XRDpolykrystalické tenké vrstvy

• Conventional Bragg-Brentano symmetric geometry – θ/2θ scan

• Asymmetric BB geometry – θ/2θ scan

• Parallel beam geometry – 2θ scan

Phase analysisLattice parametersSize, strainTexture

Bragg-Brentano conventional powder diffraction geometry

1

2

3

h1k1l1

h2k2l2

h3k3l3

Information from the grainsoriented with the

corresponding planesparallel to the surface

Symmetric - 2 scan

Absorpce

sin0

abAIdI

Energie z hloubky t za 1 s

a b

GteA

Lineární absorpční koeficient

sinsin

sinsin G

2

22 sinsin

cossin2

sin

2

cossin

2

2cos

12cos

Asymmetric powder diffraction geometry

1

2

3

h1k1l1

h2k2l2h3k3l3 2 scan

Small constant angle of incidence

Parallel beam = 2 – 10

Picture from Seifert poster

XRD Seifert - FPM

X-ray tube

Detector

Monochromator

Parallel plate collimator

Sample holder

Slits

C. Bragg-Brentano asymmetric powder diffraction geometry

1

2

3

h1k1l1

h2k2l2

h3k3l3

TextureStress

goniometer

goniometer - 2 scan

Philips X’Pert MRD

X-ray tubeParallel plate

collimator

Detector Goebel mirror

Sample stage

Eulerian cradle

Polycapillary

Texture and Stress

5 10 15 20 25 30

0

100

200

300

400

500

I(cp

s)

PbTiO3

scan

Omega sken

Korekce na absorpci a defokusaci

FWHM

- sken

Texture, stress

Pole figures

Pole figure (100) for the samples of different thickness. The asymmetry of the texture (left, middle) as well as the inclination of the texture (right) can be seen in 2.5D plot.

935 nm515 nm 2000 nm

2D reciprocal space scan

scan

scan

2 scan

Ideal single crystal

Ideal polycrystal

Textured polycrystal

0

Zbytková napětí

01211,

2012,

1 32

1, sssssss hklRhklR

Homogenní napětí 1. druhu

Může být určováno přímo známou metodou sin2 kdy musí být vzorek nakláněn na různé úhly ze symetrické polohy tak, aby difraktovaly atomové roviny různě skloněné vůči povrchu. Uvedený výraz platí přesně pouze pro jednoosá napětí 0 pro symetrickoul Braggovu-Brentanovu geometrii).

hklhkl ssd

d1

22 2sin

2

1

Rtg elastické konstanty

Elasticky izotropní materiály

Elastická anizotropie +Reussův model ( konst.

maximální závislost na hkl )

… Poissonovo číslo, E … Youngův modul

cos cot

a

111200

311400

a0

Hodnota bez napětí

tlakové napětí

222 311

Back

44121102222

222222

5.0,)(

sssslkh

lklhkh

Es

Es

1, 21

2 sken

goniometr

goniometr

422 422

Crystallite Group MethodBB - BB -

For thin films and some bulk materials the orientation of grains with respect to the surface may be very important. Differently oriented grains can have very different

defect content and/or be in very different stress state.

Therefore it is desirable to measure various crystallite families (texture components) rather than individual planes. Of course, as it is not the case of single crystals, other

crystallites always contribute to the profile (less for strong texture).

Hloubka průniku

Hloubka průniku

Efektivní hloubka průniku

Informační hloubka

Přispívající tloušťka

Ekvivalentní tloušťka

Nekonečná tloušťka

t

t

tdtdII0

11

ln rt

Poměr energií difraktovaných tenkou vrstvou

na povrchu a tenkou vrstvou v hloubce t

rzdIzdIrGr )0(/)(;1

ln1

ere

Gt

Gtt t

i e

te

GAdzdzz

1

1/

0 0

GtRR

RGR

tzI

zI

Re)1(

1ln

1

)(

)(

G

e

G

Gt

eq

1

Hloubka průniku

- 2

2SB, PB)

Titanium Oxide - At 520 KTitanium Oxidea: 3.77100

Titanium Dioxideb: 5.44900

RutileP42/mnm

4.59774.5977 2.9564

AnataseI41/amd

3.77103.77109.430

BrookitePbca

9.1745.449 5.138

400

350

300

250

200

150

100

50

0

Powder Simulation

20.0 25.0 30.0 35.0 40.0 45.0 50.0

350

300

250

200

150

100

50

0

Powder Simulation

20.0 25.0 30.0 35.0 40.0 45.0 50.0

180

160

140

120

100

80

60

40

20

0

Powder Simulation

20.0 25.0 30.0 35.0 40.0 45.0 50.0

Rutile

Anatase

Brookite

10 30 50 70

2

0

200

400

600

I(cp

s)

