ANANDH SUBRAMANIAM - IITKhome.iitk.ac.in/~anandh/presentations/Nanotech2007.pdf · At high angles...
Transcript of ANANDH SUBRAMANIAM - IITKhome.iitk.ac.in/~anandh/presentations/Nanotech2007.pdf · At high angles...
CHARACTERIZATION OF NANOSTRUCTURESCHARACTERIZATION OF NANOSTRUCTURES HRTEMHRTEM
ANANDH SUBRAMANIAMDepartment of Applied Mechanics
INDIAN INSTITUTE OF TECHNOLOGY DELHINew Delhi-
110016Ph: (+91) (11) 2659 1340, Fax: (+91) (11) 2658 1119
[email protected], [email protected]://web.iitd.ac.in/~anandh
March 2007
The entire presentation is available at:
http://web.iitd.ac.in/~anandh/Nanotech2007.ppt
Transmission Electron Microscopy
David B. Williams and C. Barry Carter
Plenum Press, New York, 1996.
Monographs in Practical Electron Microscopy in Materials Science
J.W. Edington
Philips, Eindhoven, 1974.
High-Resolution Electron Microscopy for Materials Science
Daisuke Shindo
and Kenji. Hiraga
Springer-Verlag, Tokyo, 1998.
Experimental High-Resolution Electron Microscopy John C.H. Spence Oxford University Press, 1988.
High-Resolution Electron Microscopy John C.H. Spence Oxford University Press, 2003.
REFERENCESREFERENCES
When do we see anything ? –
Contrast
How do we see fine detail ? –
Resolution
How can we see better ? –
The TEM
What is meant by ‘High-Resolution’?
What things are there to be ‘seen’
? –
Imaging (as we go along)
HRTEM
Nanostructures by HRTEM: Image Gallery
OUTLINEOUTLINE
HRTEM
= High-Resolution Transmission Electron Microscopy
How can we define nanostructures in a general way ?
What do we want to see in nanostructured
materials ?
Why do we want to see these details ?
TEM of Nanomaterials
0.66 nm
1.4 nm
IGF
Grain-1
Grain-2
0.66 nm
1.4 nm
IGF
Grain-1
Grain-2
High-resolution micrograph from a Lu-Mg doped Si3
N4
sample showing the presence of an Intergranular Glassy Film (IGF).
TEM: High-resolution phase contrast image
Atomic-resolution scanning transmission electron microscope (STEM) images ofan intergranular
glassy film (IGF) in La-doped -Si3
N4
:a) High-angle annular dark-field (HAADF-STEM)b) Bright-field (BF-STEM)
N. Shibata, S.J. Pennycook, T.R. Gosnell, G.S. Painter, W.A. Shelton, P.F. Becher
“Observation of rare-earth segregation in silicon nitride ceramics at subnanometre
dimensions”
Nature 428 (2004) 730-33.
(a) (b)[0001]
STEM: High-Angle Annular Dark Field Image + Bright Field Image
HAADF-STEM images of the interface between the IGF
and the prismatic surface of an -
Si3
N4
grain. The -Si3
N4
lattice structure is superimposed onthe images. a)
La atoms are observed as the bright spots (denoted by red arrows) at theedge of the IGF. The positions of La atoms are shifted from that of Si atoms based on theextension of the -Si3
N4
lattice structure; these expected positions are shown by opengreen circles. b)
reconstructed image of a, showing the La segregation sites more
clearly. The predicted La segregation sites obtained by the first-principles calculations are shown by the open white circles.
N. Shibata, S.J. Pennycook, T.R. Gosnell, G.S. Painter, W.A. Shelton, P.F. Becher
“Observation of rare-earth segregation in silicon nitride ceramics at subnanometre
dimensions”
Nature 428 (2004) 730-33.
