Overview of scattering, diffraction & imaging in the TEM

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1 Overview of scattering, diffraction & imaging in the TEM Eric A. Stach Purdue University

2 Scattering

3 Electrons, photons, neutrons Radiation Elastic Mean Free Path (Å)( Absorption Length (Å)( Minimum Probe Size (Å)( Neutrons X-rays Electrons Electrons interact very strongly with matter Electrons: small, negatively charged particles, directly scatter off of atom (either nucleus or electron cloud) X-rays: electromagnetic waves, field exchange with electron cloud Neutrons: heavy, uncharged particles, scatter by direct interaction ion with nucleus

4 Role of scattering in TEM Electron scattering is the underlying physics of TEM Diffraction: elastic scattering Imaging: elastic & inelastic scattering Spectroscopy: inelastic scattering Wave perspective Particle perspective

5 Myriad of scattering processes

6 Particle perspective: Collision between electron and atom No energy loss: elastic Energy loss: inelastic Wave perspective: Coherent - maintains phase Incoherent - does not maintain phase Particle vs.. wave

7 Scattering terminology Forward scattering - thin samples Elastic forward scattering is usually low angle ( ), coherent Elastic scatter is less coherent at angles > 10 Inelastic scatter is not coherent Most is very low angle (< 1 ) 1 At high angles, inelastic scatter is very sensitive to atomic weight Backscattering - thick samples Single scattering, vs. plural scattering vs. multiple scattering (>20 events) General want to be in the single to (low #) plural scattering range

8 Elastic scattering particle approach only

9 Consider the interaction between a single electron & a isolated atom Interaction is Coulombic Incident electron & electron cloud Incident electron & nucleus Elastic scattering

10 Scattering cross section - σ Describes angular dependence of the strength of atomic scatter Dependencies Angle Wavelength Atomic # Angular dependence σ σ σ of elastic scatter

11 Inelastic scattering

12 Braking radiation Electron is decelerated by Coulomb (charge) field of the nucleus, electromagnetic radiation (photon) is emitted Can have any energy less than the incident energy Results in a continuous background signal in an intensity vs.. energy spectrum Inelastic scattering Bremsstrahlung X-ray emission Angular distribution of Bremsstrahlung scatter

13 Interaction w/ inner shell electrons If energy sufficient, inner shell electron ejected Atom is ionized Atom can return to its lowest energy (ground) state Electron from outer shell to fill the hole in the inner shell Energy required is characteristic of the atom Inelastic scattering Characteristic X-raysX

14 Inelastic scattering Al K Ca L 2,3 edge O K C K edge O K edge Energy (ev) Can detect emitted X-raysX Energy dispersive spectroscopy 2. Can detect energy lost by incident electron Electron energy loss spectroscopy Energy Loss (ev) Both allow (quantitative) characterization of local chemistry

15 Scattering Comparison Plasmons (collective oscillation of free electrons) Elastic scattering L-shell ionization (X-rays) Greater frequency K-shell ionization (X-rays) Fast Secondary Electrons Slow Secondary Electrons Comparison of relative cross sections

16 Diffraction

$Diffraction - one slit d QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.$

17 Diffraction - one slit d QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. At far field sinβ I = I o β 2 β= πdsinθ λ

$Diffraction from two slits r θ d L θ Very narrow slits select just two of the wavelets These must have the same phase at the slits Path difference L$

18 Diffraction from two slits r θ d L θ Very narrow slits select just two of the wavelets These must have the same phase at the slits Path difference L = d sinθ For an arbitrary direction r, phase difference φ = 2πL/ L/λ Constructive interference when d sin(θ) = nλ Diffraction and interference combine

$Diffraction from two slits Intensity distribution at far field$

19 Diffraction from two slits Intensity distribution at far field QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

20 Diffraction from multiple slits I = I 2 o sinβ sin 2 Nα N β sin 2 α

21 A propagating plane wave

22 meets a row of atoms

23 and scatters Spherical waves emitted at each point

24 giving diffraction

25 in multiple directions

26 Bragg s s Law Incident plane wave Scattered plane wave θ θ d A θ B θ C Parallel reflecting planes Here path difference is AB + BC = 2 d sin2 sinθ Constructive interference when: nλ = 2dsinθ

27 Laue Equations asinδ 1 Incident wave δ 1 a γ 1 Scattered wave asinγ 1 Constructive interference when: a(sinγ 1 - sinδ 1 ) = hλh b(sinγ 2 - sinδ 2 ) = kλk h,k,l = integers a(sinγ 3 - sinδ 3 ) = lλl

$Each spot corresponds to diffraction from a particular plane Bi-crystal of Al on Si Patterns can$ contain information from multiple crystallites May indicated orientation relationships where

contain information from multiple crystallites May indicated orientation relationships where

