Diffraction Going further

Transcription

1 Diffraction Going further Duncan Alexander! EPFL-CIME 1 Contents Higher order Laue zones (HOLZ)! Kikuchi diffraction! Convergent beam electron diffraction (CBED)! HOLZ lines in CBED! Thickness measurements! Polarity measurements! Analysing SAED patterns! Sample/image rotation! Indexing! Simulation! Nanobeam diffraction mapping 2

2 Higher order Laue zones (HOLZ) 3 Higher-order Laue Zones ZOLZ: hu + kv + lw = 0! FOLZ: hu + kv + lw = 1! SOLZ: hu + kv + lw = 2!... Figures by Jean-Paul Morniroli 4

3 Higher-order Laue Zones Figures by Jean-Paul Morniroli 5 Higher-order Laue zone quiz ZOLZ: hu + kv + lw = 0; FOLZ: hu + kv + lw = 1; SOLZ: hu + kv + lw = 2;.! For an FCC lattice which of the zone axes [1 0 0], [1 1 0] and [1 1 1] will show a FOLZ?! FCC planes with h, k, l mixed even and odd are absent! [1 0 0]: FOLZ equation gives h = 1; possible with h k l all odd so see FOLZ! [1 1 0]: h + k = 1; impossible for h k l all even or all odd so no FOLZ! [1 1 1]: h + k + l= 1; possible with h k l all odd so see FOLZ 6

4 HOLZ for higher symmetry HOLZ reflections introduce a third dimension of reciprocal lattice into SADP (diffraction from planes inclined to e-beam)! These HOLZ reflections can show higher order symmetry not present in the ZOLZ example FCC Al on [1 1 1] zone axis. FOLZ shows 3-fold symmetry (look carefully!) ZOLZ only ZOLZ and FOLZ 7 Inelastic + elastic scattering: Kikuchi diffraction Inelastic scattering event scatters electrons in all directions inside crystal Some scattered electrons in correct orientation for Bragg scattering => cone of scattering Figures from Williams & Carter Transmission Electron Microscopy Cones have very large diameters => intersect diffraction plane as ~straight lines 8

5 Kikuchi diffraction 9 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 10

6 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 Convergent beam electron diffraction 12

7 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 13 Convergent beam electron diffraction Figures by Jean-Paul Morniroli 14

8 Convergent beam electron diffraction Figures by Jean-Paul Morniroli 15 Convergent beam electron diffraction Figures from Williams & Carter Transmission Electron Microscopy 16

9 Convergent beam electron diffraction Back-focal plane Image plane: see image of focused e-beam Figures by Jean-Paul Morniroli 17 Convergent beam electron diffraction Exact 2-beam condition Back-focal plane Near 2-beam condition Image plane: see image of focused e-beam 18

10 Convergent beam electron diffraction Kikuchi from: inelastic scattering convergent beam Figures from Williams & Carter Transmission Electron Microscopy Excess and deficient lines much less diffuse for CBED!! => use CBED to orientate sample! 19 Convergent beam electron diffraction practical example ZnO thin-film sample;! Conditions: convergent beam, large condenser aperture, diffraction mode 20

11 Convergent beam electron diffraction practical example ZnO thin-film sample;! Conditions: convergent beam, large condenser aperture, diffraction mode [1 1 0] zone axis 21 HOLZ lines in CBED If HOLZ CBED discs at have excess lines at Bragg condition these give corresponding deficient lines crossing disc Figures by Jean-Paul Morniroli 22

12 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: Fringes from 2D interactions/dynamical scattering; more thickness gives more fringes hu + kv + lw =? JEMS simulation for 300 nm thick Al, 200 kev beam energy 23 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: 24

13 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 25 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: 26

14 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 [ ] zone axis Simulation vs experiment: t = 100 nm t = 150 nm t = 200 nm t = 250 nm T. Mitate et al. Phys. Stat. Sol. (a) 192, 383 (2002) Analysing SAED patterns 28

15 Given an SADP, how do we analyse it? For indexing, choose two potential, non-parallel planes (h1 k1 l1) and (h2 k2 l2) then determine zone axis [U V W] as cross product:! Index two reflections that have correct plane spacings, making sure that angle between planes is correct! Go from there using vectorial addition, choice of planes that are consistent with [U V W] 29 Calibrating rotation Unless you are using rotation-corrected TEM (e.g. JEOL 2200FS), you must calibrate rotation between image and diffraction pattern if you want to correlate orientation with image Condenser lens Specimen Objective lens Back focal plane/ diffraction plane Use specimen with clear shape orientation Defocus diffraction pattern (diffraction focus/ intermediate lens) to image pattern above BFP Diffraction spots now discs; in each disc there is an image (BF in direct beam, DF in diffracted beams Intermediate image 1 Intermediate lens BF image (GaAs nanowire) Defocus SADP 30

16 Indexing planes example 31 Indexing planes example 32

17 Indexing planes example For cubic systems: 33 Fitting by simulation Can use e.g. Stadelmann s JEMS software to simulate diffraction patterns for known crystal structure(s), and fit to experimental data JEMS can also do active fitting from measured reciprocal lattice spacings and angles 34

18 Mapping in nano-beam diffraction mode 35 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 36

19 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, 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 Y {10-10} Z A. Brian Aebersold, CIME X {0001} {2-1-10} 38