Transcript Diffraction methods and electron microscopy

Diffraction methods and
electron microscopy
Outline and Introduction to
FYS4340 and FYS9340
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 FYS4340 + additional papers related to TEM and
diffraction.
– Teaching training.
– Perform practical demonstrations on the TEM for the master students.
Basic TEM
Electron gun
Electrons are deflected by both
electrostatic and magnetic fields
Force from an electrostatic field
F= -e E
Sample position
Force from a magnetic field
F= -e (v x B)
Electron transparent samples
Introduction
EM and materials
Electron microscopy are based on three
possible set of techniqes
Imaging
With spatial resolution
down to the atomic level
(HREM and STEM)
Spectroscopy
Chemistry and elecronic
states (EDS and EELS).
Spatial and energy
resolution down to the
atomic level and ~0.1 eV.
Electrons
BSE
AE
SE
Diffraction
From regions down to a
few nm (CBED).
E<Eo
(EELS)
Bragg diffracted
electrons
E=Eo
X-rays (EDS)
Basic principles, electron probe
Electron
Auger electron or
x-ray
Valence
M
M
3d6
3p4
3d4
2p2
Electron
shell
L
3s2
2
2p4
3p
2s2
K
L
1s2
K
Secondary electron
15/1-08
Characteristic x-ray emitted or Auger
electron ejected after relaxation of inner
state.
Low energy photons (cathodoluminescence)
when relaxation of outer stat.
MENA3100
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
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.
Resolution of the eyes 0.1-0.2 mm
Resolution of a good VLM ~300 nm
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.
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.”
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 .
λ=1.22/E1/2
• 1927, Davisson and Germer and Thomson and Reid
– Both demonstrated the wave nature of electrons by
independently performing electron diffraction
experiments
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
12 000 times magnification.
Ernst Ruska: Nobel Prize in physics 1986
Electron Microscope Deutsches
Museum, 1933 model
The first commersial microscopes
• 1939 Elmiskop by Siemens Company
Elmiskop I
• 1941 microscope by Radio corporation of America (RCA)
– First instrument with stigmators to correct for astigmatism. Resolution
limit below 10 Å.
Developments
Realized that spherical
aberration of the magnetic
lenses limited the possible
resolution to about 3 Å.
•
r2
α r1
Spherical aberration coefficient
ds = 0.5MCsα3
M: magnification
Cs :Spherical aberration coefficient
α: angular aperture/
angular deviation from optical axis
r2
α r1
2000FX: Cs= 2.3 mm
2010F: Cs= 0.5 nm
Disk of least confusion
Chromatic aberration
Disk of least confusion
Chromatic aberration coefficient:
v - Δv
v
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
Thermally emitted electrons:
2000FX: Cc= 2.2 mm
2010F: Cc= 1.0 mm
Force from a magnetic field:
ΔE/E=kT/eU
F= -e (v x B)
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.
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.
Menter, 1956
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
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.
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.
Last few years
• Development of Cs corrected microscopes
– Probe and image
• Improved energy spread of electron beam
– More user friendly Cold FEG
– Monocromator
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.
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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 1979-1981
Because electrons interact strongly with matter, elastic and
inelastic scattering give rise to many different signals which
can be used for analysis.
Electron waves
• Show both particle and wave properties
Charge e
Restmass mo
Wave ψ
Wave length λ
λ = h/p= h/mv
de Broglie (1925)
• Electrons can be accelerated to provide sufficient
short wave length for atomic resolution.
λ = h/(2emoU)1/2
U: pot. diff.
• Due to high acceleration voltages in the TEM
relativistic effects has to be taken into account.
λ = h/(2emoU)1/2 * 1/(1+eU/2moc2)1/2
The Transmission Electron Microscope
U
(Volt)
k = λ-1 (nm-1)
λ
(nm)
m/mo
v/c
1
0.815
1.226
1.0000020
0.0020
10
2.579
0.3878
1.0000196
0.0063
102
8.154
0.1226
1.0001957
0.0198
104
81.94
0.01220
1.01957
0.1950
105
270.2
0.00370
1.1957
0.5482
2*105
398.7
0.00251
1.3914
0.6953
107
8468
0.00012
20.5690
0.9988
Relations between acceleration voltage,
wavevector, wavelength, mass and velocity
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