Mechanical strainstress characterization techniques in epitaxial layers

1
Mechanical strain/stress characterization
techniques in epitaxial layers
Etienne Snoeck (HREM), F. Houdellier, Ch. Roucau
(CBED), A. Rocher, M. Cabié, A. Ponchet
(Curvature method) P. Baules (R-X), CEMES /
CNRS Toulouse V. Paillard, J. Groenen(Raman
spectrometry) Laboratoire de Physique des
Solides IRSAMC / Université Paul Sabatier
2
Epitaxial layers
Fully strained epitaxial layer
Relaxed (partly ?) epitaxial layer
al //
al //
layer
cl perp
cl perp
cs-perp
cs-perp
substrate
as-//
as-
Questions What are the layer(s) parameters
(strained ) al, cl, bl, - al, bl,
gl eij and sij of the layer(s) ? Constant
within the layers (Local measurements) ?
3
OUTLINES

• Strain measurements by TEM methods
• Quantitative measurements of strain by HRTEM
• examples Relaxed epitaxial layers
  GaAs/GaSb,
• Strained épitaxial bilayers Si/Ge/SiGe
• Measurements of strain by the moirés méthods
• Quantitative measurements of strain by Convergent
  Beam Electron Diffraction (CBED)
• example Ga0.9In0.1As/GaAs
• Quantitative measurements of stress by the
  curvature method
• Strain measurements by X-Ray diffraction
• Strain measurements by Raman spectroscopy

4
The HRTEM contrast periodicity is related to the
potential periodicity of the crystal projected
along the direction of the beam. Any changes
(not too rapid) in the periodicity in the HRTEM
image can be related to the deformations of the
lattice integrated across the sample thickness
Si (compression)
Ge (tensil)
SiGe
113 defects in silicon
Questions to be addressed Is the strain
measured in such HRTEM micrograph obtained on a
thin specimen is representative of what happens
in the bulk
5
The Geometrical Phase Analyses (GPA) method
I cos(2pg0.x)
I cos(2pg1.x)
cos(2pg0.x f(x)) cos(2pg0.(x u(x))
cos2p(g0 dg(x)).x
Martin Hÿtch
6
Quantitative HREM for the analysis of deformation
in epitaxial thin films
The GPA method is based on the analysis of the
local Fourier component of individual reflections
of the Fourier transform of an HREM image.
Displacement measurements selecting a "g0"
reflection in the Fourier Transform (FT) we get
the complex fonction
Whose filtred image after inverse Fourier
Transform FT-1 gives
with
where "u(r)" measure the local displacement at
r of the lattice planes relative to the
position they would have if they have the
periodicity of the reference lattice 1/g0 .
with
7
When selecting two systems of fringes g1 and g2
y
x
Phase image
(111) filtered image
8
Relative displacement Ux (Å) projected // to
the interface
unwrapped
f0 ref
ref.
y
y
y
x
x
x
f0 ref
ref.
y
y
y
x
x
x
9
Strain
Local strain matrix and rigid
rotations
10
Local strain matrix
E. Snoeck, A. Rocher - CEMES/CNRS
11
Strain measurements of an epitaxial Si-15nm/SiGe

• Si0.8Ge0.2 a 5.476 Å
• Si a 5.4282 Å

SixGe1-x
Si
Non relaxed epitaxial growth exx (aSi aSi)
/ aSi (aSGei aSi) / aSi exx 0.88
Biaxial strain exx eyy HREM measurements
a (d(002)Si - d(002)SiGe) / d(002)SiGe
-0.00931 cSi 5.425 Å ezz (aSi cSi) /
aSi) ezz - 0.059
Zone axis 110
15 nm
a
Out of plane displacements of the (002)-Si
planes relatively to the (002)-SiGe ones
12
But Elasticity szz 0 ezz
-2(C12/C11) exx 0.68 10 times larger to
what is measured
Si / SiGe
Possible explanations ?

