1. Tuesday, May 15 - Thursday, May 17, 2007
Thin Film Scattering:
Epitaxial Layers
Second Annual SSRL Workshop on Synchrotron X-ray Scattering Techniques in Materials and Environmental Sciences: Theory and Application
Tuesday, May 15 - Thursday, May 17, 2007

2. 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

3. 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 properties
Source: semiconductorglossary.com
Material which dimension in the out-of-plane direction is much smaller than in the in-plane direction.
A thin layer of something on a surface
Source: encarta.msn.com

4. 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 layer
the layer and substrate are the same material and possess the same lattice parameters.
Heteroepitaxial layer
the layer material is different than the substrate and usually has different lattice parameters.

5. 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 epitaxial
Layer 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”

6. 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

7. Overview of structural parameters that characterize various 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”

8. Relaxed Layer Cubic: aL> aS Cubic (00l) (10l) (20l) (000) (100)
(200)
Cubic: aL> aS
Cubic

9. Tetragonal DistortioncL aL
aL=aS aS aS aS aS
Before
deposition
After
deposition

10. Strained Layer Tetragonal: aIIL = aS, aL > aS Tetragonal
(000)
(100)
(200)
Tetragonal: aIIL = aS, aL > aS
Tetragonal
distortion
Cubic

11. Perfect Layers: Relaxed and Strained
(hkl)
(hkl)
Reciprocal
Space
(000)
(000)
aL > aS
Cubic
Tetragonal
Cubic
Cubic

12. Scan Directions Reciprocal Lattice Point q q Symmetrical Scan
Diffracted beam
Incident beam
Scattering
vector q q
(000)
(00l)
(hkl)
Symmetrical
Scan
Asymmetrical
(00l) scan
(h00) scan
(h00)
(-hkl)
Relaxed Layer
Strained Layer

13. Scan Directions Symmetrical Scan q - 2q scan q 2q Asymmetrical Scan
(hkl)
Asymmetrical Scan
w - 2q scan a
a = q - w w 2q
Sample Surface

14. (00l)
Scan Directions
(hkl)
Sample Surface

15. Scan directions w scan w scan 2q scan Symmetrical w - 2q scan
(hkl)
w scan
w scan
2q scan
Symmetrical
w - 2q scan
Asymmetrical
w - 2q scan
Sample Surface

16. Real RLP shapes cL < aS Finite thickness effect L S Homoepitaxy
Heteroepitaxy
Tensile stress
Heteroepitaxy
d-spacing variation
Heteroepitaxy
Mosaicity

17. Partially Relaxed Partially Relaxed + Mosaicity (00l) (00l) (hkl)
(000)
(00l)
(hkl)
Partially Relaxed
(00l)
(hkl)
(000)
Partially
Relaxed + Mosaicity

18. Defined by receiving optics (e.g. slits)
w-2q direction
(00l)
Defined by receiving optics (e.g. slits)
w direction
Mosaicity
(000)

19. Symmetrical Scan receiving slit analyzer crystal d-spacing variation
mosaicity
Symmetrical Scan
(000)
(00l)
w direction
w-2q direction

20. (002)
SrTiO3
With receiving slit
With channel analyzer
(220)
SrRuO3

21. Mismatch True lattice mismatch is:
Si(004)
SiGe(004)
The peak separation between substrate and layer is related to the change of interplanar spacing normal to the substrate through the equation:
If it is (00l) reflection then the “experimental x-ray mismatch”:
And true mismatch can be obtained through:
where: n – Poisson ratio

22. Layer Thickness
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 Separation
S-peak: L-peak: Separation:
Omega(°) Omega(°) Omega(°)
2Theta(°) Theta(°) Theta(°)
Layer Thickness
Mean fringe period (°):
Mean thickness (um): ± 0.003
2Theta/Omega (°) Fringe Period (°) Thickness (um)
_____________________________________________________________________________

