High Resolution X-ray Diffractometry 2 – Reciprocal Space Mapping
Jan 26, 2012 www.bruker-webinars.com
Good Diffraction Practice Webinar Series
26.01.2012 2
Welcome
Dr. Martin Zimmermann
Sr. Applications Scientist, XRD
Bruker AXS GmbH
Karlsruhe, Germany
+49.721.50997.5602
Dr. Brian Jones
Product Manager, XRD
Bruker AXS Inc.
Madison, Wisconsin, USA
+1.608.276.3000
3
Outline
• What is Reciprocal Space
• What can be measured by Reciprocal Space
maps (RSMs)
• How to measure RSMs
• RSMs with 1D-detectors
• RSMs with 2D-detectors
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• What is Reciprocal Space
• What can be measured by Reciprocal Space
maps (RSMs)
• How to measure RSMs
• RSMs with 1D-detectors
• RSMs with 2D-detectors
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Scattering from a crystal: The concept of reciprocal space
Real space
1exp RGi
332211 anananR
1a
2a
q-space
321 blbkbhG
1b
2b
ikkiba 2
Crystal lattice Reciprocal lattice Fourier transform
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Accessible region in reciprocal space – Experimental constraints
1-4 0-1-2-3 2 3 4 5
0
1
3
2
4
5
h [100]
l [
001
]of a single atom
cubic crystal
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Accessible region in reciprocal space - Wavelength
1-4 0-1-2-3 2 3 4 5
0
1
3
2
4
5
h [100]
l [
001
]kQ 2
/2k
][
24.1][
keVEnm
Wavevector
Wavelength
The range of accessible reflections can be increased by using X-rays of a higher energy.
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Accessible region in reciprocal space - Geometry
1-4 0-1-2-3 2 3 4 5
0
1
3
2
4
5
h [100]
l [
001
]
0i 0f
transmission transmission
kQ 2
Reflections very close to the half-spheres have grazing incidence or grazing exit geometry surface sensitivity
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A silicon crystal in reciprocal space – Structure Factor
FCC-lattice with
Si atoms at
(0, 0, 0) and
(¼, ¼, ¼ )
1-4 0-1-2-3 2 3 4
0
1
3
2
4
5
h [110]
l [
001]
6
7
The structure factor of the crystal determines the scattered intensity.
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• What is Reciprocal Space
• What can be measured by Reciprocal Space
maps (RSMs)
• How to measure RSMs
• RSMs with 1D-detectors
• RSMs with 2D-detectors
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Analytical tasks
Lateral structure
Defects & Crystal size
Layer thickness Chemical composition
Mismatch & relaxation
Lattice parameters
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Pseudomorphic and relaxed strain state
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aL
aS Si
Si1-xGex
• Relaxed layer lattice mismatch :
S
SL
rel a
aa
a
a
0
rela
a• Compressive strain :
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Pseudomorphic and relaxed strain state
13
aL
aS
aL
aS Si
Si1-xGex
Si1-xCx
• Relaxed layer lattice mismatch :
S
SL
rel a
aa
a
a
0
rela
a 0
rela
a• Compressive strain : • Tensile strain :
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Epitaxial Layers in Reciprocal Space
Pseudomorphic Layer
substrate
fully strained layer
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Epitaxial Layers in Reciprocal Space
Completely relaxed layer
substrate
fully relaxed layer
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The relaxation line
• The reflection of a fully strained layer is located on a perpendicular line.
• A reflection of a fully relaxed layer is on a line through the substrate reflection and (000).
• Reflections of partly relaxed layers are on the relaxation line.
Theory of elasticity:
D/tantan
1,,5.0 D
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• What is Reciprocal Space
• What can be measured by Reciprocal Space
maps (RSMs)
• How to measure RSMs
• RSMs with 1D-detectors
• RSMs with 2D-detectors
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Diffractometer configuration for measuring RSMs
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X-ray tube
Goebel mirror
Rotary absorber
Monochromator crystal
Detector
Analyzer crystal
Variable slit
Sample
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How to measure RSMs? Scan Types
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How to measure RSMs? Scan Types
Rocking curve
2θ = const
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How to measure RSMs? Scan Types
Rocking curve Detector scan
2θ = const ω = const
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How to measure RSMs? Scan Types
Rocking curve Detector scan 2θ/ω , ω/2θ scan
2θ = const ω = const
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How to measure RSMs? Scan Types
Rocking curve Detector scan 2θ/ω , ω/2θ scan
2θ = const ω = const
• reciprocal space scans
• qx scan, qz = const
• qz scan, qx = const….
