Download Scanning Transmission Electron Microscopy

STEM
Scanning Transmission Electron Microscopy
STEM; Rolf Erni 2013
[email protected]
STEM
•
Forming a small electron probe
•
Scanning the probe across the sample
•
For each scan position, scattered intensity is detected in the diffraction plane.
•
Building up serially an image of the scanned area.
STEM; Rolf Erni 2013
2
Why STEM?
BF STEM
Z‐contrast STEM
4 nm
LixNd1‐xTiO3
•
•
•
•
Chemical sensitive imaging for medium and heavy elements. STEM enables local analytics (EELS, EDX).
Incoherent imaging: less artefacts, intuitive image interpretation.
Incoherent imaging: improved resolution.
STEM; Rolf Erni 2013
3
Imaging Atoms
in 1973!
Albert Crew
The development of the cold field‐emission electron source (= high brightness) and its implementation in a home‐built, dedicated STEM microscope enabled for the first time to see individual atoms (in motion). 1973 STEM resolution: 250 pm 2009 STEM resolution: 47 pm
Example 1: Complex Crystal Structure of Al0.8(Fe,Cr)0.2
About 300 atoms in unit cell.
X‐ray and neutron have failed to solve the structure.
Suggested structure (based on X‐ray diffraction):
[010]
Red: Fe, blue: Cr, green: Al [001] HRTEM
?
[010]
STEM; Rolf Erni 2013
[100] HRTEM is an coherent imaging technique: image interpretation can be quite tricky and the image contrast strongly depends on the imaging parameters.
5
HAADF STEM of Al0.8(Fe,Cr)0.2
High‐Angle Annular Dark‐Field STEM shows a favorable atomic‐number contrast (Z‐contrast), which together with the incoherent nature of the imaging technique enables imaging of the atomic structure.
[100] [010] [001] As the image contrast approximately scales with Z2, these images show the location of the Fe and Cr atoms. Al atoms give less intensity and remain “invisible” compared with the Fe and Cr. This provides direct information about the occupation of the unit cell.
STEM; Rolf Erni 2013
6
Example 2: Ba‐doped SrTiO3
Where are the Ba dopant atoms?
TEM
nanoparticles
Delocalization
Delocalization and limited atomic‐
number sensitivity limit chemically sensitive imaging in HRTEM.
Structural atomic information is “blurred” in an area of 1‐2 nm.
Aberration‐corrected microscopes solve this problem, but there is still the limited chemical sensitivity which makes image interpretation difficult.
STEM; Rolf Erni 2013
7
Through‐focal series reconstruction of HRTEM images
This makes it possible to get rid of the HRTEM imaging aberrations and to reconstruct the phase and amplitude of the exit‐plane wave: but limited chemical sensitivity remains.
Changing focus: from overfocus towards Gauss focus.
Reconstructed EPW:
Amplitude of EPW
STEM; Rolf Erni 2013
Phase of EPW
8
Ba?
3
2 1
Ba?
The phase image contains some chemical information, but it is tedious to get there: focal series reconstruction.
Ba?
STEM; Rolf Erni 2013
9
9
HAADF (or Z‐contrast) STEM
Although HAADF STEM images are noisier than HRTEM images, their chemical sensitivity allows for imaging Ba dopant atoms in SrTiO3.
STEM; Rolf Erni 2013
10
STEM and HRTEM: complementary operation modes
PROS
‐
‐
‐
‐
‐
What you see in DF‐STEM is (almost always) real.
Chemical sensitive imaging in HAADF STEM (Z‐contrast).
No delocalization in BF‐STEM.
The samples can be a bit thicker than in HRTEM.
Quality of the images can be judged directly.
CONS
‐
‐
‐
‐
Instabilities.
More noise.
Sample contamination is critical.
More tedious alignment than HRTEM? NO!!!
STEM; Rolf Erni 2013
11
Outline
• The Idea of STEM
• What determines the resolution in STEM?
• Optimizing the Electron Probe
• Wave Optical Considerations
• The Ronchigram
• How To Align a STEM Probe
• Ronchigram of crystals
STEM; Rolf Erni 2013
12
Abbreviations
(HA)ADF
BF
Z