23. Relaxed SiGe on Si(001)
Shape of the RLP might provide much more information

24. w-scan h-scan w-2q scan l-scan Symmetrical Asymmetrical Scan Scan
(hkl)
(00l)
(hkl)
Symmetrical
Scan
Asymmetrical
Scan
(000)
(h00)
(000)
(h00) scan

25. Relaxed SiGe on Si(001)
(oo4) RLM
Si(004)
SiGe(004)

26. w-scan
w-2q scan
(00l)
(hkl)
(000)
(004)
(113)

27. 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
The mosaic spread of the layer is calculated from the angle that the 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. MS
To Origin QZ LC QX

28. Superlattices and Multilayers
dhkl
Substrate

29. Superlattices and Multilayers2
(000)
(00l) 4
(000)
(00l) 6
(000)
(00l) 10
(000)
(00l)

32. Orthorhombic Tetragonal Cubic
Structure of SrRuO3
Orthorhombic Tetragonal Cubic
a = Å
b = Å
c = Å
a = Å
c = Å
a = Å C C

33. (110)
(001)
SrRuO3
(1-10)
(001)
(010)
SrTiO3
(100)

34. X-ray Diffraction Scan Types
w – 2q scan
Reciprocal Space Map
Q scan
(-2 0 4)
(0 0 2)
SrTiO3
(2 0 4)
(2 2 0)
SrRuO3
(2 6 0)
(4 4 4)
(6 2 0)
(4 4 –4)
Tetragonal
SrRuO3
Orthorhombic
SrRuO3 a b

35. Finite size fringes indicate well ordered films
w – 2q symmetrical scans
SrTiO3 (002)
Thickness
3200 Å
SrRuO3 (220)
Finite size fringes indicate well ordered films
SrTiO3 (002)
Thickness
3100 Å
SrRuO3 (220)

36. Reciprocal Lattice Map of SrRuO3 (220) and SrTiO3 (002)
w – 2q scan
(0 0 2)
SrTiO3
Distorted perovskite structure:
Films are slightly distorted from orthorhombic, g = 89.1 – 89.4
(2 2 0)
SrRuO3
f angle
0o o o o
Substrate
5.53 Å
5.58 Å g
(110)
(100)
(010)
Layer

37. High-Resolution Reciprocal Area Mappingb
Orthorhombic
SrRuO3
Substrate
Layer
Orthorombic to Tetragonal Transition
(260) (444) (620) (444)

38. Transition Orthorhombic to Tetragonal ~ 350 C
Cubic
Literature: C
Transition Orthorhombic to Tetragonal ~ 350 C

39. Structural Transition, (221) reflection
(221) Peak
Orthorhombic
Present
Tetragonal
Absent
O – T
Transition
Tetragonal
Orthorhombic
Cubic
Literature: C
Transition Orthorhombic to Tetragonal ~ 310 C
Transition Orthorhombic to Tetragonal ~ 310 C

40. Structural Transition, (211) reflection
(211) peak is absent in cubic SrRuO3 a

41. Structural Transition, (211) reflection
O – T Transition = 310 oC
Tetragonal
Attempt for
T – C Transition ?
Orthorhombic
Cubic

42. Refined Unit Cells
We used (620), (260), (444), (444), (220) and (440) reflections for refinement a b c g V
PLD 1
5.583
5.541
7.807
90.0
89.2
241.52
PLD 2
7.811
241.61
PLD 3
5.590
5.544
7.809
89.1
242.03
PLD 4
7.810
MBE 1
5.572
5.534
7.804
89.4
240.64
MBE 2
5.577
5.528
7.808
240.70
MBE 3
5.578
5.530
7.812
240.98
MBE 4
240.88
MBE 5
5.574
5.531
7.806
90.1
240.63
Bulk
5.586
5.550
7.865
243.85
242.5
242.0
PLD
241.5
Volume (Å)
241.0
MBE
240.5
240.0
Sample #
(RRR)
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)

43. 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.

44. Preferred orientation
Single crystal
Polycrystalline