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Electron and electromagnetic radiation
Generation and interactions with matter
ResponseInteraction with sampleStimuli
Waves and energy
λ
The energy is propotional to 1/λ and 1/λ2
λ1
λ2
λ1>λ2
E1<E2
Electromagnetic waves: E= hc/λ =hf =hcνh: Plancks constant, f: frequency, ν: wave number
Electron waves :E= eVo, E=½ mv2 = ½ m(h/λ)2
Stimuli
Matter waves are referred to as de Broglie waveswhere λ=h/p and p=mv.
Electron radiation
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
Relationship between acceleration voltage, wavevector, wavelength, mass and velocity
Stimuli
The speed of the electron is approaching the speed of light.
Electromagnetic radiation
GammaHard X-raysSoft X-rays
Visible light
E = Extreme N= Near F= Far
HF = high freq. MF= medium freq. LF= low freq.
Stimuli
Energy conservation
When an electron is slowed down (accelerated) and the energy of the electron drops (speed is reduced), the energy can be transformed into electromagnetic radiation.
How can an electron be slowed down?
«Bremsstrahung»
Why is the target cooled down?
Energy conservation
How can this equation be derrived?
2.1
The wavelength of X-ray radiation (λ) is relatedto the acceleration voltage of electrons (V) as shown in the equation:
Electromagnetic waves: E= hc/λ
Electron waves :E= eVo
What is the peak energy of the bremsstrahung in fig. 2.2 (Mo) from 10 and 20 keV electrons?
Interaction and penetration depth
Coulombic interaction with e-(Much stronger interaction comparedto the interaction with X-rays and neutrons)
The Coulombic force F is defined as:
F = Q1Q2 / 4πεor2
r : distance between the charges Q1 and Q2;
εo: dielectric constant. http://www.microscopy.ethz.ch/downloads/Interactions.pdf
Interaction with sample
Interaction with sample
Interaction and penetration depthE0=20 keV : Typical energy of electrons used for analytical
scanning electron microscopy studies. TEM ~200keV
t: up to a fewhundred nm.
t of interestmuch less.
X-ray penetration depth: The depth at which the intensity of the radiation inside the material falls to 1/e (about 37%) of its original value at just beneath the surface. wiki
Energy conservation
ResponseInteraction with sampleStimuli
E1 E2
If E1= E2
If E1> E2
Elastic scattering event
Inelastic scattering event
Interaction with sample
Z+
-
~Elastic example: Back scattered electrons.
Non, singel or plural/ multiple scattering of electrons
Interaction with sample
Interaction cross-section (σ, Q) and mean free path (λmfp)represents the probability of a scattering event.
Illustration based on figure in: http://www.microscopy.ethz.ch/downloads/Interactions.pdf
*tt*
t: thickness of the specimen
Inelastic scattering
Interaction with sample
Energy transfered to the specimen
ResponseInteraction with sampleStimuli
Electromagnetic waves tranfere all their energy.i.e. The initial electromagnetic wave is absorbed.
Electrons can transfere parts of their energy.i.e. The electron continues with less speed/energy
Interaction with sample
How can the sample absorb the energy E1-E2?
Inelastic scattering
E1 E2
Energy transferred to matter
• Oscillations/vibrations of• Molecules and lattice (phonon)
(Lattice vibrations are more temperature dependent than molecule vibrations) Ref. Ch. 9.0 - 9.1.3.
• Free electron gas density (plasmon)
Interaction with sample Inelastic scattering
Quantified energy states
Phonon electron energy losses ~ 0.1 - 0.5 eV,
Electromagnetic absorption (Molecules: 200-4000 cm-1) (Lattice: 20-300 cm-1)
Energy: Ep=(h/2π)ω ~10-30 eVPlasmon frequency: ω=((ne2/εom))1/2
n: free electron density, εo: dielectric constant
Example: Analysis of molecule vibrations by IRResponceStimuli
Which energy do 1000 cm-1 correspond to?
Electromagnetic waves: E= hc/λ =hf = hcνh: Plancks constant, f: frequency, ν: wave number
ν=100000 m-1 : λ=0.00001 m 1 J= 6.2415 e18 eV
Example: Electron energy loss spectroscopy; plasmon peaks (and core loss edges).