TDS
W
M
AS
rgeo
B
IS
Iprobe
D


g
C3=CS
S
C
E
E0
CC
C1=f
C1
qR

S
D
(high‐angle) annular dark‐field
bright field
atomic number
aperture (semi‐)angle
thermal diffuse scattering
solid angle
(local) magnification
source size
geometrical source size
brightness
emission (source) current
current of electron probe
diffraction limit
wavelength
scattering and/or illumination angle
reciprocal lattice vector
constant of spherical aberration
disk of least confusion due to CS
disk of least confusion due to CC
energy spread of the beam
primary energy of the beam
constant of chromatic aberration
defocus
depth of focus
point resolution
aberration function
wave surface
camera length
13
The Idea of STEM
•
•
•
•
The electron probe is a demagnified image of the source.
The condenser aperture limits the convergence angle . The lens, forming the electron probe, suffers from aberrations.
The focused electron beam is scanned in a frame on the sample: the convergent beam is called the electron probe.
Scattering and diffraction occurs in the crystal.
Behind the sample, the convergent illumination produces a convergent diffraction pattern.
Detectors behind the sample are located in the diffraction plane
Detectors collect scattered intensity according to a specific scattering‐angle range: BF, DF, ADF, HAADF. A STEM micrograph shows in each pixel the scattered intensity measured with a particular detector as a function of the position of the electron on the sample: No CCD!
STEM; Rolf Erni 2013
14
Detectors and STEM Signals
Bright field (BF)
•
•
•
•
•
collects the intensity of the forward scattered beam
strong scatterers are dark weak scatterers are bright
signal can show phase contrast: difficult interpretation
detection angle ≤  ( = semi‐convergence angle)
Annular dark‐field (ADF)
•
•
•
•
collects the intensity of low‐order diffracted beams
strong scatterers are bright, weak scatterers are dark
but: image contrast can be ambiguous
 ≤ detection angle ≤ 3
High‐Angle Annular dark‐field (HAADF)
•
•
•
•
•
collects the intensity of high‐order diffracted beams and thermal diffuse scattering (TDS)
because the detector area is large, the signal (not necessarily the scattering!) is mostly incoherent strong scatterers are very bright, weak scatterers are dark: approx. Z2 dependence
in general: image contrast can easily be interpreted: mass‐thickness contrast
detection angle ≥ 3
Other detectors: annular‐bright field detector, thin annular dark‐field detector, point bright‐field detector, 2D detectors with different segments…
STEM; Rolf Erni 2013
15
BF and (HA)ADF STEM Signals
Simultaneously recorded BF and HAADF STEM micrographs of Ce‐doped SrTiO3
nanoparticles. Which is which?
1 nm
For thin objects, BF and (HA)ADF STEM signal are complementary:
What is scattered away from a heavy object (= atomic column, heavy element) ends on the dark‐field detectors. This object thus appears dark in the BF micrographs, while it appears bright on the dark‐field micrograph.
STEM; Rolf Erni 2013
16
HAADF STEM = Z‐contrast STEM
Mott formula: scattering amplitude
1. Because electrons are detected at large scattering angles, the form factor f() is small and the scattering amplitude becomes proportional to the atomic number Z of the atom.
Therefore: Rutherford scattering dominates: the scattered intensity approximately scales with Z2.
2. The HAADF detector is large and thus “destroys” the coherence of the signal. Z‐
contrast STEM can thus be regarded as an incoherent imaging technique:
Incoherent imaging model:
I  Or   pr 
2
2
The HAADF STEM image intensity can be described as a convolution of the square of a (complex) object function O(r) (… the electrostatic crystal potential), and the square of the complex incident wave function of the electron probe p(r). BUT: the phase information of both functions is “irrelevant”.
STEM; Rolf Erni 2013
17
What Determines the STEM Resolution?
50 Hz noise
