Thin Film Scattering:Epitaxial Layers

First Annual SSRL Workshop on Synchrotron X-ray Scattering Techniques in Materials and Environmental Sciences: Theory and

Application

Tuesday, May 16 & Wednesday, May 17, 2006

Arturas Vailionis

• Thin films. Epitaxial thin films.• What basic information we can obtain from x-ray diffraction• Reciprocal space and epitaxial thin films• Scan directions – reciprocal vs. real space scenarios• Mismatch, strain, mosaicity, thickness• How to choose right scans for your measurements• Mosaicity vs. lateral correlation length• SiGe(001) layers on Si(001) example• Why sometimes we need channel analyzer• What can we learn from reciprocal space maps• SrRuO3(110) on SrTiO3(001) example• Summary

What is thin film/layer?

Material so thin that its characteristics are dominated primarily by two dimensional effects and are mostly different than its bulk propertiesSource: semiconductorglossary.com

A thin layer of something on a surfaceSource: encarta.msn.com

Material which dimension in the out-of-plane direction is much smaller than in the in-plane direction.

Epitaxial Layer

A single crystal layer that has been deposited or grown on a crystalline substrate having the same structural arrangement.Source: photonics.com

A crystalline layer of a particular orientation on top of another crystal, where the orientation is determined by the underlying crystal.

Homoepitaxial layerthe layer and substrate are the same material and possess the same lattice parameters.

Heteroepitaxial layerthe layer material is different than the substrate and usually has different lattice parameters.

Thin films structural types

Structure Type Definition

Perfect epitaxialSingle crystal in perfect registry with the substrate that is also perfect.

Nearly perfect epitaxialSingle crystal in nearly perfect registry with the substrate that is also nearly perfect.

Textured epitaxialLayer orientation is close to registry with the substrate in both in-plane and out-of-plane directions. Layer consists of mosaic blocks.

Textured polycrystallineCrystalline grains are preferentially oriented out-of-plane but random in-plane. Grain size distribution.

Perfect polycrystalline Randomly oriented crystallites similar in size and shape.

Amorphous Strong interatomic bonds but no long range order.

P.F. Fewster “X-ray Scattering from Semiconductors”

What we want to know about thin films?

Crystalline state of the layers:Epitaxial (coherent with the substrate, relaxed)Polycrystalline (random orientation, preferred orientation) Amorphous

Crystalline quality

Strain state (fully or partially strained, fully relaxed)

Defect structure

Chemical composition

Thickness

Surface and/or interface roughness

Thickness Composition Relaxation DistortionCrystalline

sizeOrientation Defects

Perfect epitaxy × × ×Nearly perfect epitaxy × × ? ? ? × ×Textured epitaxy × × × × × × ×Textured polycrystalline × × ? × × × ?Perfect polycrystalline × × × × ?Amorphous × ×

Overview of structural parameters that characterize various thin films

P.F. Fewster “X-ray Scattering from Semiconductors”

(000)

(00l)

(100) (200)

(10l) (20l)

Cubic: aL> aS

Cubic

Relaxed Layer

aL

aL aL=aS

aS

aS

cL

aS

aS

Beforedeposition

Afterdeposition

0

0

Lz

Lz

Lz

zz ddd −

==⊥ εε

Tetragonal Distortion

(000)

(00l)

(100) (200)

(10l) (20l)

Tetragonal: aIIL = aS, a⊥

L > aS

Cubic

Strained Layer

Tetragonaldistortion

Cubic

Cubic

Cubic

Tetragonal

ReciprocalSpace

(000)

(00l)

(hkl)

(000)

(00l)

(hkl)

aL > aS

Perfect Layers: Relaxed and Strained

Scan Directions

Incident beam

Diffracted beam Scattering

vectorhkl

hkl d1sin2 * ===

− dss 0

λθ

λλ

0ss −

λs

λ0s

θθθλ sin2 hkld=

Reciprocal Lattice Point

(000)

(00l)

(hkl)

SymmetricalScan

AsymmetricalScan

(000)

(00l)

(hkl)

(00l) scan

(h00) scan

(h00)

(-hkl)

(00l) scan

Relaxed Layer Strained Layer

Sample Surface

(00l)

Symmetrical Scanθ - 2θ scan

θθ

2θ

(hkl)

Asymmetrical Scanω - 2θ scan

αα = θ − ω

ω

2θ

Scan Directions

Sample Surface

(00l)

(hkl)

Scan Directions

(00l)

(hkl)

Symmetricalω - 2θ scan

Asymmetricalω - 2θ scan

Sample Surface

2θ scan

Scan directions

ω scanω scan

Homoepitaxy

L

S

HeteroepitaxyTensile stress

Heteroepitaxyd-spacing variation

HeteroepitaxyMosaicity

Finite thickness effect

cL < aS

Real RLP shapes

(000)

(00l)

(hkl)

