### X-ray diffraction and X-ray reflectivity applied to

```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
–
–
–
–
–
1
Phase analysis
Residual stress analysis
Crystallite size and strain determination
Study of the preferred orientation
Study of the crystal anisotropy
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
Glancing angle X-ray diffraction
GAXRD
Symmetrical mode
GAXRD
Penetration depth (mm)
t:
10
sin  i  sin  o
dI
1
 I 0 ; xe 
dz
e
m sin  i  sin  o 
Gold, CuKa,
m  4000 cm-1
0
a=2Q/2
o
a=20
o
a=10
o
10
a=5
-1
o
a=2
a=1
10
-2
0
20
40
60
80
100
o
Diffraction angle ( 2Q)
3
o
120
140
Other diffraction techniques used in
the thin film analysis
Conventional diffraction
with W-scanning
qy=0
Conventional diffraction
with C-scanning
qx=0
4
Grazing incidence X-ray
diffraction (GIXRD)
qz0
Penetration depth of X-rays
L.G. Parratt, Surface Studies of Solids by Total Reflection of X-rays, Physical Review
95 (1954) 359-369.

2
 1-
re 

2
0
10
re 2
n  1 e  f 0  f  - if 
2
n  1 - d  ib  1
TER
Reflectivity
Example: Gold (CuKa)
10-5
d = 4.2558
b = 4.5875 10-6
nV cos  n j cos j
re 2
 c2
1  12
2
5
; n j  cos c
; c 
re 2

-2
10
-1

10
-2
10
-3
10
-3
10
-4
0.0
0.5
1.0
1.5
2.0
o
Glancing angle ( 2Q)
2.5
3.0
10
Penetration depth ( mm)
n  1   1
-1
10
2
X-ray reflectivity measurement
Calculation of the electron density, thickness and interface roughness for
each particular layer

t [Å] s [Å]
6
10
Edge of TER
Mo
0.68
19.6
5.8
Mo
0.93 236.5 34.0
Mo
W
1.09
1.00
Si
1.00
5
Intensity (a.u.)
10
Kiessig oscillations (fringes)
4
10
3
10
2
10
1
10
0
10
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
5,0
14.1
5.0
2.7
2.7
2.8
o
Diffraction angle ( 2)
6
The surface must be smooth
(mirror-like)
Experimental set-up
Used for XRR,
SAXS, GAXRD and
symmetrical XRD
Angle of
incidence, g
Sample
Sample
inclination, y
Diffraction
angle, 2
Scintillation
detector
Sample
rotation, f
X-ray source
Diffraction vector
Normal direction
Flat monochromator
7
Goebel mirror
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
microstructure
parameters
Uranium nitride – phase analysis
GAXRD with g = 3
o
Sample deposition
600
PVD in reactive atmosphere N2
Heated quartz substrate (300°C)
400
Phase composition
200
1.
0
40
60
80
100
120
o
140
10
2.
