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

2. FYS4340 and FYS9340
FYS4340
Theory based on ”Transmission electron microscopy” by D. B. Williams and C.B. Carter
Part 1, 2 and standard imaging techniques (part 3)
Practical training on the TEM
FYS9340
Theory same as FYS additional papers related to TEM and diffraction.
Teaching training.
Perform practical demonstrations on the TEM for the master students.

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

4. Introduction EM 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.
With spatial resolution down to the atomic level (HREM and STEM)
Electrons
E<Eo
(EELS)
BSE SE AE
X-rays (EDS)
E=Eo
Bragg diffracted
electrons
This course has focus on making the master students able to do basic TEM combining imaging, diffraction and spectroscopy (EDS) but with spesial emphasis on diffraction techniques.
Diffraction
From regions down to a few nm (CBED).

5. Basic principles, electron probe
Auger electron or
x-ray
Valence K L M
Electron
shell K L M
1s2
2s2
2p2
2p4
3s2
3p2
3p4
3d4
3d6
Characteristic x-ray emitted or Auger
electron ejected after relaxation of inner
state.
Low energy photons (cathodoluminescence)
when relaxation of outer stat.
Secondary electron
15/1-08
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. Resolution limitations of the VLM
1839, George Airy: there should be a natural limit to the optical microscopes.
1872, both Ernst Abbe and Hermann von Helmholtz: Light is limited by the size of the wavelength.
As early as 1834, George Airy, the eminent British astronomer, theorized that there should be a natural limit to the resolution of optical microscopes. In 1873, two Germans, Ernst Abbe, cofounder of the Karl Zeiss Optical Works at Jena, and Hermann von Helmholtz, the famous physicist and philosopher, independently published papers on this issue. Both arrived at the same conclusion as Airy: Light is limited by the size of its wavelength. Specifically, light cannot resolve smaller than one-half the height of its wavelength. One solution to this limitation was to experiment with light, or electromagnetic radiation, or shorter and shorter wavelengths. At the beginning of the twentieth century, Joseph Edwin Barnard experimented on microscopes using ultraviolet light. Such instruments, however, only modestly improved the resolution. In 1912, German physicist Max von Laue considered using X rays. At the time, however, it was hard to turn “X-ray microscopy” into a physical reality. The wavelengths of X rays are exceedingly short, but for the most part they are used to penetrate matter, not to illuminate objects. It appeared that microscopes had reached their limit.
Resolution of the eyes mm
Resolution of a good VLM ~300 nm

8. Electron beam/cathode ray
1857, The cathode-ray tube was invented
1896, Olaf Kristian Birkeland experimenting with the effect of parallel magnetic fields on the electron beam of the cathode-ray tub concluded that cathode rays that are concentrated on a focal point by a magnet are as effective as parallel light rays that are concentrated by means of a lens.
The core component of the new instrument was the electron beam, or “cathode ray,” as it was usually called then. The cathode-ray tube was invented in 1857 and was the source of a number of discoveries, including X rays. In 1896, Olaf Kristian Birkeland, a Norwegian scientist, after experimenting with the effect of parallel magnetic fields on the electron beam of the cathode-ray tube, concluded that cathode rays that are concentrated on a focal point by means of a magnet are as effective as parallel light rays that are concentrated by means of a lens. From around 1910, German physicist Hans Busch was the leading researcher in the field. In 1926, he published his theory on the trajectories of electrons in magnetic fields. His conclusions confirmed and expanded upon those of Birkeland. As a result, Busch has been recognized as the founder of a new field later known as “electron optics.” His theoretical study showed, among other things, that the analogy between light and lenses on the one hand, and electron beams and electromagnetic lenses, on the other hand, was accurate.

9. Electron optics
1926, Hans Busch, ”Founder of the electron optics” published his theory on the trajectories of electrons in magnetic fields.
1928, Graduate student Ruska worked on refining Busch’s work.
The energy of the electrons in the beam was not uniform resulting in fuzzy images.
Knoll and Ruska were able design and construct electron lenses and the first realization of an electron microscope.”

10. Wave nature of electrons
1897, J.J. Thomson
Concludes that electrons have particle nature.
1924, Louis de Broglie
Hypothesis: Matter on the scale of subatomic particles possesses wave characteristics. The speed of low-mass subatomic particles, such as electrons, is related to wavelength .
1927, Davisson and Germer and Thomson and Reid
Both demonstrated the wave nature of electrons by independently performing electron diffraction experiments
λ=1.22/E1/2

11. The first electron microscope
Knoll and Ruska, first TEM in 1931
Idea and first images published in 1932
By 1933 they had produced a TEM
with two magnetic lenses which gave
times magnification.
Ernst Ruska: Nobel Prize in physics 1986
Electron Microscope Deutsches Museum, 1933 model

12. The first commersial microscopes
Elmiskop I
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.

13. Developments
Realized that spherical aberration of the magnetic lenses limited the possible resolution to about 3 Å. r1 r2 α
Spherical aberration coefficient
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 r1 r2
Disk of least confusion α

14. Chromatic aberration Disk of least confusionv
v - Δv
Chromatic aberration coefficient:
dc = Cc α ((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 a magnetic field:
F= -e (v x B)

15. 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.

16. 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.
One exceptions was the work of yada who got crystallographic information from chrysotile fibres

17. Menter,

18. 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
Th-compound supported on a graphite thin crystal film. Bright spots attributed to single Th atoms.

19. 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.

20. 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

21. 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
Because electrons interact strongly with matter, elastic and inelastic scattering give rise to many different signals which can be used for analysis.

22. 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/ U: pot. diff.
When we discuss the path of the electron through an electro optical system, it is often sufficient to considder the electron as a particle.
Table 1.1 show calculated wavelenghts for various accelerating voltages.
It is necessary to use the wave description of the electron when consider electron diffraction, image contrast and discuss the properties of very small concentrated electron beams with smal diameters.
The resolving power of an imaging system is limited by the wave length of the radiation.
λ = h/(2emoU)1/2 * 1/(1+eU/2moc2)1/2

23. The Transmission Electron Microscope
U (Volt)
k = λ-1 (nm-1)
λ (nm)
m/mo
v/c 1
0.815
1.226
0.0020 10
2.579
0.3878
0.0063
102
8.154
0.1226
0.0198
104
81.94
0.1950
105
270.2
1.1957
0.5482
2*105
398.7
1.3914
0.6953
107
8468
0.9988
Relations between acceleration voltage,
wavevector, wavelength, mass and velocity

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

25. JEOL 2000FX Electron gun Illumination system Wehnelt cylinder Filament
Anode
Electron gun 1. and 2. beam deflectors
and 2. condenser lens
Condenser aperture
Condenser lens stigmator coils
Condenser lens 1. and 2. beam deflector
Condenser mini-lens
Objective lens pole piece
Objective aperture
Objective lens stigmators
Image shift coils
Objective mini-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
Schematic diagram of the JEOL 2000FX analytical microscope