Upload
jena-craley
View
231
Download
2
Embed Size (px)
Citation preview
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
2
Conventional X-ray diffraction
+ 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)
Diffracting crystallites
3
Glancing angle X-ray diffraction GAXRD
0 20 40 60 80 100 120 140
10-2
10-1
100
=2/2
=20o
=10o
=5o
=2o
=1o
Pe
net
ratio
n d
epth
(m
)
Diffraction angle (o2)
Gold, CuK, 4000 cm-1
oi
oiexe
Idz
dIt
sinsin
sinsin;
1: 0
Symmetrical modeGAXRD
4
Other diffraction techniques used in the thin film analysis
Conventional diffraction with -
scanningqy=0
Grazing incidence X-ray diffraction
(GIXRD)qz0
Conventional diffraction with -
scanningqx=0
5
Penetration depth of X-rays
L.G. Parratt, Surface Studies of Solids by Total Reflection of X-rays, Physical Review 95 (1954) 359-369.
Example: Gold (CuK)
= 4.2558 10-5
= 4.5875 10-6
112
1
21
211
0
2
2
in
fiffr
n
rn
ee
e
0.0 0.5 1.0 1.5 2.0 2.5 3.0
10-3
10-2
10-1
100
Ref
lect
ivity
0.0 0.5 1.0 1.5 2.0 2.5 3.010
-4
10-3
10-2
10-1
TER
Pe
netr
atio
n d
ep
th (m
)
Glancing angle (o2)
222
;2
12
1
cos;coscos
ec
ce
cjjjV
rr
nnn
6
X-ray reflectivity measurement
0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,010
0
101
102
103
104
105
106
Inte
nsity
(a.
u.)
Diffraction angle (o2)
Si
Mo
Mo
Mo
t [Å] [Å]
0.68 19.6 5.8
0.93 236.5 34.0
1.09 14.1 2.71.00 5.0 2.7
1.00 2.8
Calculation of the electron density, thickness and interface roughness for each particular layer
W
The surface must be smooth (mirror-like)
Edge of TER
Kiessig oscillations (fringes)
7
Experimental set-up
Scintillationdetector
Flat monochromator
SampleGoebel mirror
X-ray source
Sample rotation,
Normal direction
Diffraction vector
Diffraction angle, 2
Angle of incidence,
Sample inclination,
Used for XRR, SAXS, GAXRD and symmetrical XRD
Information on the microstructure of thin films
Phase analysisResidual stress
analysisCrystallite size and
strain determinationStudy 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
20 40 60 80 100 120 1400
200
400
600
800 GAXRD with = 3o
Radiation: Cu K
Inte
nsity
(cp
s)
Diffraction angle (o2)
20 30 40 50 60 70
101
102
103
222,
UN31
1, U
N
622
, U2N
3220,
UN
440
, U2N
3
Su
bst
rate
200,
UN
111,
UN
400
, U2N
3
222
, U2N
3
Inte
nsity
(cp
s)
Diffraction angle (o2)
Phase compositionPhase composition
1. UN, 80-90 mol.%Fm3m, a = 4.8897 Å
2. U2N3, 10-20% mol.%
Ia3, a = 10.64 10.68 Å
Sample depositionSample deposition
PVD in reactive atmosphere N2
Heated quartz substrate (300°C)
0 Atomic Percent Nitrogen 50 60 67
800
T(°C)
400
U UN U2N
3
UN
2
Schematic phase diagramSchematic phase diagram
10
U2N3 versus UN2
U
N
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)
UN2 (Fm3m)
a = 5.31 ÅU: 4a (0, 0, 0)N: 8c (¼, ¼, ¼)
Cannot be distinguished in thin
films
11
Uranium nitride – residual stress analysis
0.0 0.2 0.4 0.6 0.84.91
4.92
4.93
4.94
4.95
111
200
220
311
222
400
331
420
422
511
440
531
442
Lat
tice
pat
am
eter
(Å
)
sin2
UN
a0 = (4.926 ± 0.015) Å Compressive residual stress = (1.8 ± 0.8) GPa Strong anisotropy of lattice
deformation
U2N3
a0 = (10.636 ± 0.002) Å Compressive residual stress = (6.2 ± 0.1) GPa No anisotropy of lattice
deformation
GAXRD at =3°
0.00 0.04 0.08 0.12 0.16 0.2010.74
10.76
10.78
10.80
10.82
222
400
440
622
Latti
ce p
ara
met
er (
10-1
0 m)
sin2
12
Uranium nitride – anisotropic lattice deformation
111
2
02)coscossinsin(sin1
)(
2
)( dgphk
0.0 0.2 0.4 0.6 0.84.91
4.92
4.93
4.94
4.95
111
200
220
311
222
400
331
420
422
511
440
531
442
Lat
tice
pat
am
eter
(Å
)
sin2
0.00 0.05 0.10 0.15 0.2010.74
10.76
10.78
10.80
10.82
easy
hard
0.0 0.2 0.4 0.6 0.84.91
4.92
4.93