Window for intensityprofile
40 nm
16 nm
22 n
mA
A
A A
aFWHM ~ 3.2 nm
Window for intensityprofile
40 nm
16 nm
22 n
mA
A
A A
aFWHM ~ 3.2 nm
Diffuse Dark Field image from a grain boundary in SrTiO3
TEM: Diffuse Dark Field Image
We see something if-
Light enter our eyes
-
There is contrast in the imageWe have strong or weak contrast*
Contrast (difference in intensity between
two adjacent areas)
Amplitude contrast
Phase contrast ~ Fringes
1 2
2 2
IC I II I
When do we see anything ? –
Contrast
> 5-10 % we see
* But not bright or dark contrast (these terms refer to intensity and not to contrast)
Thickness Fringes
Bend Contours
Fresnel Fringes
Moiré
Patterns
Phase contrast
Lattice Fringes
In most of the situations both type of contrasts contribute to an image-
although one will tend to dominate
~ Fringes
Contrast
Amplitude Contrast
Diffraction contrast
Absorption contrastMass-thickness contrast small effect in a thin specimen
Bright Field & Dark Field Images
Resolution of human eyes ~ (0.1 –
0.2) mm Highest useful magnification is governed by the resolution Raleigh criterion
is used for the definition of resolution
How do we see fine details ? -
resolution
0.61sin
~2
1/ 2
1.22~E
100keV electrons λ = 4pm
Optical Microscope
TEM
→ Smallest distance that can be resolved
→ Wavelength of radiation
→ Semi-angle of collection
→ Refractive index of viewing mediumGreen light= 550 nm ~ 300 nm 1000 atomic diameters
2x
30x 10x
Magnification without detail in image does not help!
Rayleigh criterion
Not a fundamental rule but a practical definition. Figure of merit in terms of the eyes ability to distinguish separate
images of two self-luminous incoherent point sources. A single point source will not be imaged as a point even if aberrations
are absent. Any physical limit in the path of the rays (outer boundary of the lens /
aperture)
will lead to diffraction effects. Diffraction → point is imaged as a disc (Airy disc).
P2P1
Fully resolved
P1 P2
Unresolved
P2P1
0.61
Just resolved according
to Rayleigh criterion
20 %
What is meant by High-Resolution?
High Spatial Resolution
microscope’s ability to process high spatial frequencies
High Energy Resolution
spectrometer’s ability to resolve two closely positioned energy peaks
High Chemical Resolution
ability to detect small quantities of a given chemical species
In general
Additionally, one would like to differentiate two structures adopted by a material of a given composition
This is essentially related to the above-mentioned points
Phase contrast (lattice fringe) image but not ‘high’-resolution
High-resolution but not a lattice fringe image
Phase contrast image of as-cast Mg37
Zn38
Y25
alloy showing a 18 R modulated phase
Picture taken in a JEOL
2000FX microscope with W filament. Resolution ~ 2.8Å
2 nm2 nm2 nm
A
A
(b)(a)
1.2 nm
2 nm2 nm2 nm
A
A
(b)(a)
2 nm2 nm2 nm
A
A
(b)(a)
1.2 nm
Fourier Filtered Fresnel Contrast Image from Si3
N4
–
grain boundary having an IGFPicture taken in a JEOL
JEM
4000 EX, with LaB6
filament. Resolution ~ 1.8 Å
OBJECT PLANE
BACK FOCAL PLANE
IMAGE PLANE(Gaussian Image Plane)
Diffraction Pattern
f
u
v
Lens
How can we see better ? – The TEM
Absorbed Electrons Electron-Hole Pairs
Incident High-kV Beam
Direct Beam
SPECIMEN
Elastically Scattered Electrons
InelasticallyScattered Electrons
BremsstrahlungX-
rays
Auger ElectronsVisible Light
BackscatteredElectrons (BSE)
Secondary Electrons (SE)
Characteristic
X-rays
Incident electronbeam direction
Thin specimen
Diffractionpattern
Forward scatteredbeam directions
Incident electron beam With
Uniform intensity
Thin specimen
Image Scattered electrons with
varying intensity
Scattering by the specimen changes the spatial
and Angular
distribution of the electrons
Scattering
Elastic
Inelastic
Coherent
Incoherent
Elastic scattering is usually coherent if specimen is thin & crystalline In TEM elastic scattering is predominant in (1 -
10)
in the forward direction Elastically scattered electrons at large angles (> 10) can be incoherent Inelastic scattering almost always incoherentMost of scattered electrons < 5
(< about 3
they are coherent)
Particle concept
Wave concept
~ (1-10)0
Forward
~ < 10
Forward
Z has important effect
SpecimenThin
Thick
Coherent forward scattering
Incoherent back scattering
Coherentincident beam
Incoherent elastic backscattered electrons Secondary electrons
from with in the specimen
Coherent elastic scattered electrons
Incoherent elastic forward scattered electrons
Thin specimen
Direct beamIncoherent inelastic scattered electrons
Bulk specimen
Incoherent elasticbackscattered electrons
Secondary electronsfrom with in the specimen
Incoherent elasticbackscattered electrons
Coherentincident beam
Interaction cross section (σ)
T elastic inelastic 2r
elastic
ZeVr
(approximate) neglects screening effects
The chance of a electron undergoing any interaction with an atom isdetermined by an interaction cross section.
