X-ray scattering methods for Joachim F. Woitokphysics-astronomy-manuals.wwu.edu/Panalytical XRD Xray...

19-05-2005

X-R A Y S C A T T E R I N G S O L U T I O N S

X-ray scattering methods for the analysis of advanced materials

Joachim F. Woitok

Almelo, The Netherlands

Contents

• M a t e r i a l s a n d t h e i r a n a l y t i c a l d e m a n d s

• X�r a y d i f f r a c t i o n , X�r a y r e f l e c t i v i t y a n d X�r a y

d i f f u s e s c a t t e r i n g

how it works?

• X�r a y s o l u t i o n s

( a l l –in �on e ) sy ste m

X-ray diffraction for today

Diffractometer

Loose Loose powders Thin film Thin film samples

Small Small amounts Epitaxial layers

Bulk Bulk samples

StressTexture

Crystallography

Phaseiden

tificat

ion/

identifi

cation

/

quantifi

cation

quantifi

cation

High-resolution

Reflectivity/

Diffuse Scattering

Flat Flat samples

Analysis of Advanced Materials - Layers

• P e r f e c t c r y s t a l s – “ n o ” d e f e c t s , b u t s t r a i n

• M i s m a t c h e d l a y e r s � r e l a x a t i o n

• L a r g e m i s m a t c h � h i g h d e n s i t y o f i m p e r f e c t i o n s

• H i g h l y t e x t u r e d – p e r f e c t i o n n o t n e c e s s a r y

• P o l y c r y s t a l l i n e – b u t i t w o r k s

• P o l y m e r l a y e r s – t h e f u t u r e ?

• M e s o s c o p i c m a t e r i a l s – c o m i n g u p

Thin Film Characterization by X-rays •• Pseudomorphic epitaxial layers. “ No” defects. Strain may be present

Example : AlGaAs/GaAs, SiGe/SiApplications: Lasers, High-frequency IC’s

• Lattice mismatched epitaxial layers. Layers are par tly (or fully) relaxedExample: Strained Si, ZnSe/GaAs, InAsSb/GaSbApplications: Blue LED’s, IR optopelectronic

• Layers with large lattice mismatch and/or dissimilar crystal structuresExample: GaN/Sapphire, YBaCuO/SrTiO3, BST, PZTApplications: Blue Lasers and LED’s, High Tc Superconductors,

Ferroelectr ics• Layers where the epitaxial relationship is weak. Highly textured.

Example: AuCo multilayers on SiApplications: Thin film media, heads

Structural Characteristics

� Pseudomorphic growth� l a t t i c e m i s m a t c h

� l a y e r t h i c k n e s s

� s u p e r l a t t i c e s t r u c t u r e � Imperfect epitaxy- � � � � �� �� � � �� � �� �

�� � �� � � �� �� �

� � �� � �� � � � � �� �� �� Incoherent growth

- all above, plus� r elax at i on � m osai c spr ead � m i sf i t d i sloc at i on d en si t y

� lay er / subst r at e t i lt s

G aseous

S t at e

Matter

L i q ui dS t at e

Amorphous (disordered)

Crystalline(ordered)

SolidState

Atoms, ions, molecules

The Crystalline State

A c r y st al i s c on st r uc t ed by t h e ‘ i n f i n i t e’ r epet i t i on i n spac e of i d en t i c al ‘ bui ld i n g bloc k s’ .

Crystal system

Building block

Crystal+

bb

aa

The Crystalline State

Crystal Lattice and Bragg’s Law

Crystal

d

θ θ

x

C DB

x

X-ray Diffraction

2·d·sinθθθθ =λλλλ

Bragg’s Law

�

�

�

Bragg Reflection

λλλλ= 2d sinθθθθ

� λλλλ is known (the wavelength of the x-ray beam)

� θθθθ is measured (the reflection angle)

� ‘d’ is calculated (the spacing between the lattice planes)

θθθθ = angle of incidence = angle of reflection(symmetrical)

N bisects incident and reflected beams

ΘΘΘΘΘΘΘΘ

N

Bragg’s Law

The “Ideal” Diffraction System

• Fast exchange of

– tubes and tube focus positions

– incident beam optics

– sam pl e pl atfor m s

– diffr acted beam optics

– detector s

w ith out r e�al ig nm ent !

