The transmission electron
microscope
Additional web resources
• http://nanohub.org/resources/3777
– Eric Stach (2008), ”MSE 528 Lecture 4: The instrument,
Part 1, http://nanohub.org/resources/3907
c
Simplified ray diagram
b
a
Parallel incoming electron beam
3,8 Å
Si
Sample
1,1 nm
PowderCell 2.0
Objective lense
Diffraction plane
(back focal plane)
Image plane
MENA3100 V08
Objective aperture
Selected area
aperture
JEOL 2000FX
Wehnelt cylinder
Filament
Anode
Electron gun 1. and 2. beam deflectors
1.and 2. condenser lens
Condenser aperture
Condenser lens stigmator coils
Condenser lens 1. and 2. beam deflector
Mini-lens screws
Specimen
Intermediate lens
shifting screws
Projector lens
shifting screws
Condenser mini-lens
Objective lens pole piece
Objective aperture
Objective lens pole piece
Objective lens stigmators
1.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
Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1,
http://nanohub.org/resources/3907
Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1,
http://nanohub.org/resources/3907
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
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
Brightness
• Brightness is the current density per unit solid
angle of the source
• β = ie/(πdcαc)2
d
Cross over
α
Image of source
The electron source
• Two types of emission sources
– Thermionic emission
• W or LaB6
– Field emission
• W Cold FEG ZnO/W Schottky FEG
The electron gun
Thermionic gun
FEG
Wehnelt
cylinder
Bias -200 V
Cathode
-200 kV
Equipotential lines
Anode
Ground potential
dcr Cross over
αcr
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
Thermionic guns
Thermionic emission
• Current density:
Jc= AcT2exp(-φc/kT)
Richardson-Dushman
–
–
–
–
Ac: Richardson’s constant, material dependent
T: Operating temperature (K)
φ: Work function (natural barrier that prevents electrons from leaving the solid)
k: Boltzmann’s constant
Maximum usable temperature T is determined
by the onset of the melting/evaporation of material.
Field emission
• Current density:
Maxwell-Boltzmann
energy distribution
for all sources
Fowler-Norheim
Field emission
• The principle:
– The strength of an electric field E is considerably increased
at sharp points.
E=V/r
• rW < 0.1 µm, V=1 kV → E = 1010 V/m
– Lowers the work-function barrier so that electrons can
tunnel out of the tungsten.
• Surface has to be pristine (no contamination or oxide)
– Ultra high vacuum condition (Cold FEG) or poorer vacuum if tip is
heated (”thermal” FE; ZrO surface tratments → Schottky emitters).
Characteristics of principal electron sources at 200 kV
W
LaB6
FEG Schottky
(ZrO/W)
FEG cold (W)
Current density Jc (A/m2)
2-3*104
25*104
1*107
Electron source size (µm)
50
10
0.1-1
0.010-0.100
Emission current (µA)
100
20
100
20~100
Brightness B (A/m2sr)
5*109
5*1010
5*1012
5*1012
Energy spread ΔE (eV)
2.3
1.5
0.6~0.8
0.3~0.7
Vacuum pressure (Pa)*
10-3
10-5
10-7
10-8
Gun temperature (K)
2800
1800
1800
300
* Might be one order lower
Advantages and disadvantages of the
different electron sources
W Advantages:
LaB6 advantages:
FEG advantages:
Rugged and easy to handle
High brightness
Extremely high brightness
Requires only moderate
vacuum
High total beam current
Long life time, more than
1000 h.
Good long time stability
Long life time (500-1000h)
High total beam current
W disadvantages:
LaB6 disadvantages:
FEG disadvantages:
Low brightness
Fragile and delicate to
handle
Very fragile
Limited life time (100 h)
Requires better vacuum
Current instabilities
Long time instabilities
Ultra high vacuum to
remain stable
Electron lenses
Any axially symmetrical electric or magnetic field has the properties
of an ideal lens for paraxial rays of charged particles.
• Electrostatic
F= -eE
– Require high voltage - insulation problems
– Not used as imaging lenses, but are used in modern monochromators or
deflectors
• Magnetic
– Can be made more accurately
– Shorter focal length
F= -e(v x B)
General features of magnetic lenses
• Focuses near-axis electron rays with the same accuracy as a glass lens
focuses 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
Electromagnetic lens
Bore
Current in the coil creates
A magnetic field in the bore.