• Thin film relaxation ( t 300 Å) surface
  relaxation gt The strain is no more biaxial
• aSiGe ¹ aSi0.8Ge0.2 at the SiGe/Si interface,
  the alloy may have a composition different to the
  one far from it.

x
exx ¹ eyy
Substrate
z
y
t
13
Non-relaxed epitaxial growth of Si /SixGe1-x
exx (aSi aSi) / aSi (aSGei aSi) / aSi
aSiGe/aSi exx 1 ezz (cSi aSi) / aSi
(cSi / aSi) - 1 (cSi / aSiGe) (aSiGe /
aSi ) - 1 (cSi / aSiGe) (exx 1)
1 ezz (cSi / aSiGe) exx (cSi / aSiGe) -
1 a measured by MEHR a (cSi aSiGe) /
aSiGe cSi/aSiGe a 1 ezz (a 1)exx a
ezz -2(C12/C11) exx with a -0.00931
C12 6.39 1010 Pa C 11 16.57 1010 Pa
MEHR measurements in agreement with
the elasticity theory aSiGe 5.457 Å, Végard law
? x 0.87
exx 0.528 10-2 ezz -0.407 10-2 sxx 0.95
GPa
14
113 defects in Si
Tensor matrix
eyy
exx
lteyygt4. 10-3
ltexxgt10-4
exy
wxx
ltwxygt10-2
ltexxgt10-4
GPA analysis using the two 111 types reflections
111
111
E. Snoeck and N. Cherkasine
15
113 defects in Si
eyy
X
Y
eyy contours 0.02 eyy Max 0.3 eyy min 0
16
Si / Ge / Si0.5Ge0.5
5.1 nm
Si
Compressive strain
Ge
Tensile strain
8.5 nm
Si0.5Ge0.5
relaxed
aSi 0.5431 nm aGe 0.5658 nm aSiGe 0.5545 nm
Theoretical
eGexx - 2 eGezz 1.4
eSixx 2.1 eSizz - 1.6
and
sGe11 - 2.79 GPa sSi11 3.78 GPa
with ezz -2.(C12/C22) exx
E. Snoeck N. Cherkasine
17
lt 0.1 gt
ezz
exx
Z
X
lt - 1.4 gt
002
220
lt 1.2 gt
lt110gt zone axis HREM FEI / SACTEM 200 kV FEG
- Cs corrector
lt 0.1 gt (ref)
Mean dilatation
18
lteSizzgt-0.027
lteGezzgt0.027
ltezzgt0.0003 (ref.)
ezz
eSixx (cSi - cSiGe)/ cSiGe - 2.7 eGezz
(cGe - cSiGe)/ cSiGe 2.7
19
eGexx (aGe - aGe)/aGe (aSiGe - aGe) / aGe
(aSiGe / aGe) - 1 aSiGe / aGe cSiGe / cGe
eGexx 1 eGezz (cGe- cGe) / cGe (cGe/ cGe)
1 (cGe/ cSiGe) (cSiGe/ cGe) 1 With
eGezz (cGe - cSiGe)/ cSiGe (cGe / cSiGe)
-1 gt (cGe / cSiGe) eGezz 1 Then eGezz
(eGezz 1) eGexx eGezz eGezz
-2.(C12/C22) eGexx
cGe12 4.4 1010 Pa cGe22 12.6 1010 Pa eGezz
2.7
With the hypothesis of a non isotropic relaxation
(biaxial strain) we then measure
eGexx - 1.56 eGezz 1.1 sGe11 - 2.2
GPa (sexpected - 2.79 GPa)
eSixx 1.5 eSizz - 1.2 sSi11 2.7
GPa (sexpected 3.78 GPa)
Similarly for Si
20
HRTEM
Studied area few 10 of nm Resolution TEM
resolution 0.2 nm Specimen thickness 10 to 50
nm Accuracy of the measurements (De)
10-3 Problems limitations - Cross
sectional thin samples gt possible thin
specimen relaxation - Reference area
needed - Destructive
21
OUTLINES

• Strain measurements by TEM methods
• Quantitative measurements of strain by HRTEM
• examples Relaxed epitaxial layers
  GaAs/GaSb,
• Strain epitaxial bilayers Si/Ge/SiGe
• Measurements of strain by the moirés methods
• Quantitative measurements of strain by Convergent
  Beam Electron Diffraction (CBED)
• example Ga0.9In0.1As/GaAs
• Quantitative measurements of strain by the
  curvature method
• Strain measurements by X-Ray diffraction
• Strain measurements by Raman spectroscopy

22
Fully strained epitaxial layer
Relaxed (partly ?) epitaxial layer
al-//
al-//
cl-perp
layer
cl-perp
Cross section
cs-perp
cs-perp
substrate
as-//
as-//
23
HR Moirés patterns
GaSb/(001)GaAs lt110gt X-TEM MBE growth 1µm buffer
layer 300 Å GaSb
30 nm
24
Translation moirés
L
d1
d2 ?
g1
g2
h
g2 // g1
d1 1 / g1
d2 1 / g2
L 1/h
25
Rotation Moirés
d1
b
L
w
b
b
g1
g2 g2 g1
L 1/h
26
Rotation translation Moirés
L
w
d2 b
d1
b
h
g1
g2
g2
h
b
w
g1
27
GaSb/(001)GaAs