Bragg-Brentano Powder Diffractometer

monochromator

Anti scatter slit

Detector

Curved crystal

(Graphite)Receiving slit

Polycrystalline sample

Soller slits

X-ray tube(line focus)

Divergence slit

Soller slits

Beam mask

20 30 40 50 60 70 802Theta (°)

0

10000

40000

90000

160000

Inte

nsity

(co

unts

)

Angular Position: d-values

Relative intensities: I

Powder Diffraction Pattern

T h e diffr action patter n is l ik e a fing er pr int of th e

cr y stal str uctur e:

� d v al ues r efl ect th e unit cel l par am eter s ( ‘ g r id’ )

� intensities r efl ect th e atom s/ m ol ecul es ( ‘ buil ding

bl ock s’ )

Powder Diffraction Pattern

MMaterialsaterials RResearchesearch DDiffractometeriffractometer ((MRDMRD))

•• interchangeable opticsinterchangeable opticsPREFIXPREFIX

•• all kinds of applicationsall kinds of applicationsHighHigh--resolutionresolutionReflectivity Reflectivity Thin Film analysisThin Film analysisStressStressTextureTextureInIn--planeplane

4 - CrystalMonochromator

X-ray tubeLine focus

X-ray mirror

Triple Axis

OpticDetector 1

Sample

Lab to Fab Instrument

200 and 300 mm Wafers

X ’ P er t P R O E xtend ed M R D X L

– F or h ig h �r esol ution diffr action studies w ith h ig h intensities

– A l l ow s m ounting of tw o incident beam P r eF I X m odul es in�l ine

Experimental techniques

� scans in reciprocal space

� rock ing cu rv es

� ω �2θ scans

� q scans

� reciprocal space m apping

X-ray Techniques

-6000 -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000Omega/2Theta (s)

0.1

1

10

100

1K

10K

100K

1M

10Mcounts/s

XRD rocking curve :

an unambiguous, standardlessmeasure of the layer

composition andthickness

The accuracy is within a few %.0.1% Ge ≅≅≅≅ 10” ∆ω∆ω∆ω∆ω

Si substrate

SiGe layer

monochromator (collimator)

X-raysource

HR X-Ray Diffraction

X-ray Reflectivity/ Diffuse Scattering

0 1 2 3 4 5 6Omega/2Theta (°)

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

Plateau: sample size, flatness, instrument

Critical edge: density

Angular separation: thickness

Shape: roughness, density

ωωωω 2θθθθ

z

ρρρρ

X-ray Reflectivity/ Diffuse Scattering

0 1 2 3 4 5 6Omega/2Theta (°)

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

Diffuse scattering

roughnessvertical correlation

ωωωω 2θθθθ

z

ρρρρ

z

2σσσσ

L

h=0.9

h=0.5

h=0.3

Sinha et al. (1988)

Fractal model

PreFIX Optical Modules

Line focus

Point focus

12 mm

0.04 mm

0.4 mm

1.2 mm

Line focus

4-crystal Mirror/ Hybrid

Lens Mono-cap

The PreFIX Concept

• 14 incident beam P r eF I X mo du l es

• 8 dif f r acted beam P r eF I X mo du l es

• H o w can I mak e th e r ig h t co mbinatio ns ?

Applications

Line focus

Point focus

12 mm

0.04 mm

0.4 mm

1.2 mm

• Phase analysis

• Rocking curve

• Reflectivity

•Omega-Stress

• Psi-Stress

• Texture

• Micro-diffraction

• In-plane diffraction

PreFIX X-ray mirror

X-ray Mirror

X-ray mirror

• M etal l ic mu l til ay er w ith p ar abo l ic s u r f ace

• G r aded d#s p acing al o ng th e mir r o r

• U s ed w ith l ine f o cu s

• C o nv er ts div er g ent beam to p ar al l el beam

• D o es no t co ntr o l ax ial div er g ence

X-ray Mirror

X-ray mirror

focus ofx-ray tube

mirrorparabolicshape

quasi-parallelout-comingbeam

divergentbeam

quasi-parallel diffractedbeam

divergent incidentbeam

X-ray Mirror

X-ray Mirror

X-ray tube(line focus)

Divergence slits Soller slits

X-ray mirror

Detector

Samples with unevensurfaces

Parallel Plate Collimator

PreFIX Hybrid monochromator

What is a Hybrid Monochromator?

