Download - Cs-corrector. - EMBO 2015
Cs-corrector.
Felix de Haas
Content
• Non corrector systems
–Lens aberrations and how to minimize?
• Corrector systems
–How is it done?
Lens aberrations
• Spherical aberration
• Astigmatism
• Coma
• Chromatic
• The aberrations of
electron optical lenses
defined a barrier that
has limited the
performance of the
electron microscopes
for a long period
Quality of electron lenses !
• the focal length is given by:
7
beam
K : constant
U : accelerating voltage
N : windings
I : lens current
2 ) ( I N
U K f
=
Lenses
Lenses
• Gaussian Law
8
F ’
f ’ f
s s ’
F
1 1 1 1
f f s s = = +
' '
Spherical aberration
What is Astigmatism
Astigmatism
Astigmatism
Astigmatism
Rotation center
Rotation center
Rotation center
Rotation center
Rotation center
Rotation center
Coma free
Coma free
Coma free
Coma free
Coma free
Coma free
Coma free
Coma free
Coma free
Coma free; Illumination passes through a symmetric path through the lens
Lenses: Chromatic Aberration
• Blurring due to energy spread in electron beam and lens current fluctuations
• Specimen thickness (mean-free-path)
31
a
Plane of least
confusion
P
D +
D =
I
I
E
E C c c
2 a d
What did we learn?
• How to optimize the microscope for;
– Astigmatism
» Stigmator for objective lens
– Rotation center
» Direct alignments
– Coma
» Direct alignments
» or script to tilt beam and observe FFT
» AutoCTF
– Chromatic aberration
» do not use areas where ice is too thick
• What and how?
Cs Corrector
BIMR Workshop
2007
History of the Transmission Electron Microscope
1931, Knoll and Ruska
Electrostatic lenses,
1933 magnetic lenses
Limited by lens defects: aberrations d=0.66Cs
1/4l3/4 resolution =1-2 Å
From H. Rose
37
Correcting Cs
• The idea of correcting for Cs: • To create a field which has an opposite character; i.e. the strength (or refraction) of this field
should decrease with increasing distance to the optical axis – which means negative Cs.
• Why not a concave electron lens? There are no concave electron lenses.
Scherzer theorem: Cs and Cc are always positive for:
• round lenses
• no charge on the axis
• systems where the field do not vary with the time
Therefore: Cs can only be corrected if the rotational symmetry is given up!
•Hexa- or dodeca-pole lenses
•Cs c
orre
cto
r
•Spherical Aberration (Cs) Correction
39
Hexapole Probe CS Corrector
Obj
Obj
Obj
Obj
Cs-corrector
40
A CS corrector corrects for coherent aberrations, in particular CS. Incoherent
aberrations (vibrations, instabilities) or Cc are not improved by a CS
corrector!
• BUT, once CS is corrected, other aberrations become important/dominant.
• Therefore, a corrector not only corrects for CS but for a whole series of
coherent aberrations; like astigmatism and coma and aberrations produced
by the corrector itself (S3, D4).
What’s not the purpose of a corrector:
• A CS corrector does not compensate for a misaligned column!
• Having a corrector, the optical axis of the microscope is given – the column
has to be aligned such that it meets this axis, NOT vice versa!
The Purpose of a CS Corrector
Contrast transfer (Correction)
9/8/2015 41
• Example
Optical axis
u f
Sample
𝐼(𝑥, 𝑦)
Lens
Ab.func. 𝜒 Back focal plane
ℱ 𝐼 𝑒−𝑖𝜒
Camera
ℱ−1 ℱ 𝐼 sin( 𝜒𝑒𝑣𝑒𝑛 𝑒−𝑖𝜒𝑜𝑑𝑑]
𝜒𝑒𝑣𝑒𝑛 𝑞 =2𝜋
𝜆(12𝜆
2𝑞2Δ𝑓+14𝐶𝑠𝑞
4)
𝜒𝑜𝑑𝑑 𝑞 = 0
Show result (e.g. as Thon
ring positions overlay)
Input image
Power spectrum Fitted Thon rings defocus + astigmatism value
•Hexa- or dodeca-pole lenses
•Cs c
orre
cto
r
•Spherical Aberration (Cs) Correction
•Defocus C1
•Twofold astigmatism A1
•Axial coma B2
•Threefold astigmatism A2
•Spherical aberration C3
•Star aberration S3
•Fourfold astigmatism A3
•……
44
The phase plate image
17mrad = 1.3 Å
Confidence limit
of detail
represented with
smaller than 45°
phase change.
10.5 mrad = 2.1 Å
6.7 mrad = 3.4 Å
1.3Å
A2: Threefold
astigmatism
Next parameter
suggested to
focus on with
optimization.
Calculated from determined parameters.
46
• Sall: 3.216nm Sused: 3.216nm (1.669%)
• C1: -5.261nm (95%: 4.31nm)
• A1: 5.626nm / -147.5deg (95%: 4.78nm)
• A2: 109.4nm / +162.7deg (95%: 49.4nm)
• B2: 58.97nm / +117.3deg (95%: 41.8nm)
• C3: 805.3nm (95%: 2.63um)
• A3: 2.746um / +13.7deg (95%: 508nm)
• S3: 1.578um / +151.7deg (95%: 231nm)
• A4: 48.34um / +123.9deg (95%: 13.1um)
• D4: 30.57um / +51.5deg (95%: 10.3um)
• B4: 60.34um / -156.9deg (95%: 17.8um)
• C5: 11.06mm (95%: 1.98mm)
• A5: 1.918mm / +86.4deg (95%: 377um)
What else do you get?
Fast tableau (15 mrad)
Standard (18-20 mrad)
Enhanced (30-35 mrad)
Adjustable
Factory adjustable or fixed
Error bar
Azimuth angle
Measured value
•2 nm
•Cs = 0.0015 mm •Cs = 1.2 mm
•Cs Corrector at work
•Atomically sharp gold specimen edge
•ON •OFF
2 nm2 nm 2 nm2 nm
Image : B.Freitag
Cs-corrected HR-TEM Non Cs corrected HR-TEM
Clear interpretation of atomic structure (Every atomic distance is transferred with the same contrast,[ see CTF])
HR-TEM on Nb7W10O 47.5 TITAN image Cs-corrector vs. non-Cs corrected TEM @ 300kV