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Lecture 11:Introduction to Thin Film
Characterization: Structural and Morphological Characterization
B. D. Cullity, S. R. Stock, Stuart Stock, Elements of X-Ray Diffraction (3rd Edition) Prentice Hall; 3nd edition (February 5, 2001)
Harold P. Klug, Leroy E. Alexander, X-Ray Diffraction Procedures: For Polycrystalline and Amorphous Materials, 2nd Edition Wiley-Interscience; 2 edition (May 1974) ISBN: 0471493694
C. Suryanarayana, M. Grant Norton,X-Ray Diffraction: A Practical Approach Plenum Publishing Corporation; (June 1, 1998) ISBN: 030645744X
David B. Williams and C. Barry Carter, Transmission Electron Microscopy I, II, III, IV (Plenum Press, New York, 1996).
John C. Vickerman, Surface Analysis – The Principal Techniques (John Wiley & Sons, New York, 1997).J.C. Vickerman and D. Briggs, ToF-SIMS: Surface Analysis by Mass SpectrometryEdited, IM Publications ISBN 1
901019 03 9
Briggs, D., Seah, M.P. Eds.; Practical Surface Analysis, 2nd ed.; John Wiley & Sons: New York, 1996;
J. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, A. D. Romig, Jr., C. E. Lyman, C. Fiori, and E. Lifshin, Scanning Electron Microscopy and X-ray Microanalysis (Plenum Press, New York, 1990).
D. C. Joy, A. D. Romig, Jr., and J. I Goldstein, Principles of Analytical Electron Microscopy (Plenum Press, New York, 1989).
Frank A. Settle, Handbook of Instrumental Techniques for Analytical Chemistry (Prentice Hall PTR, New Jersey, 1997).
J. R. Tesmer, M. Nastasi, J. C. Barbour, C. J. Maggiore, and J. W. Mayer, Handbook of Modern Ion Beam Materials Analysis (Materials Research Society, Pittsburgh, 1995), Chap. 5, p.83.
W.-K. Chu, J. W. Mayer, and M.-A. Nicolet, Backscattering Spectrometry (Academic Press, New York, 1978).
Bibliography
IonsElectronsPhotons
IonsElectronsPhotons
Vacuum
Primary beam (source)
Secondary beam (spectrometers, detectors)
imaging
High-power lithium-ion batteries failure mechanisms
spectroscopy
crystallography
elemental analysis
Diffraction of x-rays by a crystal
2n d sinλ = θBragg’s Law:
θ
d sinθ
A
B
C
d
plane normal1
2
1’
2’
{001}
{110}
{210}
X-ray analysis of polycrystalline layers and powder materials
Bragg’s Law
dhkl = λ/2sin(θ)
•Bragg-Brentano or parallel beam x-ray analysis;
•Powders, polycrystalline films or nanostructures, mineralogy, cements, ceramics, pharmaceutics, polymers, biomaterials;
•Identification, quantification (w%) and structure determination of mixtures, impurities, multiple phases and amorphous fractions;
•Quantification of crystallinity, texture, twinning, grain size and strain;
•Pattern indexing, lattice parameters determination, unit cell refinement, atomic positions, bonds distances and angles;
•Pattern simulation and structure refinement (Rietveld analysis)
0.05%Strain:
> 1000 ÅCrystallite size:
82.9 w% LiNi0.7Co0.3O2, 17.1 w% CQuantitative analysis:
Ni-O: 1.9570 Å, Ni-Li: 2.8729 Å, Ni-Ni: 2.8629 Å, Co-O: 1.9570 Å, Co-Ni: 2.8629 Å, Co-Li: 2.8729 ÅLi-O: 2.1117 Å, Li-Li: 2.8629 Å, O-O: 2.7983 Å
Average bond distances (Rietveld):
a= 2.86285 Å; b= 2.86285 Å; c= 14.17281 Åα= 90o β= 90o γ= 120o
Unit cell volume: 100.6 (Å)3
Density: 4.8383 g cm-3
Linear Absorption Coefficient: 385.5 cm-1
Cell (Rietveld refinement):
Hexagonal R-3m (166) <1/3,2/3,2/3>, Z=1, hR4
Structure:
LiNi0.7Co0.3O2, major (minor: C graphite)Search / Match: Ni
O
Li
Co
Results obtained from the measured pattern:(006)
(113)
(110)
(018)(107)(015)
(104)
(012)
(101)
C(002)
(003)
Inte
nsity
(a.u
.)