311, UN
222, UN
622, U2N3
220, UN
440, U2N3
2
Substrate
10
400, U2N3
200, UN
3
111, UN
10
222, U2N3
Intensity (cps)
Diffraction angle ( 2)
UN, 80-90 mol.%
Fm3m, a = 4.8897 Å
U2N3, 10-20% mol.%
Ia3, a = 10.64 - 10.68 Å
Schematic phase diagram
800
T(°C)
U
1
UN
UN2
20
U2N3
Intensity (cps)
800
400
20
9
30
40
50
o
Diffraction angle ( 2)
60
70
0
Atomic Percent Nitrogen
50
60
67
U2N3 versus UN2
U2N3 (Ia3), a = 10.66 Å
U: 8b (¼, ¼, ¼)
U: 24d (-0.018, 0, ¼)
N: 48e (0.38, 1/6, 0.398)
Cannot be
distinguished
in thin films
U
N
10
UN2 (Fm3m)
a = 5.31 Å
U: 4a (0, 0, 0)
N: 8c (¼, ¼, ¼)
Uranium nitride – residual stress
analysis
10.82
4.91
0.0
0.2
0.4
2
sin y
0.6
0.8
10.74
0.00
0.04
a0 = (4.926 ± 0.015) Å
Compressive residual stress
s = - (1.8 ± 0.8) GPa
Strong anisotropy of lattice
deformation
11
0.12
0.16
0.20
2
sin Y
U2N3
UN




0.08
622
10.76
440
531
442
440
511
422
331
420
400
311
222
220
4.92
10.78
400
4.93
10.80
222
-10
Lattice parameter (10 m)
4.94
111
200
Lattice patameter (Å)
4.95
GAXRD
at g=3°




a0 = (10.636 ± 0.002) Å
Compressive residual stress
s = - (6.2 ± 0.1) GPa
No anisotropy of lattice
deformation
Uranium nitride – anisotropic lattice
deformation
Measured
Calculated
4.94
 2
( p )
g ( b )db
hk  
2
2
0 1 - (siny sin f sin b  cosy cosf )

4.93
UN
531
442
0.8
10.78
4.94
10.74
0.00 0.05 0.10 0.15 0.20
4.93
0.2
331
420
400
4.92
4.91
0.0
12
10.76
311
222
directions
10.80
220
hard
easy
10.82
111
200
111
Lattice patameter (Å)
4.95
0.4
2
sin y
0.6
531
442
440
511
0.6
440
2
sin y
511
0.4
422
331
420
400
311
222
0.2
 a0 = (4.9270 ± 0.0015) Å
 s = - (1.0 ± 0.1) GPa
422
4.91
0.0
220
4.92
111
200
Lattice patameter (Å)
4.95
0.8
-3
1.04
1.00
111, 222, 333
331
442
220, 440, 422
531
511
0.88
311, 420
0.96
200, 400, 600
-2e3/e1 = 2n/(n-1)
1.08
0.92
Relative deformation (10 )
UN – anisotropic lattice deformation
0.84
0.0
0.2
0.4
2 2
22
0.6
0.8
2 2
2
1.0
2
5
422
511
4
3
2
1
0
-1
0.0
0.1
2 2
R.W. Vook and F. Witt, J.
Appl. Phys., 36 (1965) 2169.
Related to the anisotropy of the
elastic constants
13
0.2
0.3
0.4
sin Y
2
0.5
6
-3
Dependence of the lattice
deformation on the
crystallographic direction
Relative deformation (10 )
3G = 3(h k +k l +l h ) / (h +k +l )
440
531
442
4
2
0
-2
-4
0.0
0.2
0.4
sin Y
2
0.6
0.8
UN versus U2N3
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
U
N
14
U2N3 (Ia3), a = 10.66 Å
U: 8b (¼, ¼, ¼)
U: 24d (-0.018, 0, ¼)
N: 48e (0.38, 1/6, 0.398)
Methods for the size-strain
analysis using XRD
Crystallite size
Lattice strain
 Fourier transformation of finite
objects (with limited size)
increasing diffraction vector)
 Local changes in the d-spacing
increasing q (a result of the Bragg
equation in the differential form)
(011)
(111)
(001)
(011)
(111)
(001)
(110)
(000)
Scherrer
(100)
Williamson-Hall
P. Klimanek (Freiberg)
15
R. Kuzel (Prague)
(110)
(000)
Warren-Averbach
P. Scardi (Trento)
(100)
Krivoglaz
T. Ungar (Budapest)
40
D = 40 nm
The Williamson-Hall plot
100
30
 It recognises the anisotropy of the
20
 It is robust (weak intensity, overlap
of diffraction lines)
-3
e = 11x10
-3
0.2
0.8
 It is convenient if the higher-order
lines are not available
(nanocrystalline thin films, very
thin films, GAXRD)
440
531600/442
331
420
0.6
0.4
sin Q
16
400
222
220
0
0.0
311
10
422
511/333
111
111
200
-1
1.0
UN – texture measurement
Reciprocal space mapping
400
5
q z (1/Å)
Integral intensity (a.u.)