• Misfit dislocation network
• Square grid
• Lomer type
• u 110, b ½ lt1-10gt

001
Dexp Dcalc Dd 56 4 Å 55
Å D200 39 4 Å 38 Å
gt System fully relaxed
A. Rocher
28
Moirés method
Studied area few hundred of nm Thickness 50
to 100 nm Spatial resolution 5 nm Accuracy of
the measurements (Da) 0.01 Å Problems
limitations - Only (partly) relaxed single
layer on well known substrate -
Destructive
29
OUTLINES

• Strain measurements by TEM methods
• Quantitative measurements of strain by HRTEM
• examples Relaxed epitaxial layers
  GaAs/GaSb,
• Strain epitaxial bilayers Si/Ge/SiGe
• Measurements of strain by the moirés methods
• Quantitative measurements of strain by Convergent
  Beam Electron Diffraction (CBED)
• example Ga0.9In0.1As/GaAs
• Quantitative measurements of strain by the
  cutvature method
• Strain measurements by X-Ray diffraction
• Strain measurements by Raman spectroscopy

30
Local Strain Measurements by Convergent Bean
Electron Diffraction (CBED)
Florent Houdellier et Christian Roucau
31
General
Electron diffraction
32
Laue Zones ZOLZ, FOLZ, etc HOLZ
Electron diffraction
33
General
CBED
3D nature of the CBED diffraction
superimposition of HOLZ and ZOLZ Example Zone
axis 230
a1 ,b1 ,c1 a1 ,ß1 ,?1 V1
Accuracy 10-4nm
Spatiale resolution Spot size1nm
Resolution 50V
34
CBED
Experimental
- Very small spot size of about 1nm diameter
(nanoprobe)
Objective Lentille TWIN
- Energy filtered (Zero Loss)
35
CBED
Line detection and lattice parameter measure
Silicium Substrate 230
36
CBED
Line detection and lattice parameter measure
2. Simulation of the HOLZ lines location
(Kinematical simulation dynamical correction)
1. Lines extraction (Hough transform)
3. Least square fit on a,b,c,a,b,g parameters
4. Strain tensors e
5. Hooke relation Stress tensors sCe

• TEM voltage easy to fit
• 6 lattice parameters hardly fitted
• ? symetrical considerations

37
Influence of the variation in the lattice
parameter
CBED
GaAs 230zone axis
a 0.565 nm
a b 0.55nm c 0.57nm
a 0.58nm
38
Example Epitaxial layer
CBED
al //
al //
layer
cl perp
cl perp
cs-perp
cs-perp
substrate
as-//
as-
39
Sample preparation on cross section (XTEM)
CBED
FIB preparation method
argon ions
8
40
CBED
Examples
Ga0,9In0,1As/GaAs 230
- TEM high voltage measurement (GaAs substrate
along 230)
41
CBED
Strong effect thin film relaxation
Substrate
Layer
42
Discussion
Due to its small thickness the XTEM sample is
partly relaxed and the stress is no more biaxial.
It therefore changes the lines profiles.
43
Conclusions CBED
Convergent Beam Electron Diffraction (CBED)

• Diffraction technique very sensitive to the
  strain (even too much !!)
• Local technique
• Can be applied to all kind of strain (epiaxial
  layers, dislocations, precipitates)
• CBED can give many other informations
• Crystal symmetries
• Thickness measurements
• Structure factor determination
• Defects studies
• CBED technique is very sensitive to the
  deformation modifications along the beam path
  which induces large changes of the lines profiles
• The CBED pattern can be very tricky !!!
• The sample has to be perfectly crystalline with a
  large thickness (200nm to 600nm) and along the
  beam path in order to get thin lines.

