Image formation. Image formation

Transcription

1 Image formation Source FEG Illumination coherent specimen exit wave objective lens Spherical aberration Cs Source: coherent and monochromatic Illumination: parallel Sample: thin, nicely prepared (no amorphization), orientation (zone axis) objective lens: aberrations, focus, stability! projection lens system (magnification) image MSE Image formation Source FEG Illumination coherente Illumination: parallel beam Sample: ( r) 0 exp weak phase object: weak phase object aproximation (WPOA) 2ik r Objective lens: specimen exit wave objective lens Spherical aberration Cs image Abbé s principle transfert function coherent transfer function (CTF) Image contrast (intensity) ( x) ( x) T( x) i * Ii( x) i ( x) i ( x) o MSE

2 sample = phase objet Plane wave Cristal potential k Wave vector in vacuum: k 2me( E) h Wave vector in a potential: 2me( E V( r)) h 2 2 Exit wave Phase shift due to the cristal potential V p : Exit wave function: ( x) expiv ( x; z) o V p ( x, z) 2 E p MSE WPOA Weak phase object approximation: o iv ( x; z) 1 iv ( x; ) ( x) exp z p No absorbtion,effect of the object on the outgoing wave: only phase shift p The exit wave function contains the information about the structure of the sample Multi-slice calculation: Calculation of the exit wave function for complex structures: 0 1 V p1 1 V p V p3 The sample is cut into thin slices MSE

3 Transfer Function The optical system (lenses) can be described by a convolution with a function T(x): Point spread function (PSF): describes how a point on the object side is transformed into the image. Transfer Fonction: Décrit comment une fonction d onde objet est transformé dans une fonction d onde image T(x) The image INTENSITY observed on a screen (or a camera / negative plate etc.) MSE Transfer Function Phase factors: i( h) ( h) ( ) T ( h) a( h)exp 2 E s E t h Spherical Aberration Defocus Amplitude factors: (objective) apertures spatial coherence enveloppe (non-parallel, convergent beam) Temporal coherence envelope (non monochromatic beam, instabilities of the gun and lenses) MSE

4 Transfer Function T ( h) exp 2i ( h) 4 ( h) 0.25C h 0.5zh 3 s 2 Spherical aberration defocus Object plane z image plane MSE Image formation Source FEG Illumination ( r) 0 exp 2ik r Illumination coherent specimen exit wave objective lens Spherical aberration Cs Sample o objective lens Image, contrast ( x) ( x) T( x) i iv ( x; z) 1 iv ( x; ) ( x) exp z o p i( h) avec ( h) 0.25C h 0.5z T ( h) exp 2 s h p image * Ii( x) i ( x) i ( x) MSE

5 CTF CTF: contrast transfer function («useful» = V p ) 3 4 CTF( k) sin Cs k z k 2 2 MSE Scherzer defocus With z scherzer z 4 3C s The CTF has a wide pass band D scherzer 3/4 1/ Cs The first zero crossing of the CTF defines the «point-to-point» resolution of an electron microscope The atom columns appear as dark areas on a bright background MSE

6 Spatial and temporal coherence i( h) ( h) ( ) T ( h) a( h)exp 2 E s E t h CM300UT FEG Field emission C s : 0.7mm z= 44nm Résolution (point to point): 1.7Å Information limite : ~1.2Å Resolution (Scherzer) Information limit MSE A good microscope CM300UT FEG Emmission à éffet de champs C s : 0.7mm z= 44nm Résolution (point à point): 1.7Å Limite d information: ~1.2Å CM30ST LaB6 Emmission thermionique C s : 2mm z= 76nm Résolution (point à point): 2.1Å Limite d information: ~1.9Å MSE

7 Pass bands z=44nm z=84nm directe z=67nm z=98nm MSE Super microscopes.. Cs=0.2mm Cs=0.01mm Dilemma: Cs=0mm: low contrast. MSE

8 HRTEM image formation Source FEG specimen project. pot. atom pos. phase of exit wave Illumination coherent specimen exit wave objective lens Spherical aberration Cs projected potential Transfer Function Problems: defocusing for contrast: delocalization of information, information limit not used image image of projected potential thickness defocus MSE Wave funct. Defocus defocus proj. pot. scherzer 1. p.b. 2. p.b. 3. p.b. Au [100], thickness 20nm MSE

9 Scherzer-defocus: black-atom contrast MSE White-atom contrast Hg CuO 2 Hg MSE

10 Electron Microscopy Advanced Techniques STEM High-Resolution STEM HAADF MSE b) CTEM/SEM principles Slide Projector TV Conventional Transmission Electron Microscope Scanning Electron Microscope What you see is what the detector sees!!! MSE

