1. Electron Microscopy - References
Buseck, Cowley and Eyring, “High-Resolution Transmission Electron Microscopy” (Oxford Univ. Press, 1988).
Cowley, “Diffraction Physics”, (North-Holland, 1975).
Edington, “Practical Electron Microscopy in Materials Science” (van Nostrand, 1976).
Egerton, “Electron Energy-Loss Spectroscopy in the Electron Microscope” (Plenum, 1986).
Grundy and Jones, “Electron Microscopy in the Study of Materials” (Edward Arnold, 1976).
Hirsch, Howie, Nicholson, Pashley, and Whelan, “Electron Microscopy of Thin Crystals” (Kreiger, 1977).

2. Electron Microscopy - References
7. Hren, Goldstein and Joy, “Introduction to Analytical Electron Microscopy” (Plenum, 1979).
8. Joy, Romig and Goldstein, “Principles of Analytical Electron Microscopy” (Plenum, 1986).
9. Loretto, “Electron Beam Analysis of Materials” (Chapman and Hall, 1984).
10. Reimer, “Transmission Electron Microscopy” (Springer Verlag, 1985).
11. Thomas and Goringe, “Transmission Electron Microscopy of Materials” (Wiley, 1979).
12. Williams, “Practical Analytical Electron Microscopy in Materials Science” (Philips, 1984).

3. Electron Microscopy Electron-Matter Interactions Inelastic Scattering
Diffraction
Electron
Imaging
Structure
Microscopy
Chemical
Analysis

4. Electron Microscopy Microscopy Spatial Magnification Contrast
Resolution
Contrast

5. Electron Imaging Systems
Unlike x-rays, electrons may be focused to form an image
diffraction pattern (Fourier transform)
image
object so f f si

6. I O Diffraction in Imaging Systems
Slits, lenses, etc. in imaging systems act as
apertures resulting in diffraction
Image points are diffraction patterns not points
Image point
with diffraction
Imaging
System I O
Object
Image
Imaging system
with circular aperture
(e.g., telescope, light microscope, electron microscope)

7. Fraunhofer (Far-Field) Diffraction Pattern from a Circular Aperture
Airy disk
I(q)/I(0) Dq g
J1(g) = 0 when g = ½kDsinq ≈ 3.832
sinq ≈ 1.22l/D
Dq ≈ 2 (1.22l/D)

8. Spatial Resolution
Spatial Resolution = the minimum separation between two points in the object that can still be observed as separate in the image
If aberrations are corrected then we say the optics
are diffraction-limited
overlapping
diffraction
patterns
Imaging
System
Object
Image
From Pedrotti
& Pedrotti,
Fig. 16-8,
p. 336

9. Rayleigh’s Criteria I(q)/I(0) Dq = 1.22l/D “just” resolvable q
not
resolvable q

10. Spatial Resolution Dqmin= 1.22 l/D xmin = f Dqmin = 1.22l (f/D)
= 1.22l / 2NA
NA = numerical aperture of lens
Dqmin
objective lens
diameter, D
xmin f

11. Microscope Resolution
xmin = 0.61 l / NA
Improve resolution by reducing wavelength
Optical: l ~ 500 nm
xmin ~ 250 nm
Electrons: l = h / p
= h / (2moE)½
= 1.22 / V (nm)
(non-relativistic, E << Eo = 511 keV)
E = 100 keV (typical)
l ~ 0.04 Å
xmin ~ 0.02 Å (5 – 20 Å achieved in practice)

12. Conventional TEM (CTEM)
Diffraction pattern formed in back focal plane
From Williams,
Fig. 1.3, p. 3

13. Image Formation diffraction orders
diffraction pattern (Fourier transform) so f f si

14. Magnification (Optical Analogy)
intermediate
image Fo Fi Fi Fo
virtual image
(magnified)
back
focal
plane

15. EM Lenses Electron lenses are Cu windings that form a solenoid
Force on electron is
F = q (v x B)
Can focus/magnify image by adjusting lens currents (B)
Magnification up to 106
Can image specimen or diffraction pattern by adjusting lens currents

16. Electron Microscope Specimen Crystal structure Image (microscopy)
From Ohring, Fig. 6-10, p. 270

17. Electron Microscope
Microscope is under vacuum
(< 10-4 Torr)
Eliminate scattering of electrons from gas (need mean free path > 1 m)
Minimize contamination of specimen and microscope components

18. Electron Microscope Sources
Filament
current -
100 kV – 1 MeV +
Electron
beam

19. Electron Microscope Sources
Thermionic emission: thermal energy allows electrons to overcome work function of material (e.g., W or LaB6)
Field emission: electron can tunnel through surface potential barrier (e.g., W or ZrO-coated W)
From Reimer, Fig. 4.1, p. 80

20. Microscope Resolution
In practice, resolution is limited by:
Dispersion (energy spread) and stability of electron source
Microscope aberrations
Energy loss & scattering of electrons in sample
Typical Resolution
~ nm (thermionic
emission)
~ 0.5 – 2 nm (field emission)

21. Phosphor coated screen CRT)
Electron Detectors
Phosphor coated screen CRT)
Special photographic emulsions
From Williams,
Fig. 1.3, p. 3

22. Image Contrast
Amplitude and phase change of electron waves gives contrast
Image Contrast
Absorption
Contrast
Phase
Contrast
Diffraction
Contrast

