1. X-ray Scattering from Thin Films
Experimental methods for thin films analysis using X-ray scattering
Conventional XRD diffraction
Glancing angle X-ray diffraction
X-ray reflectivity measurement
Grazing incidence X-ray diffraction
X-ray diffraction study of real structure of thin films
Phase analysis
Residual stress analysis
Crystallite size and strain determination
Study of the preferred orientation
Study of the crystal anisotropy 1

2. Conventional X-ray diffraction
Diffracting crystallites
+ Reliable information on
the preferred orientation of crystallites
the crystallite size and lattice strain (in one direction)
- No information on the residual stress (constant direction of the diffraction vector)
- Low scattering from the layer (large penetration depth) 2

3. Glancing angle X-ray diffraction GAXRD
Gold, CuKa,
m  4000 cm-1
Symmetrical mode
GAXRD 3

4. Other diffraction techniques used in the thin film analysis
Conventional diffraction with W-scanning
qy=0
Grazing incidence X-ray diffraction (GIXRD)
qz»0
Conventional diffraction with C-scanning
qx=0 4

5. Penetration depth of X-rays
L.G. Parratt, Surface Studies of Solids by Total Reflection of X-rays, Physical Review 95 (1954)
Example: Gold (CuKa)
d = 10-5
b = 10-6 5

6. X-ray reflectivity measurement
Calculation of the electron density, thickness and interface roughness for each particular layer
r t [Å] s [Å] Mo
Edge of TER Mo
Kiessig oscillations (fringes) Mo W Si
The surface must be smooth (mirror-like) 6

7. Experimental set-up Used for XRR, SAXS, GAXRD and symmetrical XRD
Scintillation
detector
Flat monochromator
Sample
Goebel mirror
X-ray source
Sample rotation, f
Normal direction
Diffraction vector
Diffraction angle, 2q
Angle of incidence, g
Sample inclination, y 7

8. Information on the microstructure of thin films
Phase analysis
Residual stress analysis
Crystallite size and strain determination
Study of the preferred orientation
Study of the anisotropy in the lattice deformation
Investigation of the depth gradients of microstructure parameters

9. Uranium nitride – phase analysis
Sample deposition
PVD in reactive atmosphere N2
Heated quartz substrate (300°C)
Phase composition
UN, mol.%
Fm3m, a = Å
U2N3, 10-20% mol.%
Ia3, a = Å
Schematic phase diagram
800
T(°C)
400 U UN
U2N3
UN2
Atomic Percent Nitrogen 9

10. Cannot be distinguished in thin films
U2N3 versus UN2
U2N3 (Ia3), a = Å
U: 8b (¼, ¼, ¼)
U: 24d (-0.018, 0, ¼)
N: 48e (0.38, 1/6, 0.398)
UN2 (Fm3m)
a = 5.31 Å
U: 4a (0, 0, 0)
N: 8c (¼, ¼, ¼)
Cannot be distinguished in thin films U N 10

11. Uranium nitride – residual stress analysisUN
a0 = (4.926 ± 0.015) Å
Compressive residual stress
s = - (1.8 ± 0.8) GPa
Strong anisotropy of lattice deformation
U2N3
a0 = ( ± 0.002) Å
Compressive residual stress
s = - (6.2 ± 0.1) GPa
No anisotropy of lattice deformation
GAXRD at g=3° 11

12. Uranium nitride – anisotropic lattice deformationUN
a0 = ( ± ) Å
s = - (1.0 ± 0.1) GPa
111
easy
hard
directions 12

13. UN – anisotropic lattice deformation
Dependence of the lattice deformation on the crystallographic direction
R.W. Vook and F. Witt, J. Appl. Phys., 36 (1965) 2169.
Related to the anisotropy of the elastic constants 13

14. UN versus U2N3 U N UN (Fm3m) a = 4.93 Å U: 4a (0, 0, 0)
N: 4b (½, ½, ½)
Anisotropy of the mechanical properties is related to the crystal structure
U2N3 (Ia3), a = Å
U: 8b (¼, ¼, ¼)
U: 24d (-0.018, 0, ¼)
N: 48e (0.38, 1/6, 0.398) U N 14

15. Methods for the size-strain analysis using XRD
Crystallite size
Fourier transformation of finite objects (with limited size)
Constant line broadening (with increasing diffraction vector)
Lattice strain
Local changes in the d-spacing
Line broadening increases with increasing q (a result of the Bragg equation in the differential form)
(011)
(011)
(111)
(111)
(001)
(001)
(110)
(110)
(000)
(100)
(000)
(100)
Scherrer Williamson-Hall Warren-Averbach Krivoglaz
P. Klimanek (Freiberg) R. Kuzel (Prague) P. Scardi (Trento) T. Ungar (Budapest) 15

16. UN – anisotropic line broadening
The Williamson-Hall plot
It recognises the anisotropy of the line broadening
It is robust (weak intensity, overlap of diffraction lines)
It is convenient if the higher-order lines are not available (nanocrystalline thin films, very thin films, GAXRD)
100
111 16

17. UN – texture measurement
Reciprocal space mapping
Preferred orientation {110} 17

18. Reciprocal space mapping-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 q x
[1/A] z
{111}
A highly textured gold layer
Measured using CuKa radiation 18

19. Epitaxial growth of SrTiO3 on Al2O3
SrTiO3: Fm3m 111  axis -3  001 Al2O3: R-3c
Reciprocal space map
Atomic ordering in direct space Sr
O in SrTiO3 Ti
O in Al2O3 Al 19

20. SrTiO3 on Al2O3 Atomic Force Microscopy
Pyramidal crystallites with two different in-plane orientations
111
111 _
110 _
110
AFM micrograph courtesy of Dr. J. Lindner, Aixtron AG, Aachen. 20

21. Depth resolved X-ray diffraction
TiC
TiN
TiN
TiC WC
TiCN
Absorption of radiation 21

22. Surface modification of thin films
Gradient of the residual stress in thin TiN coatings (CVD) implanted by metal ions: Y, Mo, W, Al and Cr 22

23. Functionally graded materials
W. Lengauer and K. Dreyer, J. Alloys Comp. 338 (2002) 194
Nitrogen – in-diffusion from N2
N-rich zone of (Ti,W)(C,N)  Ti(C,N)
N-poor zone of (Ti,W)(C,N)  (Ti,W)C
SEM micrograph courtesy of C. Kral, Vienna University of Technology, Austria 23

24. Study of concentration profiles
The lattice parameter must depend on concentration
Copper radiation
Penetration depth: 1.8 mm
Molybdenum radiation
Penetration depth: 12.5 mm 24

25. Summary Benefits of X-ray scattering
... for investigation of the real structure of thin films
Length scale between 10-2Å and 103Å is accessible (from atomic resolution to the layer thickness)
Small and variable penetration depth of X-ray into the solids (surface diffraction, study of the depth gradients)
Easy preparation of samples, non-destructive testing
Integral measurement (over the whole irradiated area) 25