σ (in area units)Probability that a electron scattering event will occur = Actual area of atom
r → effective radius of a scattering centre Z → atomic number
→ Scattering angle (greater than this) V → potential of incoming electron e → charge in esu
(4.803 x 1010
esu)
0 TT
N tprobability of scattering by the specimen P Q t
A
Transition metals 100 keV
electrons(Mean free path ( λMFP
))
22 210elastic m
10MFP s of nm
22 26 210 10inelastic m
0
1MFP
T
AN
Mass-thickness
contrast
Electron Cloud
Nucleus
Scattering by electron cloud
Scattering by nucleus (Rutherford scattering)
Elastic Scattering
At high angles Rutherford scattered electrons become incoherent
Forward scattered
Back scattered In TEM this signal is small
Image of beam entrance surface (Z + topography) used in SEM
Z contrast imaging atomic resolution microanalysis
A
B
• A, B processes may not be truly elastic (B may produce x-rays)•
Higher the angle that an electron emerges more the chance that it would have been inelastically
scattered
0
4
8
12
0.2 0.60.4(Sinθ)/λ (Å1)
f(θ)(Å)
Al Cu
Au
Incre
asing
Z
Change in atomic scattering factor with scattering angle
Variation of Rutherford cross section with scattering angle
60 120 180
-28
-26
24
-22
(degrees) Angle, Scattering
)(m
)(Log2
10
Beam Energy = 100 KeV
0
Au
Cu
C
Decreases orders of magnitude !
Basis for HAADF
High-angle scattering is incoherent
image contrast is due to Z and not
orientation of the specimen
Inelastic Scattering (Energy Loss)
Secondary electrons
Collective interactions / Oscillations
X-ray
Radiation damage
Characteristic x-rays
Bremsstrahlung
Electron-hole pairs and cathodoluminescence
Incoming electrons
(~100 keV)
Vacuum
Energy Loss electrons
Energy
levels
KE
1LE
2LE
3LE
Nucleus
K
1L
2L
3L
Characteristic x-rays(10−16s later)
Conduction Band
Valence Band
Characteristic x-rays
Valence Band
Conduction Band
Inner shells
Fast SE( 50 -200 keV)
Auger electrons
Up to 50%Energy loss
Slow SE
~ 50 eV
100s ev-few keV
FSE
are unavoidable and undesirable One does not form images with them as they can
come from deep with in the specimen
May degrade the quality of spectroscopic data
For surface chemistry
Topography in SEM
(resolution using FEG
~ 1nm at 30 keV)
+
STEM ( high-resolution)
Secondary electrons
SemiconductorsConduction band
Valence band
Band gap
e
e
hole
Hν
cathodoluminescence
(CL)
spectroscopy
Bias Electron beam induced current ( EBIC)
Charge collection microscopy
OR
Electron-hole pairs and cathodoluminescence
100 200 300 400
10-26
10-25
10-23
10-24
10-22
10-21
)(m 2
Aluminium
Plasmons
IonizationL
K
F S E
S E
Elastic scatter
Secondary Electrons
Incident beam energy (keV) →
Cross sections for the various scattering processes
Electron properties as a function of accelerating voltage
Accelerating voltage (kV)
Nonrelativistic wavelength (nm)
Relativistic wavelength (nm)
Mass (x mo
)Velocity
(x 108 m/s)100 0.00386 0.00370 1.196 1.644
120 0.00352 0.00335 1.235 1.759
200 0.00273 0.00251 1.391 2.086
300 0.00223 0.00197 1.587 2.330
400 0.00193 0.00164 1.783 2.484
1000 0.00122 0.00087 2.957 2.823
Resolution in the TEMResolution in the TEM
Electron Source
Imaging System
Resolution
= f(Voltage), High coherency FEG
↑
voltage
Can’t increase as lens aberrations ↑
with β61.0
rth
Note : Electron sources are coherent can’t use Rayleigh criterion.