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Conversion from angular to reciprocal lattice units
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Measurement is performed in angular space
Analyses are done in reciprocal space
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The instrumental resolution function in RSM
• The recorded intensity at any point in reciprocal space is an average over the respective resolution element.
• Example : Si(004) reflection measured with
• 2xGe(004a) monochromator
• 1xGe(002) analyzer
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The instrumental resolution function in RSM
M
Monochromator streak is normal to incident beam
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The instrumental resolution function in RSM
M
A
Analyzer streak is normal to exit beam
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The instrumental resolution function in RSM
A
M
wavelength streak is along a line through (000)
W
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The instrumental resolution function in RSM
M
M
A
A
W
W
CTR
Si(224+) Si(004)
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• What is Reciprocal Space
• What can be measured by Reciprocal Space
maps (RSMs)
• How to measure RSMs
• RSMs with 1D-detectors
• Technique
• Examples
• RSMs with 2D-detectors
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Reciprocal Space Maps Measurement with 1D detectors Scintillation Counter vs. VÅNTEC-1
XRD-RSM using VANTEC / 4min
Counts
1 2 103 4 5 6 10020 30 40 50 60 1000 1e4 2e4 3e41 2 103 4 5 6 10020 30 40 50 60 1000 1e4 2e4 3e4
Operations: Import [001]
SiGe 60nm [001] - File: rsm-vantec-115-004min [001].raw - Type: PSD Fix Scan - Start: 89.000 ° - End: 100.902 ° - Step: 0.006 ° - Step time: 2. s
Sca
n O
rde
r
0
10
20
30
40
50
60
70
80
90
100
110
120
130
2-Theta - Scale
93.4 94 95 96
Counts
1 2 103 4 5 6 10020 30 40 50 60 1000 1e4 2e4 3e41 2 103 4 5 6 10020 30 40 50 60 1000 1e4 2e4 3e4
115 Si sub.
60nm SiGe
Scintillation Counter: 72 min VÅNTEC-1: 4 min
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1D-detectors for fast RSM measurements: LYNXEYE
32
• Silicon strip detector
• 192 strips of 75 µm width
• Total window width 14.4 mm
• Resolution at 300 mm ≈ 0.012°
• Subsampling in Fast-scan mode
• Can be used as a 0D-detector
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1D-detectors for fast RSM measurements: LYNXEYE and VÅNTEC-1
33
• Silicon strip detector
• Total window width 14.4mm
• 192 strips of 75µm width.
• Resolution at 300mm ≈ 0.012°
• Subsampling in Fast-scan mode
• Can be used as a 0D-detector
• Gas detector (Xe-CO2)
• 50x16 mm2 active area, simultaneous up to 12°in 2
• 1600 electronic channels
• Resolution at 300 mm ≈ 0.006°
• Low detector noise
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Influence of the measurement geometry on the resolution
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Grazing incidence geometry
𝑏 =sin(𝜔𝑖)
sin(𝜔𝑒) • Asymmetry factor 𝑑𝑒 =
𝑑𝑖𝑏
• Exit beam width
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Influence of the measurement geometry on the resolution
35
𝑏 =sin(𝜔𝑖)
sin(𝜔𝑒)
Grazing incidence geometry
Grazing exit geometry
• Asymmetry factor 𝑑𝑒 =𝑑𝑖𝑏
• Exit beam width
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Influence of the measurement geometry on the resolution (2)
• When using a 1D-detector for the RSM, the reflection should be chosen such that the beam compression is high.
• The incident beam should be adapted to achieve the highest possible resolution.
• When RSMs are measured using an analyzer crystal, the full incident beam can be used and the geometry is not critical.
