Giuseppe PortaleNWO, DUBBLE@ESRF

European Synchrotron Radiation FacilityGrenoble (France)

Grazing Incidence X-ray Scattering and DiffractionTheory and applications

Mini-school, Uthecht June 2, 2015

Outline

• Experimental considerations

• Brief introduction to the Distorted Wave Born Approximation

• Example GISAXS

• GIWAXS + example

Transmission vs Gracing incidence geometry

Sample

X-rays

1

10

100

1000

104

105

106

107

0.2 0.4 0.6 0.8 1 1.2 1.4

SiO2 R=25nm

monodisperse

polydisperse

Inte

nsity (

a.u

.)

q (nm-1

)

Transmission:

Gracing incidence:

GISAXS and GIWAXS applications

Probing polymers and soft matter length scales

Experimental setup & conventions

It

Io

ai

f

Bent mirrorS3

S2

S1

Mono

Ideally, beam as small as possible vertically and parallel

Grazing Incident Small Angle X-ray Scattering

Characterization of nanoscale density correlations and/or the shape of nanoscopic objects at surfaces, at buried interfaces, or in thin films

• Surface sensitive (minimum penetration depth 10 nm)

• 2D-GISAXS: lateral and normal ordering probed at the same time

• Complex data analysis𝑞𝑥,𝑦,𝑧 =

2𝜋

𝜆

cos 𝛼𝑓 cos 2𝜃𝑓 − cos(𝛼𝑖)

cos 𝛼𝑓 sin 2𝜃𝑓

sin 𝛼𝑓 +sin 𝛼𝑖

• Surface sensitive – possibility to study structures at the interfaces

• High scattering intensity ideal to perform in-situ and time-resolved study

Image: Prof. Andreas Meyer, Uni Hambourg

X-ray reflectivity (XRR)

• Measure strictly only along 𝑞𝑧 =4𝜋

𝜆sin 𝛼

• Point detector with collimator

• Information about re(z), roughness, thickness

10-5

0.0001

0.001

0.01

0.1

1

0 0.5 1 1.5 2

Re

flectivity

qz (nm

-1)

0.001

0.01

0.1

1

0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.1 0.15 0.2 0.25 0.3 0.35

Refle

ctivity

qz (nm

-1)

Angle (o)

ac SiO2

ac PS

Usually in GIXS ac (polym) < ai < ac (sub)

Regimes for GISAXS analysis

ai < ac (polymer) : evanescent regime

ac (polymer) < ai < ac (substrate) : dynamic regime

ai > ac (substrate) : kinematic regime

In the kinematic regime:𝑑𝜎

𝑑Ω(𝒒) =

1

𝑁

𝑖

𝑗

𝐹𝑖 𝒒 𝐹𝑗,∗ 𝒒 𝑒𝑥𝑝 𝑖𝒒(𝑹∥𝑖 − 𝑹∥

𝑗)

In the simple Born Approximation (BA): 𝐹𝑖 = 𝑉

ρ(𝐫)exp 𝑖𝒒 ∙ 𝒓 𝑑𝒓

Horizon line

Experimental considerations

Footprint of the beam:

Beam 300 mm:ai = 0.1° 17 cmai = 0.5° 3.4 cm

ai

Effect of using a small incident angle

1) ai < ac

2) ai ~ ac

3) ai > ac

ai

ai

ai

Surface scattering – reflection and refraction

Light

Index of refraction: n ≥ 1

a

a’

X-ray

Index of refraction: n = 1 – d + ib

ai > ac

a

ai < ac af = ai

Total reflection

Snell’s law: n1sin a = n2 sin a ’

Snell’s law: n1cos a = n2 cos a ’

n1

n2

Surface sensitivity (penetration depth)

Limited penetration into the sample enhanced surface sensitivity

10

100

1000

104

105

106

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Penetration depth - (Å)

Si

Au

PP

(

Å)

ai / a

c

Snell’s law: cos a = n cos a ’

Critical angle: 2 /c era d r

12 keV ( = 1.033 Å)