• The size of the electron probe!
• The overall stability of the system.
• Noise in the images: signal to noise ratio.
• The size of the object.
What determines the size of the electron probe?
• The (demagnified) image size of the source = electron probe.
• The finite convergence angle : diffraction limit.
• Coherent aberrations: spherical aberration.
• Incoherent aberrations: chromatic aberration.
• High‐frequency instabilities.
STEM; Rolf Erni 2013
18
The Size of the Source Image: rgeo
The size of the source is finite, so is its image.
The source has to be demagnified:
‐ 1st condenser lens = spot size!
‐ the stronger the spot‐size lens, the higher the demagnification
‐ BUT: the higher the demagnification, the smaller the beam current
The importance of brightness:
Brightness B = Emission current IS (Solid angle  x Emission area As)
For an electron probe ( is small):
The current Iprobe of an electron probe is then: Iprobe = B  2 As
Now we apply a demagnification M<<1: The smaller the effective AS, the higher the brightness has to be to maintain a certain beam current.
Only with field‐emission electron sources (large B), high‐resolution STEM is feasible!
STEM; Rolf Erni 2013
19
The Finite Convergence Angle: Diffraction Limit
A lens of finite size cannot make a point‐image of a point‐object!
The semi‐convergence angle  defines the size of the lens.
A finite lens forms an Airy pattern instead.
Airy pattern
The radius of the first dark ring is the diffraction limit D which
is a measure for a diffraction‐limited electron probe.
 is the wavelength.
The diffraction limit decreases (= better resolution) with
increasing semi‐angle ,
decreasing wavelength  = increasing energy
STEM; Rolf Erni 2013
20
Bragg's law:
Example
We have an electron probe with a convergence semi‐angle .  defines the radius of the diffraction disks in the diffraction plane.
We see two diffraction disks, 0 and g, that just touch each other.
This means that the scattering angle  = 2.
0 is the forward scattered beam, and g reflects a certain lattice distance dg.
The diffraction limit of the probe is:
The lattice spacing dg is smaller than the diffraction limit D and thus cannot be resolved by the electron probe!
Conclusion:
Only those spatial frequencies g can be resolved whose diffraction disk (significantly) overlap with the 0‐beam.
Note: a large  is needed to see small lattice spacing.
21
Spherical Aberration CS or C3
A homogeneous magnetic field, deflects electrons stronger whose angle to the axis is larger and whose trajectory is farther away from the optical axis.
Here the field is
homogeneous.
The larger the angle: the shorter the focal distance.
STEM; Rolf Erni 2013
= Spherical aberration!
22
Spherical Aberration – The Disk of Least Confusion
Because of the spherical aberration C3, the electron probe cannot be smaller than the disk of least confusion S.
a
Note:
The impact of the spherical aberration increases with 3.
In contrast to the diffraction limit: spherical aberration makes us choose a small !!! STEM; Rolf Erni 2013
23
Chromatic Aberration
Chromatic aberration CC focuses electrons of different energy at different focal distances.
The disk of least confusion is:
E is the energy spread, E0 is the primary energy, like 200 keV.
Note:
The impact of the chromatic aberration increases linearly with .
An alternative way to see it is:
The chromatic aberration leads to a focus blur that depends on the energy spread:
The variation in energy E leads to a variation in focus C1.
STEM; Rolf Erni 2013
24
Chromatic Aberration
Then, the electron probe can be considered as a sum of electron probes all at a slightly different focus.
T: energy distribution of the e‐source
This makes the probe larger. But luckily:
Note: the chromatic aberration is not important for "normal" STEM instruments!
STEM; Rolf Erni 2013
25
Depth of Field
An electron probe has a finite lateral extension: the smaller its lateral extension, the better the STEM resolution.
