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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

[email protected]

+49.721.50997.5602

Dr. Brian Jones

Product Manager, XRD

Bruker AXS Inc.

Madison, Wisconsin, USA

[email protected]

+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


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maps (RSMs)




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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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maps (RSMs)




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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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maps (RSMs)




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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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Rocking curve

2θ = const

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Rocking curve Detector scan

2θ = const ω = const

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Rocking curve Detector scan 2θ/ω , ω/2θ scan


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Rocking curve Detector scan 2θ/ω , ω/2θ scan


• 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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M

Monochromator streak is normal to incident beam

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M

A

Analyzer streak is normal to exit beam

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A

M

wavelength streak is along a line through (000)

W

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M

M

A

A

W

W

CTR

Si(224+) Si(004)

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maps (RSMs)



• Technique

• Examples


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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

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• 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

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• 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

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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

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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+)

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(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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maps (RSMs)



• Technique

• Examples


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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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d = 200 nm d = 400 nm

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d = 200 nm d = 400 nm d = 450 nm

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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


30 nm In0.65Ga0.35As

120 nm In0.65Al0.35As


Sample courtesy of Ian Farrer (University of Cambridge)

InP(004)

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Example: HEMT structure with graded buffer layers

substrate InP


500 nm

InxAl1-xAs x=0.52

x=0.65

x=0.65

x=0.75 200 nm

InxAl1-xAs



120 nm In0.65Al0.35As


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=10-15%


250 nm SixGe1-x x=15-20%


Extract miscut for each SiGe layer

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Si(333)

substrate Si(111)

600 nm Ge



250 nm SixGe1-x x=5-10%


250 nm SixGe1-x x=10-15%


250 nm SixGe1-x x=15-20%



Si

#1

#1

#2

#3

#4

#5

#2

#3

#4

#5

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Si(333) Si(531+)

substrate Si(111)

600 nm Ge



250 nm SixGe1-x x=5-10%


250 nm SixGe1-x x=10-15%


250 nm SixGe1-x x=15-20%



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



maps (RSMs)




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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

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• 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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Join us for X-TEAM Tour 2012

• Educational one-day seminars on X-ray Analysis

• April – November in a city near you!

• Check the tour schedule and register early!

www.bruker-axs.com/xteamtour2012

64

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26.01.2012

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