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hkl ωi ωe b dinc (75 µm)
113+ 56.2° 2.9° 15.9 1.1 mm
224+ 79.2° 8.8° 6.42 0.5 mm
115+ 63.3° 32.7° 1.7 0.1 mm
Si reflections for Cu-Ka radiation
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RSMs with a 1D detector: Choice of the loop scan
37
Looped over rocking curve Looped over 2θ/ω scan Looped over h-scan
Pseudomorphic layers Fully relaxed layers
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Choosing the appropriate reflection for the RSM: (113+) vs. (224+)
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(224+) (113+)
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Choosing the appropriate reflection for the RSM: (113+) vs. (224+)
39
(224+) (113+) + Structures are more compact.
Faster RSM.
+ Higher structure factor. More
intensity.
+ Detector Snapshot is almost like a
l-scan. Faster RSM.
+ Beam Compression factor is higher.
Better resolution.
─ Penetration depth decreases at
grazing angles. Deeper layers of
the sample may not show up.
─ Less precision in lattice parameter
determination.
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• What is Reciprocal Space
• What can be measured by Reciprocal Space
maps (RSMs)
• How to measure RSMs
• RSMs with 1D-detectors
• Technique
• Examples
• RSMs with 2D-detectors
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Samples provided by F. Rinaldi (Uni Ulm / Bruker AXS)
RSMs from In0.06Ga0.96As films on GaAs with different layer thicknesses
d = 200 nm
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Samples provided by F. Rinaldi (Uni Ulm / Bruker AXS)
RSMs from In0.06Ga0.96As films on GaAs with different layer thicknesses
d = 200 nm d = 400 nm
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Samples provided by F. Rinaldi (Uni Ulm / Bruker AXS)
RSMs from In0.06Ga0.96As films on GaAs with different layer thicknesses
d = 200 nm d = 400 nm d = 450 nm
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Samples provided by F. Rinaldi (Uni Ulm / Bruker AXS)
RSMs from In0.06Ga0.96As films on GaAs with different layer thicknesses
d = 200 nm d = 400 nm d = 450 nm d = 800 nm
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Example: LaAlO3 on STO
Sample courtesy of Dirk Fuchs (Institute of solid state physics, KIT)
substrate STO
50 nm LaAlO3
STO(002)
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Sample courtesy of Dirk Fuchs (Institute of solid state physics, KIT)
substrate STO
50 nm LaAlO3
STO(002) STO(103+)
No miscut
Relaxation
Example: LaAlO3 on STO
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Example: GaN-based HEMT structure
Sample courtesy of L. R. Khoshroo (RWTH Aachen)
substrate Al2O3
350 nm AlN
1000 nm GaN
1 nm AlN
200 nm Al0.85In0.15N
GaN(002)
GaN
AlN
AlInN
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Sample courtesy of L. R. Khoshroo (RWTH Aachen)
substrate Al2O3
350 nm AlN
1000 nm GaN
1 nm AlN
200 nm Al0.85In0.15N
GaN(002)
GaN
AlN
AlInN
GaN(104+)
GaN
AlN
AlInN
Example: GaN-based HEMT structure
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Example: HEMT structure with graded buffer layers
substrate InP
50 nm In0.52Al0.48As
500 nm
InxAl1-xAs x=0.52
x=0.65
x=0.65
x=0.75 200 nm
InxAl1-xAs
50 nm In0.65Al0.35As
30 nm In0.65Ga0.35As
120 nm In0.65Al0.35As
10 nm In0.65Ga0.35As
Sample courtesy of Ian Farrer (University of Cambridge)
InP(004)
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Example: HEMT structure with graded buffer layers
substrate InP
50 nm In0.52Al0.48As
500 nm
InxAl1-xAs x=0.52
x=0.65
x=0.65
x=0.75 200 nm
InxAl1-xAs
50 nm In0.65Al0.35As
30 nm In0.65Ga0.35As
120 nm In0.65Al0.35As
10 nm In0.65Ga0.35As
Sample courtesy of Ian Farrer (University of Cambridge)
InP(004) InP(224+)