Soft Fe pole piece
The magnetic field has axial
symmetry, but is inhomogenious
along the length of the lens.
gap
Cu coil
The soft iron core can increase the field by several
thousand times.
Electron ray paths through
magnetic fields
r
The electron spirals
through the lens field:
A helical trajectory.
θ
v
B
v2
v1
For electrons with
higher keV, we must
use stronger lenses
(larger B) to get similar
ray paths.
See fig 6.9
Simple ray diagrams
• Electron lenses act like a convex glas lens
• Thin lens
Point obj
• β: variable giving the fraction
β
of rays collected by the lens
~ 10 m rad ~0.57o
α
Point image
Never a perfect image
Changing the strength of the lens
• The further away rays are from the optical axis
the stronger they are bent by a convex lens.
• What happens to the focal and image plane
when the strength of the lens is changed?
• What happens to the image?
The strength of the lens
• Under conditions normally found in the TEM,
strong lenses magnify less and demagnify
more (not in VLM).
• When do we want to demagnify an object?
Spherical aberration
Gaussian image plane
r2
α r1
Highest intensity in the
Gaussian image plane
Plane of least confusion
ds = 0.5MCsα3 (disk diameter, plane of least confusion)
ds = 2MCsα3 (disk diameter, Gaussian image plane)
M: magnification
Cs :Spherical aberration coefficient
α: angular aperture/
angular deviation from optical axis
2000FX: Cs= 2.3 mm
2010F: Cs= 0.5 nm
Chromatic aberration
Diameter for disk of least confusion:
dc = Cc α ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0.5
v
v - Δv
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
Thermally emitted electrons: ΔE/E=kT/eU,
Disk of least confusion
LaB6: ~1 eV
The specimen will introduce chromatic aberration.
2000FX: Cc= 2.2 mm
2010F: Cc= 1.0 mm
The thinner the specimen the better!!
Correcting for Cc effects only makes sense if you
are dealing with specimens that are thin enough.
Lens astigmatism
Due to non-uniform magnetic field
as in the case of non-cylindrical lenses.
Apertures may affect the beam if not
precisely centered around the axis.
This astigmatism can not be
prevented, but it can be
corrected!
y
• Loss of axial symmetry
x
y-focus
x-focus
Disk of least confusion
Diameter of disk of least confusion:
da: Δfα
Depth of focus and depth of field (image)
• Imperfections in the lenses limit the resolution but give a
better depth of focus and depth of image.
– Use of small apertures to minimize aberrations.
• The depth of field (Δb or Dob) is measured at, and refers to,
the object.
– Distance along the axis on both sides of the object plane within which
the object can move without detectable loss of focus in the image.
• The depth of focus (Δa, or Dim), is measured in, and referes to,
the image plane.
– Distance along the axis on both sides of the image plane within which
the image appears focused.
Depth of focus and depth of field (image)
1
dob
1
2
dim
2
βob
αim
Dim
Dob
Ray 1 and 2 represent the extremes of the ray paths that remain in
focus when emerging ± Dob/2 either side of a plane of the specimen.
αim≈ tan αim= (dim/2)/(Dob/2)
Angular magnification: MA= αim/ βob
Transvers magnification: MT= dim/ dob
βob≈ tan βob= (dob/2)/(Dim/2)
MT= 1/MA
Depth of focus: Dim=(dob/ βob)MT2 Depth of field: Dob= dob/ βob
Depth of field
Depth of field: Dob= dob/ βob
Carefull selection of βob
• Thin sample: βob ~10-4 rad
• Thicker, more strongly scattering specimen: βob (defined by
obj. aperture) ~10-2 rad
Example: dob/ βob= 0.2 nm/10 mrad = 20 nm
Example: dob/ βob= 2 nm/10 mrad = 200 nm
Dob= thickness of sample
all in focus
Depth of focus
Depth of focus: Dim=(dob/ βob)MT2
Example: To see a feature of 0.2 nm you would use a
magnification of ~500.000 x
(dob/ βob)M2= 20 nm *(5*105)2= 5
km
Example: To see a feature of 2 nm you would use a
magnification of ~50.000 x
(dob/ βob)M2= 200 nm *(5*104)2= 500
m
Focus on the wieving screen
and far below!
Fraunhofer and Fresnel diffraction
• Fraunhofer diffraction: far-field diffraction
– The electron source and the screen are at infinite distance
from the diffracting specimen.
