Download High-Resolution Transmission Electron Microscopy

HRTEM
High‐Resolution Transmission Electron Microscopy
HRTEM is about observing specimen information at atomic resolution.
HRTEM; Rolf Erni 2013
[email protected]
Why and When?
• Local atomic information
– Grain boundaries, dislocations, precipitates
• (Relative) lattice distortions
– Due to defects, like dopants, dislocations, grain boundaries
• When the sample is thin enough…
– Lattice fringes observable in thick samples do not contain atomic information
• When the sample is stable enough…
– A high electron dose is usually needed, drift is a killer
• When the sample is in perfect zone axis orientation…
– This needs to be checked on the exact area, in principle at the magnification the acquisition will take place
HRTEM; Rolf Erni 2013
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When not?
• To measure an (absolute) lattice spacing
– Better use diffraction
• To identify and to differentiate chemical species
– HRTEM micrographs do not contain much relevant chemical information
• To describe an unknown atomic structure
– Peaks might appear where there are no atoms, ambiguous image interpretation
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Outline
• Image formation in HRTEM
• Weak phase‐object approximation and phase contrast images
• Phase contrast transfer function – points to consider
• Optimized imaging conditions: which criterion?
• Multi‐Slice Simulations
• A must for the interpretation of HRTEM data
• Reconstruction of the Exit‐Plane Wave(*)
• Towards true object information… yet, not quite
(*) Depending on time!
HRTEM; Rolf Erni 2013
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Abbreviations
q
r

ep
CCD

f()
fe()
elast
e
m0=me


l
d
g
k0
kg
U=U0
V

t
I
(F)FT
ta
tL
D
spatial frequency (2D)

spatial coordinate (2D)

image wave function
C1=f
C3=CS
exit plane wave function
charge coupled device
tc
S
scattering angle
R
form factor
s
elastic scattering amplitude
t
elastic scattering cross‐section
elementary charge
r
Es
rest mass of the electron
Et
relativistic factor
solid angle
S
wave length
CC
crystal spacing
Z
reciprocal lattice vector (3D)
I0
wave vector of incoming electron
I
E0
wave vector of diffracted electron
acceleration voltage
E
(crystal) potential
U
WPOA
phase shift
(complex or phase) contrast‐transfer function
EPW
intensity
(fast) Fourier transform
aperture function
lens transfer function
diffraction limit
HRTEM; Rolf Erni 2013
aperture (semi‐)angle
aberration function
defocus
constant of (3rd order) spherical aberration
coherent phase contrast transfer (PCT) function
wave surface
point resolution
info limit due to partial spatial coherence
info limit due to partial temporal coherence
image delocalization = image aberration
envelope function due to partial spatial coherence
envelope function due to partial temporal coherence
beam divergence angle
constant of chromatic aberration
atomic number
objective lens current
objective lens current fluctuation
primary electron energy
energy spread
high voltage fluctuation (=ripple)
weak phase object approximation
exit‐plane wave
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Image Formation in HRTEM
HRTEM; Rolf Erni 2013
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2 Steps
1. Diffraction in the sample = forming the exit‐plane wave
(see kinematical diffraction theory, or dynamical diffraction theory (not treated))
2. Image formation
(linear and non‐linear imaging theory)
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What's the Object?
The Exit‐Plane Wave is imaged, not the sample!
The exit‐plane wave is formed by diffraction in the sample: the exit‐plane wave contains information about the sample.
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Step1: How to get the EPW?
• What happens when an e‐‐beam hits a crystal?
Scattering. If coherent scattering: Diffraction
• What causes diffraction, what interacts with the e‐?
Coulomb interaction with the electrostatic potential.
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more scattering
Elastic (coherent) scattering factor for electrons:
Mott formula:
This describes scattering at the nucleus.
And this describes scattering at the electron cloud.
What does this mean?
The elastic differential scattering cross‐section:
(gives the probability that the electron is scattered to the angle )
… and now?
The total elastic scattering cross‐section:
(that's the "size of the atom" the electron sees)
By the way: the Fourier transform of the scattering factor gives the electrostatic potential of the atom.
HRTEM; Rolf Erni 2013
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Diffraction: Bragg’s law
2d sin