4.94
4.95
111
200
220
311
222
400
331
420
422
511
440
531
442
Measured Calculated
Lat
tice
pat
am
eter
(Å
)
sin2
UN a0 = (4.9270 ± 0.0015) Å = (1.0 ± 0.1) GPa
directions
13
UN – anisotropic lattice deformation
0.0 0.1 0.2 0.3 0.4 0.5-1
0
1
2
3
4
5 422 511
Rel
ativ
e de
form
atio
n (1
0-3)
sin2
0.0 0.2 0.4 0.6 0.8 1.00.84
0.88
0.92
0.96
1.00
1.04
1.08
111
, 222
, 33
3
200
, 400
, 60
0
220
, 440
, 42
2
311
, 42
0
33
1
44
2
53
1
51
1
2 3/
1 =
2/(
1)
3 = 3(h2k2+k2l2+l2h2) / (h2+k2+l2)2
0.0 0.2 0.4 0.6 0.8-4
-2
0
2
4
6
440 531 442
Re
lativ
e d
efor
ma
tion
(10-3
)
sin2
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
14
UN versus U2N3
U
N
UN (Fm3m)
a = 4.93 ÅU: 4a (0, 0, 0)N: 4b (½, ½, ½)
Anisotropy of the mechanical
properties is related to the crystal
structure
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)
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)
Scherrer Williamson-Hall Warren-Averbach Krivoglaz
P. Klimanek (Freiberg) R. Kuzel (Prague) P. Scardi (Trento) T. Ungar (Budapest)
(000) (100)
(001)
(011) (111)
(110)
(000) (100)
(001)
(011) (111)
(110)
16
UN – anisotropic line broadening
0.0 0.2 0.4 0.6 0.8 1.00
10
20
30
40
111
200
220
31
122
2
400
331
42
0
422
511
/33
3
440
531
600
/44
2
D = 40 nm
e = 11x10-3
Lin
e br
oad
enin
g (
10-3 Å
-1)
sin
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
17
UN – texture measurement
Preferred orientation {110}
- 3 - 2 - 1 0 1
q (1/Å )
2
3
4
5
q (
1/Å
)z
x
111
200
220
311222
400
111200
220311222
-30 -20 -10 0 10 20 30
0
10
20
30
40
50
(220) (311)
Inte
gra
l int
ensi
ty (
a.u
.)
Sample inclination (deg)
0
sinsin2
;coscos2
y
ioziox
q
Reciprocal space mapping
18
Reciprocal space mapping
Measured using CuK radiation-8 -7 -6 -5 -4 -3 -2 -1 0 1
0
1
2
3
4
5
6
7
8
9
1 1 1
-1 1 1
2 0 0
2 2 0
-2 2 0
3 1 1
3 -1 1
3 -1 -1
2 2 2
-2 2 2
4 0 0
3 3 1
-3 3 1
3 3 -1
4 2 0
4 -2 0
4 2 2
4 -2 2
4 -2 -2
3 3 3
5 1 1
5 -1 1
5 -1 -1
qx [1/A]
q z [1
/A]
{111}
-7 -6 -5 -4 -3 -2 -1 0 1
q(x), 1 /A
2
3
4
5
6
7
8
q(z
), 1
/A
111
222
220
311
4-22
33-1
420
331
422
A highly textured gold layer
19
Epitaxial growth of SrTiO3 on Al2O3
O in SrTiO3
a
b
cPowderCell 1.0
a
bcPowderCell 1.0
Sr
Al
Ti
O in Al2O3
q(x)
q(y)
100
200
300
400
500
600
700
800
900211
211
112
112
121
121
018
_118
_108
Reciprocal space map Atomic ordering in direct space
SrTiO3: Fm3m 111 axis -3 001 Al2O3: R-3c
20
SrTiO3 on Al2O3
Atomic Force Microscopy
Pyramidal crystallites with two different in-plane orientations
AFM micrograph courtesy of Dr. J. Lindner, Aixtron AG, Aachen.
111 111
_110
_110
21
TiCN
Depth resolved X-ray diffraction
122 123 124 125 126 127 128 129
30
45
60
75
90 = 10
o
= 8o
= 6o
= 4o
= 2o
Inte
nsi
ty (
a.u.
)
Diffraction angle (o2)
TiN
TiC
TiN
WC
t
t
dzz
dzzzp
p
0
0
sinsinsinsin
exp
sinsinsinsin
exp
Absorption of radiation
TiC TiN
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
23
Functionally graded materials
W. Lengauer and K. Dreyer, J. Alloys Comp. 338 (2002) 194
SEM micrograph courtesy of C. Kral, Vienna University of Technology, Austria
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
24
Study of concentration profiles
26.0 26.5 27.0 27.5 28.0
0
10
20
30
Diffraction angle (o2)
Inte
nsity
(cp
s)
0 2 4 6 8
4.30
4.28
4.26
4.24
~TiC0.75N0.25
TiN
Depth (m)
a (
Å)
122 124 126 128 130
0
5
10
15
20
Inte
nsi
ty (
cps)
Diffraction angle o2
0.0 0.5 1.0 1.54.27
4.26
4.25
4.24
~TiC0.3N0.7
TiN
Depth (m)
a (
Å)
Copper radiationPenetration depth: 1.8 m
Molybdenum radiationPenetration depth: 12.5 m
The lattice parameter must depend on concentration
25
SummaryBenefits 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)