44
OUTLINES

• Strain measurements by TEM methods
• Quantitative measurements of strain by HRTEM
• examples Relaxed epitaxial layers
  GaAs/GaSb,
• Strain epitaxial bilayers Si/Ge/SiGe
• Measurements of strain by the moirés methods
• Quantitative measurements of strain by Convergent
  Beam Electron Diffraction (CBED)
• example Ga0.9In0.1As/GaAs
• Quantitative measurements of strain by the
  curvature method
• Strain measurements by X-Ray diffraction
• Strain measurements by Raman spectroscopy

45
Stress measurements in semiconducting epitaxial
systems by the Curvature method André Rocher,
Martiane Cabié, Anne Ponchet

• Measurement of the Misfit Stress by the Curvature
  method
• Curvature method Stoney formula
• Macroscopic behaviour
• Measurement of the specimen curvature induced
  by the misfit stress (geometric relaxation)
• TEM local analysis of s and misfit
  dislocation density

46
Pseudomorphic strain interface (001)
Strained structure a//b a//a
Lattice mismatch al as (1 f) f (al-as) / as
al
al-//
cl-?
cl-?
as
cs
cs

• Model
• Abrupt interface
• Continuity of planes
• Uniform strain
• From the elasticity
• sij Cik ekj
• s// - M . e//

as-//
Elastic strain e// - f ?? 2 C12/C11 f
Interplanar distances c? al (1 ?? ) c?
as (1 f ??)
M E /(1-n)
47
Measurement of the misfit stress
Relaxation of the misfit stress gt curvature
Corrected Stoneys formula
Epitaxial layer tlayer 10 nm, f 1
sStoney gt slayer - Mlayer . f
M E /(1-n)
48

• Plane view observation
• chemical thinning of the substrate
• no perturbation of the epilayer
• Natural cleavage simple shape of the specimen
• tsubstrate lt 500 nm at 200 kV

• Data
• tlayer ? 10 to 30 nm,
• (tcrit ? 10 nm)
• substrate elastic constants

• parameters to be determined by TEM
• R curvature radius
• tsub thickness of thinned substrate
• density of misfit dislocations

49

• Principle bright field image g bend
  contours
• geometry 2 .qb D0 / R
• Bragg 2.qb l .g0
• Typical values
• 440 bend contours well defined
• l 0.0025 nm at 200 kV
• g440 10 nm-1 for GaAs

R D0 / (l . g0)
R 40 . D440
50
Curvature measurement
Experimental measurement Z lt116gt D440 1.5 µm
gt R 64 µmD331 1.3 µm gt R 62 µm
spherical shape
R D0 / (l . g0)
Uniform curvature
51
Local measurement of the substrate thickness
Principe 220 dark field related to the bend
contour Symmetric intensity profile I220 1/ (1
w2) .sin2(p.t/ xg(1 w2)1/2) minima I220 0 for
t(n) n. xg / ( 1 (w0 . Dn / D0)2)1/2 xg
extinction distance w0 (l.g02). xg
52
Experimental data D0 1.35 µm Dn
0.76 µm Dn1 0.89 µm Dn2 1.02 µm.
ttot tsub tlay
t(n) n. xg / ( 1 (w0 . Dn / D0)2)1/2
ttot 181 8 nmxg 63 2 nm
n
53
Ga0.8In0.2As/GaAs
for tl 25 nm
x 20 f 1.4 tc 10 nm
No misfit dislocation 1 gt Dd 40 nm 25
dislocations / µm
sth 1.6 GPa sexp 1.3 GPa
54
OUTLINES

• Strain measurements by TEM methods
• Quantitative measurements of strain by HRTEM
• examples Relaxed epitaxial layers
  GaAs/GaSb,
• Strain epitaxial bilayers Si/Ge/SiGe
• Measurements of strain by the moirés methods
• Quantitative measurements of strain by Convergent
  Beam Electron Diffraction (CBED)
• example Ga0.9In0.1As/GaAs
• Quantitative measurements of strain by the
  curvature method
• Strain measurements by X-Ray diffraction
• Strain measurements by Raman spectroscopy

