TEM imaging and diffraction examples Duncan Alexander EPFL-CIME 1 Diffraction examples Kikuchi diffraction Epitaxial relationships Polycrystalline samples Amorphous materials Contents Convergent beam electron diffraction (CBED) Excess and deficient lines HOLZ lines in CBED Thickness measurements Polarity measurements Nanobeam diffraction mapping 2
Measuring epitaxial relationships SADP excellent tool for studying orientation relationships across interfaces Example: Mn-doped ZnO on sapphire Sapphire substrate Sapphire + film Zone axes: [1-1 0]ZnO // [0-1 0]sapphire Planes: c-planezno // c-planesapphire 3 Ring diffraction patterns If selected area aperture selects numerous, randomly-oriented nanocrystals, SADP consists of rings sampling all possible diffracting planes - like powder X-ray diffraction Example: needles of contaminant cubic MnZnO3 - which XRD failed to observe! Note: if scattering sufficiently kinematical, can compare intensities with those of X-ray PDF files 4
Nanocrystalline sample image/diffraction Bright field image setup - select direct beam with objective aperture Diffraction mode Image mode 5 Nanocrystalline sample image/diffraction Bright field image setup - select direct beam with objective aperture Diffraction mode Image mode Contrast from different crystals according to diffraction condition 5
Nanocrystalline sample image/diffraction Dark field image setup - select some transmitted beams with objective aperture Diffraction mode Image mode Only crystals diffracting strongly into objective aperture give bright contrast in image 6 Nanocrystalline sample image/diffraction Dark field image setup - select some transmitted beams with objective aperture Diffraction mode Image mode Only crystals diffracting strongly into objective aperture give bright contrast in image 7
Amorphous diffraction pattern Crystals: short-range order and long-range order Amorphous materials: no long-range order, but do have short-range order (roughly uniform interatomic distances as atoms pack around each other) Short-range order produces diffuse rings in diffraction pattern Example: Figure from Williams & Carter Transmission Electron Microscopy Vitrified germanium (M. H. Bhat et al. Nature 448 787 (2007) 8 Diffraction contrast imaging of defects 9
Principle of diffraction contrast imaging Typically we use an objective aperture to select either the direct beam or a specific diffracted beam in the back-focal plane If the diffraction condition changes across the sample the intensity in the selected beam changes; the intensity in the image changes correspondingly In other words we make a spatial map of the intensity distribution across the sample in the selected beam: it is a mapping technique In this way we can image changes in crystal phase and structural defects such as dislocations As an example such TEM imaging was a key piece of evidence proving the existence of dislocations 10 2-beam diffraction and imaging Off-axis rays for DF image! aberrations and astigmatism! image moves when change objective lens focus Incident e-beam Specimen Objective lens BF DF Back focal plane First image plane 11
Scan coils/beam deflectors Can use deflectors in condenser lens system to shift beam (with no tilt) and to tilt beam (with no shift). Use incident beam tilt for centered dark field imaging. 12 Centred dark-field imaging Tilt incident! e-beam by 2!B Corresponds to tilting of Ewald sphere by 2"B, excite g h k l;! 0 0 0 takes place of gh k l in SADP Specimen Objective lens Can now go from BF image to DF image by pressing button, no offaxis aberrations in DF image DF Back focal plane First image plane 13
Imaging crystal defects: dislocations Burgers vector for edge (top right) and screw (bottom right) dislocations 14 Imaging crystal defects: dislocations Local bending of crystal planes around the dislocation change their diffraction condition This produces a contrast in the image => g.b analysis for Burgers vector From Williams & Carter Transmission Electron Microscopy 15
Crystal defects: dislocations - g.b analysis On a simple level, planes parallel to the Burger s vector are not distorted by the dislocation! => these planes show no change in contrast a condition corresponding to g.b = 0 Invisibility criterion! u: dislocation line vector For edge dislocation, glide plane is parallel to b but can be buckled => still gives some contrast. Plane perpendicular to u and parallel to b gives no contrast 16 Crystal defects: dislocations - g.b analysis Example: analysis of threading dislocations of hexagonal GaN grown on sapphire substrate )+*+*',!"#$%&%"#'!"#$%&%"#( F )'*'*+,-)'*'*(*+, F F )'*'*+,-)'*'*+*+,./+*+*(00./'*'*+00.. 12334%56 Images by! Emad Oveisi, CIME 12334%56 7%8%9:6;** 7%8%9:6;** F F F F F F F 1<56=*)+*+*+*',*2#$*1<56=)+*+*+*',* C$.6*'@A)(*'*'*+,B*)'*'*(*+,B)'*(*'*+,* F F F F F F F F F F F F >%?6$*'@A)(*'*'*A,B)'*'*(*A,B)'*(*'*A, >%?6$*'@A)(*'*'*A,B)'*'*(*A,B)'*(*'*A, D#E%8%9:6;** D#E%8%9:6;* F F F F F F C$.6*'@A)(*'*'*+,B*)'*'*(*+,B)'*(*'*+, F 1<56=*)+*+*+*',*2#$*1<56=)+*+*+*', 17