2
 n
 is the scattering angle! 
2

2
Because the scattering cross‐sections are large, an electron can be scattered more than once, even in a thin sample.
Therefore: dynamic scattering theories are often needed to explain (HR)TEM results!
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A simpler approach
Instead of individual atoms, we have a crystal. Instead of atomic potentials, we have a crystal potential and atomic columns.
The potentials of the atomic columns in zone axis trap the electrons = e‐ gain energy and become a bit faster.
Faster = Shorter wavelength:  
1
Energy
IMPORTANT: At the exit‐plane of the crystal, electrons show a position‐dependent phase shift.
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Phase difference depends on the "weight" of the atomic column
300 keV
in‐phase
V < 0
300’010 eV
Same intensity
Phase shift
out of phase, but
coherent!
300 keV
Translation of the phase difference into an amplitude difference = phase contrast imaging
It is the imaging characteristics of a TEM which translates the phase shift into an
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amplitude modulation.
Weak Phase Object Approximation
The object changes (locally) the phase of the incident wave by 
is proportional to the projected crystal potential V (i.e. the crystal potential integrated across the thickness t):
If the phase change is small (<< 2), then we deal with a weak phase object .  ep   in  exp(i )   in  (1  i )  1  i
WPOA
The exit‐plane wave has a phase, but no amplitude modulation.
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 ep  1  i
A micrograph shows the intensity of the e‐‐wave:
What's the intensity of the EPW?
WPOA: The intensity of the EPW is constant: no specimen information.
Where's the specimen information?
In the phase of the EPW.
To get an image which contains specimen information, the phase modulation needs to be translated into an amplitude modulation. HRTEM = Phase‐Contrast Imaging.
NOTE:
The WPOA is pretty simple: in reality, there is also some amplitude modulation in the EPW, but still a (thin enough) specimen essentially modulates the phase and not the amplitude.
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Summary: Step 1
The exit‐plane wave (EPW) in HRTEM is (approximately) a wave of constant amplitude (or intensity) but with a modulated phase.
The exit‐plane wave ep is the OBJECT that needs to be imaged.
For this, the phase modulation needs to be translated into an amplitude modulation. This is the task of Step 2.
In general: the EPW is still the result of a complex dynamic diffraction process in the sample. It contains specimen information, but because of dynamic diffraction, the EPW cannot directly be interpreted as a simple projection of the crystal! HRTEM; Rolf Erni 2013
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Step 2: How to get an image?
The image intensity is given by the modulus of the convolution of the complex EPW with a complex contrast‐transfer function t which is defined by the imaging characteristics of the microscope. Coherent imaging model:
I   ep  t
2
Both, ep and t are complex functions!
The convolution mixes phase and amplitude of the EPW. The imaginary part of t (partially) translates the phase modulation of the EPW into an amplitude modulation in the image plane.
HRTEM image formation = it's all about the complex transfer function "t"
Incoherent imaging model: I    t
2
2
(see STEM)
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The object
Convolution
The transfer function
Object  Transfer function
FFT
FFT
Multiplication
Each pixel of the picture is replace by the "convolution" function weighted by the initial pixel intensity.
HRTEM; Rolf Erni 2013
Inverse FFT
Convolution = blurring the object and in case of complex functions, phases and amplitudes get mixed up.
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What contributes to t?
• The objective aperture
(to consider: diffraction at the aperture & amplitude contrast because the aperture acts as a frequency filter)
• "Lens effects"
• Partial coherence (temporal and spatial)
• The detector: CCD
• (In)stability issues
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Let's switch to frequency space
I (r )   ep (r )  t (r )
2
I (q)   ep (q)  t (q)
2
Why?
1. We don't want to know whether a certain feature is present in the image, but we want to know whether a certain lattice spacing ghkl can be observed in the image.
2. The transfer function t affects the wave in the aperture plane: that's where we have a diffraction pattern = frequency space.
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Remarks
• Relation between q and g: • Both are vectors of the reciprocal space = momentum space
• q is a general 2D vector in the aperture plane: the 2D coordinate in the aperture, equivalent to the scattering angle .
• g is a 3D vector of the reciprocal lattice of the crystal
• We deal with small angles, therefore: 
q

 


  2   sin  
 1 
2 2

 