55
X- ray and thin films
Pierre Baules CEMES CNRS
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X-Ray Reflectivity
Interferences
e
n
The difference in path length D 2nI1I2 I1H
2eÖ(n2-cos2q) p.l gt Kiessig fringes for low
incidence angles sin2q p2l2/4e2 (1-n2)
(p1, 2,) gt Thickness, roughness and density
measurements
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INTRODUCTION
CRISTALLOGRAPHY
EXAMPLES
CONCLUSION
The reciprocal lattices
Single thin film low Q (close to the origin of
the RL)
d111
substrate
Qz
1.5
0
10.6
Si (111) d3,1355 Å QB14,221 Qz2,004
Å-1 20 planes e62,7Å
Even if the single layer is not cristalline
62
INTRODUCTION
CRISTALLOGRAPHY
CONCLUSION
EXAMPLES
The reciprocal lattices
Multilayers high Q (far from the origin of the
RL)
5 bilayers
0
1
Ge (111) d3.266 Å Qz1.924 Å-1 10 planes
e32.66 Å
-1
-2
2
-3
3
substrate
Qz
...
17,8
10,6
Si (111) d3.1355 Å Qz2.004 Å -1 5 planes
e15.68 Å
63
INTRODUCTION
CRISTALLOGRAPHY
EXAMPLES
CONCLUSION
The reciprocal lattices
Multilayers low Q (Close to the origin of the
RL)
5 bilayers
Ge (111) d3.266 Å Qz1.924 Å-1 10 planes
e32.66 Å
substrate
Qz
...
4,9
0
Si (111) d3.1355 Å Qz2.004 Å -1 5 planes
e15.68 Å
Even for non cristalline layers
64
High Q (far from the origin of the RL)
DIFFRACTION
qperp
qperp
qpar
qpar
Substrate cubic as
as-perp
.
as-par
.
65
004
66
SIMULATION automatical fit of the thickness and
mismatches
experimental
simulation
(a para layer a para subs) / a para subs -
0.00045
(a perp layer a perp subs) / a perp subs
0.006039
67
No reference from the substrate 4
measurements needed
68

Problem it is not possible to measure directly
the thickness of each layer. gt Simulation
needed (kinematical case)
69
Layers quality (2D or 3D), crystallization state,
layers mosaicity Measurement of the layers
thicknesses Quality of the interfaces Characteriza
tion of the layers strain LIMITATIONS In
reflectivity atomic diffusion at interfaces, Z
contrast, roughness gt 30 to 40 Å . In
diffraction dimension of the coherent domains,
mosaicity .
70
Some values to keep in mind
Studied area 0.1 mm 1mm Maximum layer
thickness 300 to 400 nm (reflectivity) Minimum
layer thickness 1 nm (diffraction) Accuracy
of the measurements Dd/d Dl/l cotgQ
DQ Exple Si (004) Q 34.57 Dl 0.0002
nm l 0.15406 nm Dd/d 1.3 10-3 3.05 10-4
1.6 10-3 double monochromators low
divergence monochromaticity
71
OUTLINES

• Strain measurements by TEM methods
• Quantitative measurements of strain by HRTEM
• examples Relaxed epitaxial layers
  GaAs/GaSb,
• Strain épitaxial bilayers Si/Ge/SiGe
• Measurements of strain by the moirés méthods
• Quantitative measurements of strain by Convergent
  Beam Electron Diffraction (CBED)
• example Ga0.9In0.1As/GaAs
• Quantitative measurements of strain by the poutre
  method
• Strain measurements by X-Ray diffraction
• Strain measurements by Raman spectroscopy

72
Strain measurement usingRaman spectrometry

• V. Paillard, J. Groenen
• Laboratoire de Physique des Solides
• IRSAMC / Université Paul Sabatier
• Toulouse, France, U.E.

73
Raman scattering in crystals
Incident light
Scattered light
Selection rules function of crystal symmetry
74
Raman spectrometer (Dilor XY)
75
Role of the electrons optical absorption
coefficient
Raman probe depth (nm)
Absorption coefficient (cm-1)
5 nm
Si
10 mm
Energy (eV)
76
Resonance Raman scattering selection of
structural and chemical phases
InAs/InP QWs and QDs
Resonant excitation on QDs
Resonant excitation on the wetting layer
Groenen et al., APL 99
77
Advantages-hindrances

• Non destructive probe
• No specific preparation of samples
• Good spatial resolution (down to 0.7 mm)
• Bulk to surface probe
• Sensitive and selective (resonant Raman
  scattering)
• Cartography, imaging
• Laser heating under microscope
• No universal spectrometer
• Laser excitation lines adapted to the materials

78
Raman scattering in siliconInfluence of biaxial
stress

• Compressive stress (bond contraction )
• Tensile stress (bond extension)

79
The Si1-xGex virtual substrateStrain relaxation
and Ge concentration
wx
w0


80
The SiGe virtual substrateStrained Si layer (10
nm thick)
81
After transfer sSOI wafers (before and after
SiGe etching)
82
Strained silicon on insulatorThe strain is
conserved
After transfer (SSOI)
Before transfer (virtual substrate)
83
Strain imaging crosshatch in SSi/Si0.8Ge0.2
Strain variation in SSi/Si0.8Ge0.2
Strain variation in Si0.8Ge0.2 (weak compressive
strain)
C. Villeneuve et al., JSFV conf. (2005)
84
Strain measurements