Birch - Characterization of Epitaxial Material by High Resolution X-ray Diffraction

7/30/2019 Birch - Characterization of Epitaxial Material by High Resolution X-ray Diffraction

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Thin Film Analysis by X-ray Scattering

Lecture 7:

Characterization of Epitaxial Material by

High Resolution X-Ray Diffraction

Jens Birch

Thin Film Physics, IFM, Linkping University, Linkping [email protected]

PAN-3 Winter Schoolon

SiC epitaxial growth: from thin layers to bulk material

Linkping, January 26, 2010


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Increasin

gstructuralorder

Polycrystalline

Amorphous ornanocrystalline

Epitaxial

Superlattices

Textured

Multilayers

Substrate

Strained layer epi

Substrate

Substrate

Substrate

Thin film structures and common XRD optics

Bragg-Brentano(-2)

High Resolutioncrystal optics

(4-axis gonio)

Most thin filmsin this region


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Diffraction in Real and Reciprocal Space

An FCC crystal

Real Space


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Set ofplanes(hkl)=(222)

d222

a*b*

c*

200

222

111

000

020

002022 222

202

220

Miller indices(sets of planesin Real Space)

Reciprocal Lattice Coordinates(scattering directionsin Reciprocal Space)


G222 =Reciprocal

lattice vector

Place reciprocal lattice points in the directionsof the planes normals at distances inversely

proportional to their plane spacings.

Reciprocal Space

Real Space


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X-Raysout

2

diffraction angle

X-Rays in


Wavevectors: |K0|=|K|=2/x


222

Incident Wavevector

K0

Diffracted Wavevector

K2


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X-Raysout

2

diffraction angle

X-Rays in


Incident Wavevector

K0

Diffracted Wavevector

K

ScatteringVector

Q=K-K0

2,-2,2

2



Braggs law:

=2d222sinLaue condition

Q=G222

Q=K-K0=2|K|sin=4/X sinG=2/dhkl4/X sin=2/dhkl

2dhklsin=X


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K0 K

Scattering

VectorQ=K-K0

2,-2,2

2


Diffraction in Reciprocal Space

The Laue ConditionQ=G222

Constructive interference(diffraction) occur wheneverthe Ewald sphere coincides

with a reciprocal lattice point

Ewalds sphere concept:A sphere in reciprocal spaceradius = |K0|center at start of K0All possible scattering vectorswill start and end on theEwalds sphere


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Epitaxial Layer Definitions

In-plane or lateral lattice parameter, a//= lattice parameter parallel to sample surface

Out-of-plane or transverse lattice parameter, a= lattice parameter perpendicular to sample surface

Lattice mismatch (a0F-aS)/aS = lateral lattice parameter difference between layerand substrate relative to substrate

film

substrate

aS

a0Ff

aS

relaxed film

a0Ff

as

a//F

aF

as

strained film


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Substrate Layer & Reciprocal Lattice

Qx

Qz

000

004 404

400

202

206

202

206

404

400

Substrate


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Qx

Qz

000

Substrate

RelaxedEpilayer

aS

a0F > aS


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Qx

Qz

000

Substrate

StrainedEpilayer

aS

a0F > aS


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Qx

Qz

000

Substrate

RelaxedEpilayer

aS

a0F < aS


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Qx

Qz

000

Substrate

StrainedEpilayer

aS

a0F < aS


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2/ scan

Qx

Qz

000

Substrate

StrainedEpilayer

aS

a0F < aS

=

2


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scan = Rocking curve

Qx

Qz

000

Substrate

StrainedEpilayer

aS

a0F < aS

2222

222


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Diffraction scan definitions

Rocking curve = -scan(circumferential scan around reciprocal space origin)

2/ - scan = the diffraction (2) to incidence () angle scan rate = 2/1(radial scan from origin in reciprocal space, i.e., perpendicular to a rocking curve)

Reciprocal space map = a sequence of 2/ scans with a little offset in between each

(2-dimensional scan producing a map of reciprocal space)

Symmetric reflection = reflection from lattice planes parallel to the sample surface Asymmetric reflection = reflection from lattice planes inclined to the sample surface Glancing incidence = 2/2

2/

2/

Reciprocal lattices of strained film + substrate

as

a//F

aF

as

strained film

substrate

real space:


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Sampling volume

000

Divergence ofincident beamoptics

Acceptance angleof detector optics

Diffractometersampling volume

Ewalds sphere(thickness ~)

2

2

Sampling volume is - 3D- depends on diffractometer


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Increasin

gstructural

order

Polycrystalline

Amorphous ornanocrystalline

Epitaxial

Superlattices

Textured

Multilayers

Substrate

Strained layer epi

Substrate

Substrate

Substrate

XRD optics selection for thin films

Bragg-Brentano

HR crystal optics

Low and medium

resolution opticsExamples


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Applications: New semiconductors

