Diffraction methods and electron microscopy

1. Diffraction methods and electron microscopy Outline and Introduction to FYS4340 and FYS9340

2. FYS4340 and FYS9340 • FYS4340 • Theory based on ”The theory and practice of analytical electron microscopy in material science” by Arne Olsen • Chapter: 1-10, 12 + sample preparation • Practical training on the TEM • FYS9340 • Theory same as FYS4340 + additional papers related to TEM and diffraction. • Teaching training. • Perform practical demonstrations on the TEM for the master students.

3. Basic TEM Electrons are deflected by both electrostatic and magnetic fields Force from an electrostatic field F= -e E Force from amagnetic field F= -e (v x B) Electron transparent samples Electron gun Sample position

4. IntroductionEM and materials Electron microscopy are based on three possible set of techniqes Spectroscopy Imaging Chemistry and elecronic states (EDS and EELS). Spatial and energy resolution down to the atomic level and ~0.1 eV. Electrons With spatial resolution down to the atomic level (HREM and STEM) BSE X-rays (EDS) AE SE Diffraction E<Eo (EELS) From regions down to a few nm (CBED). Bragg diffracted electrons E=Eo

5. Valence M 3d6 M 3p4 L 3d4 3s2 2p4 3p2 K Electron shell 2s2 2p2 1s2 L K Basic principles, electron probe Electron Auger electron or x-ray Characteristic x-ray emitted or Auger electron ejected after relaxation of inner state. Low energy photons (cathodoluminescence) when relaxation of outer stat. Secondary electron MENA3100

6. Introduction EM and materials The interesting objects for EM is not the average structure or homogenous materials but local structure and inhomogeneities Defects Interfaces Precipitates Defects, interfaces and precipitates determines the properties of materials

7. Introduction History of EM: from dream to reality • 1834 William Rowan Hamilton • 1876 Ernst Abbe • 1897 J.J. Thomson • 1924 de Broglie • 1925/26 E. Schrӧdinger • 1926/27 Hans Busch • 1927 C. Davisson and L.H. Germer/ G. Thomson and A. Reid • 1928 Max Knoll and Ernst Ruska

8. The first electron microscope • Knoll and Ruska • By 1933 they had produced a TEM with two magnetic lenses which gave 12 000 times magnification. Ernst Ruska: Nobel Prize in physics 1986

9. The first commersial microscopes • 1939 Elmiskop by Siemens Company • 1941 microscope by Radio corporation of America (RCA) • First instrument with stigmators to correct for astigmatism. Resolution limit below 10 Å. Elmiskop I

10. r2 r1 α Disk of least confusion Developments Realized that spherical aberration of the magnetic lenses limited the possible resolution to about 3 Å. • Spherical aberration coefficient r2 r1 α ds = 0.5MCsα3 M: magnification Cs :Spherical aberration coefficient α: angular aperture/ angular deviation from optical axis 2000FX: Cs= 2.3 mm 2010F: Cs= 0.5 nm

11. v - Δv v Chromatic aberration Disk of least confusion Chromatic aberration coefficient: dc = Ccα ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0.5 Cc: Chromatic aberration coefficient α: angular divergence of the beam U: acceleration voltage I: Current in the windings of the objective lens E: Energy of the electrons 2000FX: Cc= 2.2 mm 2010F: Cc= 1.0 mm Thermally emitted electrons: ΔE/E=kT/eU Force from amagnetic field: F= -e (v x B)

12. Developments ~ 1950 EM suffered from problems like: Vibration of the column, stray magnetic fields, movement of specimen stage, contamination. Lots of improvements early 1950’s. Still far from resolving crystal lattices and making direct atomic observations.

13. Observations of dislocations and lattice images • 1956 independent observations of dislocations by: Hirsch, Horne and Wheland and Bollmann -Started the use of TEM in metallurgy. • 1956 Menter observed lattice images from materials with large lattice spacings. • 1965 Komoda demonstrated lattice resolution of 0.18 nm. • Until the end of the 1960’s it was mainly used to test resolution of microscopes.

