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