Electron and electromagnetic radiation - Forsiden Electron radiation U (Volt) k = ®»-1(nm...

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Transcript of Electron and electromagnetic radiation - Forsiden Electron radiation U (Volt) k = ®»-1(nm...

  • 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

  • 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

    Gamma Hard X-rays Soft 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 related to 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 compared to 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 depth E0=20 keV : Typical energy of electrons used for analytical

    scanning electron microscopy studies. TEM ~200keV

    t: up to a few hundred nm.

    t of interest much 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 eV Plasmon frequency: ω=((ne2/εom))

    1/2

    n: free electron density, εo: dielectric constant

  • Example: Analysis of molecule vibrations by IR ResponceStimuli

    Which energy do 1000 cm-1 correspond to?

    Electromagnetic waves: E= hc/λ =hf = hcν h: 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

  • 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 eV Plasmon frequency: ω=((ne2/εom))

    1/2

    n: free electron density, εo: dielectric constant

  • K

    L

    M

    1s2

    2s2 2p2

    2p4 3s2

    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 spectroscopy and 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-ray Commonly: Al Kα

    Can also probe occupied and unoccupied

    valence states

    More on XPS later in the semester!

    https://xpssimplified.com/whatisxps.php

  • 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 electron The probability to emit an Auger electron or X-ray

    Siegbahn notation Ex.: Kα1

    Intensity: α>β>γ> and 1>2>3

    Fluorescence: electromagnetic radiation generate new electromagnetic radiation

    http://upload.wikimedia.org/wikipedia/commons/5/5e/Auger_Yield.svg

  • Fluorecent yield The relative effectiveness of X-ray generation

  • Example: Detection of continuous and 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 continuous and 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 Inelastic E1 = E2 E1 > E2

    Excitations: phonon, plasmon, ionization

    Zero, single, multiple scatteing events

    Kinematic condition

    Dynamic conditions