14. Menter, 1956

15. Use of high resolution electron microscopy (HREM) in crystallography • 1971/72 Cowley and Iijima • Observation of two-dimensional lattice images of complex oxides • 1971 Hashimoto, Kumao, Hino, Yotsumoto and Ono • Observation of heavy single atoms, Th-atoms

16. 1970’s • Early 1970’s: Development of energy dispersive x-ray (EDX) analyzers started the field of analytical EM. • Development of dedicated HREM • Electron energy loss spectrometers and scanning transmission attachments were attached on analytical TEMs. • Small probes making convergent beam electron diffraction (CBED) possible.

17. 1980’s • Development of combined high resolution and analytical microscopes. • An important feature in the development was the use of increased acceleration voltage of the microscopes. • Development of Cs corrected microscopes • Probe and image • Improved energy spread of electron beam • More user friendly Cold FEG • Monocromator Last few years

18. Electron beam instruments • Transmission Electron microscope (TEM) • Electron energies usually in the range of 80 – 400 keV. High voltage microscopes (HVEM) in the range of 600 keV – 3 MeV. • Scanning electron microscope (SEM) early 1960’s • dedicated Scanning TEM (STEM) in 1968. • Electron Microprobe (EMP) first realization in 1949. • Auger Scanning Electron Microscopy (ASEM) 1925, 1967 • Scanning Tunneling Microscope (STM) developed 1979-1981 Because electrons interact strongly with matter, elastic and inelastic scattering give rise to many different signals which can be used for analysis.

19. Electron waves • Show both particle and wave properties • Electrons can be accelerated to provide sufficient short wave length for atomic resolution. • Due to high acceleration voltages in the TEM relativistic effects has to be taken into account. Charge e Restmass mo Wave ψ Wave length λ λ = h/p= h/mv de Broglie (1925) λ = h/(2emoU)1/2 U: pot. diff. λ = h/(2emoU)1/2 * 1/(1+eU/2moc2)1/2

20. The Transmission Electron Microscope Relations between acceleration voltage, wavevector, wavelength, mass and velocity

21. 3,8 Å 1,1 nm Simplified ray diagram Parallel incoming electron beam Si Sample Objective lense Diffraction plane (back focal plane) Objective aperture Selected area aperture Image plane MENA3100 V08

22. Microscopy and diffraction condition Focal plane Image plane Intermediate lens Projector lens

23. JEOL 2000FX • Wehneltcylinder • Filament • Anode • Electrongun 1. and 2. beam deflectors • and 2. condenser lens • Condenseraperture • Condenser lens stigmator coils • Condenser lens 1. and 2. beam deflector • Condensermini-lens • Objective lens pole piece • Objectiveaperture • Objective lens pole piece • Objective lens stigmators • Image shift coils • Objectivemini-lens coils (low mag) • 2. Image shift coils • 1., 2.and 3. Intermediate lens • Projector lens beam deflectors • Projector lens • Screen Electron gun Illumination system Mini-lens screws Specimen Intermediate lens shifting screws Projector lens shifting screws

24. The requirements of the illumination system • High electron intensity • Image visible at high magnifications • Small energy spread • Reduce chromatic aberrations effect in obj. lens • High brightness of the electron beam • Reduce spherical aberration effects in the obj. lens • Adequate working space between the illumination system and the specimen

25. The electron microscope

26. Additional literature and web resources • http://nanohub.org/resources/3777 • Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http://nanohub.org/resources/3907 • D.B. Williams and C.B. Carter, Transmission Electron Microscopy- A textbook for Material Science, Plenum Press New York. Second edition 2009

27. Repetition from 1st lecture • What type of techniques can be done in an analytical TEM? • Why are electrons suitable for imaging with atomic resolution? • What is changing when one goes from diffraction to imaging mode?

28. 3,8 Å 1,1 nm Simplified ray diagram Parallel incoming electron beam Si Sample Objective lense Diffraction plane (back focal plane) Objective aperture Selected area aperture Image plane MENA3100 V08

29. Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http://nanohub.org/resources/3907

30. JEOL 2000FX • Wehneltcylinder • Filament • Anode • Electrongun 1. and 2. beam deflectors • and 2. condenser lens • Condenseraperture • Condenser lens stigmator coils • Condenser lens 1. and 2. beam deflector • Condensermini-lens • Objective lens pole piece • Objectiveaperture • Objective lens pole piece • Objective lens stigmators • Image shift coils • Objectivemini-lens coils (low mag) • 2. Image shift coils • 1., 2.and 3. Intermediate lens • Projector lens beam deflectors • Projector lens • Screen Electron gun Illumination system Mini-lens screws Specimen Intermediate lens shifting screws Projector lens shifting screws

31. Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http://nanohub.org/resources/3907

32. The requirements of the illumination system • High electron intensity • Image visible at high magnifications • Small energy spread • Reduce chromatic aberrations effect in obj. lens • Adequate working space between the illumination system and the specimen • High brightness of the electron beam • Reduce spherical aberration effects in the obj. lens

33. Brightness • Brightness is the current density per unit solid angle of the source • β = ie/(πdcαc)2

34. The electron source • Two types of emission sources • Thermionic emission • W or LaB6 • Field emission • W ZnO/W Cold FEG Schottky FEG

35. The electron gun • The performance of the gun is characterised by: • Beam diameter, dcr • Divergence angle, αcr • Beam current, Icr • Beam brightness, βcr at the cross over d Cross over α Image of source

36. The electron gun Thermionic gun FEG Bias -200 V Wehnelt cylinder Cathode -200 kV Anode Ground potential Equipotential lines dcr Cross over αcr

37. Thermionic guns • Filament heated to give • Thermionic emission • Directly (W) or • indirectly (LaB6) • Filament negative • potential to ground • Wehnelt produces a • small negative bias • Brings electrons to • cross over

38. Thermionic guns

39. Thermionic emission • Current density: • Ac: Richardson’s constant, material dependent • T: Operating temperature (K) • φ: Work function (natural barrier to prevent electrons to leak out from the surface) • k: Boltzmann’s constant Jc= AcT2exp(-φc/kT) Richardson-Dushman Maximum usable temperature T is determined by the onset of the evaporation of material.

40. Field emission • Current density: Fowler-Norheim Maxwell-Boltzmann energydistribution for all sources

41. Field emission • The principle: • The strengthof an electricfield E is considerablyincreased at sharppoints. E=V/r • rW < 0.1 µm, V=1 kV → E = 1010 V/m • Lowersthework-functionbarrier so thatelectronscan tunnel outofthetungsten. • Surface has to be pristine (nocontamination or oxide) • Ultra highvacuumcondition (Cold FEG) or poorervacuumiftip is heated (”thermal” FE; ZrOsurfacetratments → Schottkyemitters).

42. Characteristics of principal electron sources at 200 kV * Might be one order lower

43. Advantages and disadvantages of the different electron sources

44. Electron lenses Any axially symmetrical electric or magnetic field have the properties of an ideal lens for paraxial rays of charged particles. • Electrostatic • Require high voltage- insulation problems • Not used as imaging lenses, but are used in modern monochromators • Magnetic • Can be made more accurately • Shorter focal length F= -eE F= -e(v x B)

45. General features of magnetic lenses • Focus near-axis electron rays with the same accuracy as a glass lens focusses near axis light rays • Same aberrations as glass lenses • Converging lenses • The bore of the pole pieces in an objective lens is about 4 mm or less • A single magnetic lens rotates the image relative to the object • Focal length can be varied by changing the field between the pole pieces. (Changing magnification) http://www.matter.org.uk/tem/lenses/electromagnetic_lenses.htm

46. Strengths of lenses and focused image of the source http://www.rodenburg.org/guide/t300.html If you turn up one lens (i.e. make it stronger, or ‘over- focus’ then you must turn the other lens down (i.e. make it weaker, or ‘under-focus’ it, or turn its knob anti-clockwise) to keep the image in focus.

47. Magnification of image, Rays from different parts of the object http://www.rodenburg.org/guide/t300.html If the strengths (excitations) of the two lenses are changed, the magnification of the image changes

48. The transmission electron microscope Chapter 2 The TEM (part 2) Chapter 3 ElectronOptics

49. Some repetition • Whatcharacterizestheperformanceof an electrongun? • Whatkindofelectronsourcesare used in EM? • Whatkindof lenses can be used in a TEM? • In whatwaydoesthetrajectoryof an electrondiffer from an opticalraythrough a lens? • Whatarethedeflection coils used for? • What is thefocallength for a lens and howcan it be changed in the TEM?

50. The Objective lens • Often a double or twin lens • The most important lens • Determinesthe reolving powerofthe TEM • All theaberationsoftheobjective lens aremagnified by theintermediat and projector lens. • The most importantaberrations • Asigmatism • Spherical • Chromatical