Download TEM Image Contrast

TEM Image Contrast
(W&C Vol. 3, and Vol. 1 chapter 13)
2. Phase: electron optics and sample
introduce phase differences between
1. Amplitude: fluctuations in number of electrons
scattered and transmitted beams
scattered outside the objective aperture
• All types of fringes, thickness,
• Mass-Thickness
Moiré, lattice fringes, Fresnel
• absorption determines primary contrast
fringes
eg. amorphous materials;
• Important for detail ≤ 1.5 nm
• at high angles (> 5°) incoherent scattering
gives mass sensitive imaging in STEM
• Diffraction
• BF, DF objective aperture defines beams
producing primary image contrast
• Important for detail ≥ 1.5 nm
Amplitude Contrast
Mass-Thickness
• scattering factor f ∝ Z so intensity ∝ Z2
• the number of unscattered electrons decreases exponentially with thickness
• amorphous materials generate no diffraction so the only contrast mechanism is via absorption.
Density and thickness determine contrast.
• At high detector angles STEM mode: Z-contrast imaging
annular dark field detector (ADF) or high angle ADF detects electrons scattered through
larger angles than for diffraction.
Absorption varies with degree of diffraction
• away from strong Bragg diffraction conditions – leads to a uniform influence on the overall
background intensity
• under strong diffraction conditions: called anomalous – (historical name only) since depends
on phase of beam, responsible for many of the detailed features of contrast when near a Bragg
condition (Bloch waves do not have the same phase and hence absorption coefficient is
different.)
Example of mass/thickness contrast from biology:
Z- Contrast
1 µm
A dendritic cell sensing a lymphocyte,
(Nature Cell Biology 6, 188 (2004)
Olivier Schwartz, Virus and Immunity Group,
Institut Pasteur, Paris, France).
Diffraction Contrast - Perfect Crystals
Perfect crystals display only contrast from bending or thickness variations
• kinematical amplitude of the diffracted beam:
rn =lattice vector so g•r = integer leaving only s
• For a narrow column of the crystal thickness t:
assuming |s| ≈ sz
integral becomes:
ψg =
ψo
ξg
exp[−2
π
i(
g
+ s ) • ( rn )]dV
∫
ψo t / 2
=
∫ exp[−2πi(sz)]dz
ξ g −t / 2
• Integration gives the result:
Applies for finite s, does not apply when s = 0
• ξg is the extinction length for a particular g.
ψg =
• Intensity:
 I  sin 2 πts
Ig =  o 
2
 ξ g  (πs)
ψ o sin πts
ξ g (πs)
2
 π  sin 2 πts
eff
Ig =  
2
 ξ g  (πseff )
2
• Using dynamical theory this expression
changes slightly to:
2
where seff = s +
1
ξ g2
if s = 0 (exact Bragg condition) then seff = 1/ ξg
Contrast seen in perfect crystals:
1. Thickness fringes from variations in sample thickness
2. Fringes in convergent beam patterns from beam tilt.
3. Bend contours from sample curvature
Thickness Fringes
when s = 0, t varies
Ig = sin 2
πt
ξg
1
Intensity
0
BF Intensity
Io
ξg/2
Ig
Io = 1− Ig
ξg
Intensities
the same
t
z
Figure 23.2 W & C
Dark fringe
in image
z
Bright fringe
in image
100 nm
Convergent Beam Pattern
Uniform sample thickness t in focussed beam, beam tilt varies so s varies.
 π  sin 2 πts
eff
Ig =  
2
 ξ g  (πseff )
2
seff = s2 +
1
ξ g2