For ai ≤ ac

Evanescent regime

Reflection and Transmission coefficients

For the bare substrate: E r, k = 𝐸0𝑒−𝑖𝑘∥𝑟∥

𝑒−𝑖𝑘𝑖,𝑧𝑧 + 𝑟𝑒𝑖𝑘𝑖,𝑧𝑧 𝑓𝑜𝑟 𝑧 > 0

𝑡𝑒−𝑖𝑘t,𝑧𝑧 𝑓𝑜𝑟 𝑧 < 0

𝑟 =𝑘𝑖,𝑧 − 𝑘𝑡,𝑧𝑘𝑖,𝑧 + 𝑘𝑡,𝑧

𝑡 =2𝑘𝑡,𝑧𝑘𝑖,𝑧 + 𝑘𝑡,𝑧

Fresnel reflectivity: 𝑅𝐹 = 𝑟2

Fresnel transmission: 𝑇𝐹 = 𝑡2

Yoneda peak

𝑛 = 1 − 𝛿 + 𝑖𝛽

Nano-objects supported on a substrate

𝑑𝜎

𝑑Ω= 𝑟𝑒2 Δ𝜌 2 ℱ(𝒒∥, 𝑘𝑧

𝑖 , 𝑘𝑧𝑓)2

𝒒 = 𝒌𝑓 − 𝒌𝑖

𝑞𝑧1 = 𝑘𝑧

𝑓− 𝑘𝑧𝑖

1

𝑞𝑧2 = 𝑘𝑧

𝑓+ 𝑘𝑧𝑖

2

ai

𝑞𝑧3 = −𝑘𝑧

𝑓− 𝑘𝑧𝑖

3

af

𝑞𝑧4 = −𝑘𝑧

𝑓+ 𝑘𝑧𝑖

4

ℱ 𝒒∥, 𝑘𝑧𝑖 , 𝑘𝑧𝑓= 𝐹(𝒒∥, 𝑞𝑧

1) +𝑟(𝛼𝑖)𝐹(𝒒∥, 𝑞𝑧2) +𝑟(𝛼𝑓)𝐹(𝒒∥, 𝑞𝑧

3) +𝑟(𝛼𝑖)𝑟(𝛼𝑓)𝐹(𝒒∥, 𝑞𝑧2)

Classican Born Approx. (SAXS)

Distorted Wave Born Approximation - DWBA

For a simple sphere:

𝐹𝑠𝑝ℎ𝑒𝑟𝑒 𝑞, 𝑅 = 4𝜋𝑅3sin 𝑞𝑅 − 𝑞𝑅𝑐𝑜𝑠(𝑞𝑅)

(𝑞𝑅)3𝑒𝑖𝑞𝑧𝑟

Classical SAXS

Nano-objects supported on a substrate

1

2

3

4

Si substrate

PS bead R = 5nm

Yoneda peak for Si substrate: af = ac

Nano-objects supported on a substrate: effect of increasing ai

0.1° 0.2° 0.3° 0.4°0.15°

Au nanoparticles R = 25nm on glass substrate

For supported nano-object the maximum scattered intensity is at the critical angle of the substrate

Particle shape sensitivity

Calculations performed using the IsGISAXS software (R. Lazzari)

𝑞𝑥,𝑦,𝑧 =2𝜋

𝜆

cos 𝛼𝑓 cos 2𝜃𝑓 − cos(𝛼𝑖)

cos 𝛼𝑓 sin 2𝜃𝑓

sin 𝛼𝑓 +sin 𝛼𝑖

Calculated form factors under the DWBA

Renaud G., Lazzari R., Leroy F., Surf. Sci Rep. 64 (2009), 255-380

Now with spatial correlation between nano-objects

If spatial correlation exists between objects, an interference function has to be considered:

Decoupling approximation (DA):

Local monodisperse approximation (LMA):

𝐼 𝑞 ∝ 𝐼𝑑 𝑞 + 𝐹 𝑞2𝑆(𝑞)

𝐼 𝑞 ∝ 𝐹 𝑞 2 𝑆(𝑞)

PS cylinders with 2D hexagonal latticePS spheres with 2D hexagonal lattice

q* 3q* 4q*

Supported nanoparticles: Pt deposit on MgO (001)

J. Olander et al. Phys. Rev. B 76 (2007) 075409.

TEM

Disks with 1D paracrystalline lattice

Au clusters on a substrate@BM26B

Au clusters with R = 3nm and H/R = 1.6

H

2R

10

100

0 1 2 3 4 5

Au:Ag 20:80

ai = 0.13

o

Fit

Inte

nsity (

a.u

.)

