Transmissions electron microscopy Sample preparation Basic principles Imaging

Transmissions electron microscopy Sample preparation Basic principles Imaging aberrations (Spherical, Chromatic, Astigmatism) contrast (Mass-thickness, Diffraction, Phase) A. E. Gunnæs MENA 3100 V 10

Sample preparation for TEM • Crushing Plane view or cross section sample? • Cutting – saw, diamond pen, ultrasonic drill, FIB • Mechanical thinning – Grinding, dimpling • Electrochemical thinning • Ion milling • Coating • Replica methods • FIB A. E. Gunnæs Is your material brittle or ductile? Is it a conductor or insulator? Is it a multi layered material? MENA 3100 V 10

TEM sample preparation: Thin films Cut out cylinder • Top view Cut out a cylinder and glue it in a Cu-tube Cut out slices • Cross section • Glue the interface of interest face together with support material Focused Ion Beam (FIB) Grind down/ dimple Ione beam thinning Grind down and glue on Cu-rings or Cut a slice of the cylinder and grind it down / dimple Cut off excess material Ione beam thinning A. E. Gunnæs MENA 3100 V 10

Basic principles, first TEM Electrons are deflected by both electrostatic and magnetic fields Force from an electrostatic field (in the gun) F= -e E Force from a magnetic field (in the lenses) F= -e (v x B) Wave length: λ= h/(2 me. V)0. 5 (NB non rel. expr. ) λ= h/(2 m 0 e. V(1+e. V)/2 m 0 c 2)0. 5 (relativistic expression) 200 k. V: λ= 0. 00251 nm (v/c= 0. 6953, m/m 0= 1. 3914) a) The first electron microscope built by Knoll and Ruska in 1933, b) The first commercial electron Microscope built by Siemens in 1939. Nobel prize lecture: http: //ernst. ruska. de/daten_e/library/documents/999. nobellecture/lecture. html A. E. Gunnæs MENA 3100 V 10

Basic TEM Electron gun Electron source: ●Tungsten, W ● La. B 6 ● FEG A. E. Gunnæs MENA 3100 V 10

Electron guns Field emission gun (FEG) Thermionic gun A. E. Gunnæs MENA 3100 V 10

Technical data of different sources Tungsten La. B 6 Cold FEG Schottky Heated FEG Brightness (A/m 2/sr) (0. 3 -2)109 1011 -1014 Temperature (K) 2500 -3000 1400 -2000 300 1800 Work function (e. V) 4. 6 2. 7 4. 6 2. 8 4. 6 Source size (μm) 20 -50 10 -20 <0. 01 Energy spread (e. V) 3. 0 1. 5 0. 3 0. 8 0. 5 http: //dissertations. ub. rug. nl/FILES/faculties/science/1999/h. b. groen/c 1. pdf H. B. Groen et al. , Phil. Mag. A, 79, p 2083, 1999 A. E. Gunnæs MENA 3100 V 10 Monochromator: Energy spread less than 0. 15 ev

Basic TEM Electron gun Electron source: ●Tungsten, W ● La. B 6 Cold trap ● FEG Sample position Vacuum requirements: - Avoid scattering from residual gas in the column. - Thermal and chemical stability of the gun during operation. - Reduce beam-induced contamination of the sample. La. B 6: 10 -7 torr FEG: 10 -10 torr A. E. Gunnæs MENA 3100 V 10

The lenses in a TEM Filament Anode The diffraction limit on resolution is given by the Raleigh criterion: 1. and 2. condenser lenses δd=0. 61λ/μsinα, μ=1, sinα~ α Sample Objective lens Intermediate lenses Projector lens A. E. Gunnæs MENA 3100 V 10 Compared to the lenses in an optical microscope they are very poor! The point resolution in a TEM is limited by the aberrations of the lenses. -Spherical - Chromatic -Astigmatism

Spherical aberrations • Cs corrected TEMs are now available Spherical aberration coefficient ds = 0. 5 MCsα 3 M: magnification Cs : Spherical aberration coefficient α: angular aperture/ angular deviation from optical axis r 2 α r 1 2000 FX: Cs= 2. 3 mm 2010 F: Cs= 0. 5 nm Disk of least confusion The diffraction and the spherical aberration limits on resolution have an opposite dependence on the angular aperture of the objective. A. E. Gunnæs MENA 3100 V 10

