Transmission Electron Microscopy
David Stokes
2DX Workshop
University of Washington
8/15-8/19/2011
Kinds of Electron
Microscopes
TEM
transmissive
resolution determined by optics
analogous to bright field light microscope
detector is film or CCD

SEM
reflective, surface imaging
resolution determined by spot size
x-ray microanalysis or EELS possible
STEM
transmissive, small spot with scan coils
resolution determined by spot size
analogous to confocal
detector is PMT
x-ray microanalysis or EELS possible
SEM vs. TEM
TEM sectioned cell
TEM metal shadowed molecules
250 nm
TEM of frozen, isolated macromolecules
TEM of 2D membrane protein crystal
TEM images are 2D projections
Source of electrons
Tungsten:
- outer electrons of W are made free by heating the metal.
- W has excellent yield when heated just below its melting temp of 3653K.
- Heat to 2600K for good yield without melting and evaporating tip (saturation point)
- 100 hrs with W wire.
- Make filament (cathode) at neg potential (e.g. -100 kV).
- As electrons boil off the W, they are repelled by the cathode.
- Potential difference relative to the anode provides the accelerating voltage
- Make Weihnolt several hundred volts more negative
electrons pass through the aperture in the Weihnolt cap.
bias controls output of electrons and shapes field
- Anode is grounded so electrons are accelerated towards it.
- Electrostatic field causes crossover at the anode - this is effective source size
LaB6
- has lower work function: amount of energy necessary to free electrons.
- 1000K with higher electron yield and longer life.
- get small beam crossover size with high flux (10x emission of W)
Field emission
- single crystal of W oriented relative its xtal lattice
- no heating - series of high voltage anodes draw electrons out of lattice
- electrostatic lens of anodes -> 10 nm source size
- need very high vacuum -> contamination
- Zirconium to reduce work function, heating to reduce contamination
from Reimer
Properties of Electrons
Energy of electrons is work W required to move electron
from anode to cathode against force F=-eE:
c
c
c
a
a
a
P  W   F  ds  e E  ds  e   ds  e(c  a )  eU
U=accelerating voltage
charge on electron is -1.602x10-19 Coulombs,
when accelerated through 1V potential difference has kinetic energy of 1.602x10 -19 Nm (joule)
define this kinetic energy as 1 eV.
With accelerating voltage of 200kV – electrons have energy of 200keV (= 3.2x10-14 joules)
compare to C-C bond of 5.8x10-19 joules (3.6 eV) or lattice binding energy of 1-2 eV
Speed of electrons
at 100kV: v=1.64x108m/sec 
Have to consider relativity
1MeV = 2Eo  m=3m0
Wavelengths of electrons ()
0.0349 Å at 120kV,
0.025 Å at 200 kV,
0.01969 Å at 300 kV
more than 1/2 speed of light
compare with wavelength of light: 2000 Å
or X-rays:
1.5 Å for Cu K
1 Å synchrotron radiation
diffraction limit for
resolution of
any optical system:
D = /2
Force on an electron
electrostatic:
electromagnetic:


F  q0 E

 
F  q0v  B
Typical electron lenses
single lens (e.g. condensor)
split lens (e.g. objective)
Magnetic lenses like Glass lenses
are governed by Newton’s lens equation
http://members.shaw.ca/quadibloc/science/opt05.htm
and
Focal length of Electromagnetic lens
f  K (U / i 2 )
f = focal length K = lens const,
U = voltage, i = current
electromagnetic lens:
can change focal length by changing current
glass lens:
change focus by moving specimen up and down
change magnification by switching lenses
Lens Strength affects focal length
f  K (U / i )
2
f = focal length K = lens const,
U = voltage, i = current
A stronger lens demagnifies the image!!!
Trajectory of electrons through a homogeneous B field