PartiallyRelaxed + Mosaicity

(000)

(00l)

(hkl)

Partially Relaxed

(000)

(00l)

ω direction

ω-2θ direction

Defined by receiving optics (e.g. slits)

Mosaicity

(000)

(00l)

ω direction

ω-2θ direction

Symmetrical Scan

receivingslit

analyzercrystal

mosaicity

receivingslit

analyzercrystal

d-spacing variation

44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.52Theta/Omega (°)

0.1

1

10

100

1K

10K

100K

1Mcounts/s

With receiving slitWith channel analyzer

(002)SrTiO3

(220)SrRuO3

65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 70.0 70.52Theta/Omega (°)

0.1

1

10

100

1K

10K

100K

1M

10Mcounts/s

Si(004)

SiGe(004)

The peak separation between substrate and layer is related to the change of interplanarspacing normal to the substrate through the equation:

Mismatch

θδθδ cot−=dd

If it is (00l) reflection then the “experimental x-ray mismatch”:

dd

aam δδ

==*

True lattice mismatch is:S

SL

aaam −

=

⎭⎬⎫

⎩⎨⎧

+−

=νν

11*mm

And true mismatch can be obtained through:

where: ν – Poisson ratio 2*

31

mm ≈

≈ν

6 5 .5 6 6 .0 6 6 .5 6 7 .0 6 7 .5 6 8 .0 6 8 .5 6 9 .0 6 9 .5 7 0 .02 The ta /O m e g a (°)

1 0 0

1 K

1 0 K

1 0 0 K

1 M

1 0 Mco unts /s

S

L

F

F

F

F

F

F

F

F

FF

F

F

F

F

F

F

F

F

Interference fringes observed in the scattering pattern, due to different optical paths of the x-rays, are related to the thickness of the layers

( )( )

Substrate Layer SeparationS-peak: L-peak: Separation: Omega(°) 34.5649 Omega(°) 33.9748 Omega(°) 0.590172Theta(°) 69.1298 2Theta(°) 67.9495 2Theta(°) 1.18034

Layer ThicknessMean fringe period (°): 0.09368 Mean thickness (um): 0.113 ± 0.003

2Theta/Omega (°) Fringe Period (°) Thickness (um) _____________________________________________________________________________

66.22698 - 66.32140 0.09442 0.11163766.32140 - 66.41430 0.09290 0.11352866.41430 - 66.50568 0.09138 0.11548166.50568 - 66.59858 0.09290 0.11364866.59858 - 66.69300 0.09442 0.11187866.69300 - 66.78327 0.09027 0.117079

Layer Thickness

21

21

sinsin2 ωωλ

−−

=nnt

Relaxed SiGe on Si(001)

64 65 66 67 68 69 70 71 72 73 742Theta/Omega (°)

0.1

1

10

100

1K

10K

100K

1M

10Mcounts/s

0 0 4Omega 34.565502Theta 69.13090

Phi 0.00Psi 0.00

X 0.00Y 0.00 013106c_TA.xrdml

Shape of the RLP might provide much more information

(000)

(00l)(hkl)

SymmetricalScan

AsymmetricalScan

(000)

(00l)

(hkl)

(00l) scan

(h00) scan(h00)

ω-scan

ω-2θ scan

h-scan

l-scan

64 65 66 67 68 69 70 71 72 73 742Theta/Omega (°)

0.1

1

10

100

1K

10K

100K

1M

10Mcounts/s

0 0 4Omega 34.565502Theta 69.13090

Phi 0.00Psi 0.00

X 0.00Y 0.00 013106c_TA.xrdml

Relaxed SiGe on Si(001)

66

67

68

69

7(oo4) RLM

Si(004)

SiGe(004)

(004) (113)

(000)

(00l)(hkl)

ω-scan

ω-2θ scan

The mosaic spread of the layer is calculated from the angle thatthe layer peak subtends at the origin of reciprocal space measured perpendicular to the reflecting plane normal.

The lateral correlation length of the layer is calculated from the reciprocal of the FWHM of the peak measured parallel to the interface.

Mosaic Spread and Lateral Correlation Length

The Mosaic Spread and Lateral Correlation Length functionality derives information from the shape of a layer peak in a diffraction space map recorded using an asymmetrical reflection

LC

MS

To OriginQZ

QX

Λ

t dhkl

Superlattices and Multilayers

Substrate

6

(000)

(00l)

10

(000)

(00l)

2

(000)

(00l)

4

(000)

(00l)

Superlattices and Multilayers

61 62 63 64 65 66 67 68 69 70 712Theta/Omega (°)

10

100

1K

10K

100K

1M

10Mcounts/s

0 0 4Omega 33.006502Theta 66.01310

Phi 0.00Psi 0.00

X 0.00Y 0.00 3683ssl.xrdml

a = 5.586 Åb = 5.555 Åc = 7.865 Å

a = 5.578 Åc = 7.908 Å

a = 3.956 Å

275-550 °C 510-702 °C

Orthorhombic Tetragonal Cubic

Structure of SrRuO3

SrRuO3

SrTiO3

(110)