Aberrations in a nutshell Before Cs correction After Cs correction Core of the M 100 galaxy seen through Hubble (source: NASA) A. E. Gunnæs Q. M. Ramasse MENA 3100 V 10

Resolution limit Year 1940 s 1950 s 1960 s 1970 s 1980 s 1990 s 2000 s Resolution ~10 nm ~0. 5 -2 nm 0. 3 nm (transmission) ~15 -20 nm (scanning) 0. 2 nm (transmission) 7 nm (standard scanning) 0. 15 nm (transmission) 5 nm (scanning at 1 k. V) 0. 1 nm (transmission) 3 nm (scanning at 1 k. V) <0. 1 nm (Cs correctors) http: //www. sfc. fr/Material/hrst. mit. edu/hrs/materials/public/Elec. Micr. htm A. E. Gunnæs MENA 3100 V 10

Chromatic aberration Disk of least confusion Chromatic aberration coefficient: v - Δv dc = Cc α ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0. 5 Cc: Chromatic aberration coefficient α: angular divergence of the beam U: acceleration voltage I: Current in the windings of the objective lens E: Energy of the electrons v Thermally emitted electrons: ΔE/E=KT/e. V 2000 FX: Cc= 2. 2 mm 2010 F: Cc= 1. 0 mm Force from a magnetic field: F= -e (v x B) A. E. Gunnæs MENA 3100 V 10

Lens aberrations • Lens astigmatism Loss of axial asymmetry This astigmatism can not be x prevented, but it can be corrected! y-focus y A. E. Gunnæs x-focus MENA 3100 V 10

Operating modes Convergent beam Parallel beam Can be scanned (STEM mode) Specimen Spectroscopy and mapping (EDS and EELS) Imaging mode or Diffraction mode A. E. Gunnæs MENA 3100 V 10

Image or diffraction mode Filament Anode 1. and 2. condenser lenses Spesimen Objective lens Bi-prism Objective aperture Selected area aperture Diffraction plane Image plane Intermediate lenses Projector lens Viewing screen A. E. Gunnæs STEM detectors (BF and HAADF) Image or diffraction pattern MENA 3100 V 10

Advanced nanotool JEOL 2010 F FEGTEM Ultra high resolution version with analytical possibilities A. E. Gunnæs MENA 3100 V 10

Imaging / microscopy TEM - High resolution (HREM) - Bright field (BF) - Dark field (DF) - Shadow imaging (SAD+DF+BF) STEM - Z-contrast (HAADF) - Elemental mapping (EDS and EELS) Bi. Fe. O 3 Pt Ti. O 2 Si 200 nm GIF - Energy filtering Holography A. E. Gunnæs MENA 3100 V 10 Glue

Simplified ray diagram Parallel incoming electron beam 3, 8 Å Si Sample 1, 1 nm Objective lense Diffraction plane Objective aperture (back focal plane) Selected area Image plane aperture A. E. Gunnæs MENA 3100 V 10

Apertures Condenser aperture Objective aperture Selected area aperture A. E. Gunnæs MENA 3100 V 10

Use of apertures Condenser aperture: Limits the number of electrons hitting the sample (reducing the intensity), Reducing the diameter of the discs in the convergent electron diffraction pattern. Selected area aperture: Allows only electrons going through an area on the sample that is limited by the SAD aperture to contribute to the diffraction pattern (SAD pattern). Objective aperture: Allows certain reflections to contribute to the image. Increases the contrast in the image. Bright field imaging (central beam, 000), Dark field imaging (one reflection, g), High resolution Images (several reflections from a zone axis). A. E. Gunnæs MENA 3100 V 10

Objective aperture: Contrast enhancement Si Ag and Pb hole glue (light elements) All electrons contributes to the image. Intensity: Thickness and density dependence A small aperture allows only electrons in the central spot in the back focal plane to contribute to the image. Diffraction contrast Mass-thickness contrast (Amplitude contrast) One grain seen along a 50 nm low index zone axis. A. E. Gunnæs MENA 3100 V 10

Diffraction contrast: Bright field (BF), dark field (DF) and weak-beam (WB) Objective aperture BF image DF image Weak-beam Dissociation of pure screw dislocation In Ni 3 Al, Meng and Preston, J. Mater. Scicence, 35, p. 821 -828, 2000. A. E. Gunnæs MENA 3100 V 10