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

2.5000 3.5000 4.5000 5.5000

Lattice parameter

Band

gap

BN

AlN

SiC

GaN

InN

Diamond

ZnS

CdS

PbS

AlAsGaAs

Si

Ge

Possibility to Tailor: bandgap

lattice mismatch


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Double Crystal DiffractometerDetector

Samplecrystal

Collimatorcrystal

X-ray source

All wavelength components are diffracted - DISPERSED - in the collimator crystalEach wavelength component diffracts at different s at the SAME -setting of the sample

+ simple+ intense

- only rocking curves

- sample crystal and reflection must be same as the collimator crystal

+

+


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Multiple crystal monochromator diffractometer

Detector

sample

4 -crystal monochromator

x-raysource

+ well collimated beam = 0.001-0.008

+ well monochromized beam/ = 10-5 - 10-4

+ any crystal and reflection can be measured

- low intensity500k - 3M ct/s in primary beam- NO 2 resolution

"2"


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The 4 crystal monochromator


x-raysource

Dynamical Simulation ofoneGe 022 Rocking Curve

1

10-1

10-2

10-3

10-4

10-5

4 reflections useful dynamic range >106

+

-

-+

(+, -, -, +) configuration(+, -) = dispersion(-, -) = monochromation (compare double xtal)


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Sampling volume

000




Ewalds sphere

(thickness ~)

2

2

0

0


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Sampling volume

000




Ewalds sphere

(thickness ~)

2

2

A thin Ewalds shell

0

0


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Sampling volume in reciprocal space with 4-crystal

monochromator & open detector

asymetricgrazing exit

-scan

symetric-scan

2

and

E.S.

asymetricgrazing incidence

-scan


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Determination of unstrained lattice paremeters

as

a0f

as

fictiverelaxed film

a0f

as

af

cf

as

strained film

Elastic distortion duringepitaxial growth

measure strainedlattice parameters

calculate unstrainedlattice parameters

a c 1 21c a

af0f f

f f= +

AxB(1-x)

Calculatecomposition(Vegard's law) a (x) x a (1 x)a

xa a

a a

0f 0A 0B

0f 0B

0A 0B

= +

=

Process feedback,Bandgap, etc.

AxB(1-x)

S

S


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Example of a rocking curve

31.4 31.5 31.6 31.7 31.8 31.90.1

1

10

100

1K

10K

1M

31.7 31.8 31.931.631.5

100k

10k

1000

100

10

1

InP substrate004

GaInAs film

004

Layer thicknessfringes

Intens

ity

(ct/s)

omega (degrees)

s f


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Materials characterization from simple rocking curve

Lattice parameter:

Assume as is known calibrates s s Measure peak separation

d004,f cf

Composition:

Calculate a0ffrom cf Assume strained if thickness fringes visible:

No thickness fringes assume a0f= a0f= cf Calculate AxB(1-x) composition x from Vegards law:

a c 1 21c a

af0f f

f f= +

a (x) x a (1 x)a

xa aa a

0f 0A 0B

0f 0B

0A 0B

= +

=

aInP = 5.8688 = 0.046= 1.540562

d004,f= 1.4653 cf = 5.8612

GaInAs/InP example:

a0GaInAs = 5.8688 (strained)a0GaInAs = 5.8612 (relaxed)

GaInAs/InP example:(nGaAs=0.311InAs = 0.352)

0.477 < x < 0.487


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Example of a rocking curve

31.4 31.5 31.6 31.7 31.8 31.90.1

1

10

100

1K

10K

1M

31.7 31.8 31.931.631.5

100k

10k

1000

100

10

1

InP substrate004

GaInAs film

004

Layer thicknessfringes

Intens

ity

(ct/s)

omega (degrees)

s f


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Rocking curve calculations III

Film thickness tf:

Measure fringe separation (radians) Calculate tf from:

or

NB. Useful for superlattice periods as well

GaInAs/InP - Example:

= 0.012=2.09410-4 radians=1.540562 s = 31.77

tf= 4326 t

f

=

2 cos

t n

n

f=

20

sin sin

Materials characterization from simple rocking curve


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Simulations of Rocking curves


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Reciprocal Space Mapping RSM


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Qx

Qz

000

Substrate

RelaxedEpilayer

aS

a0F > aS


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Qx

Qz

000

Substrate

Strained

epilayerDifferentcomposition

aS

a0F > aS

Removes guesswork:Strained/non-strained


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Qx

Qz

000

Substrate

RelaxedEpilayer

aS

a0F > aS


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Triple axis multiple crystal diffractometer

Detector

sample


x-raysource

Analyzer(triple axisCrystal)

+ well collimated beam

= 0.001-0.008+ well monochromized beam

/ = 10-5 - 10-4

+ very good 2 resolution2 = 0.003

+ any crystal and reflection can be measured+ the shape af reciprocal lattice points can be recorded