2-theta (o)
Pattern from a Li-Ni-based battery cathode
Data: Sardela, Abraham et al
Ta/SiO2 vs Ts
30 40 50 60 70 80 90 100
(212
)
(831
) (33
4)
(202
)(0
02)
(820
) (82
1)
(413
)
350 癈
Ts = 100 癈
Inte
nsity
(a.u
.)
2θ (deg)
430 癈
(311
)
(220
)
(211
)
(200
)
(110
)
tetragonal β-Tabcc α-Tat = 500 nm
fN2 = 0
Ta/SiO2/Si(001)
30 35 40 45 50 55 60
α-T
a 11
0
β-Ta
002
430 癈
Inte
nsity
(a.u
.)
2θ (deg)
α-T
a 11
0β-
Ta 2
02
β-Ta
002
350 癈
Ts = 100 癈 10 20 30
Inte
nsity
(a.u
.)
Γω = 3.5�
ω (deg)
10 20 30
Inte
nsity
(a.u
.)
Γω = 4.3�
ω (deg)
GA-XRD 2θ scans XRD ω-2θ scans
TaNx/SiO2 vs fN2
20 30 40 50 60 70 80
++0.013 (211
)
(200
)
(110
)
Inte
nsity
(a.u
.)
2θ (deg)
+
(101
)
0.025 (002
)
(112
)
(110
)
0.050
0.063
0.125
0.150
0.250
(311
)
(220
)
*
*
*
(200
)
fN2 = 1
(301
)
(200
)
(110
)
Ts = 100 癈t = 500 nm
(111
)
cubic TaN0.1
hexagonal γ-Ta2Ncubic δ-TaNbct-TaNx
+
*TaNx/SiO2/Si(001)GA-XRD 2θ scans TEM
δ-TaNx: ao = 0.443 nmbct-TaNx: a = 0.590 nm, c = 0.443 nm
N/Ta = 1.96
110
200
111
200 002
112
301
321220
400
fcc bct
Growth phase map for TaNx
Pure Ar: tetragonal β-Ta @ Ts < 150 °Cbcc α-Ta @ Ts > 400 °C.
fN2 < 0.1: three consecutive narrow lower nitride regions, defined by tilted boundaries toward higher fN2 with increasing Ts.
0.1 <fN2 < 0.3 and Ts ≤ 650 °C: single-phase δ-TaNx.
0.1 <fN2 < 0.3 and Ts > 650 °C:hexagonal ε-TaNx + δ-TaNx.
Pure N2: δ-TaNx + bct-TaNx.
0 0.1 0.2 0.3 1.00
200
400
600
800
1000= α-Ta= α-Ta + β-Ta= β-Ta = TaN0.1
= δ-TaN + ε-TaN= δ-TaN= δ-TaN + bct TaN
= Ta4N+TaN0.1
= Ta4N= γ-Ta2N = γ-Ta2N + δ-TaN
TaNx growth phase map
T s (癈
)
fN2
Stress measurements (sin2ψ method)
aψ is expected to depend linearly on sin2ψ.
[ ] ξ+ψδ=+ν−ψν+σ
=
σν
−ψσν+
=−
=ε
φψ
φφψ
ψ
20
20
2
0
0
sina2sin)1(E
aa
E2sin
E1
aaa
ψ
θ
Diffracting planes
Lφ,ψ
Film Normal
IncidentX-rays
ReflectedX-rays
ψ
θ
Diffracting planes
Lφ,ψ
Film Normal
IncidentX-rays
ReflectedX-rays
ψaψ
a0
a⊥
σφ
stressed
unstressed
film surfaceψ
aψ
a0
a⊥
σφ
stressed
unstressed
film surface
Stress measurement (sin2ψ method)
aψ is expected to depend linearly on sin2ψ.
