalt islands on a –dislocations network at the Ag/MgO(001) interface

• Significant surface strain if : H<∆

Ordering of nanostructures induced by a dislocation network : principle

• Misfit dislocation network

aMgO-aAg aAg

= 3%

∆ = 10 nm

Ag and MgO(001) ∆

H

MgO Ag Co

Ag/MgO(001) ultra-thin film: in situ GIXS, XRR and GISAXS

MgO

Ag

10 nm ≈ 5 nm

Ion bombardment

• 3. Ion Beam thinning

down to 5 nm while keeping large terraces and low roughness.

MgO

Ag

10 nm 100 nm

• 1. Growth of 100 nm Ag(001)/MgO

Ultra-thin (5nm) Ag film of homogeneous thickness, with an ordered array of dislocation

Ordered dislocation network Very low roughness Large terraces (100nm)

200 400 600 800 1000 1200

I( u.a.) time (s)

IB at 200°C IB at 300°C 200°C

180 200 220 240 260 280 300 320 340

time (s)

I( u.a.)

Monitored in situ by Anti-Bragg GIXS

• 2. Annealing 900 K

1.95 2.00 2.05 2.10 2.15

h

MgO(220)

Dislocations peaks

and reflectivity

0.4 0.8 1.2 10

10

10

10

10

Intensité (coups/s)

θ

• 4. Co Deposition
• Room temperature : trap energy >> thermal energy
• Deposition rate (0.05 Å/min): diffusion length of Co adatoms >>10 nm

X

MgO Ag D= 10 nm

dislocations rods

4π/D Q// Q⊥ Ag Ag(111) (111) facet facet rod rod

2nd order

No cobalt No cobalt

Self-organized growth of magnetic cobalt dots on an interfacial dislocation network : Co/Ag/MgO(100)

With With 1.2 1.2Å Å

• f Co
• f Co

2π/e

e≈5 nm

Co

Interferences Co islands are

• rdered

Position of Co islands / dislocation cores

Simulations 1 2 3

• 50

50

Intensity (photons) q┴ (nm-1)

• before

negligible interferences

( )

e q d q q I q I q I q I q I

Co disloc Co disloc ⊥

+ × × + = −

// //

cos ) ( ) ( 2 ) ( ) ( ) ( r r r r r r r

After

π =

// //d

q r r

// //

= d q r r

e π 2

Size and shape evolution of Co dots upon deposition time

Interference(q┴,time)

q┴ (nm-1)

Time (mn) 10 60 50 40 30 20

0.1 0.2 0.3

100 200 300

Intensity (photons)

1,2 ML 0,2 ML

( )

H q d q time q I q I time q I

Co disloc erference ⊥

+ × × =

// // int

cos ) , ( ) ( 2 ) , ( r r r r r

Fit : 2ML height islands Time (mn) A m p l i t u d e ( u . a . )

20 40 60 0,0 0,4 0,8

• GISAXS for the first time in situ during growth
• Combined with GIXS Atomic structure + Morphology
• Quantitative information on nano-particles shape/size/ordering
• Very sensitive to the ordering of nanostructures

Conclusions

Determination of the nucleation site, size and shape of islands during organized growth of :

• Co on Au(111)
• Co on kinked Au(677) : in between kinks and at the step edges
• Co on Ag/MgO(001) : upon the dislocation core
• In situ surface X-ray diffraction and GISAXS combined

for determining conditions for ordering of Co islands on a Ag/MgO dislocation network

• Eventually probing the shape & 2D organization of biological molecules

deposited on surfaces? Conformation and function of selected bio-molecules?

Potential and future directions

• GISAXS extremely sensitive to the very premisses of organization
• used to monitor organized growth in real-time and quickly reach the

right thermodynamical and kinetic conditions for the organization.

• In situ studies during
• surface reactivity (e.g. catalytic reactions, annealings ...)
• growth (during MBE, (MO)CVD, LPE );
• use of gaseous, liquid or solid surfactants, at High p, T …

10

• 4

10

• 3

10

• 2

10

• 1

10 10

1

10

2

12 10 8 6 4 2

a

i

= a

c

Coherent interferences between 4 waves with different qz !

Distorted Wave Born Approximation (DWBA) for supported islands

• M. Rauscher, T. Salditt et H. Spohn, Phys. Rev. B 52, 16855 (1995)
• M. Rauscher et al. J. Appl. Phys. 86 (12), 6763 (1999)

4th term : qz=-kfz+kiz

Ri RF

2nd term : qz=kfz+kiz

Ri

3rd term : qz=-kfz-kiz

RF

1st term : qz=kfz-kiz ki kf

ai af

10

5

10

4

10

3

10

2

10

1

10

Intensity (a.u.)