P2P1
Fully resolved
P1 P2
Unresolved
P2P1
0.61
Just resolved according
to Rayleigh criterion
Can be increased by a larger lens aperture but electron lenses are not good
Electron Source
Lenses
Imaging System
Resolution
= f(Voltage), High coherency FEG
Apertures
Control the quality of• Images• Diffraction patterns• Analytical signals
•Lens defects affects the resolution but give us increased ‘Depth of Focus’
& ‘Depth of Field’• Can suffer from 10 kinds of aberration
Spherical Aberration
Chromatic Aberration
Control • Beam current and Convergence• Cutoff paraxial rays which suffer aberration• Image contrast• Type of image (BF / DF)• Select areas from which we want diffraction patterns (SAD)
Astigmatism
“The current best electromagnetic lens is like using a coke bottle for a magnifying lens” “If the lens of our eyes was as good as the best electromagnetic lens available then we
would be legally blind”
Lenses aberrations
Spherical Aberration
Chromatic Aberration
3sph sr = C β
chr cEr = C β
E
Most important in objective lens in TEM & condenser lens in STEM
Cs
~ Focal lengh
~ (1-3 mm)
Current high tension supplies are stable to 1 in 106
(100 keV
beam 0.1 eV) For electrons passed through a sample (50-100 nm thick) E = (15-25) eV
Astigmatism astr = β f Maximum difference in focus introduced by astigmatism
Due to non-uniform magnetic field in the path of electrons Can be corrected with a stigmator
Gaussian image planeDisk diameter = 2CS
β3
Plane of least confusionDisk diameter = CS
β3
P
P’
CS = 0
β0
dmin
CS
≠
0 The spherical aberration of the lens
causes wavefronts
from a point object P
to be spherical distorted
The point is imaged as a disc with a
minimum radius in the plane of least confusion
The disc is larger in the Gaussian image plane
Lens
This figure has been exaggerated in the angular dimension
Effect of Spherical Aberration
Spherical aberration
AssumeSpecimen is thin → low chromatic aberration
Astigmatism is corrected
14
min30.91
opt scr 143
sc
1 14 4
0.77opt
s sc c
rsph
limits the resolution Further resolution f(Rayleigh
criterion, aberration error)
0.0037nm 3
smmc
15opt
mrad min 0.3nmr
HREM min 0.15nmr
100 kev electrons
Useful magnification
Take resolution on specimen ~ 2 Å
→ Magnify the resolution of eye 0.2 mm3
69
0.2 10 100.2 10usefulM
Inelastic scattering causes loss of the energy of electrons Electron-electron interaction Loss in energy + Change in momentum Thin specimen required EELS spectrometer has a very high energy resolution
[(FEG
~ 0.3 eV), (XEDS
→ resolution ~ 100eV)]
Note: beam energy can be 400 kV Can be used in forming energy filtered images + diffraction patterns
Electron Energy Loss Spectrometry (EELS)Electron Energy Loss Spectrometry (EELS)
EELS
Inter of intra band transitions
Plasmon excitation
Phonon excitation
Inner shell ionization
Part of the zero loss peak. Not resolved. Causes specimen to heat up.(~ 0.2 eV, 5-15 mrad)
(5-25 eV, 5-10 mrad)
(~5-25 eV, < 0.1 mrad)
(~30-1000 eV, 1-5 mrad)
Bulk plasmon
Surface plasmon
λp
~ 100nm
• Transverse waves•
Half the energy of bulk plasmons
Signature of the structure
• Longitudinal waves
COLLECTIVE OSCILLATIONS
PLASMONS PHONONS
Collective oscillations of free electronsMost common inelastic interaction Damped out in < 1015
s Localized to < 10 nm
Predominant in metals (high free electron density)
Collective oscillations of atoms Can be generated by other inelastic
processes. (Auger / X-ray energy)Will heat up the specimen Small energy loss < 0.1 eV