11 TEM-SEM interaction of electrons with the sample Auger electrons Backscattered electrons BSE Incident beam secondary electrons SE Characteristic X-rays visible light 1-100nm absorbed electrons Specimen electron-hole pairs elastically scattered electrons direct beam Bremsstrahlung X-rays inelastically scattered electrons MSE Reciprocity Specimen Lens Cowley, 1989 A 2 2 CTEM B Source A STEM 2 2 B Detector Lens Cowley (1969): for the same lenses, apertures and system dimension the image contrast must be the same for CTEM and STEM 2 STEM = 2 CTEM 2 STEM = 2 CTEM MSE

12 Au particles on a C film STEM BF: Detection of transmitted electrons: contrast similar to CTEM BF image (objective aperture selects only transmitted electrons) Diffraction pattern STEM ADF: Detection of diffracted electrons on the annular DF detector: (integration of multiple CTEM DF images) MSE Bright field TEM <->STEM MSE

13 ADF STEM Single atoms (or small groups of atoms) of Pt on crystalline Al 2 O 3 The ADF image provides a signal which depends strongly on the bragg scattering (Al 2 O 3 ). DIFFRACTION CONTRAST Single atoms scatter electrons incoherently to higher angles ~ z-contrast MSE c) High Angle Annular Dark Field z-contrast (atomic resolution) Ultramicroscopy 30 (1989) North-Holland, Amsterdam Z-CONTRAST STEM FOR MATERIALS SCIENCE S.J. PENNYCOOK Ultramicroscopy 37 (1991) 14-38; North-Holland High-resolution Z-contrast imaging of crystals S.J. Pennycook and D.E. Jesson MSE

14 MSE High Angle Annular Dark field detector HAADF Big camera length small camera length ADF BF MSE

15 High angle incoherent scattering The annular DF detector is placed beyond the braggscattered electrons Small camera length and large diameter of the detectors inner diameter The image is formed by high angle incoherently scattered electrons -> Rutherford scattering at the nucleus of the atoms z 2 Z-Contrast Si nano-crystals in SiO 2 formed by implantation MSE HAADF <-> HRTEM HAADF BF Pt catalyst on Al 2 O 3 Pt particles become visible in the HAADF image MSE

16 HRTEM <-> STEM HAADF HRTEM STEM-HAADF MSE Twist boundaries and stacking defects in Bi 2 Sr 2 Ca 2 Cu 3 O 10 MSE

17 Stacking fault MSE Cs-corrected STEM Atomic resolution EELS analysis of defects and interfaces R.F. Klie*, Y. Zhu Micron 36 (2005) ADF images of Si[112] recorded with aberration corrected STEM Probe size = 60pm (0.06nm) Resolution 78pm EELS spectrum of single atom columns Ti-L edge in SrTiO 3 8 grain boundary MSE

18 Characterization Methods for Materials Science Electron Microscopy Advanced Techniques HR-TEM, STEM Analytical-TEM 3D-Microscopy MSE summary Energy dispersive X-ray spectroscopy (EDS, EDX or EDXRF) is an analytical technique used for the elemental analysis or chemical characterization of a sample. It is one of the variants of XRF. As a type of spectroscopy, it relies on the investigation of a sample through interactions between electromagnetic radiation and matter, analyzing x-rays emitted by the matter in response to being hit with charged particles. Its characterization capabilities are due in large part to the fundamental principle that each element has a unique atomic structure allowing x-rays that are characteristic of an element's atomic structure to be identified uniquely from each other. To stimulate the emission of characteristic X-rays from a specimen, a high energy beam of charged particles such as electrons or a beam of X-rays, is focused into the sample being studied. At rest, an atom within the sample contains ground state (or unexcited) electrons in discrete energy levels or electron shells bound to the nucleus. The incident beam may excite an electron in an inner shell, ejecting it from the shell while creating an electron hole where the electron was. An electron from an outer, higher-energy shell then fills the hole, and the difference in energy between the higher-energy shell and the lower energy shell may be released in the form of an X-ray. The number and energy of the X-rays emitted from a specimen can be measured by an energy dispersive spectrometer. As the energy of the X- rays are characteristic of the difference in energy between the two shells, and of the atomic structure of the element from which they were emitted, this allows the elemental composition of the specimen to be measured. MSE

19 Basics of EDX a) Generation of X-rays b) Detection c) Quantification EDX in SEM, Interaction volume Monte-Carlo-Simulations EDX in TEM d) Examples MSE X-ray generation: Inelastic scattering of electrons at atoms E electron_in > E electron_out SE inner shell ionization Characteristic X-ray emission Continuum X- ray production (Bremsstrahlung, Synchrotron) SE, BSE, EELS MSE