An electron probe also has a finite axial extension. The finite axial extension defines the depth of field.
The depth of field defines the slice of the sample
that sees a focused electron probe.
For conventional STEMs: C1  20 nm
For aberration‐corrected STEMS: C1  5 nm
NOTE:
The larger , the smaller the depth of field.
The larger , the better the lateral resolution.
For normal HR‐STEM the depth of field is not important as the sample thickness is thin enough.
For tomography, where samples tilted to high angles are imaged, it can be the resolution limiting factor.
STEM; Rolf Erni 2013
26
Dependencies: Log‐Log Plot
Source size:
No dependency on 
Spherical aberration
Chromatic aberration
Diffraction limit:
This probe does not exist!
Often seen in literature: the probe size is:
STEM; Rolf Erni 2013
27
Summary: Resolution‐Limiting Factors
•
Instabilities: not too much a user can do about it.
•
The most important parameter for the resolution is the size and shape of the electron probe. It depends on the effective source size, spherical and chromatic aberration and the diffraction limit! •
Source size: choose a small spot size, but this comes on the expense of beam current and a reduced signal‐to‐noise ratio in the image
•
Diffraction limit: choose a large aperture
•
Spherical aberration: choose a small aperture
•
Chromatic aberration: not critical, if there is no aberration corrector
STEM; Rolf Erni 2013
28
Optimizing the Electron Probe
Because spherical aberration and the diffraction limit are the important parameters for a conventional STEM instrument: they need to be balanced to optimize the electron probe:
• Under the assumption that the chromatic aberration is negligible
• Under the assumption that the source size is small enough
We can apply the Scherzer incoherent condition:
Optimized focus:
Optimized semi‐convergence angle:
Which gives a STEM resolution (probe size):
Example: 200kV: =2.5 pm, C3 = 1 mm
C1opt = ‐50 nm, opt = 10 mrad (The third condenser aperture measures: 10.8 mrad)
Yielding a STEM resolution of: 1.52 Å
STEM; Rolf Erni 2013
29
Probe Shapes: Focus Effect
Parameters: 200kV, C3 = 1 mm,  = 10 mrad, C1opt = ‐50 nm
The optimal focus minimizes the diameter of the probe AND
minimizes the intensity of the side maxima
accumulates most intensity in a narrow peak
The correct focus is found by optimizing the contrast in the HAADF STEM image.
STEM; Rolf Erni 2013
30
Probe Shapes: Effect of the Convergence Angle
opt
too large 
C3=0, large 
A too large semi‐convergence angle:
•
is good for the diffraction limit!
•
impairs the probe shape because of the spherical aberration!
•
reduces the image contrast!
•
BUT: provides higher "resolution"
Only if the spherical aberration C3 is corrected, a large angle makes sense: then the probe is not limited by C3 anymore, but by the diffraction limit.
In general, an optimized probe provides a directly interpretable (DF) STEM micrograph. If  is too large, this is not the case anymore.
STEM; Rolf Erni 2013
31
Comment: Resolution in TEM vs. STEM
TEM Resolution at Scherzer condition:
STEM Resolution at Scherzer incoherent condition:
STEM resolution is roughly 30% better than TEM resolution!
… but there are more noise and more instabilities in STEM.
In general: an incoherent imaging technique (STEM), shows a better resolution than an equivalent coherent imaging technique (Rayleigh criterion).
It’s similar in light optics:
STEM; Rolf Erni 2013
OPD: optical path difference
32
Wave Optical Considerations
1st part: the probe
2nd part:
How to evaluate the probe based on the diffraction pattern?
STEM; Rolf Erni 2013
33
TEM vs. STEM mode
The sample is immersed in the field of the objective lens (OL).
In TEM mode, the objective lens forms a “point” image of each point of the exit‐plane wave.
In STEM mode, the objective lens forms a ”point” image of the source on the specimen.