- low intensity 200k - 3M ct/s in primary beam

2


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Multiple crystal optics High Resolution

point focusx-ray tube

detector

2

channel-cutGe 220 analyser

2~0.003

4-xtal Ge 220monochromator

~0.003

sample

Euleriancradle

(omega) = angle between incident beam and the sample surface2 (two theta) = angle between the incident and diffracted beams(psi) = sample tilt, about axis in the diffraction plane andthe sample surface (phi) = azimuthal rotation about sample normal

Diffractometer angles:


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Multiple crystal optics High Resolution

point focusx-ray tube

detector

2

channel-cutGe 220 analyser

2~0.003

4-xtal Ge 220monochromator

~0.003

sample

Euleriancradle

Epitaxial thin films

Substrate

Typically semiconductors:II-VI:s CdS, ZnSe, etc.III-V:s GaAs, AlAs, InP, etc.

GaN, AlN, InN, etc.IV:s SiGeSiC

and their alloyson highly perfect substrates


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Sampling volume

000




Ewalds sphere

(thickness ~)

2

2

A thin Ewalds shell

0

0

0


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Sampling volume

000




Ewalds sphere

(thickness ~)

2

2

A narrow Ewalds cigar

0

0

0

S li l i i l


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Sampling volumes in reciprocal spacewith 4-crystal monochromator & triple axis

grazing exit symetric grazing incidence

Mapping of reciprocal space possible bysuccessive 2/-scans each offset by

2/

2/

2=0.003 and

E.S.

2/


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Projection on reciprocal axes

Qx

Qz2/

2

Q//

Q

( )

( )//

//2

sinsin4

2

cossin

4

dQ

dQ

==

==


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Example of High Resolution RSM

ZnSe on GaAs

0.1680 0.1700

0.6860

0.6880

24102250

111247551

12282738GaAs1 1 5

ZnSe1 1 5

-0.0200 -0.0180

0.5410

0.5420

0.5430

0.5440

25

122867

159376

89021074990

004GaAs

004ZnSe

2/

2/

2/

Relaxed ZnSe layer

Somewhat tilted with respectto the GaAs substrate

Lattice parameters obtainedby projection to x-y and z - axes


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Shapes of the Reciprocal Lattice Points

Film = greySubstrate = blackScattering vector = red

Relaxed film peaks at relaxed QMisfit defects Broadening along surface

Mosaic relaxed film

Tilted crystallites circumferential broadening (purely )

Thin strained film

Thicknessbroadeningalong surfacenormal

Curved substrate circumferential broadening(Mosaic substrate multiple peaks)


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Examples of high resolution RSM

AlAs/AlGaAs/GaAs LED-structures

0

0.5435

0.5440

0.5445

0.5450

0.5455 26

1746

122324865

2307615416416

-0.0005 0.0005

AlAs

AlGaAsGaAs

Thin strained structure Thick stressed structurewafer bending

-0.0100 -0.0090

0.5430

0.5440

0.5450 2511266013932274717314009

GaAs

AlGaAs

AlAs

Reciprocal Lattice Units: 2d/


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3C-SiC epitaxially grown onto on-axis 6H-SiC

Symmetric reflections[111]3C

6H-SiC substrate 0006 reflection

3C-SiC film 111 reflection

Broad 3C 111 reflection lattice strain relaxation (MDs)stacking faultsstacking mismatch domains

?

[0006]6H

M. Beskova, M. Syvjrvi, et al., Mater.s Sci. Forum 615-617, 181, (2009)


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StackingFault

AB

CACB

AB

CA

BC A

B

CA

BC

70.53[-111]

[111]

ABC

A

diffraction

plane

70.53

Stacking faults in 3C SiC (111)/6H-SiC (0006)

6H SiC substrate

3C SiC epilayer

*A. Boulle et al. Journal of Crystal Growth 310 (2008) 982987

shape 111reciprocal

lattice point *

E l f hi h l i RSM


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M. Beskova, M. Syvjrvi, et al., Mater.s Sci. Forum in press (2009)

Stacking faults in 3C SiC (111)/6H-SiC (0006)

1113C

7055

Why 2 sets of streaksin the experiment?

HR RSM

Stacking Faults andDouble Positioning Domains (DPB) !

A

A

AA

A

BC

CBBC

BC

B

CAB

CA

BC

A

[111]3C

CC

C

AB

CAC

BBA

BA

B

ACB

AC

BA

C

[111]3C___

3D sampling volumecigar-shaped

F h R di


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Further Reading

D. K. Bowen & B. K. TannerHigh Resolution X-ray Diffractometry andTopography

Paul Fewster X-Ray Scattering fromSemiconductors

Documents

Birch - Characterization of Epitaxial Material by High Resolution X-ray Diffraction