Bending contours sample Obj. lens Obj. aperture BF image DF image A. E. Gunnæs MENA 3100 V 10

Thickness fringes/contours e In the two-beam situation the intensity of the diffracted and direct beam is periodic with thickness (Ig=1 - Io) 000 g Ig=1 - Io Sample (side view) t Hole Sample (top view) Ig=(πt/ξg)2(sin 2(πtseff)/(πtseff)2)) t = distance ”traveled” by the diffracted beam. ξg = extinction distance A. E. Gunnæs Positions with max Intensity in Ig MENA 3100 V 10

Thickness fringes, bright and dark field images Sample BF image A. E. Gunnæs DF image MENA 3100 V 10

Phase contrast: HREM and Moire’ fringes Long-Wei Yin et al. , Materials Letters, 52, p. 187 -191 HREM image 2 nm Interference pattern http: //www. mathematik. com/Moire/ 200 -400 k. V TEMs are most commonly used for HREM A. E. Gunnæs A Moiré pattern is an interference pattern created, for example, when two grids are overlaid at an angle, or when they have slightly different mesh sizes (rotational and parallel Moire’ patterns). MENA 3100 V 10

Moire’ fringe spacing Parallel Moire’ spacing dmoire’= 1 / IΔg. I = 1 / Ig 1 -g 2 I = d 1 d 2/Id 1 -d 2 I g 2 g 1 Rotational Moire’ spacing dmoire’= 1 / IΔg. I = 1 / Ig 1 -g 2 I ~1/gβ = d/β β g 2 Parallel and rotational Moire’ spacing dmoire’= d 1 d 2/((d 1 -d 2)2 + d 1 d 2β 2)0. 5 A. E. Gunnæs g 1 MENA 3100 V 10 Δg Δg

Simulating HREM images Contrast transfer function (CTF) In order to take into account the effect of the objective lens when calculating HREM images, the wave function Ψ(u) in reciprocal space has to be multiplied by a transfer function T(u). In general we have: Ψ(r)= Σ Ψ(u) T(u) exp (2πiu. r) CTF (Contrast Transfer Function) is the function which modulates the amplitudes and phases of the electron diffraction pattern formed in the back focal plane of the objective lens. It can be represented as: k = u The curve depend on: • Cs (the quality of objective lens) l (wave-length defined by accelerating voltage) Df (the defocus value) u (spatial frequency) T(u)= A(u) exp(iχ), A(u): aperture function 1 or 0 Χ(u)= πΔfλu 2+1/2πCsλ 3 u 4 : coherent transfer function A. E. Gunnæs MENA 3100 V 10

Simulating HREM images Contrast transfer function (CTF) Effect of the envelope functions can be represented as: where Ec is the temporal coherency envelope (caused by chromatic aberrations, focal and energy spread, instabilities in the high tension and objective lens current), and Ea is spatial coherency envelope (caused by the finite incident beam convergence). http: //www. maxsidorov. com/ctfexplorer/webhelp/background. htm A. E. Gunnæs MENA 3100 V 10

Scherzer defocus Δ f = - (Csλ)1/2 Δ f = -1. 2(Csλ)1/2 Scherzer condition Extended Scherzer condition http: //www. maxsidorov. com/ctfexplorer/webhelp/effect_of_defocus. htm A. E. Gunnæs MENA 3100 V 10

HREM simulations One possible model for which the simulated HREM images match rectangular region I HREM simulation along [0 0 1] based on the above structures. The numbers before and after the slash symbol “/” represent the defocus and thickness (nm), respectively ”The assessment of GPB 2/S′′ structures in Al–Cu–Mg alloys ” Wang and Starink, Mater. Sci. and Eng. A, 386, p 156 -163, 2004. A. E. Gunnæs MENA 3100 V 10

Combined HAADF and EELS HAADF image of an icosahedral Fe. Pt particle (false colors): thanks to the small probe size, it is possible to probe precisely the chemical structure of samples at the atomic level, revealing here a small crystalline layer of iron oxide surrounding the outermost shell of the particle. A. E. Gunnæs MENA 3100 V 10

Energy filtering A. Thøgersen et al. , Collaboration with Prof. T. Finnstad, Ui. O, S. Diplas, SINTEF and Uni. S, UK and NIMS, Japan A. E. Gunnæs MENA 3100 V 10