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RSM from a SiGe graded heterostructure: Miscut, Relaxation and Concentration
Si(333)
substrate Si(111)
600 nm Ge
250 nm SixGe1-x x=0-5%
250 nm SixGe1-x x=5%
250 nm SixGe1-x x=5-10%
250 nm SixGe1-x x=10%
250 nm SixGe1-x x=10-15%
250 nm SixGe1-x x=15%
250 nm SixGe1-x x=15-20%
500 nm SixGe1-x x=20%
Extract miscut for each SiGe layer
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RSM from a SiGe graded heterostructure: Miscut, Relaxation and Concentration
Si(333)
substrate Si(111)
600 nm Ge
250 nm SixGe1-x x=0-5%
250 nm SixGe1-x x=5%
250 nm SixGe1-x x=5-10%
250 nm SixGe1-x x=10%
250 nm SixGe1-x x=10-15%
250 nm SixGe1-x x=15%
250 nm SixGe1-x x=15-20%
500 nm SixGe1-x x=20%
Extract miscut for each SiGe layer
Si
#1
#1
#2
#3
#4
#5
#2
#3
#4
#5
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RSM from a SiGe graded heterostructure: Miscut, Relaxation and Concentration
Si(333) Si(531+)
substrate Si(111)
600 nm Ge
250 nm SixGe1-x x=0-5%
250 nm SixGe1-x x=5%
250 nm SixGe1-x x=5-10%
250 nm SixGe1-x x=10%
250 nm SixGe1-x x=10-15%
250 nm SixGe1-x x=15%
250 nm SixGe1-x x=15-20%
500 nm SixGe1-x x=20%
Extract miscut for each SiGe layer
Relaxation Concentration
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RSM from superlattices with large offcut
Sample courtesy of Uni Sheffield
substrate GaAs(001) with 10°offcut
43 nm GaInP
23 nm GaAs
x10
(004)
Evaluated Parameters: Concentration Layer thickness SL period
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Sample courtesy of Uni Sheffield
substrate GaAs(001) with 10°offcut
43 nm GaInP
23 nm GaAs
x10
(004) (002)
Evaluated Parameters: Concentration Layer thickness SL period
Periodic lateral structure due to substrate steps
RSM from superlattices with large offcut
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Outline
• What is Reciprocal Space
• What can be measured by Reciprocal Space
maps (RSMs)
• How to measure RSMs
• RSMs with 1D-detectors
• RSMs with 2D-detectors
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(103)STO
Phase 1
Phase 2
Scintillation Counter
• Measurement time:
8 hours
• Just one (103) diffraction
spot
• High resolution not
needed
Fast RSM with a 2D-detector Example: BiFeO3(200nm)/(001)SrTiO3
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Fast RSM with a 2D-detector: The VÅNTEC-500
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• Xe-based gas detector
• Window diameter of 140 mm
• 2048 x 2048 pixels with 68 x 68 µm size
• Detector noise <0.0005 cps/mm²
• 2θ range
• 23°at 300 mm
• 56°at 100 mm
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Fast RSM with a 2D-detector: Measurement mode
59
• 2D detector used in fixed
position --> fixed range in
2 and g is measured
simultaneously
• w scanned for one frame
for half of the 2 range of
the detector --> Ewald
sphere (red) is rotated to
integrate the reflection
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• Integration time ≈ 45 min
• In-plane epitaxial relation
as well as exisitence of
second phase (impurity
phase) is clear.
• Sample from Osaka
University
.
001S 002S
102S
103S 001 002
102
003 103
001 002
102 101
Fast RSM with a 2D-detector Example: BiFeO3(200nm)/(001)SrTiO3
𝜒
2𝜃
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• Very fast, no alignment required
• Good indication of degree of orientation / quality of layers
• Do I have the layer structure that I want?
• Can spot certain sample-to-sample differences immediately
• Use it as a very fast feedback loop to optimize the making
of your sample
Benefits of RSM with 2D-detector
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Q & A
Any Questions?
Please type any questions you may have in the Q&A panel and click Send.
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26.01.2012