3 deg, 100 C3 deg, 300 CBB, 300 C

Thickness - 0.6 mParallel beam geometryBragg-Brentano symmetric geometry

Anatase

Amorphous

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0 0.1 0.2 0.3 0.4 0.5 0. 6 0.7 0.8 0.9 1

measurements from both XRD7 and X’Pert diffractometers-2 scans2 and

Williamson-Hall plot

sin

Inte

gral

bre

adth

(1

/d) h = 800 nm

ann. 300 Co

Williamson-Hall plot

Crystallite size> 100 nm

Microstrain~ 0.15 %

~ 1/crystallite size

~ microstrain

sin41

)/1( hkl

hkl

hkl e

Dd

Apparent crystallite sizeLattice strain e=d/d

Texture indices

2.0/250 2.0/300 1.7/300 1.5/300 1.2/300

101 1.2 1 1.2 1.6 1.7

004 3 2.1 1.3 1.1 1.1

112 0.5 0.5 0.8 1 0.9

200 1.2 0.9 0.7 1 1.1

105 1.6 1.2 1.1. 0.9 1

211 0.6 0.5 0.6 0.9 0.9

Thicker Thinner

Fiber texture

Residual stress

• isotropic elastic constants (E = 190 GPa, ν = 0,31)

• tensile stress• at 500 C drop of stress• stresses ~ 200 - 300 MPa • typical stress anisotropy

1.2632

1.2634

1.2636

1.2638

1.2640

1.2642

1.2644

1.2646

1.2648

1.2650

1.2652

1.2654

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d-sp

acin

g (A

)

sin ² (Psi)

Stress: 383,5 ± 19,9 MPaPhi = 0,0°

1,54 m at 300 C for (215)

Typical linear dependence

Isotropic stress, absence of tri-axial stresses

Stress

Thickness [nm]

[MPa]

300 C

350 C 500 C

200 341 151

630 187 187 42

800 219 209 -

1000 184 154 -

1500 240 163 -

1700 280 232 -

2000 293 252 -

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 6 9 8

1 . 6 9 9

1 . 7 0 0

1 . 7 0 1

d(

10

5)

[A]

s in2

1 . 5 m , 3 0 0 ° C

1 . 5 m , 3 5 0 ° C

Stress anisotropy

(103

)

(004

)

(112

)

(200

)

(105

)

(211

)

(116

)

(220

)

(215

)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

sl

ope

of s

in2

plo

t

diffraction peak

0.2 m, 300°C 0.8 m, 300°C 0.8 m, 350°C 1.5 m, 300°C 1.5 m, 350°C

105 211

300 ºCTensile stress~ 200 MPa

500 ºCno stress

Diffraction peaksFor different inclinations

X-ray reflectivity

1n

510~,),(1 in

Refraction index

eer 2

2

4

re = 2.818 10-15 m - wavelength

electron densityabsorption length

2c

Critical angle

)(2

1 21

20 iffN

rn at

Total reflection

Surface roughness, film thickness

1 2 3100

101

102

103

104

105

106

107

Ref

lect

ivity

angle (deg)

t=0,054m

1 2 310-5

10-4

10-3

10-2

10-1

100

Ref

lect

ivity

2 (degrees)

Perfectly smooth surface

0.3 nm roughness

)/sin16exp( 2220 igRR

Reflectivity is sensitive onlyto the projection of the surface profileto its normal direction

It cannot distinguish betweenmechanically and chemically rough surface

~ 1/t

Kiessig maxima mt cim

22 sinsin2

Visible up to ~ 300 nm

250 ºC

350 ºC

450 ºC

TiO2 200 nm

Increasing roughness with annealing temperature

TiO2 200 nm250 ºC

Ω scans

TiO2 1 700 nm

Ω scan

350 ºC

Reflectivity curves

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.510-2

10-1

100

101

102

103

104

105

106

107

t= 1.0 m t= 1.7 m t= 0.054 m t= 1.24 m

Re

flekt

ivita

úhel (stupně) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

10-2

10-1

100

101

102

103

104

105

106 as deposited

350 oC

450 oC

Ref

lect

ivity

2

Increase of roughness with film thicknessReduction of very thin surface layer with

annealing temperature

2

Reflectivity curves fitting

Incident angle (°)1.110.90.80.70.60.50.40.30.20.10

Inte

nsity

(co

unts

/s)

0

1

10

100

1,000

10,000

100,000

Incident angle (°)0.50.40.30.20.10

Inte

nsity

(co

unts

/s)

0

1

10

100

1,000

10,000

100,000 0,054 m 350 C

0,8 m 300 CTwo layer model necessarySurface porous layer

Fitted

Experimental

Surface roughnessThickness

[nm]Fitted

thickness[nm]

Electron density[g.cm-3]

Roughness [nm]

54 57 3.42 1.2

100 93 3.58 1.7

200 200 3.48 1.8

630 569 3.53 4.12nd layer 57 3.64 7

1000 968 3.89 22nd layer 49 3.68 5

1700 1791 3.89 22nd layer 55 3.74 5

Depth profiling

Rutile growths on the interface while anatase is on the top

Different angles of incidence ()