Phonon scattered electrons
to large angle (5 –
15 mrads) Diffuse background
Plasmon excitation
Longitudinal wave like oscillations of weakly bound electrons Rapidly damped (lifetime ~10-15
sec, localized to < 10 nm) Dominate in materials with free electrons (n) (Li, Na, Mg, Al )
But occur in all materials EP
= f(n) microanalytical
information Carry contrast formation, limit image resolution through chromatic aberration Can be removed by energy filtering
Inter of intra band transitions
Change in orbital state of the core electron Interactions with molecular orbital → can be used for finger printing Secondary electron emission (< 20eV)
(hence in same energy-loss regime as band transitions) Weakly bound outer-shell electrons control the reaction of a material to an
external field → controls the dielectric response (can measure with the signal
from the < ~ 10eV region)
Inner shell ionization
The other side of the coin of XEDS. Small cross section (ΔE ↑
cross section ↓) K , L (L1
, L2
, L3
) , M (M1
, M2
, M3
, M4;5
). Combination of ionization loss with plasmon loss can occur.
There are intensity variations superimposed on the ionization edge
ELNES
(starting from about 30 eV
of the edge and extending ~100s of eV)
EXELFS
(~50 eV
after ELNES) ELNES
and EXELFS
arise due to the ionization process imparting more than critical energy (Ec
) for ionization
0 40 80v
Io
Plasmon peak
250 300 350 400 450Energy-loss (eV)
ELNES
EXELFS
Zero loss peak
Forward scattered (cone of few mrad) 000 spot of DP Bragg diffracted peak (~20mrad) rarely enters the spectrometer) Includes energy loss of ~0.3 eV Includes phonon loses EELS does not resolve phonon loses
FWHM
defines the energy resolution
E resolution
kV resolution
Low loss region ~ 50 eV
Ionization Edge
Bonding effects
~50 eV
after ELNES
Diffraction effects from
the atoms surrounding
the ionized atom
The EELS spectrum
ELNES-
Energy Loss Near Edge StructureEXELFS-
EXtended
Energy Loss Fine StructureCoordination, Bonding effects,
Density of states, Radial distribution function
Thin specimen is better (plasmon peak intensity < 1/10 th
zero loss peak) Use high E0
(scattering cross-section , but benefit is in
of plural scattering + edge signal to noise ratio )
Energy resolution limited by electron source
Chemical analysis (structural and elemental) using EELS
Spatial ResolutionTEM
STEM Limited by size of probe (~1nm)
Limited by selecting aperture at spectrometer entrance (its effective size at the plane of the specimen)
Energy Resolution 1 eV
(incident energy 200-400 eV!)
• Somewhat better than XEDS• FEG
< 1nm resolution
• Using FEG
DSTEM
Krivanek
et al. [Microsc. Microanal. Microst. 2,
257 (1991).] detected single atom of Th
on C film
No visible Grain Boundary
2.761 Å
Fourier filtered image
Dislocation structures at the Grain boundary
counts
eV
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
counts
1850 1900 1950 2000 2050 2100 2150 2200 2250eV
counts
eV
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
counts
1850 1900 1950 2000 2050 2100 2150 2200 2250eV
Si peak at 1839 eV Sr
L2,3
peaks
Grain Boundary
Grain
eV1900 2000
EELS
2100 2200
~8º
TILT BOUNDARY IN THE SrTiO3
POLYCRYSTALGB23x4
MX23x4
Dist 5 nm
VG microscope
[1] Using FEG
DSTEM
Krivanek
et al. [Microsc. Microanal. Microst. 2,
257 (1991).] detected single atom of Th
on C film[2] Chapter 40 in Transmission Electron Microscopy by David B. Williams and C. Barry Carter, Plenum Press, New York, 1996.