• A co mbinatio n o f an X #r ay mir r o r and a

ch annel #cu t G er maniu m cr y s tal

• O nl y C u K α � is tr ans mitted

• P ar al l el , mo no ch r o matic X #r ay beam o f

h ig h #intens ity ,

• T w o ty p es :

– two bounces in the monochromator

– f our bounces in the monochromator

What is a Hybrid Monochromator?

Hybrid monochromatorHybrid Monochromator

Performance ComparisonR

esol

utio

n

Intensity (log scale) (c/s)107 108 109

0.003º

0.006º

0.009º

0.012º

0.015º

0.018º

4x(220)

4x(220 )asym 4x(220 )asym + mirror

Hybrid

4x(220)+ mirror

2*106

Si (333)Si (111)

Powder diffractionPowder diffraction

Potential Analyzers for Parallel Beam Set-up

Analyzer Resolution

Perfect crystal < 0.02° Too narrow

Multilayers 0.02° … 0.06° ? Optimal ?

Parallel plate collimators

> 0.06° Too broad

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500Omega/2Theta (s)

0.1

1

10

100

1K

10K

100K

1M

10Mcounts/s

AlGaN/GaN MQW0 0 2

Omega 17.606602Theta 34.60000

Phi 0.00Psi 0.00

X -2.00Y 0.00

1mm

TA

Hybr idHybr idAlGaNAlGaN//GaN GaN MQWMQW

Effect of Diffracted Beam Optics

High-resolution Diffraction

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000Omega/2Theta (s)

0.1

1

10

100

1K

10K

100K

1M

10Mcounts/s

Ge %Si substrate

SiGe

SiGeSi cap

16.15.1

Ge[220] 4 – Crystalmonochromator

X-ray tube(line focus)

X-ray mir ror

Detector 2

Tr iple Axis

Detector 1

Optional slit

Beam size:1.4 x 2.5mm2

SiGe HBT

Analysis of Boron Doping

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000

Omega/2Theta(seconds)

1

10

100

1K

10K

100K

1M

Inte

ns

ity

(a.u

.)

Si (001)

SixGe1-x

Si (001)

SixGe1-x

SixGe1-x:B

SixGe1-x Si(004)

Reciprocal Space Mapping (TA)

-100 -50 0 50 100Qx*10000(rlu)

5600

5620

5640

5660

5680

5700

5720

5740

Qy*10000(rlu) #1_M1.A00

1.6

3.0

5.4

9.8

17.9

32.5

59.0

107.3

195.0

354.5

644.5

1171.6

2129.6

3871.2

7037.1

12792.0

23253.1

42269.2

76836.5

139672.5

253895.1

Graded SiGe to 20%(relaxed)

Si0.8Ge0.2

Si substrate

Strained SiSiGe 5x

Si(004)

SL

SiGe

Ge gradient

Poly silicon001 silicon wafer

2Theta/omega projections: comparison of polycrystalline and single crystal Si

111 220113

004

133224 115

335444

!002!

Layer structure

X-ray tube

(line focus)

Hybr id monochromator

X’Celerator

X’Per t PRO MRD

Set-up Fast Reciprocal Space Mapping

-800 -600 -400 -200 0 200 400 600 800Qx*10000(rlu)

23600

23800

24000

24200

24400

24600

24800

Qy*10000(rlu) F2113_7_M1.xrdml

1.6

2.7

4.7

8.1

14.1

24.4

42.2

73.1

126.7

219.5

380.3

658.9

1141.7

1978.2

3427.6

5938.9

10290.2

17829.5

30892.8

53527.1

92744.9

GaN (0002)

AlGaN/GaN MQW

X’Celerator (total time: 40 min)

0 1 2 3 4 5 6Omega/2Theta (°)

0.1

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

Si substrate

SiGe

SiGe

Si cap 39.0 nm 38.1 nm

29.4 nm 28.9 nm

54.9 nm 55.1 nm

XRR XRD

0 1 2 3 4 5 6Omega/2Theta (°)

0.1

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

0 1 2 3 4 5 6Omega/2Theta (°)

0.1

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

Si substrate

SiGe

SiGe

Si cap 39.0 nm 38.1 nm

29.4 nm 28.9 nm

54.9 nm 55.1 nm

XRR XRD

Si substrate

SiGe

SiGe

Si cap 39.0 nm 38.1 nm

29.4 nm 28.9 nm

54.9 nm 55.1 nm

XRR XRD

Reflectivity

Detector

Parallel platecollimator

Flat crystalmonochromator

Slit 0.1 mm

X-ray tube(line focus)