50
(220)
(311)
40
30
222
311
4
222 311
3
20
200
10
111
2
200
0
-30
-20
-10
0
10
20
-3
30
Sample inclination (deg)
Preferred orientation {110}
17
220
220
qx 
2

-2
111
-1
0
q x (1/Å)
cos o - cos i 
; qz 
qy  0
1
2

sin  o  sin  i 
Reciprocal space mapping
A highly textured gold layer
9
3 3 3
8
8
422
4 2 2
7
7
5 1 1
331
3 3 1
qz [1/A]
4 2 0
2 2 2
420
5
4
6
222
6
5 -1 1
3 3 -1
3 1 1
4 -2 2
4 0 0
2 2 0
311
5
4
33-1
111
220
3
5 -1 -1
3 -1 1
1 1 1
2
4 -2 0
-2 2 2
2 0 0
1
-3 3 1
3 -1 -1
-1 1 1
0
-8
18
4 -2 -2
-7
-7
-5
-4
-3
qx [1/A]
-2
-6
-5
-4
-3
q(x), 1/A
-2 2 0
-6
-1
0
3
4-22
1
Measured using
-2
-1
0
1
2
q(z), 1/A
{111}
Epitaxial growth of SrTiO3 on Al2O3
SrTiO3: Fm3m 111  axis -3  001 Al2O3: R-3c
Reciprocal space map
Atomic ordering in direct
space
121
211
q(y)
121
_
118
018
211
_
108
112
Sr
900
800
700
600
500
400
300
200
100
Ti
112
O in Al2O3
b
O in SrTiO3
Al
Powde r Ce l l 1. 0
c
q(x)
19
a
c
b
a
Powde r Ce l l 1. 0
SrTiO3 on Al2O3
Atomic Force Microscopy
Pyramidal crystallites with two
different in-plane orientations
111
_
110
111
_
110
AFM micrograph courtesy of Dr. J. Lindner,
Aixtron AG, Aachen.
20
Depth resolved X-ray diffraction
TiN
TiC
TiN
TiCN
TiC
TiN
WC
Intensity (a.u.)
90
g = 10
o
g= 8
60
o
g= 6
45
o
g= 4
30
o
g= 2
123
124
125
126
127
o
Diffraction angle ( 2Q)
21

sin a  sin b 



dz
p
z
exp
m
z

0
sin
a

sin
b


p  t

sin a  sin b 

exp
m
z
0  sin a  sin b dz
t
75
122
o
128
129
Surface modification of thin films
Residual stress (GPa)
35keV, 10 cm
35keV, 10 cm
-2
-3
265 nm
0
0
1000 nm
-3
1
10
Angle of incidence (deg)
22
1
10
-1
-2
270 nm
-3
-4
1
10
Angle of incidence (deg)
-1
stress in thin TiN coatings
(CVD) implanted by metal
ions: Y, Mo, W, Al and Cr
-1
-2
-3
1170 nm
-4
-1
C VD TiN , C r-im planted
70keV, 10 cm
-2
-4
250 nm
17
-1
-1
17
-2
-3
C VD TiN , W -im planted
35keV, 10 cm
Angle of incidence (deg)
C VD TiN , A l-im planted
70keV, 10 cm
0
-1
-1
-4
1
10
Angle of incidence (deg)
17
C VD TiN , M o-im planted
17
-1
-4
Residual stress (GPa)
0
-1
Residual stress (GPa)
17
Residual stress (GPa)
C VD TiN , Y-im planted
Residual stress (GPa)
0
1
10
Angle of incidence (deg)
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
Study of concentration profiles
The lattice parameter must depend on concentration
4.24
15
4.26
~TiC0.3N0.7
4.27
0.0
10
0.5
1.0
1.5
Depth ( mm)
5
124
126
128
o
Diffraction angle 2
Penetration depth: 1.8 mm
24
4.28
~TiC0.75N0.25
20
0
2
4
6
Depth ( mm)
4.30
8
10
0
0
122
4.26
30
Intensity (cps)
a (Å)
Intensity (cps)
4.25
a (Å)
4.24
TiN
TiN
20
130
26.0
26.5
27.0
27.5
o
Diffraction angle ( 2)
Penetration depth: 12.5 mm
28.0
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