Defocus 
Spherical aberration
For a twin‐type lens, it is the same bending of the wave front caused by the objective lens, which is relevant in STEM or TEM mode. The pre‐field and the post‐field of the OL can be treated with the same formalism and the corresponding aberration function . For TEM, 
is the scattering angle, and for STEM,  is the illumination angle ( = max).
STEM; Rolf Erni 2013
34
Good and Bad Wave Fronts
A point source emits rays whose wave front is spherical.
To make an ideal image of the source point, the imaging system needs to transfer the incoming spherical wave front into an outgoing spherical wave front.
Non ideal imaging systems don't do that.
Conclusion: Good wave fronts are spherical.
STEM; Rolf Erni 2013
35
Bad Wave Front = Aberrated Wave Front
An aberrated wave front can be described as a spherical wave front plus a difference. This difference is the aberration function .

y

x

For axial aberrations:
the aberration function depends only on the angle  under which a ray passes the lens, i.e. not on the distance from the optical axis. STEM; Rolf Erni 2013
36
STEM Electron Probe
The aberrations of the pre‐field of the OL define the STEM probe.
(…and the aberrations of the post‐field of the OL define TEM imaging)

This is the aberrated wave front in STEM.
The aberration function is:

It depends on defocus C1 and spherical aberration C3.
The electron probe is not a point because the lens suffers from aberrations.
Defocus C1 and spherical aberration C3.

STEM; Rolf Erni 2013
37
Spherical Wave Front: Overfocus / Underfocus
No spherical aberration: CS=C3=0
Making lens stronger: overfocus
Making lens weaker: underfocus
Focusing = Changing the radius of the spherical wave front!
Underfocus = Negative Focus = Weak Lens
Overfocus = Positive Focus = Strong Lens
STEM; Rolf Erni 2013
38
Note:
Focus C1: It's not spherical but parabolic
This is not a sphere but a parabola scaling with 2!
Reasoning: We normally use a semi‐convergence angle of 10‐30 mrad = 0.5‐1.5°.
Because  is small, the sphere can be approximated by a parabola.
This does not change the basic concept that spherical wave fronts are good!
Think about spherical wave fronts anyhow…
STEM; Rolf Erni 2013
39
C = 80 nm
Impact of Spherical Aberration and its Compensation
1
No spherical aberration.
Positive spherical aberration.
and underfocus = negative focus.
Disk of least confusion.
C1= 0
In the presence of spherical aberration:
A point image is not feasible.
The best image is the disk of least
confusion.
C1= -80 nm
Negative focus moves the disk of least
confusion to the sample: Scherzer focus!
STEM; Rolf Erni 2013
40
The Impact of Spherical Aberration
No spherical aberration:
Electron beam is (point‐)focused to the specimen.
With (positive) spherical aberration:
Disk of least confusion is above the sample.
C1= 0
STEM; Rolf Erni 2013
41
C = 80 nm
Compensating Spherical Aberration with Defocus
1
Positive spherical aberration and underfocus
= negative focus:
Disk of least confusion is moved to the image plane.
C1= 0
This corresponds to the Scherzer incoherent
condition and is equivalent in HRTEM where a
negative defocus is needed to reach Scherzer
conditions
Scherzer incoherent focus
In the presence of spherical aberration:
with optimized convergence angle
A point image is not feasible.
C1= -80 nm
The best image is the disk of least confusion.
Negative focus moves the disk of least confusion to the sample: Scherzer focus!
STEM; Rolf Erni 2013
42
Beyond Defocus and Spherical Aberration
In general, there is a whole zoo of axial aberrations!
Each of the aberrations modulates the wave front in a specific way.
For non CS‐corrected STEM instruments:
Aside from C1 and C3 only two‐fold astigmatism A1 is important. A0 is beam shift.
The axial aberration function up to 7th order:
Bx: coma of x‐th order
Sx: star aberration of x‐th order
Ax: astigmatism of x‐th order (x+1 fold)
Cx: spherical aberration of x‐th order
43
Alignments: How Can We See What We Do?
2 Strategies
1. Form an image of the electron probe and align it according to its image
•
Advantage: it's intuitively clear what needs to be done
•
Disadvantage: it's an image of the electron probe and not the electron probe itself
Hence, it can suffer from image aberrations, like HRTEM
2. Use the shadow image in the diffraction disk of the forward scattered beam on an amorphous sample area: Ronchigram
‐ Advantage: you see how the electron probe sees the specimen
‐ Disadvantage: it's less intuitively clear what it means.
STEM; Rolf Erni 2013
44
The Ronchigram
The Ronchigram is the shadow(?) image observable in the diffraction disk of the forward scattered beam.
1
2
1
2
3
3
Ronchigram
No aberrations
CS‐corrected
CS = 0.5mm
The Ronchigram contains a (distorted) image of the sample. The area of the sample we see in the Ronchigram depends on the defocus. STEM; Rolf Erni 2013
45
Relation Between Ronchigram and the Electron Probe
The radius of the Ronchigram is the radius of the diffraction disk, which is .
The choice of aperture defines the size of the Ronchigram.
The electron probe is determined by the aberrations of the lens
Defocus C1 and Spherical aberration C3 (and two‐fold astigmatism A1).
It is the aberration function  that determines the probe!
The distortions in the Ronchigram must be related to this aberration function ‐ somehow.
The local magnification M in the Ronchigram is given by:
(D is the camera length)
M
D 1
D
1