 
1

 
q  
2 2
 is small
q
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Objective aperture
The objective aperture acts as a top‐hat function in the diffraction plane.
The aperture removes high spatial frequencies.
The aperture removes high‐angle scattering.
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Diffraction limit
Airy disk
 semi‐angle of the aperture
A large aperture gives "sharper" peaks and thus better resolution.
But lens effects (aberrations) increase with the aperture angle .
To decrease the impact of the aberrations, a small  is desirable.
A balance between D and  is necessary.
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Lens effects: Aberrations
Aberrations lead to a frequency‐dependent phase shift. is the aberration function.
C1: defocus, C3 = CS: (third order) spherical aberration
The phase contrast is given by the imaginary part: therefore
Note: the amplitude contrast is given by the real part of tc!
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The meaning of 
Ideal: a spherical wave surface remains spherical
Non‐ideal: a spherical wave surface gets warped
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= (axial) aberration function
Scattering angle 
 describes the deviation from the spherical wave surface. It's unit is a length.
optical axis

The phase shift is then given by the optical path (difference) each electron travels on its particular route. This route is given by the scattering angle . HRTEM; Rolf Erni 2013
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Optimizing the Imaging Conditions
A point is a point: spherical aberration C3 = 0
A point becomes a disk: C3 > 0
Idea: to have the disk of least confusion in the Gaussian image plane:
Scherzer focus:
Example: CS = C3 = 1 mm, = 2.5pm (200 kV), therefore Scherzer focus = ‐58 nm
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Point Resolution
Otto Scherzer
q 
The first zero‐crossing of t at Scherzer focus defines the point resolution.
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Scherzer focus
HRTEM; Rolf Erni 2013
Gauss focus
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The "sin" function implies that there is no phase contrast at q=0: HRTEM: we see "edges" and fine details but no volume information!!!
Inverse FFT
FFT
HRTEM; Rolf Erni 2013
FFT: with vanishing intensity at q=0 30
The importance of optimizing the imaging conditions
Scherzer defocus, Cs=1mm
Defocus = 0, Cs = 1mm
At Scherzer focus, the interpretability of the images is maximized, because there is a broad passband where t is almost constant.
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Impact of defocus: LiNdTiO3
200 kV, CS = C3 = 1 mm, HRTEM
Changing the focus, changes the phase contrast transfer function and the image contrast.
‐ The contrast of the atomic columns changes with focus: direct image interpretation is
often impossible: whether the atomic columns appear bright or dark, depends on the
focus setting and on the sample thickness
‐ Image interpretation often requires simulations
‐ Fringes in vacuum: image delocalization
‐ The images provide the correct symmetry
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Impact of defocus: SrTiO3
Overfocus: C1 > 0
Gauss focus
Overfocus
Underfocus: C1 < 0
300 kV, CS = C3 = 0
Aberration corrected HRTEM
‐ The contrast of the atomic
columns changes with
focus:
direct
image
interpretation is often
impossible.
‐ Close to Gauss focus, when
there are no aberrations:
the phase contrast transfer
function is 0, and no image
contrast is present.
‐ No fringes in vacuum are
observable.
‐ In thick areas, HRTEM
images show fringes, but
cannot be interpreted
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Defocus C1
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Aberration = Image artifacts
Scherzer focus optimizes the "point resolution".
But other aspects need to be considered as well…
Aberrations
Image artifacts = Image delocalization
Image delocalization r depends on the defocus and on the spatial frequency:

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Aberration = Image artifacts
Fringes in vacuum
Aberration corrected
Image delocalization
No aberrations (C1=CS=0) = no delocalization
If CS (=C3) is finite, defocus can be adjusted such that exactly ONE spatial frequency has zero delocalization!!!
In periodic crystals image delocalization is
often not apparent (but still present). Delocalization becomes obvious (and
problematic) at defects, grain boundaries, interfaces etc.
Where is the surface of the particles?
HRTEM; Rolf Erni 2013
Delocalization compensated for one spatial frequency
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Lichte focus
How to optimize the imaging conditions in respect to image delocalization?...
Hannes
Lichte
Lichte focus minimizes the image delocalization for the whole spectrum of image frequencies from zero to a maximum spatial frequency qmax:
qmax is given by the aperture or by the information limit.
Example: C3 = 1mm, qmax = 10 nm‐1,  = 2.5pm… Lichte focus = ‐470nm (!)
The Lichte focus is different from Scherzer focus!
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Other factors contributing to t
The imaging process is not coherent, but partially coherent.
1. Partial Spatial Coherence = The Electron Source is not a Point
2. Partial Temporal Coherence = The Electron Source is not Monochromatic
3. The point spread function of the detector.
While  describes coherent aberrations that lead to aberrations due to interference effects in the image, the above factors describe incoherent aberrations!
• Coherent aberrations: information is misplaced in the image.
• Incoherent aberrations: information is lost.
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Partial Spatial Coherence
Each point of the source forms an independent image.
Analogon: A broad light source does not form a sharp shadow.
The sum of all these slightly independent images forms the HRTEM micrograph = dampening of high frequent object information.
Damping envelope function due to partial spatial coherence.
Scattering angle .
Beam divergence semi‐angle S.
  2S2 2 2