[ ]
νσ−+ψ
ν+σ=+ν−ψν+
σ=
σν
−ψσν+
=−
=ε
φφφψ
φφψ
ψ
E2
1asinE
)1(aa2sin)1(
Ea
a
E2sin
E1
aaa
020
020
2
0
0
ψ
θ
Diffracting planes
Lφ,ψ
Film Normal
IncidentX-rays
ReflectedX-rays
ψ
θ
Diffracting planes
Lφ,ψ
Film Normal
IncidentX-rays
ReflectedX-rays
ψaψ
a0
a⊥
σφ
stressed
unstressed
film surfaceψ
aψ
a0
a⊥
σφ
stressed
unstressed
film surface
δ ξ
Stress measurement using XRD
0.0 0.2 0.4 0.6 0.8 1.04.515
4.520
4.525
4.530
4.535
4.540
sin2ψ
ξν++δνδ
=σ
ν+δν
+ξ=
φ )1(2E
12a0
ν+ν
=ψ12sin2
= −757.9 MPa (compressive stress)
= 4.5280 Å
δ = -0.01751ξ = 4.53503
a (Å
)
HfN1.18/SiO2
a0
orientation plane ψ 2θ sin2ψ
1 1 1 0 01 1 1 70.529 0.88892 0 0 54.736 39.853 0.66672 2 0 35.264 57.601 0.33333 1 1 29.496 0.24243 1 1 58.518 0.72733 1 1 79.975 0.96971 1 1 54.736 34.333 0.66672 0 0 0 39.853 02 2 0 45 57.601 0.53 1 1 25.239 0.18181 1 3 72.452 0.9091
2 0 0
34.333
1 1 1
68.825
68.825
1.0 1.1 1.2 1.3 1.4 1.5 1.64.50
4.52
4.54
4.56
4.58
a 0 (A)
x
Stress and a0 of HfNX/SiO2
1.0 1.1 1.2 1.3 1.4 1.5 1.6-2
-1
0
1
2
σ φ (GPa
)
x
• X ≤ 1.17 : (111) preferred orientation, tensile stress
• X ≥ 1.18 : (200) preferred orientation, compressive stress
• X ↑ ⇒ a0 ↑
(200) P.O.(111)
HfNX/SiO2
X-ray analysis of textured materials
Texture results from a rolled Cu foil
•Texture orientation and quantification•Volume fraction of textured grains,
twinning and random distributions•Texture strength and sharpness•Crystallographic orientation•Crystallographic relationship between
layers and substrate
x-ray source
Pole figures
Orientation distribution
function (ODF)
φ
ψ
ψφ
(111)
Φ2
Φ1
Φ
Φ
Data: Sardela et al
φ
ψdetector
2θ sample
Si1-xGex on Si(001)
Si1-xGex on Si(001)
substratesubstrate
film
film
thicknessfringes
(224) (224)
0.1 nm-1 0.1 nm-1
Mosaicity(diffuse
scattering)
∆q001
∆q110
substrate substrate
film film
a// = as
a┴
as as
a// ≠ as
a┴
X-ray analysis of lattice mismatched epitaxial films•High resolution reciprocal lattice mapping requires multi-reflection monochromator and analyzer crystal in order to separate strain from mosaicity
•Sensitive to lattice distortions within 10-5
•Accurate lattice parameter determination (in and out of plane)
•Determination of strain and composition variations, strain relaxation, mosaic size and rotation, misfit dislocation density, nanostructure dimensions, lattice disorder and diffuse scattering
No strain relaxation: Strain relaxation:
Data: Sardela et al
HR-XRD and TEM: CeN /MgO(001):fN2 = 0.25, Ji/JMe = 15, Ei = 30 eV
Cube on cube epitaxial relationship:(001)CeN||(001)MgO with [100]CeN||[100]MgO
aCeN = 5.021 Å, aTiN = 4.242 Å
0 90 180 270 360
MgO(113)
CeN(113)
I (a.
u.)
φ(deg)
MgOCeN
000 020
022002
2.16°
17 18 21 220
10
20
30
40
50
60
t = 70 nm MgO(002)
CeN(002)
CeN/MgO(001)TS = 700 癈
I (10
4 cou
nts s
-1)
ω−2θ (deg)
I (
coun
ts s-1
)
0
1
2
3
15 18 210
10
20
30
ω (deg)
I (co
unts
s-1)
HR-RLM
The degree of in-plane layer relaxation:
|||| k2a =
⊥⊥ = k3a
+−
−=⊥
⊥⊥ ν)1(a
)aaν(2 1aa ||
o
so
s||L a-a
aaR
−=
Relaxed lattice constant:
for 113 reflection
0.04 nm-1
TaN
MgO 113
∆(ω
−2θ)
∆(ω)k
k (nm )-1
(nm
)-1
δ-TaN /MgO(001)1.17
T = 600 癈s
113 RL = 94±4% for δ-TaNx (1.0 ≤ x ≤ 1.37)
X-ray reflectometry of thin films
•Film thickness measurements: 2 – 300 nm
•Applicable to ultra-thin films, amorphous or crystalline materials, multilayers and liquids
•Simulation and fitting: determination of interface roughness (rms) at each interface, and roughness correlation.