  2   C1  3 2C3
 2


What does this mean?
STEM; Rolf Erni 2013
46
Spherical wave front: over‐/underfocus
1st case: No spherical aberration: CS=C3=0, only defocus C1 is active.
The "local" magnification M 
Making lens stronger: overfocus
C1= 80 nm
D 1
 C1
C1= 0
Making lens weaker: underfocus
C1= -80 nm
If only C1 is considered:
The magnification is homogeneous. No ‐dependence.
If C1= 0, the magnification is infinite!
STEM; Rolf Erni 2013
47
The impact of spherical aberration
C1= 80 nm
With spherical aberration: C3= 0.5 mm
M
D
1
 C1  3 2C3
Disk of least confusion
C1= 0
C1= ‐240 nm
C1= -80 nm
The local magnification depends on .
For each negative C1, there is an angle  for which the local magnification is infinite: circle of infinite magnification!
The probe is in focus when the circle merges in the center of the Ronchigram such that the sweet spot has its maximum size.
48
In Summary: Wave Optical Considerations
1. A good wave front is spherical (… approximated by a parabola because angles are small)
2. The deviation from a spherical wave front is described by the aberration function: 3. The local magnification in the Ronchigram reflects the curvature of the wave front.
4. The Ronchigram can be used to adjust the wave front in a controlled way.
3
2
1
C1= 80 nm
The local magnification depends on the curvature of the wave front! M (1 )
STEM; Rolf Erni 2013
M ( 2 )
M ( 3 )
49
Balancing Spherical Aberration, Defocus and Aperture
For a suitable choice of focus (Scherzer focus), this area of the incoming wave front behaves like a spherical wave front.
q
Sweet spot:
A flat area in the Ronchigram indicates that within this angular area the illuminating wave front is "spherical".
The electrons that illuminate the sample within this angular area have the "same" phase = no aberration effects.
Hence, the aperture needs to be adjusted that only those electrons form the electron probe that are within the angular area of the sweet spot.
9 mrad
STEM; Rolf Erni 2013
3 mrad
The angular range that behaves like a spherical wave front is very limited (like 10 mrad) – that's why the electron probe is then limited by the diffraction limit.
50
Aligning the Electron Probe: the Ronchigram
On an electron microscope with spherical aberration:
‐ the sweet spot needs to be as large as possible: focus
‐ the sweet spot needs to be round: no astigmatism
‐ the sweet spot opens and closes concentrically when the focus is varied
‐ the aperture opening should just cover the sweet spot
A1
C3
A2
On an electron microscope without spherical aberration:
‐ the sweet spot needs to be as large as possible: focus
‐ the sweet spot opens and closes concentrically when the focus is varied
‐ the aperture opening should just cover the sweet spot
STEM; Rolf Erni 2013
51
2‐fold Axial Astigmatism A1
In the presence of astigmatism, the focusing power of the lens depends on the direction.
At this defocus: an isotropic image is formed!
Even in the presence of 2‐fold astigmatism, an isotropic image can be formed. But it's resolution is lower.
