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

Sample position

Electrons are deflected by both electrostatic and magnetic fields

Force from an electrostatic field F= -e E

Force from a magnetic field F= -e (v x B)

Electron transparent samples

IntroductionEM and materials

Electron microscopy are based on three possible set of techniqes

Imaging

Diffraction

SpectroscopyWith spatial resolution down to the atomic level (HREM and STEM)

Chemistry and elecronic states (EDS and EELS).Spatial and energy resolution down to the atomic level and ~0.1 eV.

From regions down to a few nm (CBED).

Electrons

E<Eo(EELS)

BSE

SEAE X-rays (EDS)

E=Eo

Bragg diffracted electrons

15/1-08 MENA3100

Basic principles, electron probeValence

K

L

M

Electronshell

Characteristic x-ray emitted or Auger electron ejected after relaxation of inner state. Low energy photons (cathodoluminescence)when relaxation of outer stat.

K

L

M

1s2

2s22p2

2p43s2

3p2

3p4

3d4

3d6

Auger electron or x-ray

Secondary electron

Electron

Introduction EM and materials

The interesting objects for EM is not the average structure or homogenous materials but local

structure and inhomogeneities

Defects

Precipitates

Interfaces

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 .

• 1927, Davisson and Germer and Thomson and Reid– Both demonstrated the wave nature of electrons by

independently performing electron diffraction experiments

λ=1.22/E1/2

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

• 1941 microscope by Radio corporation of America (RCA)– First instrument with stigmators to correct for astigmatism. Resolution

limit below 10 Å.

Elmiskop I

Developments

• Spherical aberration coefficient

ds = 0.5MCsα3

M: magnificationCs :Spherical aberration coefficientα: angular aperture/ angular deviation from optical axis

2000FX: Cs= 2.3 mm2010F: Cs= 0.5 nm

r1

r2

Disk of least confusion

α

r1

r2

α

Realized that spherical aberration of the magnetic lenses limited the possible resolution to about 3 Å.

Chromatic aberration

vv - Δvdc = Cc α ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0.5

Cc: Chromatic aberration coefficientα: angular divergence of the beamU: acceleration voltageI: Current in the windings of the objective lensE: Energy of the electrons

2000FX: Cc= 2.2 mm2010F: Cc= 1.0 mm

Chromatic aberration coefficient:

Thermally emitted electrons:ΔE/E=kT/eU

Force from a magnetic field:F= -e (v x B)

Disk of least confusion

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.

• Development of Cs corrected microscopes– Probe and image

• Improved energy spread of electron beam– More user friendly Cold FEG – Monocromator

Last few years

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.

• 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

• Electrons can be accelerated to provide sufficient short wave length for atomic resolution.

• Due to high acceleration voltages in the TEM relativistic effects has to be taken into account.

Charge eRestmass mo

Wave ψWave length λ

λ = h/p= h/mv de Broglie (1925)

λ = h/(2emoU)1/2 U: pot. diff.

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

MENA3100 V08

Objective lense

Diffraction plane(back focal plane)

Image plane

Sample

Parallel incoming electron beamSi

a

b

cP

ow

derC

ell 2.0

1,1 nm

3,8

Å

Objective aperture

Selected area aperture

Simplified ray diagram

JEOL 2000FX Wehnelt cylinderFilamentAnode

Electron gun 1. and 2. beam deflectors

1.and 2. condenser lensCondenser apertureCondenser lens stigmator coilsCondenser lens 1. and 2. beam deflector

Condenser mini-lensObjective lens pole pieceObjective apertureObjective lens pole pieceObjective lens stigmators1.Image shift coilsObjective mini-lens coils (low mag)2. Image shift coils

1., 2.and 3. Intermediate lens

Projector lens beam deflectorsProjector lensScreen

Mini-lens screws

Specimen

Intermediate lensshifting screws

Projector lensshifting screws