EELS microanalysis detection of a single atom of Th
on C film
EELS microanalysis
Si L edge ELNES
changes across a Si- SiO2
interface due to change in Si bonding atomic level images with spectra localized to individual atomic columns
[1]
[2]
Energy-loss (eV) →
v
280 290 300 310 320
Graphite
Diamond
Differences between C edge between graphite and diamond
Change in Cu L edge as Cu metal is oxidized
Energy-loss (eV) →
v
920 940 960 980
CuO
Cu
L3
L2
[1] [1]
[1] Chapter 40 in Transmission Electron Microscopy by David B. Williams and C. Barry Carter, Plenum Press, New York, 1996.
ELNES
2D image of 3D specimen
Diffraction contrast
Contrast depends on lenses + apparatus
Absorption contrast is usually small
Phase contrast related to specimen and not to topography (or “depth”)
“Seeing is believing “
? ! ?
High Resolution Microscopy
With Reference to Lattice Fringe Imaging in a TEM
)( ),( rfyxf
)( ),( rgyxg
)(rh
Point spread function )(uHContrast transfer function
Specimen
Image
Diffraction patternBack focal plane
( )F u
( )G u
Rea
l spa
ceR
eciprocal space
Fourier transform
2 ) ()(
432 uCufu s
)()()( rhrfrg
)()()( uFuHuG
Point spread function
Convolution in real space gives multiplication in reciprocal space
Contrast transfer function
Aperture function
Envelope function
Aberration function
)()()()( uBuEuAuH
Property of lens
) , , ,()( sCuffu
)](exp[)( uiuB
Specimen transmission function
Phase distortion function
High resolution implies ability to see two closely spaced features in the sample (real ‘r’
space) as distinct
This corresponds to high spatial frequencies large distances from the optic axis in the diffraction pattern (reciprocal (u) space)
Rays which pass through the lens at such large distances are bent through a larger angle by the objective lens
Due to an imperfect lens (spherical aberration) these rays are not focused at the same point by the lens
Point in the sample disc in the image (spreading of a point in the image)
Objective lens magnifies the image but confuses the detail (hence the resolution is limited)
Each point in the final image has contributions from many points
in the specimen (no linear relation between the specimen and the image)
Is a linear relationship possible?
yxieyxAyxf , ),(),(
f(x,y) → specimen function
→ phase (function of V(x,y,z))
V(x,y,z) → specimen potential Vt
(x,y) → projected potential
→ Interaction constant (=/E)
Phase Object approximation
yxieyxf ,),(
Weak Phase Object approx.
),( 1),( yxVyxf t
d
V(x,y,z) Specimen
Phase change = f(Vt
)
yxVi teyxf , ),(
WPOA For a very thin specimen the amplitude of the transmitted wave function will be linearly related to the projected potential
Specimen and approximations
)],(, [),( yxyxVi teyxf
dzzyxVyxVt ),,(),(
),( ),( yxVyxVE
d tt
Including
absorption
meEh
2In vacuum
),,((2'
zyxVEmeh
In the specimen
dzdzd
22'
Phase change dzzyxVE
d ),,( dzzyxVd ),,(
dzzyxVyxVt ),,(),(),( ),( yxVyxVE
d tt
→ Interaction constant (=/E) tends to a constant value as V increases(energy of electron proportional to E & 1, variables tend to compensate)
2 3 4
11! 2! 3! 4!