1` 
2
t  si + 2  = n i2 minima occur where n i is an integer
ξg 

2
 s 2
11 1
s
1
1
1
i
  = − 2  2  + 2 plot of i versus 2 gives intercept 2 and slope − 2
ξ g  ni  t
ni
ni
t
ξg
 ni 
x
g
0
si = g 2 λ i
R
s x 2θ x gx
Note : = =
=
g L
kR
R
R
xi
Thickness Fringes
t varies, s constant
Near strong diffraction condition, strength of the fringes die away in the thickest
regions due to preferential absorption of one of the Bloch waves.
BF Aluminum. Fringes are regions of constant thickness. Many dislocations also visible.
http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/microscopy/fringes.html
Bend Contours
when s varies, t constant
S=0
S<0
S>0
BF Al again near a zone axis pattern (ZAP) bend contour.
http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/microscopy/bend.html
S=0
S>0
Zone Axis Pattern (bend contour pattern around a zone axis) Example from [110] Au zone axis, Y.
Takai, J. Elec. Microscopy 41 (1992) 116. (a) image (b) method to measure local curvature: tilt the
beam by angle α and measure image shift
distance L. Radius of curvature = L/α
Bend contour
small radius of curvature
Fe (001) bcc
Planview TEM
• large black band is a bend
contour (220)
• planar defects visible (250 nm
long)
• Fine spots ion milling damage
Diffraction Contrast - Defects
Perfect crystals display only contrast from bending or thickness variations
If there is a defect, obtaining the strongest contrast and the most information about it requires:
1) setting up a two-beam strong diffraction condition such that the diffraction vector g is
known
2) setting the deviation s to be slightly positive (the excess Kikuchi line outside the hkl spot).
Consider a perfect crystal now with a distortion R (z) from a defect
•
•
•
•
kinematical amplitude of the diffracted beam: ψ = ψ o exp[−2πi( g + s ) • ( r + R)]dV
∫
g
n
ξg
rn =lattice vector so g•r = integer
For a narrow column of the crystal thickness t:
ψo t / 2
=
assuming |s| ≈ sz and s •R is small
∫ exp[−2πi(sz + g • R)]dz
ξ
g −t / 2
integral becomes:
Flat sample, no bending, no thickness variation: it is the g•R term that will impact the
intensity
Let α = 2πg•R
Defect Imaging
Planar defect such as a stacking fault (SF):
• For example: R = 1/3{111} is a very common type of SF in FCC materials.
• R = 1/2{110} in some intermetallics where ordering occurs eg. NiAl, CuAu or oxides
if g = <100> then α =nπ ; called π fringes
• Antiphase boundary (APB), R can be very small giving rise to δ fringes.
A
b
C
B
A
C
Intrinsic SF
(vacancy
loop)
B
A
B
C
B
A
a
b = {111}
3
B
A
C
B
A
C
B
A
Extrinsic SF
(interstitial
loop)
C
B
A
B
A
C
B
A
C
B
A
SF from
mechanical
deformation
along arrow
SFs in ZnSe/BeTe/GaAs (001)
SFs in ZnSe/BeTe/GaAs - planview
Side view
Top view
Growth, branching, and kinking of molecular beam epitaxial <110> GaAs nanowires, Z.
H. Wu, J. Q., Liu, X. Mei, D. Kim, M. Blumin, K. L. Kavanagh, and H. E. Ruda, APL 83
(2003) 3368.
Planar defects in <111> GaAs nanowires
[110]
[110]
(a)
(b)
(111) planar twin boundary: Faulted stacking sequence (b).
The density of planar defects varies. The broader the
nanowire, the higher the possibility for finding these defects.
InAs wires grown by MOCVD on
InAs (111)B substrates.
[2ĪĪ0]
20 nm
0002
BF from two regions of the
same wurtzite InAs NW
observed from two different
zone axis orientation [0lĪ0]
and [2ĪĪ0]; Stacking faults
are visible only from the
[0lĪ0] orientation while NW
appears defect free at [2ĪĪ0]
orientations;
5 nm
0002
[0lĪ0]
20 nm
[0lĪ0]
5 nm
(110)
(100)
Z.L. Bao
Ph.D. Thesis
(2006)
Twinning modulation in ZnSe nanowires,
Y.Q. Wang, U. Philipose, H.E. Ruda, and K.L. Kavanagh,
Semicond. Sci. Technol. 22 (2007) 175
Au/ZnSe/Si
C
B A B
C
{111}
Twinned
Interface
40˚
Dislocation formation at a strained interface (“plastic” deformation)
as
Pseudomorphically strained
InGaAs
af > as
GaAs
as
Partially relaxed
Strain relaxation = bi/D,
where:
bi = interfacial slip vector,
D = dislocation spacing
PtC
amorphous
capping
material
InGaAsP
QW’s
No defects,
pseudomorphically
strained
Ortel optical
device structure
cross-sectioned
via FIB
(002)
InP
Plastic deformation: Interfacial Dislocations
• GaAsInN/GaAs (N=1.5%)
• Bright field TEM g = (220)
• MBE grown Tsub= 500°C
• b is 60° tilted out of the interface
along a <110>
g
Diffraction Contrast – Dislocations
Deformation R now dependent on b
Dark image contrast is slightly displaced
from the core of the dislocation and
depends on s.
No contrast from dislocation since
deformation is out of plane.
http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_6/backbone/r6_3_1.html
Dislocations
Pure screw dislocations:
b || u || z
bβ
R=
cylindrical coordinates
2π
 β 
g • R = g • b
 = 0 when g ⊥ b or u
 2π 
AFM image of surface step from real
screw dislocation; u into surface.
Watkins et al. J. Crystal Growth 170
(1997) 788.
φ
z
r
u
b
Deformation is parallel b and
independent of angle φ.
More Dislocations
Deformation R dependent on b
Pure edge dislocation :
b ⊥u
and b and u both || to the surface:
u
1  be sin 2 β 