20 Core shell ionisation: chemical microanalysis by X-ray, Auger electron and Electron Energy Loss Spectrometries e- Designation of x-ray emission lines + L 1 K L2 L3 e- M 5 K2 RX + L 1 L2 K L 3 Ionisation 1ps + e- KL 2L3 L 1 L2 K L 3 Ka 1 Ka2 Kb La 1 La2 KL 1L2 KL1L3 KL2L3 L 1M1M2 M 4 M 3 M 2 M 1 L 3 L 2 L 1 K Rayons X Electrons Auger Emission X Emission Auger MSE Forbidden transitions! quantum mechanics: conservation of angular momentum MSE

21 Efficiency of X-ray generation Relative efficiency of X-ray and Auger emission vs. atomic number for K lines Ionization cross-section vs. overvoltage U=Eo/Eedge (electron in -> X-ray out) Light elements Auger Spectroscopy Heavy elements EDS SEM TEM -> Cu-K 8.1kV, HT 15kV U = 15/8.1 = 1.85 Light element atoms return to fundamental state mainly by Auger emission. For that reason, their K-lines are weak. In addition their low energy makes them easily absorbed. To ionized the incident electron MUST have an energy larger than the core shell level U>1. To be efficient, it should have about twice the edge energy U>2. MSE Characteristic lines: Moseley's Law Frequency of X-rays emitted from K-level vs. atomic number E= h et =c/ Z with the Planck constant:h= (52) J s and 1eV = J EDS range ~ kev! To assess an element all detectables lines MUST be present!!! known ambiguities: Al K = Br Ll S K = Mo Ll MSE

22 Characteristic X-ray peaks EDX spectrum of (K,Na)NbO 3 Continuum, Bremsstrahlung Max Energy, 10keV Electron beam: 10keV Duane-Hunt limit MSE b) Detection of X-rays (EDX) MSE

23 Right: Si(Li) detector Cooled down to liquid nitrogen temperature modern silicon drift (SDD) detector: no LN cooling required MSE X-Ray energy conversion to electrical charges: 3.8eV / electron-hole pair in average electronic noise+ imperfect charge collection: 130 ev resolution / Mn Ka line Detector acts like a diode: at room temperature the leak current for 1000V would be too high! The FET produces less noise if cooled! Li migration at room temperature! ->Detector cooling by L-N MSE

24 Detection limit EDS in SEM Acquisition under best conditions Flat surface without contamination (no Au coating, use C instead) Sample must be homogenous at the place of analysis (interaction volume!!) Horizontal orientation of the surface High count rate Overvoltage U=Eo/Ec > %at Sn in Cu For acquisition times of 100sec. : detection of ~0.5at% for almost all elements MSE Continuum, Bremsstrahlung (K,Na)NbO 3 Overvoltage, 10keV Duane-Hunt limit MSE

25 c) Quantification First approach: compare X-ray intensity with a standard (sample with known concentration, same beam current of the electron beam) c i : wt concentration of element i I i : X-ray intensity of char. Line k i : concentration ratio c c i std i Yes, but. I I i std i k i MSE Intensity ~ Concentration? How many different samples? MSE

26 MSE Quantification When the going gets tough.. Correction matrix c c i i Z A F ki std i I I std i "Z" describe how the electron beam penetrates in the sample (Zdependant and density dependant) and loose energy "A" takes in account the absorption of the X- rays photons along the path to sample surface "F" adds some photons when (secondary) fluorescence occurs MSE

27 Flow chart of quantification Measure the intensities and calculate the concentrations without ZAF corrections Calculate the ZAF corrections and the density of the sample Calculate the concentrations with the corrections Is the difference between the new and the old concentrations smaller than the calculation error? no Yes! stop MSE Quantitative EDX in SEM Acquisition under best conditions Flat surface without contamination, horizontal orientation of the surface (no Au coating, use C instead) Sample must be homogenous at the place of analysis (interaction volume!!) High count rate (but dead time below 30%) Overvoltage U=Eo/Ec >1.5-2 For acquisition times of 100sec. : detection of ~0.5at% possible for almost all elements Standardless quantification possible with high accuracy (intensities of references under the given conditions can be calculated for a great range of elements), test with samples of known composition, light elements (like O) are critical Spatial resolution depends strongly on HT and the density of the sample MSE

28 Spectrum imaging Data cube Synthesized spectrum Extraction of element maps MSE PZT bulk EDS in TEM High spatial resolution! 20nm thick PZT MSE