x x x x xe
POA
holds good only for thin specimens
If specimen is very thin {Vt
(x,y) << 1} WPOA
In WPOA
{f(x,y) = 1
i
Vt
(x,y)} the amplitude of the transmitted wave will be linearly related to the projected potential of the specimen
)()()( rhrfrg
),()],( 1[),( yxhyxVyx t
WPOA
)],( ),([)],( 1[),( yxSiniyxCosyxVyx t
[1 2 ( , )] ( , )tI V x y Sin x y
I = * Neglecting 2
Only imaginary part of B(u) contributes
to intensity
)](exp[)( uiuB
)]([2)( uSinuB
)]([2 )()()( uSinuEuAuT
Objective lens transfer function Incoherent illumination T(u) = H(u)
T(u) ve
+ve
phase contrast (atoms would appear dark)
In WPOA
T(u) is sometimes called CTFApproximately
)]([)(2)( uSinuAuT
Or
coherencespatialchromaticeffective EEuTuT )()(
Envelope is like a virtual aperture at the back focal plane
u (nm1)
→
T(u)
= 2
Sin
()→
+2
2
v
2 4 6
Cs
= 1 mm, E0
= 200 keV, f = 58 nm)
2.5Å
)]([)(2)( uSinuAuT
u (nm1)
→
T(u)
= 2
Sin
()→
Cs
= 2.2 mm, E0
= 200 keV, f = -100 nm)
)]([)(2)( uSinuAuT
T eff
ectiv
e(u)→
u (nm1)
→
coherencespatialchromaticeffective EEuTuT )()(
Scherzer
defocus and Information Limits 124
3Scherzer sf C
1 34 4
Scherzer su =1.51 C
1 34 4
Scherzer s= 0.66 C r
Instrumental resolution limit
can use nearly intuitive arguments to interpret the contrast
Information limit
Damping envelope
IMAGE SIMULATIONIMAGE SIMULATION
Computer simulation (a) and electron micrograph (b) of a Cu Cubeoctahedron
consisting of seven shells (1415 atoms) in [001] orientation. Structures of nanoclusters
by high-resolution transmission electron microscopy by J. Urban, Volume 10, p.161 in Encyclopedia of Nanoscience
and Nanotechnology (Ed.: Hari
Singh Nalva), American Scientific Publishers, Stevenson Ranch, 2004.
(a) (b)
Thickness dependency of lattice images of a Si crystal (200 kV, f = 65 nm). Thickness changes from 1nm (a) to 86 nm (r) in steps of 5 nm.
High-Resolution Electron Microscopy for Materials Science by Daisuke Shindo
and Kenji Hiraga, Springer-Verlag, Tokyo, 1998.
Defocus dependency of lattice images of a Si crystal (200 kV, t = 6 nm). Thickness changes from 20 nm (a) to 90 nm (l) in steps of 10 nm.
High-Resolution Electron Microscopy for Materials Science by Daisuke Shindo
and Kenji Hiraga, Springer-Verlag, Tokyo, 1998.
In lattice fringe imaging mode:
Things which look like ‘atoms’
are not atoms!
Use image simulation to confirm what you see
Do not interpret details below the resolution limit of the microscope
HRTEM-
some tips
Spherical aberration correctors for illumination as well as imaging lens systems,
Electron beam monochromators
reducing the energy spread of the electron beam
to < 0.1 eV
High-energy resolution spectrometers (Sub-eV
mandoline
filter for EELS)
Imaging energy filters
Advanced specimen holders for in-situ experiments
High-sensitivity and high-dynamic-range detectors for images, diffraction patterns,
electron energy loss spectra (EELS) and energy dispersive X-ray spectra (EDXS)
Advanced methods Focal series reconstruction
Electron Holography
In-focus ‘Fresnel’
reconstruction
It is possible to record phase contrast images with point resolutions of well below
0.1 nm, or alternatively, scan electron probes of size < 0.1 nm
across the
specimen, recording high-angle scattering or high-energy resolution spectra from
areas as small as a single atomic column.