R=
2π  4(1 −ν ) 
If b and u both parallel to the surface then:
1 
be sin 2 β  (1 − 2ν )
cos 2 β  
bβ +

R=
+
b
×
u
ln
r
+



2π 
4(1 −ν )
4(1 −ν )  
 2(1 −ν )
General dislocations: mixed screw and edge, b not parallel to line direction u:
g • (b × u ) = 0
1 
be sin 2 β 


R=
bβ +
where be is the edge component
2π 
4(1 −ν ) 
Example: Dislocations at the interface of a single layer (15 nm) InGaAsN/GaAs. u || surface
Invisibility Criteria:
g• b = 0 and g• b× u = 0
What types of dislocations are
here?
g = (220)
Plastic deformation: Interfacial Dislocations
• GaAsInN/GaAs (N=1.5%)
• Bright field TEM g = (220)
• MBE grown Tsub= 500°C
• b is 60° tilted out of the interface
along a <110>
g
GaSb islands grown on GaAs - quantum dots; Planview TEM g = (004)
Pure edge dislocations in both directions visible since b = a/2<110>. Moiré fringes visible
perpendicular to [002]
20 nm
Strained QW
Partially relaxed QW via a dislocation loop.
GaAs
InGaAs
GaAs
Stacking fault
Viewed along a <100> direction. The stacking faults
occur on {110} planes. R ∝ <110>
GaAs/In0.27Ga0.73As/GaAs buried Quantum Wells
- planview TEM micrographs
10 nm
s >> 0
s=0
BF
WB
<100>
100 nm
12 nm
s >> 0
s>0
BF
Bright Field
WB
Weak Beam Dark Field
Dislocations running perpendicular to surface of sample
W & C Text: Fig. 25.19
• Edge dislocation contrast is weak but strong contrast from screw dislocations.
• g • b = 0, so all contrast is from surface relaxation
Dislocation Loops
• often form after rapid quenching from high temperatures
• or after ion implantation (eg. Ga ion beam milling)
• resulting points defects precipitate into dislocation loops
Cracks from brittle strain relaxation:
GaAsN Growth on GaAs
• N content = 2.2%
• Substrate temp.
500°C
• Bright field TEM,
g= (004)
• Film 340 nm thick
• Crack seen to
propagate from
surface