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]