Es (q)  exp 2  C1  2 4C1C3   6C32 
 


HRTEM; Rolf Erni 2013

q 
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Partial Temporal Coherence
Electrons of different energy form independent images which differ in focus.
Chromatic focus blur: AGAIN… The sum of all these slightly independent images forms the HRTEM micrograph = dampening of high frequent object information.
Damping envelope function due to partial temporal coherence.

 2
Et (q)  exp 2 C12 4 

 2
Example: with Cc = 2mm, an electron of 1eV difference from 200keV has a focus offset of 4nm (!) 40
Coherent = No dampening at high ‐values
Damping envelope function: partial coherence
The total complex transfer function is the product of all contributions: aperture, coherent lens effects (C1, C3), partial coherence. The phase contrast transfer function is the imaginary part of t (sin‐term).
t (q)  ta (q)tc (q) Es (q) Et (q)
q 
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Impact of the Coherence of the Electron Source
Schottky Field Emission Source
Thermionic LaB6
Source
A highly coherent electron source (field emission source) allows for a higher information transfer as it has a smaller effect on the damping envelope functions.
However: the highly oscillating phase contrast transfer function makes image interpretation difficult: image contrast depends on spatial frequency and image delocalization.
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Information limit
Aside from the point resolution, the information limit is a critical parameter to
describe the HRTEM imaging performance.
Information Limit = When the damping envelope function reaches a value of 1/e2
Information limit due to partial temporal coherence:
strongly depends on the energy spread of the beam
Information limit due to partial spatial coherence:
strongly depends on the type of source (FEG, thermionic)
HRTEM; Rolf Erni 2013
Comment: Phase contrast transfer function
In the sample:
•
Kinematical diffraction describes the basic (linear) interaction between the electron beam and the sample.
•
In general, dynamical diffraction should be applied to electron diffraction as it considers multiple scattering effects.
In the imaging system:
•
The phase contrast transfer (PCT) function describes linear imaging: the interference of diffracted beams g with the forward scattered beam 0.
•
In general, non‐linear imaging theory is necessary to describe HRTEM imaging. Then, the PCT function is replaced with a transmission cross‐coefficient which describes interferences between diffracted beams g’ and g’’ as well.
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MTF at Nyquist
Pixel size
CCD: Point Spread Function (r)
or
Modulation Transfer Function (q)
An electron leads to a cloud of photons in the scintillator = information is always blurred over several pixel = Point Spread Function
The point spread function in frequency space is called the MTF.
Characteristic value: The value of the MTF at Nyquist frequency.
Nyquist frequency = 1/(2 x pixel‐size)
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Summary: Step 2
Imaging in HRTEM is described by a convolution of the complex exit plane wave with a complex contrast transfer function.
The contrast transfer function is solely defined by microscope parameters: aperture, lens, partial coherence.
Imaging conditions can be optimized to allow for a maximal interpretability of the images: Scherzer focus.
Because the aberration function depends on the defocus, the image contrast can be changed by changing the defocus.
HRTEM; Rolf Erni 2013
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HRTEM Keywords
Aperture radius
High tension
Wavelength 
MTF at Nyquist
Pixel size
Scherzer focus
Information limit
Chromatic aberration CC
Energy spread
Focus spread
Divergence angle
Lichte focus
Divergence angle
Point resolution
HRTEM; Rolf Erni 2013
Spherical aberration C3
Defocus
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HRTEM Simulations
HRTEM; Rolf Erni 2013
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Step 0: Make a model of the sample
Step 1: Getting an Exit‐Plane Wave
Step 2: Forming an HRTEM image
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STEP 0: The Model
A model is usually a super‐cell which can consist of several unit‐cells.
It is essentially a list of atoms giving their coordinates within the super‐cell.
It can be kept simple, but it can even contain small atomic shifts due to vacancies, interfaces, ordering etc.
Each atomic site is then "decorated" with the corresponding electrostatic atomic potential (whose Fourier transform is the scattering factor). The atomic potential (or scattering factors) are listed, e.g.,: Doyle & Turner (like X‐ray), Weickenmeier &Kohl
Approximation
independent atom model defines the crystal potential
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STEP 1: The Exit‐Plane Wave
First: the illumination is a plane wave
 in  1
How to calculate all the dynamic scattering of the electron beam in the crystal?
Bloch wave calculations… …one possibility for fully periodic objects, not treated here.
Weak Phase‐Object Approximation:  ep  1  i
too simple…. There are no real WPO!!!
But, if we treat the crystal as a series of WPO… it works
= Multi‐Slice Calculation
John Cowley and Alex Moodie (1957)
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Multi‐Slice Algorithm
‐ The crystal is sliced in thin "phase objects"
‐ The electron beam interacts with the projected potential of one slice
like in the WPOA
‐ Then, the electron wave is propagated to the next slice (Fresnel propagator)
‐ This is repeated at each slice, until the wave reaches the exit plane of the crystal
phase shift
phase shift
phase shift
phase shift
phase shift
HRTEM; Rolf Erni 2013
propagator
propagator
propagator
propagator
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Multi‐Slice Algorithm
The potentials of the slices can be complex (to describe absorption and a small amplitude modulation)
 in  1
 t ,1 (r )  t1 (r ) in (r )
 t , 2 (r )  t 2 (r ) t ,1 (r )  pz ( x)
 t ,3 (r )  t3 (r ) t , 2 (r )  pz ( x)
...
 t ,n 1 (r )  t n 1 (r ) t ,n (r )  pz ( x) ...   ep (r )
Transmission function of one slice: t n ( x)  exp- in ( x)
like the WPOA… projected potential of the n‐th slice defines n