0.5 0.75 1.01.52.0

Anatase 101

Rutile 110

thickness – 1 m

0.5 0.75 1.01.52.0

Angles of incidence in degreesAnatase

Rutile

Rutile growths on the interface while anatase is on the top

thickness 935 nm

Effective penetration depth

100 nm

4

150 nm200 nm300 nm00 nm

Reflection on multilayers

Bragg maxima of multilayer

Period d

Kiessig maxima

Total thickness T

indk 22 cos2

BA ddd

)sin(sin2 12

k

d

d = T

Number of ML periods

10x(GaAs 7nm/AlAs 15 nm),CuK1

Kinematical approx:No total reflection region,wrong positions of the satellites (refraction not considered)

1 2 3 410-6

1x10-5

1x10-4

10-3

10-2

10-1

100

101

102

103

104

Ref

lect

ivity

2 (degrees)

Annealing of amorphous9x(5 nm Si/ 1 nm W)

Experimental set-up

X-ray tubeCuK

Göbel mirror

Sample

Secondary graphite monochromator

Detector

Slit 0.1mm

Slit 0.05 mm

Diffuse scatteringnon-specular conditions Thermal fluctuations

Correlated layer distortions

Height-height correlationfunction

)0,0(),(),( zYXzYXC

hRRC 22 )/exp()(

Effective cut-off length of theself-affine surface

)0,0(),(),( kjjk zYXzYXC

For multilayers

)/||exp( kjkjjk ZZCCC

Vertical interface roughnesscorrelation

Fe/Au (70Å/21Å)x13

-6000 -4000 -2000 0 2000 4000 60002000

4000

6000

1.11

2.22

3.33

Sample inclination

Dete

ctor

angle

-0.56 -0.560-1.11 1.11 1.67-1.67

Low correlation of the interface roughness

Dynamická difrakce

Dynamical diffraction Shift from the kinematical Bragg position (due to refraction)

Finite width of the diffraction curve (even for T→0)

Asymmetry of the maximum – due to the Borrmann effect

Strongly interacts with the atoms – Anomalously high absorption

Weakly interacts with the atoms – Anomalously low absorption

The Borrmann effectThe Borrmann effect

Wavefields in crystal

Tloušťka

strain

Epitaxní vrstvy

ImplantaceSi – B+

bez implantace

D = 6,2.1015

D = 3,1.1014

D = 6,2.1015

a žíhání 1000 ºC

X-ray grazing incidence diffraction

W ~ 1.8 nm na Al2O3

a|| = 0.3184 nma0 = 0.3165 nm|| = 0.6 %<D||> 5 nm

sken

Mozaiková rozorientace ~ 1.1º

MBEMo 22 nm (111)na(001) GaAs

Tři doményMo[110] || GaAs [110] GaAs [1-10] GaAs [100]Mismatch B || -10.2 % ┴ +3.7 % C ┴ +27 %<D> ~ 13 nm

Jedna doménaNb[110] || GaAs [100]Nb(001) || GaAs (001)

Mismatch 21.1 %

Standing waves

Standing waves

)cos(

||

||2

||

||1||)(

02

0

22

0 rhE

E

E

EErI hh

Reciprocal lattice vectorAmplitude of incoming wave

Phase of (Eh/E0)Amplitude of diffracted wave

Reflection curve – 1Phase – 2Intensity at atomic planes – 3

Maximum interactionfor = 0, at high angle side of reflection curve

Monolayer of adsorbed atoms

Yield of the fluorescent radiation

High sensitivity to displacement of layer~ 1 % !!!

Adsorbed layersThree adatomsat 0, 1/3, 2/3

Parallel planes

Inclined planes

ExperimentMeasurements of secondary radiationunder the condition of diffraction

Determination of coherent position – mean plane of the adsorbed atomsand coherent fraction – static and dynamic displacement of atoms from the coherent position

FluorescencePhotoelectronsAuger electronsCompton radiation

Chemical selectivitySpatial resolution on atomic scaleDepth-resolved studies

Organic materialsLong-period standing waves are necessary

Total reflection SW is formed as an interference between incidentand specularly reflected waves

Bragg diffraction from layered synthetic microstructures with large period

10-200 layer pairs (low and high electron density)

Fixed period XSW

Height dependence of electric field intensitygenerated during specular reflection of an X-ray plane wave from the mirror surfaceat three angles of incidence

Marker atom A – two E-field maximamarker atom B – five E-field maxima

= 0.1 c

= c

XSW applicationMonitoring of membrane-related dynamic processes

membrane-lipid phase transitionsion movement in membrane

Protein foldingMembrane-protein insertionLipid and/or protein distributionsSurface binding

Distribution of marker atom above the substrate surface

Theoretical model Experimental fluorescence, Reflectivity data

Layered model of refractive indexbased on the known structure

Adjusting of interfacial roughness

Features of XSW

Resolution ~ 1 % of LSM d (for 50 Å - 0.3 Å, 925 Å - 3 Å)

Element specificity (not suitable for light elements, O, P, S)

Structure-determination measurement on isolated lipid membranes(protein monolayers ~ 10 pmol (100 ng) of cytochrome c)

Calculation of the angle-dependent electric-field profileand fluorescence-yield profile normal to the surfaceAdjusting two parameters

Membrane-topology measurements on minimally perturbed systems(Fe XSW on Fe-cytochrome c)