12 10 8 6 4 2

BA α c/2 α c

2α c

Diffuse scattering due to size distributions, and sizes-distances and sizes-sizes correlations

) q ( S F F F ) q , q ( I

// 2 2 2 //

× + − ∝

⊥

Diffuse scattering Coherent scattering

1 – DA (Decoupling Approximation): Size and positions completely un-correlated 2 - LMA : Local monodisperse approximation

) q ( S F ) q , q ( I

// 2 //

× ∝

⊥

Coherency zones of the X-ray beam

Two usual extreme approximations neglecting correlations:

• Correlations deduced from analysis of TEM images Pd/MgO(001)

Island diameter (nm)

20 40 60 30 45 60 Distance between first NNs (nm)

Sizes-separations correlations

First NN diameter (nm) 20 40 60 20 40 60

Island diameter (nm)

No sizes-sizes correlation ฀ LMA wrong

∑

= ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ω σ

p p p p

P F A ) ( ) ( const. d d

2 diff

Q Q

• ver the processes

amplitude

• f the p-th process

form factor

• f a single object

correlation function

• f the positions

Result from scattering theory

Short range order Short range order Long range order Long range order P(Qp) = FT of pair correlation in real space

Courtesy of V. Holy

Anneal to T>750K Simulation

Another template for 2D organization : nano-facetted surface

Shape: FDWBA

I(Q)= |FDWBA(Q, ki

z, kf z)|2 S(Q)

ω=0° ω=30° 19.5°

Q

⊥

Q// Q// Q⊥

Exp. Exp. Exp.

ω= -30°

Late stages of facetting: Large nano-pyramids

S from ds with facets

Evolution of facetting as a function

• f annealing time

GISAXS on Bimolecules

• B. Krause, ID01

0.04 0.02 0.00

• 0.04
• 0.02

0.04 0.00 0.02

• 0.02
• 0.04

log(Intensity) qx[Å-1] qy[Å-1] [1 1 0]

αi=0.2° < αc α f=0.4° > α c R0=270 Å R1=130 Å H=170 Å 10 % size distribution Model: Formfactor of double-disk

[110]

1.8 µm

z

substrate (000) (hk 0) radialqr angularqa decreasing lateral size Intensity 2θ

αf αi αi

GISAXS

G I D

: information on shape q

angular

strain q

radial

depth q

z

Scans in 3D reciprocal space

I n A s ( 2 2 ) G a A s ( 2 2 )

a n g u l a r d i r e c t i

• n

: q a radial direction: q r

( )

Distance from radial path q a in Å-1

• 0,10
• 0,05

0,00 0,05 0,10 Intensity 10-4 10-3 10-2 10-1 100 fit for single disk fit with model

• exp. data

lateral size height

Results: data analysis ISS

50 100 100 100 200 nm 300 100 200 300

Linear relation between strain and size is found from fits at all radial positions

f(Q,E) = fo(Q) + f ’(E) + i f ”(E)

5

GID with contrast variation using anomalous ISS

Energy dependence For Si negligible

Example III: composition of Ge domes on Si

Use energy and Q dependence to amplify contrast:

measure at high Q !

• T. Schülli et al PRL, 90, 66105 (2003)

60 eV

• 10
• 5

5

11043 11103

E2 E1

f ''Ge f 'Ge

f ' or f '' Energy [eV]

anomalous correction enhanced at high Q higher resolution for ∆a/a = -qr/Q Si content from deviation of IE1/IE2 for pure Ge All possible GID reflections should be measured

IE1/IE2=1.7 IE1/IE2=4.7

Isi > IGe

1 2 3 4 5 6 7 8 9 10

5 10 15 20 25 30

Q [Å

• 1]

f Ge(K-edge)

fSi

fGe(K-60ev)

Q(660) Q(800) Q(620) Q(440) Q(400) Q(220)

f0+f ' [electron units]

Contrast variation: Q dependence

• 30
• 20
• 10

10 20 30 2 4 6 8 10 12 14

2

3

4

5 6

H eig ht (Å )

Lateral Size (Å)

strained Si substrate

20 40 60 80 100 0,0 0,4 0,8 1,2 1,6 2,0 2,4 2,8 3,2 3,6 4,0

20 40 60 80 100 Ge content (%) (b) ∆a/a (%) Height (Å)

Si interdiffusion : vertical composition profile from (A)-GID at (800)

RESULTS Sharp Si/Ge interface Ge plateau at 85% ∆a/a monotonic dot is highly strained

7 ML MBE growth at 600oC Ge domes Small size dispersion

• T. Schülli et al PRL, 90, 66105 (2003)

5,42 5,44 5,46 5,48 5,50 5,52 5,54

E1: K-Edge-60 eV E2: K-Edge-2 eV

Intensity (a.u.) Lattice Parameter (Å)

qradial Direct method!