Wiki magnunor
Similar to the absorption spectra of the electromagnetic radiation.
Thin specimen
Inelastic scatteringResponce
Effect of tecnical improvments (TEM and STEM) EELS can now be used to detect energy losses due to lattice vibrations (phonon)
The progress has taken place on three principal fronts: (1) the energy resolution of EELS carried out in the electron microscope has been improved to around 10 meV; (2) the EELS–STEM instrument has been optimized so that the electron probe incident on the sample contains a current sufficient to perform EELS experiments even when the energy width of the probe is ∼10 meV and its size <1 nm; and (3) the tail of the intense zero loss peak (ZLP) in the EELS spectrum has been reduced so that it does not obscure the vibrational features of interest.
Inelastic scatteringResponce
Why?
Measurement of bandgap. Spatial resolution!
Inelastic scatteringResponce
Energy transferred to matter• Oscillations/vibrations of
• Molecules (200-4000 cm-1) and lattice (20-300 cm-1) (phonon) (Lattice vibrations are more temperature dependent than molecule vibrations) Ref. Ch. 9.0 - 9.1.3.
• Free electron gas density (plasmon)
• Exitation/ionisation• Electrons goes from a ground energy state to a higher energy state above the fermi level.
- Ionization- Excitation
(Above 50 eV and typically more than thousand eV for the ionization of inner electron shells (core electrons).)
Interaction with sample Inelastic scattering
Quantified energy states
Energy losses ~ 0.1 eV
Energy: Ep=(h/2π)ω ~10-30 eVPlasmon frequency: ω=((ne2/εom))1/2
n: free electron density, εo: dielectric constant
K
L
M
1s2
2s2
2p2
2p43s2
3p2
3p4
3d4
3d6
Electron
Ionization of inner shells
K
L
M
Photo electron
x-ray
Secondary electron
Interaction with sample Inelastic scattering
1st. responce
EELS X-ray photo electron spectroscopyand X-ray absorption spectroscopy
X-ray absorption and photo electron spectroscopy
https://xpssimplified.com/elements/germanium.php
https://xpssimplified.com/whatisxps.php http://www.fis.unical.it/files/fl178/9232XASChap6.pdf
When the energy of the photons increases,
the absorption coefficient μ(ω) decreases.
Synchrotron radiationSinge wavelength X-rayCommonly: Al Kα
Can also probeoccupied and unoccupied
valence states
More on XPS later in the semester!
X-ray energy filtering http://pd.chem.ucl.ac.uk/pdnn/inst1/filters.htm
The absorption edge of nickel metal at 1.488 Å lies between the Kα (λ = 1.542 Å) and Kβ (λ = 1.392 Å) X-ray spectral lines of copper. Hence nickel foil of an appropriate thickness can be used to reduce the intensity of the Cu Kβ X-rays
Anode Cu Co Fe Cr Mo
Filter Ni Fe Mn V Zr
RelaxsationResponce
K
L
M
Characteristic
x-ray
Auger electronThe probability to emit an Auger electron or X-ray
Siegbahn notationEx.: Kα1
Intensity: α>β>γ> and1>2>3
Fluorescence: electromagnetic radiation generate new electromagnetic radiation
Fluorecent yieldThe relative effectiveness of X-ray generation
Example: Detection of continuousand characteristic x-rays
http://www.emeraldinsight.com/journals.htm?articleid=1454931&show=html
Continous X-ray energies
The cut-off energy for
continous x-rays.
Characteristic X-ray energies.EK>EL>EM
?
Example: Detection of continuousand characteristic x-rays
http://www.emeraldinsight.com/journals.htm?articleid=1454931&show=html
Characteristic X-ray energies.EK>EL>EM
Two peaks
Limited resolution of the detection method (EDS)
Overlapping peaks
Improved resolution with wavelength dispersive spectroscopy
A very short summary: Stimuli Interaction with sample
Elastic InelasticE1 = E2 E1 > E2
Excitations: phonon, plasmon, ionization
Zero, single, multiple scatteing events
Kinematic condition
Dynamic conditions