(001)

(1-10)

(001)

(010)

(100)

(2 6 0)(4 4 4)(6 2 0)

(4 4 –4)

(2 2 0)

(0 0 2)(-2 0 4) (2 0 4)

ω – 2θ scan Reciprocal Space Map

Q scan

SrTiO3

SrRuO3

ab

OrthorhombicSrRuO3

TetragonalSrRuO3

X-ray Diffraction Scan Types

4 5 .4 4 5 .6 4 5 .8 4 6 .0 4 6 .2 4 6 .4 4 6 .6 4 6 .8 4 7 .02 The ta /O m e g a (°)

1

1 0

1 0 0

1 K

1 0 K

1 0 0 K

co unts /s

4 5 .4 4 5 .6 4 5 .8 4 6 .0 4 6 .2 4 6 .4 4 6 .6 4 6 .82 The ta /O m e g a (°)

0 .1

1

1 0

1 0 0

1 K

1 0 K

1 0 0 K

co unts /s

Thickness3100 Å

SrTiO3 (002)SrRuO3 (220)

SrTiO3 (002)

SrRuO3 (220)

Thickness3200 Å

Finite size fringes indicate well ordered films

ω – 2θ symmetrical scans

φ angle0o 90o 180o 270o

(2 2 0)

(0 0 2)

ω – 2θ scan

SrTiO3

SrRuO3

Reciprocal Lattice Map ofSrRuO3 (220) and SrTiO3 (002)

Substrate

Layer

5.53 Å 5.58 Å

Distorted perovskite structure:

Films are slightly distorted from orthorhombic, γ = 89.1° – 89.4°

γ

(110)

(110)

(100) (010)

ab

OrthorhombicSrRuO3

(260) (444) (620) (444)

High-Resolution Reciprocal Area Mapping

Substrate

Layer

Orthorombic to Tetragonal Transition

Orthorhombic

Tetragonal

Cubic

Literature: 510-702 °C

Transition Orthorhombic to Tetragonal ~ 350 °C

Temperature ( oC)

150 200 250 300 350 400

Inte

nsity

(arb

uni

ts)

0.0

0.2

0.4

0.6

0.8

1.0

Structural Transition, (221) reflection

Orthorhombic

Tetragonal

Cubic

Literature: 510-702 °C

Transition Orthorhombic to Tetragonal ~ 310 °C

O – TTransition

(221) Peak

Orthorhombic Present

Tetragonal Absent

Transition Orthorhombic to Tetragonal ~ 310 °C

α

Rotation Angle (deg)

0 2 4 6 8 10 12 14 16

Cal

cula

ted

Inte

nsity

(arb

uni

ts)

0

10000

20000

30000

40000

50000

60000

(211) peak is absent in cubic SrRuO3

Structural Transition, (211) reflection

Temperature (oC)

200 300 400 500 600 700

Inte

nsity

(a.u

.)

550 600 650 700

Orthorhombic

Tetragonal

Cubic

Attempt forT – C Transition ?

O – T Transition = 310 oC

Structural Transition, (211) reflection

We used (620), (260), (444), (444), (220) and (440) reflections for refinement

240.0

240.5

241.0

241.5

242.0

242.5

PLD 1(3)

PLD 2(3)

PLD 3(4)

PLD 4(5)

MBE 1(10)

MBE 2(18)

MBE 3(26)

MBE 4(40)

MBE 5(60)

Vo

lum

e (

Å)

MBE

PLD

Sample #(RRR)

a b c a b g VPLD 1 5.583 5.541 7.807 90.0 90.0 89.2 241.52PLD 2 5.583 5.541 7.811 90.0 90.0 89.2 241.61PLD 3 5.590 5.544 7.809 90.0 90.0 89.1 242.03PLD 4 5.583 5.541 7.810 90.0 90.0 89.2 241.61MBE 1 5.572 5.534 7.804 90.0 90.0 89.4 240.64MBE 2 5.577 5.528 7.808 90.0 90.0 89.4 240.70MBE 3 5.578 5.530 7.812 90.0 90.0 89.4 240.98MBE 4 5.577 5.530 7.811 90.0 90.0 89.4 240.88MBE 5 5.574 5.531 7.806 90.1 90.1 89.4 240.63Bulk 5.586 5.550 7.865 90.0 90.0 90.0 243.85

Refined Unit Cells

Summary

Reciprocal space for epitaxial thin films is very rich.

Shape and positions of reciprocal lattice points with respect tothe substrate reveal information about:

• Mismatch• Strain state• Relaxation• Mosaicity• Composition• Thickness ….

Diffractometer instrumental resolution has to be understood before measurements are performed.

PolycrystallinePreferred orientationSingle crystal