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

Quality of electron lenses! The aberrations of electron optical lenses defined a barrier that has limited the performance of the electron microscopes for a long period

Lenses the focal length is given by: f = K U ( N I ) 2 K U N I : constant : accelerating voltage : windings : lens current beam 7

Lenses Gaussian Law f f 1 = 1 = 1 + 1 f f ' s s ' F s s F 8

Spherical aberration

What is Astigmatism

Astigmatism

Rotation center

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) Plane of least confusion P a D E 2 D I d = C a c c + E I 31

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

History of the Transmission Electron Microscope 1931, Knoll and Ruska Electrostatic lenses, 1933 magnetic lenses BIMR Workshop 2007 Limited by lens defects: aberrations d=0.66c s 1/4 l 3/4 resolution =1-2 Å From H. Rose

Correcting C s The idea of correcting for C s : 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 C s. Why not a concave electron lens? There are no concave electron lenses. Scherzer theorem: C s and C c are always positive for: round lenses no charge on the axis systems where the field do not vary with the time Therefore: C s can only be corrected if the rotational symmetry is given up! 37

Spherical Aberration (Cs) Correction Cs corrector Hexa- or dodeca-pole lenses

Hexapole Probe C S Corrector Obj Obj Obj Obj Cs-corrector 39

The Purpose of a C S Corrector A C S corrector corrects for coherent aberrations, in particular C S. Incoherent aberrations (vibrations, instabilities) or C c are not improved by a C S corrector! BUT, once C S is corrected, other aberrations become important/dominant. Therefore, a corrector not only corrects for C S 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 C S 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! 40

Contrast transfer (Correction) Sample I(x, y) Lens Ab.func. χ Back focal plane F I e iχ Camera F 1 F I sin ( χ even e iχ odd] Optical axis Show result (e.g. as Thon ring positions overlay) u Example Input image f Power spectrum χ even q = 2π λ (1 2 λ2 q 2 Δf+ 1 4 C sq 4 ) χ odd q = 0 Fitted Thon rings defocus + astigmatism value 9/8/2015 41

Spherical Aberration (Cs) Correction Cs corrector Hexa- or dodeca-pole lenses Defocus Twofold astigmatism Axial coma Threefold astigmatism Spherical aberration Star aberration Fourfold astigmatism C1 A1 B2 A2 C3 S3 A3

The phase plate image 17mrad = 1.3 Å Confidence limit of detail represented with smaller than 45 phase change. A2: Threefold astigmatism Next parameter suggested to focus on with optimization. 10.5 mrad = 2.1 Å 6.7 mrad = 3.4 Å 1.3Å Calculated from determined parameters.

What else do you get? 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) Fast tableau (15 mrad) Standard (18-20 mrad) Enhanced (30-35 mrad) Error bar Adjustable Factory adjustable or fixed Azimuth angle Measured value 46

Cs Corrector at work Cs = 1.2 mm Cs = 0.0015 mm 2 nm Atomically sharp gold specimen edge OFF ON

HR-TEM on Nb 7 W 10 O 47.5 TITAN image Cs-corrector vs. non-cs corrected TEM @ 300kV 2 nm 2 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])