Thin Film Scattering:Epitaxial Layers

5th Annual SSRL Workshop on Synchrotron X-ray Scattering Techniques in Materials and Environmental Sciences: Theory and Application

June 1 - 3, 2010

Arturas VailionisGLAM, Stanford University

SIMES, SLAC

• 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 we need channel analyzer

• What can we learn from reciprocal space maps

• SrRuO3 and La0.67Sr0.33MnO3 films 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 epitaxial Single crystal in perfect registry with the substrate that is also perfect.

Nearly perfect epitaxial Single 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 polycrystalline Crystalline 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”

Mosaic spread

Curvature

Relaxation

Inhomogeneity

Mismatch

Misorientation

Dislocation content

Thin films structural properties

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

What we want to know about thin films?

Thickness Composition Relaxation Distortion Crystalline size Orientation Defects

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

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

Overview of structural parameters that characterize various thin films

Beforedeposition

AfterdepositionR

L

RLL

RL

RLL

zz ddd

aaa −

=−

==⊥⊥

⊥ εε

Tetragonal Distortion

Lattice mismatch betweencubic lattice parameters:

S

SRL

aaa

aa −

=∆

Lattice mismatch induces lattice strain:

RLa

RLa

SaSa

Lc

SL aa =

SaSa

RLa

RLa

SaSa

0≠∆φ

0=∆φ

Relaxed

Strained, coherent, pseudomorphic

Partially relaxed

(000)

(00l)

(100)

(10l)

(200)

(20l)

Cubic: aL> aS

Cubic

Relaxed Layer

(000)

(00l)

(100)

(10l)

(200)

(20l)

Tetragonal:

CubicTetragonaldistortion

SL

SIIL

aaaa

>

=⊥

Strained Layer

Compressive strain

Cubic

Cubic

Cubic

Tetragonal

ReciprocalSpace

(000) (000)

(00l) (00l)

(hkl) (hkl)

aL > aS

Perfect Layers: Relaxed and Strained

Reciprocal space – Ewald sphere

θλθλ

sin22

121sin1 *

hklhkl

hkl dd

=→=== dOC

*hkldOB =

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

Reciprocal space – Scattering vector

Scan Directions

Sample Surface

(00l)

Symmetrical Scanθ - 2θ scan

θθ

2θ

(hkl)

Asymmetrical Scanω - 2θ scan

αα = θ − ω

ω

2θ

Sample Surface

(00l)

(hkl)

Scan Directions

(00l)

(hkl)

Symmetricalω - 2θ scan

Asymmetricalω - 2θ scan

Sample Surface

2θ scan

ω scanω scan

Scan Directions

Compressive strain

L

S

Tensile strain d-spacing variation Mosaicity

Finite thickness effect

cL < aScL > aS

Real RLP shapes

Mismatch

Si(004)

Si1-xGex(004)For cubic (001) oriented material the experimentally measured normal component of the mismatch:

The experimental mismatch, m⊥, can be related to the mismatch through the equation:

True lattice mismatch is:S

SRL

aaam −

=

where ν is Poisson ratio.For Si, ν = 0.28

2*

31

mm ≈

≈ν

( )( )θθ

θθθ∆+

∆+−=

∆

=

∆

=−

=⊥

⊥⊥

S

SS

S

S

dd

aa

aaam

sinsinsin

⊥+−

=−

= ma

aamS

SRL

νν

11

The composition of the A1-xBx alloy can be calculated from Vegard’s law:

( ) ( ) BARL xaaxxa +−= 1

AB

A

aaamx−

=

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

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

( )( )21

21

sinsin2 ωωλ

−−

=nnt

Layer Thickness

(000)

(00l)

(hkl)

Partially Relaxed + Mosaicity

(000)

(00l)

(hkl)

Partially Relaxed + Thin

(000)

(00l)

ω direction

ω-2θ direction

Mosaicity

Defined by receiving optics (e.g. slits) Defined by incident

optics – monochromator

S

L

Symmetrical scan

(000)

(00l)

ω direction

ω-2θ direction

Symmetrical Scan

receivingslit

analyzercrystal

mosaicity

receivingslit

analyzercrystal

d-spacing variation

Ge content: 50% 40% 30% 20% 10%

Triple axis diffractometry

Open detector

Triple axis

Open detector

Triple axis

(000)

(00l)(hkl)

SymmetricalScan

AsymmetricalScan

(000)

(00l)

(hkl)

(00l) scan

(h00) scan(h00)

ω-scan

ω-2θ scan

h-scan

l-scan

Relaxed SiGe on Si(001)

Shape of the RLP might provide much more information

Relaxed SiGe on Si(001)

(oo4) RLM

Si(004)

SiGe(004)

(004) (113)

(000)

(00l)(hkl)

ω-scan

ω-2θ scan

100×−−

=S

RL

SL

aaaaR

The relaxation is defined as:

Relaxation

Grazing incidence Grazing exit Symmetrical scan

To separate the layer tilt from the true splitting we can make grazing incidence and grazing exit measurements:

The effect of tilt on the peak splitting is reversed if the specimen is rotated by 180o about its surface normal.