X-ray mir rorbeam knife

Beam size:0.13 x 5 mm2

Model Based on XRD

0 1 2 3 4 5 6Omega/2Theta (°)

0.1

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

Si substrate

SiGe

SiGe

Si cap

Best Fit Simulation

0 1 2 3 4 5 6Omega/2Theta (°)

0.1

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

Si substrate

SiGe

SiGe

Si cap

Roughness Parameters

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Omega (°)

0.1

1

10

100

1K

10K

100K

1M

10M

100Mcounts/s

L: 45±±±±10nm, h:0.5

Thin film phase analysisX-ray tube(line focus)

Soller slits

X-ray mir ror

Thin layers

Detector

Sample

Parallel platecollimator

Incident angles

Depth resolved phase analysis

Zn

Zn

CuGaInSe

CdSe/Mo

Zn

CuGaInSe

SBT (SrBi2Ta2O9) and PZT (Pb(Zrx,Ti1-x)O3) are key materials for:

• FeRAM (ferroelectric random access memories)• MEMS (mircro-electromechanical systems)

Goal X-ray characterization:

Distinguish cubic non-ferroelectric phase from Pervoskite ferroelectric phase

Ferroelectric Films

SBT – possible phases:

• Pervoskite• Fluorite (low T SBT)• Pyrochlore (Bi-deficient composition)

The Material Problem

X-ray Lens (Point Focus)

X-ray tube(point focus)

θ = 0.3°

Stressed and textured samples,highly textured layers

X-ray lens

Detector

Flat graphite crystalmonochromator(optional)∆

25.0 30.0

35.0 40.0 45.02 Theta/Omega [deg]

45.0

85.0

5.0

Psi

[de

g]

25.0

65.0

Pt(111)

Pt(111)

113 008 115 200 202 0010 119 0012 208SBTPyrochlore 222 400

Pyrochlore (222)

Psi- 2Theta/Omega map for phase determinationPt/SBT/Pt/TiO2/SiO2/(100)Si

hkl

Texture

111 200

220 311

111 200

220 311

X-ray tube

∆θ∆θ∆θ∆θ= 0.3°

Stressed and textured samples,Highly textured layers X-ray lens

Detector

Flat graphite crystalmonochromator (optinal)

Parallel platecollimator

X-(point focus)

= 0.3°

Stressed and textured samples,Highly textured layers X-ray lens

Detector

Flat graphite crystalmonochromator (optinal)

Parallel platecollimator

Rolled Cu

Micro-Diffraction

X-ray tube(point focus)

∆θ∆θ∆θ∆θ= 0.3°

Sample with small areaof interest Mono-cap

X’Celerator

0.4 0.4 mm

Cu plating

Cu(111)

xx

In-plane - Low Resolution Setup

XX--ray lensray lens

CrossedCrossed--slits slits 0.1 x 5 mm0.1 x 5 mm2222θθθθθθθθ

Parallel plate collimatorParallel plate collimator

ωωωωωωωω, , φφφφφφφφ

Co

CrNiPAl

Textured polycrystalline Co(CrPtTa) alloy layers in hard discs

Co-based magnetic thin film• typically 25nm thick•hexagonal phase•highly textured

Polycrystalline Cr

Polycrystalline textured Al

Amorphous NiPCo signals lost amongst others

Optics: X-Ray lens, Soller slits, Parallel plate collimator

The Co reflections, if present, are buried under the NiP amorphous hump.

Conventional diffraction geometryvs In-plane

Al (200)

Co (002)

Co (100) Co (101)

Amorphous NiP

40 45 50°2Theta

0

200

400

600

800

counts/s

Co(100)

Co(002)

Co(101)

In-plane diffraction geometry

Co(100)

Co(002)

Co(101)

Conventional diffraction

High temperature studies

DHS 900

TA Scans as Function of T

34.40 34.45 34.50 34.55 34.60 34.65 34.70 34.75 34.80Omega/2Theta (°)

0.1

1

10

100

1K

10K

100K

1Mcounts/s Si_100TA.xrdml

Si_150TA.xrdml

Si_180TA.xrdml

Si_500TA.xrdml

Si_700TA.xrdml

100°C700°C

Si(004)

1.355

1.357

1.359

1.361

1.363

1.365

0 200 400 600 800 1000 1200

T [K]d

004

[An

g]