29 STEM point analysis PbMg 1/3 Nb 2/3 O 3 (bulk) Processing option : Oxygen by stoichiometry (Normalised) Spectrum Mg Si Nb Pb O Total Spectrum Spectrum Spectrum Spectrum Spectrum Spectrum Spectrum Spectrum Spectrum Max Min All results in Atomic Percent MSE STEM linescan Pb(Zr,Ti)O 3 (thick film), slight Pb excess MSE

30 STEM Element Mapping PMN/PT 90/10 (bulk) MSE Analytical TEM of multifilament Nb 3 Sn superconducting wires Superconducting Nb 3 Sn cables for high magnetic fields 10-20T: increase current density, lower cost Potential Applications: NMR, Tokamak fusion reactors Large Hadron Collider (LHC), CERN Typical cable: 1 x 1.5mm cross-section 121x121 filaments of Nb 3 Sn in a bronze (Cu/Sn) matrix 0.5 mm Prof. R. Flükiger, V. Abächerli, D. Uglietti, B. Seeber Dept. Condensed Matter Physics (DPMC), University of Geneva MSE

31 Processing bronze route Nano -engineering: controlled creation of imperfections of nm scale (coherence length) Cu and Ti are believed to play an important role at the grain boundaries: dirty grain boundaries = pinning Cu,Sn bronze Nb Ta Ti Nb 3 Sn Ti Heat treatment Is it possible to detect Cu and Ti at the grain boundaries? What is the difference between the grain boundaries depending on where the additives are added to the unreacted material? Nb Cu,Sn SEM: reacted filament (1 out of ) MSE Typical problems: thinning of heterogeneous specimens: selective thinning bronze Nb 3 Sn filament Cross-section, polished mechanically to 30 um, ion milled until perforation STEM, Dark field: core of filament too thick, preferential etching of bronze matrix MSE

32 Preparation by Focused Ion Beam defining and cutting of lamella 15um Lift-out TEM grid, 3mm diameter MSE Preparation by Focused Ion Beam final thinning, two windows 20um two windows, 5x5 um Top view: final thickness of nm MSE

33 Specimen preparation by focused Ion Beam (FIB): large areas with uniform thickness ideally for EDX Analysis in the TEM (STEM mode) 15um SEM (FIB) thickness:40-50nm STEM-DF Ion milling EDS, element maps STEM, Bright field FIB Sample #21 MSE grain boundary without Ti Cu Nb Ta Ti Quantitative Line-scan Sn Sample #24 MSE

34 OSIRIS EPFL CIME 1 TECNAI based TIA, Compustage (sample holders..) 2 boxed LN 1time/week, no viewing screen, motorized apertures 3 X-FEG (5x higher brightness) 4 SUPER-X, EDX Detector (0.9 srad) 5 STEM HAADF, ADF,BF MSE Sn Nb Cu 400x400 pixels (5umx5um) 4msec., (10min.) 2.5nA MSE

35 400x400 pixels (500nmx500nm) 4msec., (10min.) 2.5nA MSE Characterization Methods for Materials Science Electron Microscopy Advanced Techniques HR-TEM, STEM Analytical-TEM 3D-Microscopy MSE

36 Field emission (electron, ion) microscopy +/- HV D FEM: FIM: vacuum HV<0 low pressure rare gas HV>0 Sharp tip (R radius of curvature): Electric field (E10 9 V/m) E=V/R V1 kv R0.1 m Magnification (M 10 6 ) M=D/R D0.3 m 1.5 (tip shape) MSE Field Ion Microscopy Gas Field Ionisation Source (GFIS) atoms (molecules) are trapped by polarizations forces Trapped atoms hop on the surface until they are ionised Ionisation: tunnelling process with probability D: D e I : Ionisation potential -c(i- ) V : Work function of emitter V : El. Potential c : constant Ions are ejected from the surface MSE

37 Atom probe Tomography Use the sample atoms as imaging ions.! APFIM: Atom Probe Field Ion Microscopy Measure the Time Of Flight (TOF), to determine the mass of the ion! elemental analysis on atomic level Use Laser to assist ablation of ions LAWATAP: Laser Assisted Wide Angle Tomographic Atom Probe Insulating samples become possible MSE Wide Angle position sensitive detector Sample needs to have tip shape: metals: etching, insulators: FIB MSE