•Very sensitive to density variations
•Determination of critical angle, refractive index and density
2 4 6 8 10 12
Log
inte
nsity
(a.u
.)
2-theta (o)0.5 1.0 1.5 2.0 2.5 3.0 3.5
Log
inte
nsity
(a.u
.)Theta (o)
0 2 4 6 8 10 12
Log
inte
nsity
(a.u
.)
2-theta (o)
Metallic multilayer
2.3 nm thick polymer on Si
AmorphousPZT film
Log
Ref
lect
ivity
RR ~ θ -4
One sharp surface(density ρe variation: step function at surface)
One rough interface (“broad”ρe variation
at surface)∆θ = λ/[2*(thickness)]
∆I ~∆ ρe
decay ~ roughness
Critical angle θc
Two interfaces
Thickness fringes
θ
θ
Data: Heitzman et al Data: Sardela, Auoadi et al Data: Mikalsen et al
Atomic Force MicroscopyAtomic Force Microscopy
Schematic of a typical AFM system
AFM is a technique which uses a smalltip to physically scan the sample surfacetopography on a sub-nm scale and produce a quantitative map of height vs location.
(c) t = 1000 � (d) t = 2300 �
(b) t = 500 �(a) t = 250 �
[100][100] 1000 � Universal Scaling Theory
M aterial β γ ξG e* 1 0.4 0.02Fe** 0 .16 0.16 0.1T iN 0.25 0.25 0.006
β = roughening exponent
γ = coarsening exponent
ξ = aspect ratiodw
td
tw
=ξ
∝
∝
γ
βTiN/TiN(001)TiN/TiN(001)
( )2
i jG( ) h hρ = −
Surface Morphological Evolution of TM NitridesSurface Morphological Evolution of TM Nitrides
2 phases
1 phase
Ti1-xCexN/SiO2 (x = 0 - 0.23), TS = 350 ºC, Ji/JMe = 15, Ei = 14 eV
x 0.1:• a0 increases linearly with x.• Γ2θ (FWHM) remains small.• ρ increases linearly with x.
x > 0.1:• extensive CeN segregation• 2 phases (TiN-rich / CeN-rich)• Γ2θ jumps and then increases
linearly with x.• ρ increases faster than x < 0.1.
2 cosvKDθ
λθ
⋅=
Γ ⋅Dv = Volume weighted crystallite size,K = Scherrer constant (0.87-1.0),λ = The wavelength of the radiation,Γ2θ= The integral breadth of a reflection
(in radians 2θ) located at 2θ.
Ti1-xCexN (14 eV) surface morphology f(x)
w = surface width (RMS roughness)
x > 0.1:• CeN segregation.• 2 phases (TiN-rich & CeN-rich).• w drops below 2 nm.• w reaches 0.32 nm when x = 0.2.
x = 0
w = 6.82 nm w = 4.57 nm
x = 0.1
w = 1.31 nm
x = 0.15
w = 0.32 nm
0.5 µm
x = 0.2
SiO2100 nm100 nmSiO2100 nm
XTEM as f(x) at Ei = 14 eVTiN Ti0.9Ce0.1N Ti0.8Ce0.2N
Kinetic roughening:• Low adatom mobility in the
presence of Ehrlich barriers* Eb.• Local epitaxial growth in
individual columns facetsatomic shadowingunderdense structure.
*G. Ehrlich, Surf.Sci. 331-333, 865 (1995).
Eb
Polycrystalline ScN/MgO(001)
MgO(001)ScN
30 35 40 450
100
200
300
400 Ts = 750 oCt = 180 nm
x 500 ScN(002)
ScN(111)
MgO(002)
ScN/MgO(001)
Inte
nsity
(arb
. uni
ts)
2θ (degrees)
ScN layers on MgO(001) are polycrystalline with 111- and 002-oriented grains, as observed by x-ray diffraction θ-2θscans.
7%mismatch
Plan-view electron diffraction pattern
12-fold symmetry is due to 4-different azimuthal orientations of the ScN three-fold 111-grains on MgO(001)
X-ray Diffraction Pole Figures and Electron Diffraction Patterns
ScN(111)(2θ = 34.415°)
Pole figure