Electron Microscopy - References
1. Buseck, Cowley and Eyring, “HighResolution Transmission Electron
Microscopy” (Oxford Univ. Press, 1988).
2. Cowley, “Diffraction Physics”, (NorthHolland, 1975).
3. Edington, “Practical Electron
Microscopy in Materials Science” (van
Nostrand, 1976).
4. Egerton, “Electron Energy-Loss
Spectroscopy in the Electron
Microscope” (Plenum, 1986).
5. Grundy and Jones, “Electron
Microscopy in the Study of Materials”
(Edward Arnold, 1976).
6. Hirsch, Howie, Nicholson, Pashley, and
Whelan, “Electron Microscopy of Thin
Crystals” (Kreiger, 1977).
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).
Electron Microscopy
Electron-Matter
Interactions
Elastic
Scattering
Electron
Diffraction
Structure
Inelastic
Scattering
Electron
Imaging
Microscopy
Chemical
Analysis
Electron Microscopy
Microscopy
Spatial
Resolution
Magnification
Contrast
Electron Imaging Systems
• Unlike x-rays, electrons may be focused to
form an image
diffraction pattern (Fourier transform)
image
object
so
f
f
si
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
O
I
Imaging
System
Object
Image
Imaging system
with circular aperture
(e.g., telescope, light microscope, electron microscope)
Fraunhofer (Far-Field) Diffraction
Pattern from a Circular Aperture
Airy disk
I(q)/I(0)
1
0.8
0.6
Dq
0.4
0.2
g
0
-10
-5
0
5
10
J1(g) = 0 when g = ½kDsinq ≈ 3.832
 sinq ≈ 1.22l/D
 Dq ≈ 2 (1.22l/D)
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
Rayleigh’s Criteria
I(q)/I(0)
Dq = 1.22l/D
“just”
resolvable
q
I(q)/I(0)
Dq < 1.22l/D
not
resolvable
q
Spatial Resolution
Dqmin= 1.22 l/D
xmin = f Dqmin
= 1.22l (f/D)
= 1.22l / 2NA
NA = numerical aperture of lens
Dqmin
xmin
f
objective lens
diameter, D
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)
Conventional TEM (CTEM)
Diffraction pattern
formed in back focal
plane
From Williams,
Fig. 1.3, p. 3
Image Formation
diffraction orders
diffraction pattern (Fourier transform)
so
f
f
si
Magnification
(Optical Analogy)
intermediate
image
Fo
Fo
virtual image
(magnified)
back
focal
plane
Fi
Fi
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
Electron Microscope
Specimen
Crystal
Image
structure
(microscopy)
From Ohring, Fig. 6-10, p. 270
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
Electron Microscope Sources
Filament
current
-
100 kV – 1 MeV
+
Electron
beam
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
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
~ 5 - 10 nm (thermionic
emission)
~ 0.5 – 2 nm (field emission)
Electron Detectors
• Phosphor
coated screen
CRT)
• Special
photographic
emulsions
From Williams,
Fig. 1.3, p. 3
Image Contrast
• Amplitude and phase change of
electron waves gives contrast
Image Contrast
Absorption
Contrast
Diffraction
Contrast
Phase
Contrast
Image Contrast
Contrast is formed by using
aperture in back focal plane
to block scattered electrons
From Williams,
Fig. 1.3, p. 3
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
91
17
96
83
4
objective
aperture
Diffraction Contrast
Smaller lattice constant diffracts to larger angles
 diffracted electrons blocked by aperture
 darker contrast
blocked electrons
Diffraction Contrast
• Only one beam (transmitted or
diffracted) is allowed to pass through
the objective aperture
• Incident beam → bright field
• Diffracted beam → dark field
diffracted
transmitted 2q beam
beam
Ewald
sphere
g
transmitted
beam
diffracted
beam
Ewald
sphere
2q
g
aperture
Bright field
aperture
Dark field
Phase Contrast
The more diffraction orders captured, the greater
the specimen detail that can be resolved (more
Fourier components)
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
Phase Contrast
• Can combine transmitted and
diffracted beams to produce highresolution lattice images
• Uses amplitude & phase
from Ohring, Fig. 14-17, p. 664
Electron Microscopy
Electron
Microscopy
SEM
(bulk)
TEM
(thin foil)
small scanning
electron beam
(~ 50 Å)
CTEM
STEM
large diameter
(10’s mm’s)
stationary
electron beam
small diameter
(~ 10 Å)
scanning
electron beam
Conventional TEM (CTEM)
• Large diameter, stationary electron
beam (~10’s mm)
From Williams,
Fig. 1.3, p. 3
Scanning TEM (STEM)
• Small diameter electron beam (~0.5
nm) scanned across surface
From Williams, Fig. 1.7, p. 5
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
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
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
SEM
• Electrons undergo elastic and inelastic
scattering with sample resulting in tearshaped 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)
X-rays
(0.2 – 2 mm)
Auger
electrons (1 nm)
Backscattered
electrons
(0.1 – 1 mm)
SEM
• 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)
Secondary
Electrons
Electron
Yield
Elastic
Backscattered
Electrons
Auger Electrons
5
50
2000
Electron Energy (eV)
Eo
SEM
• Secondary electrons
• Originate from a depth < 10
nm
• Surface-sensitive technique
• Best resolution
Probability
of SE
1
escape
0.5
0
25
50
75
Depth at which SE are generated (Å)
SEM
• Low energy electrons are detected by
scintillator (e.g., NaI) - PMT system
From Williams, Fig. 1.14, p. 8
SEM
• Edges and slopes appear brighter
due to greater SE yield from volume
projection
Electron beam
to SE detector
SEM
• Can also use backscattered
electrons
• Backscattering yield is sensitive
to the atomic number
• Greater elemental sensitivity
than secondary electrons
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
l
Area scanned
on specimen
xxxx
xxxxxx
L
Area scanned
on CRT
SEM
• Maximum magnification :
M=
pixel size on CRT
beam diameter
~ 105
xxxx
xxxxxx
l
Area scanned
on specimen
xxxx
xxxxxx
L
Area scanned
on CRT
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
Channeling
• Electrons incident along a major
crystallographic orientation
experience channeling effect
• Electron backscattering yield is
reduced
Channeling
• Channeling pattern can be used
to deduce crystal structure
From Loretto, Fig. 4.20, p. 137