Propagator function: Pz (q )  FT ( pz ( x))  exp  i z q 2

Fresnel propagator
2 Å
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Characteristics of MS
‐ A convolution is a multiplication in the frequency space.
Hence, multi‐slice is about Fourier transforms and multiplication
‐ It can be used for non‐periodic crystals (unlike Bloch wave approach)
‐ Dynamic scattering is fully considered (like Bloch wave approach)
‐ The atomic potentials can have an absorption part
‐ The thinner the slices, the better the approximation. HRTEM; Rolf Erni 2013
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Practical Aspects of MS
‐ What's a suitable thickness of the slices?
1‐2 atomic layers, around 0.2‐0.3 nm
‐ Calculation time depends on the amount of slices, i.e. on the thickness of the crystal and also on the size of the supercell and on the sampling. For TEM simulations, time is not critical (a few secs ‐ min).
Multi‐Slice only gives the exit‐plane wave, i.e. the object. Now we need to form an image… Step 2.
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STEP 2: Getting an Image
‐ The EPW (exit‐plane wave)is determined by the illumination and the diffraction in the sample
The EPW thus contains "pure" object information, but it is still the  ep (r )
result of dynamic scattering in the sample
‐The intensity of the Fourier transform of the EPW is the diffraction pattern!!!
‐ To get a HRTEM image I(r), one has to consider the transfer function of the microscope
t (q)  ta (q)tc (q) Es (q) Et (q)
I (q)   ep (q)  t (q)
2
I (r )   ep (r )  t (r )
2
Experimental parameter need to be known or at least estimates: trying to match the experimental data or vice versa!
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Summary: Multi‐Slice Simulations
•
The multi‐slice algorithm solves the dynamic diffraction problem by dividing a crystal in thin slices.
•
In the case of infinitely thin slices, the multi‐slice algorithm is equivalent to the (fully analytic) Bloch wave formalism.
•
It can be applied to non‐periodic or amorphous «objects»
•
•
Online simulation software (Bloch wave): http://emaps.mrl.uiuc.edu/
Free simulation software (multi‐slice): http://elim.physik.uni‐ulm.de/?page_id=137
HRTEM; Rolf Erni 2013
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Reconstruction of the Exit‐Plane Wave
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The Problem
How to get from
Here
To There
?
A real image:
Intensity distribution
Complex transfer function
A complex wave function (phase and amplitude)
(contains phase and amplitude information: mixed)
Image formation
HRTEM; Rolf Erni 2013
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Strategy
Even though the (complex) transfer function is "known", a single HRTEM micrograph does not contain enough information to retrieve the EPW.
Recording a focal series means to vary the transfer function in a controlled manner: the object remains the same (the EPW)
the image formation is systematically changed
From a focal series, the EPW can be iteratively reconstructed.
different algorithms are coded…
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FEG
Field‐emission vs. thermionic
Why?
Information limit
Point resolution
Thermionic microscope: Point resolution ≈ Information limit
Field emission microscope: Point resolution << Information limit
The information tranferred in the oscilating part of the transfer function cannot
directly be interpreted. Oscillating transfer function = Loss of information
Micrographs might look nicer, but do not contain more "useful" information.
The gap between information limit and point resolution needs to be retrieved.
NOTE: In an aberration corrected microscope, a transfer function can be adjustes such that
there is a broad pass band, and the information limit becomes the point resolution.
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Why?
Restoring the EPW
• Restores the "lost" information
•
•
Solves the "phase" problem
one ends up with the complex wave function = holography
•
For thin samples, the imaginary part of the wave function is proportional to the projected potential = quantitative atomic information
•
Because EPW‐Restoration removes the effect of Cs, it is a kind of numerical aberration correction!
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How?
How is the complex exit‐plane wave restored from a focal series:
• Imaging parameters need to be known precisely
