Dynamical Scattering and Defect Imaging

Transcription

1 Dynamical Scatterin and Defect Imain Duncan Alexander! EPFL-CIME 1 Contents Dynamical scatterin! Thickness frines! Double diffraction! Defect imain! 2-beam (stron beam) set-up!.b dislocation analysis! Stackin fault analysis! Weak beam imain 2

2 TEM diffraction recap Reciprocal lattice + relrods => multi-beam scatterin Excitation error s => deviation from Bra condition 3 Dynamical scatterin 4

3 Dynamical scatterin For interpretation of intensities in diffraction pattern, sinle scatterin would be ideal - i.e. kinematical scatterin However, in electron diffraction there is often multiple elastic scatterin:! i.e. dynamical behaviour This dynamical scatterin has a hih probability because a Bra-scattered beam is at the perfect anle to be Bra-scattered aain (and aain...) As a result, scatterin of different beams is not independent from each other 5 Dynamical scatterin for 2-beam condition For a 2-beam condition (i.e. stron scatterin at ϴB) from the Howie-Whelan equations it can be derived that*: where: and ξ is the extinction distance for the Bra reflection: Further: i.e. the intensities of the direct and diffracted beams are complementary, and in anti-phase, to each other. Both are periodic in t and seff If the excitation distance s = 0 (i.e. perfect Bra condition), then: *see Williams & Carter Chapter 13 on Diffracted Beams 6

4 Extinction and thickness frines Dynamical scatterin in the dark-field imae => Intensity zero for thicknesses t = nξ (inteer n) See effect as dark thickness frines on wede-shaped sample: Composition chanes in quantum wells => extinction at different thickness compared to substrate 7 Dynamical scatterin for 2-beam 2-beam condition: direct and diffracted beam intensities beams π/2 out of phase: Model with absorption usin JEMS: Briht-field imae showin modulation with absorption: 8

5 Double diffraction Special type of dynamical scatterin: diffracted beam travellin throuh a crystal is rediffracted Example 1: rediffraction in different crystal - NiO bein reduced to Ni in-situ in TEM Epitaxial relationship between the two FCC structures (NiO: a = 0.42 nm Ni: a = 0.37 nm) Formation of satellite spots around Bra reflections Imaes by Quentin Jeanros, EPFL 9 Double diffraction Example 1: NiO bein reduced to Ni in-situ in TEM movie 10

6 Double diffraction Example 1I: rediffraction in the same crystal; appearance of forbidden reflections Example of silicon; from symmetry of the structure {2 0 0} reflections should be absent However, normally see them because of double diffraction Si [1 1 0]: 2-beams simulation Si [1 1 0]: all-beams simulation Defect imain 12

7 Principle of diffraction contrast imain 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 chanes across the sample the intensity in the selected beam chanes; the intensity in the imae chanes correspondinly! In other words we make a spatial map of the intensity distribution across the sample in the selected beam: it is a mappin technique! In this way we can imae chanes in crystal phase and structural defects such as dislocations! As an example such TEM imain was a key piece of evidence provin the existence of dislocations 13 2-beam diffraction and imain Off-axis rays for DF imae aberrations and astimatism imae moves when chane objective lens focus Incident e-beam Specimen Objective lens BF DF Back focal! plane First imae! plane 14

8 Centered dark-field imain Tilt incident e-beam by 2!B Corresponds to tiltin of Ewald sphere by 2"B, excite h k l; takes place of h k l in SADP! Can now o from BF imae to DF imae by pressin button, no offaxis aberrations in DF imae DF Specimen Objective lens Back focal! plane First imae! plane 15 Crystal defects: dislocations Burers vector for ede (top riht) and screw (bottom riht) dislocations 16

9 Crystal defects: dislocations Local bendin of crystal planes around the dislocation chane their diffraction condition! This produces a contrast in the imae =>.b analysis for Burers vector From Williams & Carter Transmission Electron Microscopy 17 Crystal defects: dislocations -.b analysis On a simple level, planes parallel to the Burer s vector are not distorted by the dislocation => these planes show no chane in contrast a condition correspondin to.b = 0 Invisibility criterion! u: dislocation line vector For ede dislocation, lide plane is parallel to b but can be buckled => still ives some contrast. Plane perpendicular to u and parallel to b ives no contrast 18