 
F  ev  B
F  evBsin 
where  is angle between v and B
Energy of electron conserved – no change in |v|
If force is  to v: electron moves in a circle
If force is || to v, path unchanged.
Generally, path is spiral, with v|| and v components
So electrons passing through given point P will intersect again at
point P'
PP' = v||Tc = vTccos,
where Tc is time to complete circle,
which is independent of 
P
If many angles focused in same plane, get image formed
P'
For small angles of , cos ~1 and get image formed at P'.
Larger angles of  reduces the distance to P' (cos = (1 - 2/2 + . . .)
and thus gives rise to spherical aberration
Real lens is non-homogeneous field - so-called bell-shaped field
Aberrations: astigmatism, coma, spherical, field curvature,
distortion (pincushion/barrel)
chromatic and Contrast Transfer Function
TEM lens configuration
Condenser Lenses:
Demagnifies source
Define “spot size”
Objective lens:
Defines image focus
Has fixed magnification (20-50x)
Intermediate lens:
Controls whether
Image or diffraction pattern
Is recorded
Projector lenses:
Controls image magnification
or
Diffraction “camera length”
Condenser lenses
C1 lens produces image of source
C2 lens demagnifies onto sample
C2 aperture reduces beam current
and makes beam more parallel
C1 lens controls spot size
Strong C1 lens produces
small probe size and
weak beam
Weak C1 lens produces
larger probe size and
bright beam
This is known as
“spot size”
C1 crossover produces
image of source and
Mag = u/v for C2 lens
Beam convergence
Increasing strength of C2 lens
Upper
Objective
lens
~parallel
convergent
divergent
parallel
magnification of objective: 20-50x
angle for 2.5 Å resolution at 200kv:
 = /d = 0.025/2.5 = 10 mrad = 0.5°
most of mag range achieved
with projection lenses
Much smaller angles and
aberrations therefore less
important
Diffraction vs. Imaging
controlled by
Intermediate lens
Back focal plane of objective lens
corresponds to diff pattern
Selected area aperture
is at first image plane
Intermediate lens selects either
BFP or 1st image plane as its
object
Diff pattern or 2nd image serves
as object for projector lens
Coma
For high resolution images, you want the apparent source
aligned with the real source on the optical axis and the beam
to run parallel to this axis. This is coma-free alignment.
Deflectors produced by transverse fields:
E field (parallel plate capacitor)
B field (electromagnetic lens)
electrostatic
Deflectors
electromagnetic
deflector coils generally come in pairs
gun tilt coils
pivot points aligned
pivot points misaligned
Apertures
source
condensor
lens
condensor
aperture
specimen
A typical scattering event
i
s
ikr
e
 (r , ,  )   i  s  eikz  f ( ,  )
r
Proportionality constant for scattering:
 is scattering cross-section for one atom (cm2/atom)
elastic, inelastic, absorption, fission
Electron Scattering
Elastic Scattering: Rutherford scattering
F
b
electrostatic
force:

q1q2
Ze 2
F

2
4R
4R 2

z

+
+
+
+
+
+
+
+
Z = atomic number,
but, actually need to consider screening of
electrons on nuclear charge
Solving Scrodinger’s equation for the
potential and making
approximations for screening of
nuclear charge by electron cloud:
 tot
1  Z  R 2 1 2 2 43
 (
)    Z
 a0

N.B. Elastically scattered electrons have same wavelength as incident
beam and are most effective for generating phase contrast image because
they interfere with the unscattered beam
Inelastic Scattering
Energy transferred from incident electrons to the specimen
1. Oscillations of molecular bonds and phonon excitations: 20 meV – 1 eV
too small to generally observe given ~1 eV spread of beam energy
2. Excitation of outer electrons and valence/conduction band electrons (metals): 1-50 eV
3. Ionization of inner electrons (K,L,M shells) to unoccupied shells: 10 – 100s eV
Why do we hate inelastic collisions?
Inelastic electrons are focused at “undesirable” places
And therefore produce a blurred image due to
Chromatic aberration
Inelastic scattering produces chemical changes radiation damage
differential cross-section
total scattering cross-section
scattered outside 2.4 A aperture
unscattered
inelastics within aperture
differential scattering vs. 
25 keV electrons with Ar gas
elastics within aperture
The inelastic scattering “blurs” the low spatial frequencies
electrons
X-rays
But they can be filtered out (after they damaged the specimen)
-filter
+filter