Convergent beam electron diffraction 18 Convergent beam electron diffraction Instead of parallel illumination with selected-area aperture, CBED uses! highly converged illumination to select a much smaller specimen region Small illuminated area =>! no thickness and orientation variations There is dynamical scattering, but it is useful! Can obtain disc and line patterns! packed with information: Figures by Jean-Paul Morniroli 19
Convergent beam electron diffraction Figures by Jean-Paul Morniroli 20 Convergent beam electron diffraction Figures by Jean-Paul Morniroli 21
Convergent beam electron diffraction Figures from Williams & Carter Transmission Electron Microscopy 22 Convergent beam electron diffraction Back-focal plane Image plane:! see image of focused e-beam Figures by Jean-Paul Morniroli 23
Convergent beam electron diffraction Exact 2- beam condition Back-focal plane Near 2- beam condition Image plane:! see image of focused e-beam 24 Excess and Deficient lines Look at Ewald sphere construction!here Ewald sphere intersects a HOLZ reflection exactly.! In this condition this HOLZ reflection must give 2#B scattering angle. If we draw in rays for excess and deficient lines at +#B and #B relative to the planes making the! reflection we see excess line intersects HOLZ reflection and deficient 0 0 0 exactly. If we plot full angular range of incident beam it is clear that deficient HOLZ line crosses 0 0 0 disc. k I k D 0 0 0 25
Excess and Deficient lines Look at Ewald sphere construction!here Ewald sphere intersects a HOLZ reflection exactly.! In this condition this HOLZ reflection must give 2#B scattering angle. If we draw in rays for excess and deficient lines at +#B and #B relative to the planes making the! reflection we see excess line intersects HOLZ reflection and deficient 0 0 0 exactly. If we plot full angular range of incident beam it is clear that deficient HOLZ line crosses 0 0 0 disc. k I k D Note: Excess and deficient lines! are often called Kikuchi lines 0 0 0 26 HOLZ lines in CBED If HOLZ CBED discs at have excess lines at Bragg condition these give corresponding deficient lines crossing 0 0 0 disc Figures by Jean-Paul Morniroli 27
HOLZ lines in CBED Because HOLZ lines contain 3D information, they also show true symmetry! e.g. three-fold {111} symmetry for cubic Al - unlike apparent six-fold axis in SADP or from ZOLZ Kikuchi lines Deficient lines for inclined planes: -3-7 11 5 7-11 7 5-11 hu + kv + lw =? Fringes from 2D interactions/dynamical scattering; more thickness gives more fringes JEMS simulation for 300 nm thick Al, 200 kev beam energy 28 Thickness measurement by CBED Within CBED discs also obtain patterns from dynamical scattering. These patterns show fringes that are somewhat analogous to thickness fringes in the TEM image. Can measure thickness e.g. by comparing experimental data to simulation Example: Blochwave simulations for Al on [0 0 1] zone axis: 29
Thickness measurement by CBED Easier to think about in 2-beam Bragg scattering condition Different rays in the scattered beam sample different excitation errors for the reflection g Effectively we make a map of intensity for different excitation errors s along a chord in the disc g As thickness increases nodes in sinc 2 function move to smaller s (reciprocal relationship with thickness) => more fringes in the disc Intensity vs s for 2-beam condition, different specimen thicknesses t t = 10 nm t = 25 nm t = 50 nm 30 Thickness measurement by CBED Therefore to obtain CBED discs with 1-D fringes for thickness measurement tilt to 2-beam condition Possible to calculate thickness analytically (e.g. see Williams & Carter) Example: Blochwave simulations for Al with (0 0 2) reflection excited: 31
Identifying polarity in CBED Patterns from dynamical scattering in direct and diffraction discs allow determination of polarity of non-centrosymmetric crystals because dynamical scattering patterns are sensitive to channeling down particular atomic column JEMS simulation: GaN [1-1 0 0] zone axis Simulation vs experiment: t = 100 nm t = 150 nm t = 200 nm t = 250 nm 000-2 0000 0002 A. Brian Aebersold et al. Acta Materialia, Volume 130, 2017, 240 248.! http://dx.doi.org/10.1016/j.actamat.2017.03.021 32 Zone axis CBED Instead of spot pattern, obtain disc pattern Larger convergence semi-angle " => larger discs Parallel beam SADP Si [001] " = 1.6 mrad " = 3.9 mrad 33
Zone axis CBED Instead of spot pattern, obtain disc pattern Larger convergence semi-angle α => larger discs α = 3.9 mrad α = 8.6 mrad α = 19.3 mrad See fringes in discs, and symmetry 34 Convergent beam electron diffraction practical example ZnO thin-film sample; Conditions: convergent beam, large condenser aperture, diffraction mode 35
Convergent beam electron diffraction practical example ZnO thin-film sample; Conditions: convergent beam, large condenser aperture, diffraction mode [1 1 0] zone axis 36 Kikuchi diffraction 37