10 Crystal defects: dislocations -.b analysis Example: analysis of threadin dislocations of hexaonal GaN rown on sapphire substrate [0*0*1] Condition1 Condition2 [1*1*0]=[1*1*2*0] [1*1*0]=[1*1*0*0] (0*0*2)) (1*1*0)) Sapphire Imaes by Emad Oveisi, CIME Sapphire Visible:** Visible:** Screw*[0*0*0*1]*and*Screw[0*0*0*1]* Ede*1/3[2*1*1*0],*[1*1*2*0],[1*2*1*0]* Mixed*1/3[2*1*1*3],[1*1*2*3],[1*2*1*3] Mixed*1/3[2*1*1*3],[1*1*2*3],[1*2*1*3] Invisible:** Invisible:* Ede*1/3[2*1*1*0],*[1*1*2*0],[1*2*1*0] Screw*[0*0*0*1]*and*Screw[0*0*0*1] 19 Planar defects stackin faults Similarly to Burers vector analysis, stackin faults with displacement vector R! are invisible for.r = 0 Example: analysis of basal plane stackin faults in ZnO SADP on [1 1 00] zone axis Briht-field = Dark-field = parallel to R: stackin faults visible 20

11 Planar defects stackin faults Similarly to Burers vector analysis, stackin faults with displacement vector R! are invisible for.r = 0 Example: analysis of basal plane stackin faults in ZnO SADP on [1 1 00] zone axis Briht-field = Dark-field = perpendicular to R: stackin faults invisible 21 Weak beam analysis If we imae dislocations or other defects usin with the crystal tilted to an exact 2-beam condition i.e. excitation error s = 0 then:! the dislocation has a dark contrast in the dark-field imae! this dark contrast extends over the strain field and so ives an imprecise imae of the dislocation or defect location (see exercises later)! In this condition we also have stron dynamical interaction; it is called stron beam imain! Weak beam imain provides a way to avoid these problems! Called weak beam because you imae usin a very weak diffracted beam 22

12 Weak beam; kinematical approximation Before we saw for 2-beam condition: where: Weak-beam imain: make s lare (~0.2 nm 1 )!! Now I is effectively independent of ξ kinematical conditions!!! => dark-field imae intensity easier to interpret Fiures from Williams & Carter 23 Settin up a weak beam condition A typical weak beam condition is the so-called (3) where sample is tilted so that the Ewald sphere intersects 3 reflection at s = 0 and we use to take the imae! Stron beam with the same vector is instead called 0()! Same set-up as stron beam, but tilt incident beam 2θB in other direction 0() stron beam (3) weak beam Fiures from Williams & Carter 24

13 Thickness frines in weak beam where: Since s is lare, periodicity in thickness frines occurs at smaller distances Δt! E.. for s = 0.2 nm 1, effective extinction distance ξeff = 5 nm Fiures from Williams & Carter 25 Weak beam imain of strain fields When we use diffraction contrast to imae dislocations we are in fact imain their strain fields i.e. the structural distortion of the crystal around their core! In the weak beam dark field imae, the dislocation shows as a sharp briht line on a dark backround see exercises Weak beam imae Stron beam (s > 0) imae Fiures from Williams & Carter Comparison of dislocation imaes in Cu alloy 26

14 Weak beam imain of strain fields The briht line corresponds to where planes are tilted towards satisfyin the Bra condition for diffraction vector, which only happens close to the dislocation core! The intensity peak is always displaced to one side of the dislocation core; if you o from to it oes to the other side of the core! Hirsch s kinematical approximation for screw dislocations finds half-width of dislocation iven by:!! s = 0.2 nm 1 => Δx = 1.7 nm (c.f. typically Δx > 10 nm for stron beam) Fiures from Williams & Carter 27 Weak beam example:.b analysis on GaN (0*0*2)) Visible:** Screw*[0*0*0*1]*and*Screw[0*0*0*1]* Mixed*1/3[2*1*1*3],[1*1*2*3],[1*2*1*3] Invisible:** Ede*1/3[2*1*1*0],*[1*1*2*0],[1*2*1*0] (1*1*0)) Visible:** Ede*1/3[2*1*1*0],*[1*1*2*0],[1*2*1*0]* Mixed*1/3[2*1*1*3],[1*1*2*3],[1*2*1*3] Invisible:* Screw*[0*0*0*1]*and*Screw[0*0*0*1] Imaes by Emad Oveisi, CIME 28

15 When diffraction and diffraction contrast imain is not enouh InAs nanoabbiani: to identify nucleation zone and imae dense planar stackin faults! conventional BF/DF TEM and diffraction studies lack sufficient spatial resolution => HRTEM 29