ADVANCESADVANCES
ELECTRON HOLOGRAPHYELECTRON HOLOGRAPHY
High-resolution (a) amplitude and (b) phase images of the aberration-corrected object wave reconstructed from an electron hologram of [110] Si, obtained at
300 kV on a CM 30 FEG
TEM. The characteristic Si dumbbell structure is visible only after aberration correction. A. Orchowski
et al., Phys. Rev. Lett. 74, 399, 1995.
(a) (b)
-40 0 40-20 20Distance (Å)
RTHTCooled to RT
20 nm20 nm20 nm
A
A2.3 nm
20 nm20 nm20 nm
B
B
2.5 nm
20 nm20 nm20 nm
C
C 3.2 nm
RT
HT
Cooled to RT
FRESNEL RECONSTRUCTIONFRESNEL RECONSTRUCTION
Exit face wave reconstructed profiles, of the imaginary part of the inner potential, using
zero-defocus Fresnel fringe images
NANOSTRUCTURESNANOSTRUCTURES
IMAGE GALLERYIMAGE GALLERY
HRTEM
micrographs of MWNT: (a) 5-walled, diameter = 6.7 nm; (b) 2-walled, diamter
= 5.5 nm; (c) seven-walled, diameter = 6.5 nm (hollow
diameter = 2.2 nm).
S. Iijima, Nature, 354, p.56, 1991.
HRTEM
image of a BN
multi-walled nanotube
(inner shell distance of ~ 0.33 nm).D. Golberg
et al., J. of Appl. Phys. 86, 2364, 1999.
NANOTUBESNANOTUBES
(a) (b) (c)
Cross section of TiN/NbN
nanolayered
coatings: (a) Conventional TEM micrograph with SAD patterns, (b) HRTEM
of {200} lattice fringes.M. Shinn et al., J. Mater. Res. 7, 901, 1992.
(a) (b)
NANOLAYERSNANOLAYERS
High-resolution micrograph of Si3
N4
–
TiN
composite prepared by CVD.High-Resolution Electron Microscopy for Materials Science by Daisuke Shindo
and Kenji Hiraga, Springer-Verlag, Tokyo, 1998.
Gas atomized Al-Si powders:
(a) HREM, (b) SEM, (c) BFI.High-Resolution Electron Microscopy for Materials Science by Daisuke Shindo
and Kenji Hiraga, Springer-Verlag, Tokyo, 1998.
[001][110]
(a)
(b)
(c)
[110]Al
NANOPARTICLESNANOPARTICLES
NANOTWINSNANOTWINS
[011]
Twin Plane
HREM
of ZrO2
showing formation of nanotwins.High-Resolution Electron Microscopy for Materials Science by Daisuke Shindo
and Kenji Hiraga, Springer-Verlag, Tokyo, 1998.
NANO(poly)CRYSTALLINENANO(poly)CRYSTALLINE
MATERIALMATERIAL
HREM
image of nanocrystalline
PdG.J. Thomas et al., Scripta
Metall. Mater. 24, 201, 1990.
MOIRMOIRÉÉ
FRINGESFRINGES
HRTEM
image of a Kr nanocluster
on a Mg substrate showing Moiré
fringes. The lattice parameter of Kr can be calculated from the Moiré
fringe spacing: [1/dfringes
= |(1/dMgO
)
(1/dKr
)|] Encyclopedia of Nanoscience
and Nanotechnology (Ed.: Hari
Singh Nalva), American Scientific Publishers, Stevenson Ranch, 2004.
Incident convergent beam
Specimen
BF detector
HAADF detector
θ3
θ2
θ1 > 50 mrad off axis
θ3 < 10 mrad
θ2 >10-50 mrad
θ1
ADF detector
High-Angle Annular Dark Field Imaging
HAADF-STEM images of the interface between the IGF
and the prismatic surface of an -Si3
N4
grain.N. Shibata, S.J. Pennycook, T.R. Gosnell, G.S. Painter, W.A. Shelton, P.F. Becher
“Observation of rare-earth segregation in silicon nitride ceramics at subnanometre
dimensions”, Nature 428 (2004) 730-33.
Intergranular Glassy FilmIntergranular Glassy Film