qy (nm

-1)

10

100

0 1 2 3 4 5 6

Au:Ag 20:80

ai = 0.13

o

Fit

Inte

nsity (

a.u

.)

qz (nm

-1)

GISAXS from a monolayer of core-shell gold-PNIPAM nanoparticles

10

100

1000

104

105

106

107

108

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

0.1o

Sim. IsGISAXS

Inte

nsity

qy (nm

-1)

Spheroidal Gold coresR = 25nm

2D Hex witha = 230 nm

a

High resolution GISAXS (GIUSAXS)

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06

Standard GISAXS

High resolutionGIUSAXS

Inte

nsity (

a.u

.)

qy (nm

-1)

0th order

1st order

7th

order

q* = 0.0048 nm-1 d = 1.3 mm

AFM GIUSAXS

Au linear assembly

Several possible geometries

Renaud G., Lazzari R., Leroy F., Surf. Sci Rep. 64 (2009), 255-380

Buried interfaces: Pb clusters implanted in Si substrate

0

5

10

15

20

25

-1,5 -1 -0,5 0 0,5 1 1,5

sample 2

Inte

nsity (

a.u

.)

qy (nm

-1)

ai ~ ac (substrate) ai >> ac (substrate)

Dintercluster = 9nm

x x

Scattering from facets: pyramid

z = 0°

X-rays

z = 45°

X-rays

54.7°

Scattering from facets: Ge/Si(001) quantum dots

A.V. Zozulya, et al. Phys. Rev. B 78 (2008) 121304

Bragg rod is proportional to the facet area

Laser Induced Periodic Surface Structures (LIPSS)

Film surface

so : Molecular Roughnessll : longest wavelengthls : shortest wavelength

• Roughness :

C. Bollinne, S. Cuenot, B. Nysten, and A.M. Jonas. Eur. Phys. J. E 12, 389–396 (2003).Z. Guosheng, P.M. Fauchet, A.E. Siegman. Phys. Rev. B, 5366 (1982)

Laser beam • Interference of the incident and reflected light at

the interface produces Ripples with a period L :

isin

n

l: light wavelength: angle of incidence n : refraction index

In-situ GISAXS: study of LIPSS formation

ai

af

w

ai

LIPSS Film

Film LIPPS

H

2R2W

=

AFM

T. Etzquerra (CSIC Madrid)

(a) (b)(a) (b)

Poly(tri methylene terephthalate)(PTT)

•

Mirrors

Sample

I

A

I: IrisA: Attenuator

Laser

00306090120210310

F=7 mJ/cm2 @ N pulses (8ns)

N pulses (8ns)

Set-up @ BM26, ESRF

Final height about 50nm, periodicity about 200 nm

-90 nm

-50 nm

50 nm

-50 nm

60 nm

80 nm

-80 nm

80 nm

10 nm

0 nm

5 nm

0 nm

2 nm

0 nm

5 nm

0 nm

5 nm

-70 nm

0 nm

2 nm

-2 nm

40 nm

0 nm

40 nm

-20 nm

20 nm

0 nm

50 nm

(a) Non-irrad.

(b) 4 mJ/cm2

(c) 5 mJ/cm2

(d) 6 mJ/cm2

(e) 8 mJ/cm2

(f) 10 mJ/cm2

(g) 14 mJ/cm2

(b) 100 (c) 300

PTT_sc_3_9

100 vs nanometros_PTT_sc_3_9

0 (mm) 2

160

0nm

PTT_sc_3_2

X Data

h(nm)

300 vs nanometros_PTT_sc_3_2

0 (mm) 2

160

0nm

(d) 600 (e) 1200 (f) 6000

PTT_sc_3_1

X Data

h(nm)

600 vs nm_PTT_sc_3_1

0 (mm) 2

160

0nm

2D Graph 5

X Data

h(nm)

1200 vs nm_PTT_sc_2_3

0 (mm) 2

160

0nm

2D Graph 6

X Data

h(nm)