Always play with focus when adjusting the stigmator!!!
STEM; Rolf Erni 2013
52
The Ronchigram of Crystals
Uncorrected, with CS = C3
Aberration corrected
Silicon
25 mrad
Silicon
25 mrad
The local magnification changes across the field of view.
The local magnification is constant across the field of view.
M
STEM; Rolf Erni 2013
D
1
 C1  3 2C3
53
The Ronchigram Defines the Orientation of the Crystal
Aperture
Overlapping diffraction disks
Focus
Specimen
Aligned
Off axis
Aligning the zone axis of the crystal in respect to the axis of the electron beam means that the Ronchigram looks symmetric, flower‐like.
STEM; Rolf Erni 2013
54
Atomic‐resolution contrast in STEM
Where the diffracted beams overlap, they interfere and reveal their phases.
Focal series of Ronchigrams:
1
2
3
6
7
8
5
4
9
10
If the probe is focused onto the sample, the size of the fringes is the size of the disk.
STEM; Rolf Erni 2013
55
The Coherent STEM Signal
Each beam, i.e. each disk, carries a specific phase given by the structure factor of the crystal. The overlapping diffraction disks interfere: interference fringes.
When the probe is focused on the sample, the fringes have the size of the aperture disk.
Scanning the focused probed across the sample moves bright and dark fringes across the detectors: This yields the (coherent) STEM signal.
Only those fringes give "true" image information that are transferred undistorted.
If fringes are transferred to the image that are distorted = too large aperture, then, the image becomes ambiguous.
The Ronchigram contains those spatial frequencies whose diffraction disks coherently interfere with the disk of the forward scattered beam.
STEM; Rolf Erni 2013
56
The Ronchigram Reveals the STEM Resolution
In order to see a certain g fringe in the Ronchigram and the corresponding spatial frequency in the STEM micrograph, the central 0‐beam has to interfere with this g beam.
‐ Beams can only interfere if they overlap: increasing the resolution means that a large convergence angle is necessary.
‐ Coherent aberrations need to be corrected up to this spatial frequency.
FFT of Ronchigram
Like a TEM micrograph, the FFT of the Ronchigram shows which spatial frequencies are present: this is equivalent to a measure of the resolution.
STEM; Rolf Erni 2013
57
Ronchigram and STEM Resolution: Diamond
Ronchigram
25 mrad
300 kV
HAADF‐STEM
Ronchigram “resolution” like HRTEM resolution can be ambiguous: dynamical effects
Go to a “simple” zone axis.
STEM; Rolf Erni 2013
Dumbbell distance in diamond [110] is 89 pm
58
Summary
•
The electron probe defines the STEM resolution
Stability, Aberrations, Diffraction limit
•
The impact of the spherical aberration is minimized by adjusting the
focus and by limiting the convergence angle
Scherzer incoherent conditions
•
The Ronchigram reflects the distortion of the incoming wave front
Local magnification
•
The Ronchigram can thus be used to align the electron probe
•
Z-contrast STEM (HAADF STEM) is a powerful, atomic-number
sensitive & (mostly) incoherent imaging technique.
STEM; Rolf Erni 2013
59