• The exit plane wave is restored iteratively
• A «guess» wave function is used to calculate the focal series corresponding to the experiment.
• The difference between the calculated and the experimental focal series is used to correct the first guess function = a second guess function is produced. And so on… till the deviation is small.
•
BUT: The reconstructed exit plane wave still does not necessarily contain directly interpretable specimen information: it is still the result of a complex diffraction process in the specimen.
•
BUT: A focal series is a time series as well! Sample damage and dynamics are «forbidden».
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Through focal series of SrTiO3
See also slide 34
300 kV, monochromated, CS‐corrected,
focus step: ‐1.2 nm
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Raw Exit‐Plane Wave
Real part
Imaginary part
010
HRTEM; Rolf Erni 2013
100
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When it's local – it's useful
Reconstructed phase image
Ba‐doped SrTiO3 particles
Where are the dopants?
Experimental parameters (derived from optimizing the iteration of the reconstruction):
To get Focal step: -2 nm (nominal), -1.28 nm (effective)
Sampling: 0.02592 nm/pix
Focal spread: 2 nm (assuming a residual energy spread of 0.3 eV, and Cc of 1.2 mm)
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Intensity line profiles of the phase image reveal the location of some Ba atoms.
Ba?
Ba?
3
2 1
Ba?
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‐ Atomic structure of grain boundaries
‐ Surface configurations
‐ Point or line defect
… but a focal series is always also a time series
Phase image of graphene oxide
Phase image of graphene
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Summary: HRTEM
• HRTEM allows for accessing atomic‐resolution information
• The interpretation of HRTEM micrographs is often not trivial and needs simulations
• The crucial quantity for HRTEM is the phase contrast transfer
function, it defines point resolution and information limit.
• Imaging parameters, defocus in particular, need to be selected
carefully.
• Aberration‐corrected microscopes solve many HRTEM problems of conventional microscopes, but the sample is still a limiting parameter.
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HRTEM Alignment and Fine‐Tuning
Gun alignment/setting
Objective aperture
Voltage centering
Current centering
Condenser astigmatism
Objective astigmatism
Rotation Center
Wobble Tilt
Lens Alignment
Focus
Condenser aperture
Beam‐shift pivot‐point
Wobble Shift
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Beam‐tilt pivot‐point
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Practical Aspects… to discuss
‐The smaller the energy spread of the beam, the better the transfer.
Reduce the extraction voltage when working at reduced HT.
‐ A large beam convergence angle might impact the transfer.
Don't use the largest C2 aperture.
‐ Use a large magnification, such that the MTF is not resolution limiting.
Spots in the FFT should be in the inner half of the CCD.
‐ Rotation center or high‐voltage center is extremely important for HRTEM.
This increases the "homogeneity" of the transfer = increases the usable field of view.
‐Use the filter to form zero‐loss filtered images.
Reduces the chromatic image blur due to plasmon‐loss contributions.
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Gun Alignment and Gun Setting
Gun Tilt, Gun Shift
Extraction Voltage, Gun Lens, Filament, Emission
Affects what?
‐ "virtual" source size and eventually the beam divergence angle. Impacts the info limit.
‐ energy spread of the beam and thus the chromatic focus blur. Impacts the info limit.
Why important?
‐ take full benefit of the (limited) brightness of the source
‐ homogeneous illumination
‐ warrants that the initial beam is on the optical axis of the microscope
remember the iterative alignment: gun‐shift (spot 2) / beam‐shift (spot 9)
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Condenser alignment
Spot size
Condenser aperture: size and position
Condenser astigmatism
Affects what?
‐ Spot size: "virtual" source size and eventually the beam divergence angle = info limit… normally a large spot is selected = more intensity is better
‐Aperture: beam divergence angle: small aperture might be better, but on expenses of intensity… balance needs to be found
‐ Round illumination
Why important?
‐ Defines the illumination