6000_ripples vs PTT_sc_1_8

0 (mm) 2

160

0nm

PTT_sc_2

X Data

Y Data

0 vs PTT_sc_2 0 (mm) 2

160

0nm

AFM F=7 mJ/cm2 @ N pulses (8ns)5x5 mm2

GISAXS at the liquid-air interface

Colloidal CdSe/CdS nanorods

F. Pietra et al. Nano Letters 12 (2012) 5515-5523

Deflecting crystal

Adjustable z-table

GIWAXS – crystallinity and orientation

Isotropic:

Textured – slightly oriented:

Highly oriented:

Detector

Rings

Arcs

Spots

Maps of constant qr values in pixel space

GIWAXS images

𝑞𝑟 = 𝑞𝑥2 + 𝑞𝑦

2 𝑞 = 𝑞𝑟2 + 𝑞𝑧

2

GIWAXS (1) - Block-copolymer additives in OPVs

Why P3HT- b -P4VP:non-covalent supramolecular interactions between P4VP and PCBM

P3HT- b -P4VP is blended with P3HT:PCBM

Inverted OPV devices◉ Glass/ITO/TiOx/active layer/MoO3/Ag

Goal:◉ Exploit the PCBM - P4VP interactions to trigger the morphology and

improve the power conversion efficiency (PCE)

P3HT:PCBM:P3HT-b-P4VP blends

as cast devices annealed

Prof. G. Hadziioannou (Uni Bordeaux)

* Adv. Mat. 2012, 24, 2196-2201

P3HT- b -P4VP as nanostructuring agent in the P3HT:PCBM blend*

0.5 1.0 1.5 2.0

q [Å-1]

P3HT:PCBM

+4% P3HT-b-P4VP

P3H

T (

10

0)

PC

BM

P3H

T (

01

0)

PC

BM

P3H

T (

10

0)

Inte

nsity (

a.u

.)

qxy

[Å-1]

P3H

T (

20

0)

P3H

T (

10

0)

qz [Å

-1]

Upon P3HT- b -P4VP incorporation:

• PCBM is less aggregated → more interfaces for exciton

dissociation

• Minor decrease in the crystallinity of P3HT

• Increase in the population of the face-on oriented P3HT

crystallites

GIWAXS (1) - Block-copolymer additives in OPVs

GIWAXS (2) – Ordering in organic thin film transistors

Yoneda peak

(001) peak

(002) peak

Low angle diffuse scattering

qy (nm-1)

qz

(nm

-1)

GIWAXS

001002

010

GISAXS

MM1320 (5 nm)MM1325 (50 nm)

GIWAXS (2) – Ordering in organic thin film transistors

qy (nm-1)

qz

(nm

-1)

qy (nm-1)

qz

(nm

-1)

qy (nm-

1)q

z(n

m-1

)

001

0020

10

MM1322 (15 nm)

<001>

Software for DWBA

• IsGISAXS from R. Lazzary (Windows)R. Lazzari, (U. Curie, Paris) J. Appl. Cryst. 35:406-21 (2002)

• FitGISAXS from D. Babboneau (Igor Pro)D. Babboneau (U. Poitiers) J. Appl. Cryst. 43 929-936 (2010)

• BornAgain (Python)C. Durniak et al, (Juelich)

1. Als-Nielsen, Jens, and Des McMorrow. Elements of modern X-ray physics. John Wiley & Sons, (2011).

2. Daillant, J., and A. Gibaud. "X-ray and Neutron Reflectivity and Scattering." (1999).

3. Müller-Buschbaum, P. "Grazing incidence small-angle X-ray scattering: an advanced scattering technique for the investigation of nanostructured polymer films." Analytical and bioanalytical chemistry 376.1 (2003): 3-10.

4. Renaud, Gilles, Rémi Lazzari, and Frédéric Leroy. "Probing surface and interface morphology with grazing incidence small angle X-ray scattering." Surface Science Reports 64.8 (2009): 255-380.

Books and references

Conclusions

• GISAXS and GIWAXS are powerful tools to obtain statistical structural information on sub-monolayers, monolayers and multilayers of soft and hard condensed matter

• GISAXS 1-100 (1000) nm

• GIWAXS down to 0.1 nm

• Surface sensitivity

• High intensity allows for in-situ study

Thank you for your attention!

Questions?