• Flat wavefront
• Fresnel diffraction: near-field diffraction
– Either one or both (electron source and screen) distances
are finite.
Electron diffraction patterns correspond closely to the Fraunhofer case
while we ”see” the effect of Fresnel diffraction in our images.
Airy discs (rings)
• Fraunhofer diffraction from a circular aperture will give a
series of concentric rings with intensity I given by:
I(u)=Io(JI(πu)/ πu)2
http://en.wikipedia.org/wiki/Airy_disk
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.
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
The Objective lens
• Often a double or twin lens
• The most important lens
– Determines the resolving power of the TEM
• All the aberations of the objective lens are magnified by
the intermediate and projector lens.
• The most important aberrations
– Astigmatism
– Spherical
– Chromatic
Astigmatism
Can be corrected for with stigmators
The objective lens
• Cs can be calculated from information about
the shape of the magnetic field
– Cs has ~ the same value as the focal length (see
table 2.3)
• The objective lens is made as strong as possible
– Limitation on the strength of a magnetic lens with an iron core
(saturation of the magnetization Ms)
– Superconductiong lenses (give a fixed field, but need liquid
helium cooling)
Apertures
Apertures
We use apertures in the lenses to control the divergence or convergence
of electron paths through the lens which, in turn, affects the lens aberrations
and controls the current in the beam hitting the sample.
Use of apertures
Condenser apertures:
Limit the beam divergence (reducing the diameter of the discs in the
convergent electron diffraction pattern).
Limit the number of electrons hitting the sample (reducing the intensity).
Objective apertures:
Control the contrast in the image. Allow certain reflections to contribute to
the image. Bright field imaging (central beam, 000), Dark field imaging (one
reflection, g), High resolution Images (several reflections from a zone axis).
A.E. Gunnæs
MENA3100 V08
Objective aperture: Contrast enhancement
Bright field (BF)
glue
hole
(light elements)
Ag and Pb
Objective
aperture
Si
BF image
All electrons contribute to the image.
Only central beam contributes to the image.
Small objective aperture
Bright field (BF), dark field (DF) and weak-beam (WB)
Objective
aperture
BF image
DF image
Diffraction contrast
Weak-beam
Dissociation of pure screw dislocation In Ni3Al, Meng
and Preston, J. Mater. Scicence, 35, p. 821-828, 2000.
Large objective aperture
High Resolution Electron Microscopy (HREM)
HREM image
Phase contrast
Use of apertures
Condenser aperture:
It limits the beam divergence (reducing the diameter of the discs in the
convergent electron diffraction pattern).
It limits the number of electrons hitting the sample (reducing the intensity).
Objective aperture:
It controls the contrast in the image. It allows certain reflections to
contribute to the image. Bright field imaging (central beam, 000), Dark field
imaging (one reflection, g), high resolution images (several reflections from a
zone axis).
Selected area aperture:
It selects diffraction patterns from small (> 1µm) areas of the specimen.
It allows only electrons going through an area on the sample that is limited
by the SAD aperture to contribute to the diffraction pattern (SAD pattern).
Selected area diffraction
Parallel incoming electron beam
Specimen with two crystals (red and blue)
Objective lense
Pattern on the screen
Diffraction pattern
Image plane
Selected area
aperture
Diffraction with no apertures
Convergent beam and Micro diffraction (CBED and µ-diffraction)
Convergent beam
Focused beam
C2 lens
Convergent beam
Illuminated area less than
the SAD aperture size.
Small probe
CBED pattern
Diffraction information from an area with
~ same thickness and crystal orientation
µ-diffraction pattern
Shadow imaging
(diffraction mode)
Parallel incoming electron beam
Sample
Objective lense
Diffraction plane
(back focal plane)
Image plane
Magnification and calibration
Resolution of the photographic emulsion: 20-50 µm
Magnification depends on specimen position in the objective lens
Microscope
Lens
Mode
Magnification
JEM-2010
Objective
MAG
2 000-1 500 000
LOW MAG
50
-
Twin
TEM
25
- 750 000
Super twin
TEM
25
- 1 100 000
Twin
SA
3 800 - 390 000
Super twin
SA
5 600 - 575 000
Philips CM30
6 000
Magnification higher than 100 000x can be calibrated by using lattice images.
Rotation of images in the TEM.