28 Single crystal materials When a material is composed of a single crystal, a spot pattern is formed Each spot corresponds to diffraction from a particular plane Bi-crystal of Al on Si Patterns can contain information from multiple crystallites May indicated orientation relationships where specific planes and directions are parallel Hex & cubic GaN HCP / FCC: 110 fcc 1120 hcp & ( 111) fcc ( 0001) hcp

is not random, but one direction is preferred Readily

29 In small grained samples, random distribution of grains results in rings in DP Texture: Distribution of orientations is not random, but one direction is preferred Readily visible in ring patterns as arcs of intensity Polycrystalline materials

30 Amorphous materials do not have random placement of atoms Instead distance between neighbors follows a probability function Radial distribution function Can be recorded and measured Amorphous materials DP from amorphous TiO 2 and measured RDF

31 Helical molecules

32 Diffraction contrast

$Diffraction Contrast Imaging Strain fields preferentially diffract electrons Can image: Dislocations Stacking faults Grain boundaries Precipitates Secondary phases$

33 Diffraction Contrast Imaging Strain fields preferentially diffract electrons Can image: Dislocations Stacking faults Grain boundaries Precipitates Secondary phases Typical bright field image Dislocation configurations at the interface between a SiGe heteroepitaxial layer and a Si (100) substrate viewed in plan view (along [100])

34 Diffraction Contrast Imaging Defects cause a change in the local scattering of electrons One beam selected for imaging Transmitted - bright field" Diffracted - dark field Result is contrast that is local to the defect

$Diffraction Contrast Imaging$ heteroepitaxial film GaN GaN

35 Diffraction Contrast Imaging Dislocations in a GaN heteroepitaxial film GaN GaN GaN Bright field image Al 2 O 3 Al 2 O 3 Dark field image Al 2 O 3 Weak beam dark field image

$diffraction$ contrast

36 Examples of diffraction contrast Dislocation slip along an inclined plane A complex dislocation tangle Stacking Faults Interfacial misfit dislocations Cold rolled alloy

37 Phase contrast imaging or High-resolution TEM

38 High-resolution EM general idea Incident electron wave Sample (very thin!) Transmitted & Diffracted waves Transmitted & diffracted waves each have a different phase Result is an interference pattern - our phase contrast or HREM image

39 High-resolution EM Image courtesy U. Dahmen, NCEM, LBNL

40 High-resolution EM Image courtesy U. Dahmen, NCEM, LBNL

41 High-resolution EM Not quite so simple, though The TEM has very poor lenses Spherical aberration in particular Result is that phases of diffracted waves are scrambled by the objective lens Complex dependence on wavelength, C s and diffraction vector Causes difficulty in interpretation Sample Objective lens Back focal plane Objective aperture Image plane Scattering Calculation f(x) Diffraction pattern F(u) Y G(u) = H(u)F(u) Y Image g (x)

$defoci are matched with calculations of the effect of defocus, aberration and diffraction vector Image courtesy C.$

42 Exit wave reconstruction Can descramble the images by computationally reconstructing the exit wave Multiple images at different defoci are matched with calculations of the effect of defocus, aberration and diffraction vector Image courtesy C. Kisielowski, NCEM, LBNL

43 Exit wave reconstruction Image courtesy C. Kisielowski, NCEM, LBNL

$nanowire In fact, electron diffraction is superior for establishing single crstallinity this (though less visually appealing) Image: P.$

44 High-resolution imaging Often high-resolution imaging is used in nanoscience to show single crystalline nature of nanostructures Here, from a Si nanowire In fact, electron diffraction is superior for establishing single crstallinity this (though less visually appealing) Image: P. Yang, UC Berkeley

$some nanomaterials Can computationally extract diffraction$ information from HREM images Would never get this directly

45 High-resolution imaging But, can be only way to characterize some nanomaterials Can computationally extract diffraction information from HREM images Would never get this directly Scattering is too weak at this size scale Ge Nanoparticles 5 nm

46 Scattering tering Elastic scattering No energy loss Diffraction Inelastic scattering Conclusions Energy loss can either be characteristic (i.e. specific to a particular atom) But it doesn t t have to be Leads to both EDS & EELS Spectroscopies

47 Diffraction Conclusions Coordinated scatter from an array of atoms Yields local structural information Distinct spots indicative of single crystal diffraction Ring patterns from polycrystalline materials Indistinct rings from amorphous materials

48 Conclusions Diffraction contrast imaging Local contrast from defects Defects diffract electrons differently from the bulk Chose specific beams to image Can determine fault vectors HREM imaging Phase contrast formed by interference of multiple beams Resolutions < 1 Å possible Image interpretation can be complex

Transmission Electron Microscopy

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