38 Annu. Rev. Mater. Res : MSE Detection speed Electrical pulsing The pulse repetition rate is variable in discrete steps from 1 khz to 250 khz, and a detection rate of up to ion min 1 ( ion h 1 ) can be achieved. This implies that a data set containing 10 9 atoms can be obtained in 8 1/3 h from a single cooperative specimen. For electrical pulsing, the full-width half-maximum (FWHM) value of m/m is 500. Laser (picosecond) Pulsing For the LEAP 3000X Si XTM, the laser pulse repetition rate is variable in steps from 1 khz to 500 khz, and a detection rate of up to ion min 1 ( ion h 1 ) can be obtained. Therefore, a data set containing 10 9 atoms is attainable from a single very cooperative specimen in 3 1/3 h, which is a factor of 2.5 faster than with electrical pulsing. MSE

39 Al 2.2 at.% Mg 0.12 at.% Sc alloy MSE MSE

40 MSE MSE

41 Introduction to Tomography Tomography is imaging by sections or sectioning. A device used in tomography is called a tomograph, while the image produced is a tomogram. The method is used in medicine, archaeology, biology, geophysics, oceanography, materials science, astrophysics and other sciences. In most cases it is based on the mathematical procedure called tomographic reconstruction. The word "tomography" is derived from the Greek tomos (slice) and graphein (to write). Wickipedia MSE Introduction to Tomography Tomography is a method in which a 3-D structure is reconstructed from a series of 2-D projections (images) acquired at successive tilts (Radon 1917). First developed for use in medical imaging (1963, Nobel Prize for Medicine in 1979) using X-rays, ultrasound and magnetic resonance (e.g. cat-scans ).. Found further application in geology, astronomy, materials science, etc P. Midgley, tomo workshop in Berlin MSE

42 Introduction to Tomography Recording Series of 2D images Destructive: serial sectioning, FIB, LEAP Non-destructive: X-rays, TEM Reconstruction and «viewing» Registration (alignment of images) Back-projection, reconstruct (tilt-series) Tomogram Segmentation (image processing), extraction of the desired information MSE D imaging in medicine Non-invasive methods are preferred! The disadvantage of conventional X- radiographs is its inability to discriminate between organs of close absorptivity or overlapping organs in the viewing direction. X-ray computed tomography overcomes that limitation: X-radiographs are made in many different directions and combined mathematically to to reconstruct cross-sectional maps. reconstruction tomography or computer assisted tomography. MSE

43 Tomograph MSE Radon 1917 Ber. Sächs. Akad. Wiss. Leipzig, Math. Phys. Kl. 69, 262 (1917) English translation in: Deans, S.R. (1983) The Radon transform and its applications. John Wiley & Sons, NY) MSE

44 Radon Transform MSE Radon Transform MSE

45 Radon Transform MSE Back projection Projection recording Back projection reconstructing MSE

46 Back projection MSE back projection MSE

47 Tomography in medicine MSE D imaging in materials science 360degree X-ray tomography Milan Felberbaum STI-IMX-LSMX Cylinder of an Al-Cu Alloy MSE

48 3D imaging in materials science Tomogram MSE D imaging in materials science Reconstructed pore MSE

49 Tomography with electrons Stopping range for electrons (99% absorbed) Element (specific weight) 4-Be 13-Al 29-Cu 82-Pb 1.84 g/cm g/cm g/cm g/cm 3 X-rays Cu-Kα λ=1.54 Å Mo-Kα λ=0.71 Å 16 mm 83 mm 0.35 mm 3.3 mm 0.10 mm 0.10 mm mm mm Neutrons λ 1.08 Å 89 m 6 m 0.26 m 14 m Électrons λ=0.037 Å à 100 kv λ=0.020 Å à 300 kv 39 µm 42 µm ~330 µm 11 µm 0.6 µm MSE Bio-EM, Tomography MSE

50 Tilt series, degree tilt MSE Tomogram MSE

51 Tomo workflow MSE resolution MSE

52 geometrical limit, the missing wedge MSE Missing wedge MSE

53 Weighted back projection WBP Limited number of projections Limited tilt MSE projection requirement projection requirement: monotonically varying function of a physical property: mass-thickness dominant in biological samples! Si-Ge multiple quantum well structure MSE

54 Tomography in Electron Microscopy From P. Midgley MSE Tomography with HAADF (z-contrast) nanoparticle bimetallic catalysts supported on mesoporous silica Dogan Ozkaya,Paul Midgley; Catalysis Letters 60 (1999) STEM HAADF: heterogeneous catalyst composed of Pd 6 Ru 6 nanoparticles (~ 1 nm) on mesoporous silica support with mesopores of ~ 3 nm diameter. Pd 6 Ru 6 nanoparticles anchored to the wall of mesopore MSE

55 Electron Tomography in materials science Acquisition and alignment of 2x71 tilted images Back-projection: missing wedge Projection requirement (image contrast) Thickness limitation (samples rather thin) MSE