The splitting due to mismatch will not be affected by such rotation

ϕθθ ∆+∆=∆ gi– grazing incidence

– grazing exitϕθθ ∆−∆=∆ ge

giθ∆ geθ∆ symθ∆

ϕθ −BBθ2 ϕθ +B Bθ2

Bθ2Bθ

Relaxation

Considering (tetragonal distortion):

φφφθθθ

∆+=∆+=

SL

SL

φ – angle between reflecting plane and the surface

LLL cba ≠=

we obtain cell constants for the (00l )-oriented layer:

2

22

sin2

cossin2

lkhla

lc

LL

LLL

+=

=

θλ

φθλ

−−

−−

=

νν

νν

121

12 LL

RL

aca

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

L

qz

L3

L2

L1∆qx

∆qzξ

ϕ

( )ξϕξ+

−=cos

cos

2

1

LL

ξϕ

cossin

2

3 −=LL

∆∆

=

=

∆+∆=

z

x

z

x

zx

qq

qq

qqL

tan

1

tan

1

223

ξ

ϕand

Lateral correlation length

222

1

1

zx qqL

L

+=

=

Microscopic tilt

qx

(000)

Analysis of Laterally Inhomogeneous Layers

∆ω

L

qz

(000)

∆qx1

∆qx2

∆ω

Analysis of Laterally Inhomogeneous Layers

21

2

2

1

1

11

2tan

2

2tan

2

xLxL

z

x

z

x

qqL

qq

qq

∆=

∆=

∆=

∆=∆

ωω

ω

If the contributing profiles have Gaussian shape:

21

21

212

122

21

222

1

222

1

ω

ω

ω

xx

zzz

xxx

xLnnxxn

qqL

qqq

qqq

qqq

∆−∆=

+∆−∆

=∆

∆+∆=∆

Two symmetrical reflections

Λ

t dhkl

Superlattices and Multilayers

Substrate

6

(000)

(00l)

10

(000)

(00l)

2

(000)

(00l)

4

(000)

(00l)

Superlattices and Multilayers

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

[1-10]

[110]

NGOLayer

3.85 3.86 3.87 3.88 3.89 3.90 3.91 3.92 3.93 3.94 3.95 3.96

SrTi

O3

NdG

aO3

LSA

T

La0.

67Sr

0.33

MnO

3

SrR

uO3

DyS

cO3

Pseudo-cubic lattice parameters:

Samples:

SrRuO3 on SrTiO3 and DyScO3

La0.67Sr0.33MnO3 on NdGaO3, LSAT, SrTiO3 and DyScO3

a b

c

γ

[1-10]

[110]

STOLayer

[100]

[001]

SrTiO3 (002)SrRuO3 (220)

Finite size fringes indicate well ordered films

ω – 2θ symmetrical scans

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2

H-K (rlu)

Inte

nsity

(a.u

.) LSMO(220)

SrTiO3 (002)

(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 for [110] growth

(0 0

1)

(1 -1 0)

a b

c

γ

Untwinned

(0 0

1)

+ (

1 -1

0)

(1 -1 0) + (0 0 1)

Twinned

Twinning in SrRuO3/SrTiO3

ab

OrthorhombicSrRuO3

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

High-Resolution Reciprocal Area Mapping

Substrate

Layer

Orthorhombic to Tetragonal Transition

Orthorhombic

Tetragonal

Cubic

Literature: 510-702 °C

Transition Orthorhombic to Tetragonal ~ 350 °C

Appl. Phys. Lett. 91, 071907 (2007)

O – T Structural Transition, (620) & (260) reflections

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

O – T 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

Appl. Phys. Lett. 91, 071907 (2007)

Appl. Phys. Lett. 93, 051909 (2008)

Compressive Stress Unit cell is orthorhombica ≠ b

a b

c

γ

Tensile Stress Unit cell is tetragonala = b

a b

c

γ

89.0

89.5

90.0

90.5

91.0

91.5

92.0

92.5

5.45

5.46

5.47

5.48

5.49

5.50

5.51

5.52

NGO LSAT STO DSO

γan

gle

(deg

)

aan

d b

latt

ice

par

amet

ers

(Å)

a b γ

C C T T[110] γ angle accommodates the stress along [1-10]

[1-10]

γ

a b

Substrate a (Å) b (Å) ab (Å) c (Å) Layer a (Å) b (Å) ab (Å) c (Å) γ (O)

NdGaO3 5.428 5.498 7.726 7.708 LSMO/NGO 5.477 5.513 7.725 7.707 89.32

LSAT 5.476 5.476 7.744 7.740 LSMO/LSAT 5.471 5.507 7.744 7.740 89.72

SrTiO3 3.905 LSMO/STO 5.480 5.483 7.809 7.809 90.87

DyScO3 5.444 5.721 7.897 7.904 LSMO/DSO 5.478 5.483 7.895 7.902 92.16

LSMO (O) 5.488 5.524 7.762 7.787

Strain (%)

NdGaO3 LSAT SrTiO3 DyScO3

along ab = -0.79along c = -1.02

along ab = -0.55along c = -0.60

along ab = 0.28along c = 0.28

along ab = 1.39along c = 1.48

Appl. Phys. Lett. 95, 152508 (2009)

Summary

Reciprocal space for epitaxial thin films is very rich.

Shape and positions of reciprocal lattice points with respect to the 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