‐ "Defines" the axis of the beam in respect of the objective lens.
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Height of the Sample
"Eucentric" height vs. standard focus
Different strategies… ‐ most reproducible: using the standard focus of the lens and moving the sample to the position of minimum contrast.
‐ if the standard focus of the lens is set properly, it minimizes unwanted aberrations.
‐ Alternative: tilting the sample and moving the sample to the position where the sample shift is minimal (= eucentric height): not very reproducible, not to be recommended if one wants to "measure" distances or spacing precisely.
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Beam deflector
Jeol
Wobble Shift
Wobble Tilt
Philips/FEI
=
=
Beam‐Shift Pivot Point
Beam‐Tilt Pivot Point
Affects what?
‐ Decouples the beam shift from the tilt and vice versa: to have a pure beam shift and to have a pure beam tilt
Why important?
‐ It's not crucial for TEM performance
‐ Makes the microscope more user‐friendly
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Deflectors: Double deflection units
… We start with the tilt
‐
+
One defines the ratio of the excitation of the two deflectors in such a way that there is pure beam tilt on the sample.
For this; the beam is "tilted" on the sample (x & y directions) and by changing the ratio of the excitation of the deflectors one tries to match the position of the beam on the sample for two tilt values = beam does not move when tilted.
Sample
One deflector always causes shift and tilt on the sample!
Not user‐friendly!!!
HRTEM; Rolf Erni 2013
Beam‐tilt pivot point alignment
= Wobble Tilt alignment:
Two deflectors properly excited can cause a pure tilt.
Important: The pivot point is on the sample!
Now we have an optical unit that causes a pure beam tilt on the sample = user‐friendly deflector.
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‐
… and now Shift
+
Beam‐shift pivot point alignment
= Wobble Shift alignment:
One defines the ratio of the excitation of the two deflectors in such a way that there is pure beam shift on the sample.
Sample
One deflector always causes shift and tilt on the sample!
Not user‐friendly!!!
Sample
Objective lens
Back focal plane = diffraction pattern
Two deflectors properly excited can cause a pure shift.
HRTEM; Rolf Erni 2013
For this; the beam is "shifted" on the sample (x & y directions) and by changing the ratio of the excitation of the deflectors one tries to match the position of the beam in the diffraction pattern.
Important: The pivot point is at infinity = diffraction plane!
Now we have an optical unit that causes a pure beam shift on the sample = user‐friendly deflector.
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Comments
The "alignment" of the beam tilt PP (or Wobble tilt) depends
on the height of the sample
on the excitation of the Objective lens
= the height of the object
The "alignment" of the beam shift PP (or Shift tilt) depends
on the excitation of the Objective lens
on the excitation of the diffraction lens
= the height of the diffraction plane
For normal operation conditions, the object plane and the diffraction plane are pre‐defined by the microscope… the PP should be quite constant.
The same concept is used for the gun deflector (gun tilt, gun shift … usually not very good decoupled) or the image deflector (diffraction shift = image tilt, image shift = diffraction tilt)!
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Lens Alignment
CM30: Rotation Center: Voltage or Current
Jeol: Wobbler High‐Tension or Wobbler Objective Lens
Since we now have the tools to shift and tilt the beam, we can align the beam in respect of the optical axis of the objective lens
= most important alignment step Affects what?
• Optimizes the transfer
• Minimizes lens aberrations
• Maximizes the usable field‐of‐view
Why important?
• It's not crucial for TEM performance
• Makes the microscope more user‐friendly
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Finally…
Once the axis of the lens is found
• residual objective astigmatism is normally small: use FFT or judge by eye
• transfer should be isotropic (provided there is "no" drift or vibrations) … check the FFT) Use FFT or judge by eye.
Comments:
‐ Fine‐tuning of the alignment depends on magnification
‐ Filter alignment (isochromaticity) needs to be done for ZL filtering
What's your experience?
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