Kikuchi lines Formation of bright and dark lines ( excess and deficient lines) by combination of incoherent scattering followed by elastic scattering in parallel incident beam geometry (e.g. SADP) The incoherent scattering (no preferential scattering vectors) is generally in forwards direction Cones of incoherently-scattered electrons then scattered by coherent elastic scattering, creating arcs in the diffraction plane. Because angles are small the arcs look straight. Resultant lines are very similar to the excess and deficient lines of CBED. They are equally sensitive to specimen orientation, and we use them e.g. to set a 2-beam condition. However the specimen must be thick (for sufficient inelastic scattering) and flat (to have sharp lines) to see them well. 38 Kikuchi line formation Treat problem in real space "B "B "B Treat 2-beam Bragg scattering condition "B "B Yellow volume represents intensity distribution of incoherent scattering event; mainly forward scattered h k l 2"B "B h k l origin of incoherent scattering event: h k l h k l 39
Treat problem in reciprocal space; Ewald sphere construction Forward scattering from incoherent scattering gives diffuse intensity at low scattering angles around 0 0 0 Kikuchi line formation h k l "B "B ki 0 0 0 Exact Bragg condition: Kikuchi lines coincide Deficient line: incoherent forwardscattered intensity removed from with Bragg spots Kikuchi line! dark line on brighter background kd ghkl h k l Excess line: incoherent forward-scattered intensity redistributed into Kikuchi line! bright line on low background 40 Kikuchi line formation Treat problem in real space Treat zone axis condition "B "B h k l "B "B h k l h k l h k l 41
Kikuchi line formation Treat problem in reciprocal space; Ewald sphere construction Remember Bragg spots only visible because of relrods and excitation error s Zone axis condition: (by geometry) Kikuchi lines halfway between Bragg spots ghkl h k l 2"B ki 0 0 0 kd h k l Symmetrical relationship so both Kikuchi lines should have same intensity s ghkl 42 Kikuchi diffraction Figures by Jean-Paul Morniroli Position of the Kikuchi line pairs of (excess and deficient) very sensitive to specimen orientation Can use to identify excitation vector; in particular s = 0 when diffracted beam coincides! exactly with excess Kikuchi line (and direct beam with deficient Kikuchi line) Quiz: what happens to width of Kikuchi line pairs as (h k l) indices become bigger?! Answer: larger indices (h k l)! greater scattering angle "B! larger width of line pairs 43
Kikuchi lines road map to reciprocal space Kikuchi lines traverse reciprocal space, converging on zone axes - use them to navigate reciprocal space as you tilt the specimen! Examples: Si simulations using JEMS Si [1 1 0] Si [1 1 0] tilted off zone axis Si [2 2 3] Obviously Kikuchi lines can be useful, but can be hard to see (e.g. from insufficient thickness, diffuse lines from crystal bending, strain). Need an alternative method... 44 Mapping in nano-beam diffraction mode 45
Nano-beam set-up In nano-beam mode, use small C2 condenser aperture and excited 3rd condenser lens (e.g. condenser mini-lens) to make near-parallel beam of 2 3 nm diameter on specimen surface Typical convergence semi-angle alpha ~0.5 1 mrad; therefore obtain spot-like diffraction patterns from very small probe 46 Orientation image mapping in TEM The NanoMEGAS ASTAR system scans the nanobeam across sample while recording diffraction patterns to make a map with one diffraction pattern for every pixel positions x, y Template matching then used to identify phase and orientation; each pattern correlated with 100s-1000s of patterns simulated at different orientations and for different phases Much higher spatial resolution than EBSD in SEM, and angular resolution of 1 Can combine with precession for greater reliability of indexing [1] E.F. Rauch et al., Micros. Anal. Nanotech. Supplement, 22(6), S5-S8,2008 47
ASTAR example: nanocrystalline ZnO Plan-view sample of textured, nanocrystalline ZnO thin-film 750 x 750 pixel map, 2 3 nm probe size, 2 nm step size {10-10} Y Z X {0001} {2-1-10} A. Brian Aebersold, CIME 48 Imaging and diffraction examples summary Diffraction useful for measuring orientation relationships and polycrystalline crystal structures For correct dark-field imaging we tilt incident beam to do centred dark-field imaging free of aberrations from displacing the objective aperture Can use centred dark-field e.g. for analysing dislocations Parallel beam diffraction can also give excess and deficient lines via incoherent followed by coherent scattering: Kikuchi diffraction Automated crystal orientation and phase mapping is also now possible and can give high quality data on nanocrystalline materials nature Convergent beam electron diffraction is a powerful technique allowing to see excess and deficient lines which are very sensitive to specimen orientation, and dynamical scattering patterns that inform e.g. on sample thickness and polarity 49
Resources Transmission Electron Microscopy by Williams and Carter Large Angle Convervent Beam Electron Diffraction, Jean-Paul Morniroli JEMS Pierre Stadelmann s electron microscopy simulation software: http://www.jems-saas.ch/ Open access database of.cif files: http://www.crystallography.net/cod/ 50