2 4 6 8 10 12 14

• 20
• 10

10 20

Height(nm)

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.000

2 4 6 8 10 12 14

• 20
• 10

10 20 Ge concentration Elastic energy (meV/atom)

Height(nm) Position(nm)

3.030 6.061 9.091 12.12 15.15 18.18 21.21 24.24 27.27 30.30

Si Ge

“Nano –Tomography”: 3D real space image

shape, size, strain and composition of Ge/Si alloy islands

11.2 ML Ge domes on Si (001) grown by CVD at 600°C Lateral coordinate (nm)

Results:

the lateral variation of the Ge concentration changes with height Si rich core covered by Ge rich alloy concentration from pure Si at bottom to pure Ge at top

T.Schülli et al. PRL90, 66105 (2003)

• A. Malachias et al. PRL91, 176101 (2003)

Oxide layer and crystalline core

amorphous oxide layer (2-3 nm)

• xidation ⇒ foot of the dot was

part of the substrate

Marquez et al., APL 78 (16), 2310 (2001)

Oxide layer and crystalline core

amorphous oxide layer (2-3 nm)

• xidation ⇒ foot of the dot was

part of the substrate

Marquez et al., APL 78 (16), 2310 (2001)

Away from L3 Co edge 770 eV Specular peak Structural peaks At L3 Co edge 780 eV Peak from AF magnetic order Magnetic peaks

Magnetic resonant X-ray scattering from an array of CoPt multilayers

Pinhole 20 µm

• K. Chesnel at al, PRB 2003

FePd thin film,

• perp. magn.

AF order Pinhole 20 µm

X

8 µm 22 µm

Coherent scattering on magnetic microstructures

Specular spot Magnetic satellite Speckle Interference fringes

Beutier – Chesnel CF les PRBs.

2D detector

d D h

ω

αi αf

2θ

qx qz qy

GID

GISAXS Strain state In-plane lattice parameter Shape, size In UHV in situ during growth Grazing Incidence X-ray Scattering Incident beam

slits detector

2θ

2D image around direct beam: Fourier transform

• f the objects

to decrease the bulk scattering as much as possible (to be sensitive to surface)

80 cm 18 cm 4.2 m 40 µm 100 µm CCD Sample

Coherent Diffraction from a 5 µ made of Au Simulation Measurement

Next steps Phase retrieval and reconstruction

Christian Schroer,Edgar Weckert, Andreas Schropp, I. Vartanyants, Hasylab and ID01

• Elements of modern X-ray physics, J. Als-Nielsen et D. McMorrow, John

Wiley&Son (2001)

• X-ray scattering from soft-matter thin films, M. Tolan, Springer Tracts in

Modern Physics, Vol148 (1998)

• High-resolution X-ray scattering from thin films and multilayers, V. Holy, U.

Pietsch et T. Baumbach, Springer Tracts in Modern Physics, Vol149 (1998)

• Scattering of X-rays and neutrons at interfaces, D. Dietrich et A. Haase,
• Phys. Rep. 260 (1995) 1-138
• Critical phenomena at surfaces and interfaces, H. Dosch, Springer Tracts in

Modern Physics, Vol126 (1992)

• Surface X-ray diffraction, K. Robinson et D.J. Tweed,Rep. Prog. Phys. 55

(1992) 599-651

• Surface structure determination by X-ray diffraction, R. Feidenhans ’l, Surf.
• Sci. Rep. 10 (1989) 105-188

General references

• F. Leroy, C. Revenant, A. Létoublon, T. Schülli, M. Ducruet, O. Ulrich,

CEA-Grenoble (France) C.R. Henry, C. Mottet CRMCN, Marseille (France)

• O. Fruchart,

LLN, Grenoble, France

• R. Lazzari, S. Rohart, Y. Girard, S. Rousset

GPS, Paris (France)

• A. Coati, Y. Garreau

LURE, Orsay (France)

Aknowledgments

Thank you for your attention