23. Image Contrast
Contrast is formed by using aperture in back focal plane to block scattered electrons
From Williams,
Fig. 1.3, p. 3

24. Absorption Contrast
Increase in scattering (elastic and inelastic) with higher atomic number Z and thickness of material
Scattered electrons are blocked by objective aperture in rear focal plane producing darker contrast
10 nm
carbon
lead 9 96 17 91 83 4
objective
aperture

25. Diffraction Contrast
Smaller lattice constant diffracts to larger angles
diffracted electrons blocked by aperture
darker contrast
blocked electrons

26. Incident beam → bright field Diffracted beam → dark field
Diffraction Contrast
Only one beam (transmitted or diffracted) is allowed to pass through the objective aperture
Incident beam → bright field
Diffracted beam → dark field z z
transmitted
beam
diffracted
beam
transmitted
beam 2q
diffracted
beam 2q
Ewald
sphere g
Ewald
sphere g
aperture
aperture
Bright field
Dark field

27. Phase Contrast The more diffraction orders captured, the greater
the specimen detail that can be resolved (more Fourier components)

28. Fourier Analysis of Square Wave
0.5
0.5 + (2/p)sinkx
0.5 + (2/p)sinkx
- (2/3p)sin3kx
0.5 + (2/p)sinkx
- (2/3p)sin3kx
+ (2/5p)sin5kx

29. Phase Contrast
Can combine transmitted and diffracted beams to produce high-resolution lattice images
Uses amplitude & phase
from Ohring, Fig , p. 664

30. Electron Microscopy small scanning electron beam (~ 50 Å)
TEM
(thin foil)
SEM
(bulk)
small scanning electron beam (~ 50 Å)
CTEM
STEM
large diameter (10’s mm’s) stationary electron beam
small diameter (~ 10 Å) scanning electron beam

31. Conventional TEM (CTEM)
Large diameter, stationary electron beam (~10’s mm)
From Williams,
Fig. 1.3, p. 3

32. Scanning TEM (STEM)
Small diameter electron beam (~0.5 nm) scanned across surface
From Williams, Fig. 1.7, p. 5

33. By Bx Scanning TEM (STEM)
An electron beam (incident into the page, along the z direction) will be deflected by a perpendicular magnetic field
The electron beam can be scanned in a raster pattern across the sample By Bx

34. Disadvantage of TEM : Sample Preparation
Specimen must be thin enough to transmit electrons
e.g., range of 100 keV electrons in Si ~ 0.6 mm
Sample preparation
Many hours
Epoxy sections together
Polish to produce thin foil
Ion beam milling (thin by sputtering)
Hole appears in middle
Thickness at edge of hole ~ 2000 Å

35. SEM Incident electron energy ~ 1- 50 keV
Pairs of scanning coils (x, y) deflect a small diameter (~ 50 Å) electron beam across a specimen surface
From Williams,
Fig. 1.4, p. 3

36. SEM
Electrons undergo elastic and inelastic scattering with sample resulting in tear-shaped interaction volume
Inelastic processes include production of x-rays, secondary electrons, light, phonons, e-h pairs, Auger electrons
Electron Beam
Secondary
electrons
(1-10 nm)
Auger
electrons (1 nm)
Backscattered
electrons
(0.1 – 1 mm)
X-rays
(0.2 – 2 mm)

37. Usually use secondary electrons (1 – 50 eV) to form SEM image
Secondary electrons: electrons in CB are ejected due to collision with incident electron (inelastic scattering)
Elastic
Backscattered
Electrons
Secondary
Electrons
Electron
Yield
Auger Electrons 5 50
2000 Eo
Electron Energy (eV)

38. Originate from a depth < 10 nm Surface-sensitive technique
SEM
Secondary electrons
Originate from a depth < 10 nm
Surface-sensitive technique
Best resolution
Probability of SE escape 1
0.5 25 50 75
Depth at which SE are generated (Å)

39. SEM
Low energy electrons are detected by scintillator (e.g., NaI) - PMT system
From Williams, Fig. 1.14, p. 8

40. SEM
Edges and slopes appear brighter due to greater SE yield from volume projection
Electron beam
to SE detector

41. SEM
Can also use backscattered electrons
Backscattering yield is sensitive to the atomic number
Greater elemental sensitivity than secondary electrons

42. xxxx xxxxxx SEM Image magnification : M = scan length on CRT, L
scan length on specimen, l
Magnification achieved electronically by changing the scan area on the specimen via the scanning coils
xxxx
xxxxxx
xxxx
xxxxxx l L
Area scanned
on specimen
Area scanned
on CRT

43. xxxx xxxxxx SEM Maximum magnification : M = pixel size on CRT
beam diameter
~ 105
xxxx
xxxxxx
xxxx
xxxxxx l L
Area scanned
on specimen
Area scanned
on CRT

44. SEM Can detect other signals in the SEM for compositional analysis
Cathodoluminescence (CL)
X-rays (EDX)
e-h pairs (EBIC)
From Schroder,
Fig. 10.4, p. 655

45. Channeling
Electrons incident along a major crystallographic orientation experience channeling effect
Electron backscattering yield is reduced

46. Channeling pattern can be used to deduce crystal structure
From Loretto, Fig. 4.20, p. 137