Electron and electromagnetic radiation

Transcription

1 Electron and electromagnetic radiation Generation and interactions with matter Stimuli Interaction with sample Response

2 Stimuli Waves and energy The energy is propotional to 1/λ and 1/λ 2 λ λ 1 Electromagnetic waves: E= hc/λ =hf =hcν h: Plancks constant, f: frequency, ν: wave number λ 1 >λ 2 Electron waves :E= ev o, E=½ mv 2 = ½ m(h/λ) 2 Matter waves are referred to as de Broglie waves where λ=h/p and p=mv. λ 2 E 1 <E 2

3 Stimuli Electron radiation Relationship between acceleration voltage, wavevector, wavelength, mass and velocity U (Volt) k = λ -1 (nm -1 ) λ (nm) m/mo v/c * The speed of the electron is approaching the speed of light.

4 Stimuli 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.

5 «Bremsstrahung» 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? Why is the target cooled down?

6 Energy conservation The wavelength of X-ray radiation (λ) is related to the acceleration voltage of electrons (V) as shown in the equation: 2.1 How can this equation be derrived? Electromagnetic waves: E= hc/λ Electron waves :E= ev o What is the peak energy of the bremsstrahung in fig. 2.2 (Mo) from 10 and 20 kev electrons?

7 Interaction with sample 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. pdf

8 Interaction with sample Interaction and penetration depth E 0 =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

9 Interaction with sample Energy conservation Stimuli Interaction with sample Response - E 1 E 2 If E 1 = E 2 If E 1 > E 2 Elastic scattering event Inelastic scattering event Z+ ~Elastic example: Back scattered electrons.

10 Interaction with sample Non, singel or plural/ multiple scattering of electrons Interaction cross-section (σ, Q) and mean free path (λ mfp ) represents the probability of a scattering event. t * *t t: thickness of the specimen Illustration based on figure in: downloads/interactions.pdf

11 Interaction with sample Inelastic scattering

12 Interaction with sample Inelastic scattering Energy transfered to the specimen 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 Stimuli Interaction with sample Response E 1 E 2 How can the sample absorb the energy E 1 -E 2?

13 Interaction with sample Inelastic scattering Energy transferred to matter Oscillations/vibrations of Molecules and lattice (phonon) Phonon electron energy losses ~ ev, Electromagnetic absorption (Molecules: cm -1 ) (Lattice: cm -1 ) Quantified energy states (Lattice vibrations are more temperature dependent than molecule vibrations) Ref. Ch Free electron gas density (plasmon) Energy: E p =(h/2π)ω ~10-30 ev Plasmon frequency: ω=((ne 2 /ε o m)) 1/2 n: free electron density, ε o : dielectric constant

14 Example: Analysis of molecule vibrations by IR Stimuli Responce Which energy do 1000 cm -1 correspond to? ν= m -1 : λ= m 1 J= e18 ev Electromagnetic waves: E= hc/λ =hf = hcν h: Plancks constant, f: frequency, ν: wave number

15 Responce Inelastic scattering Example: Electron energy loss spectroscopy; plasmon peaks (and core loss edges). Wiki magnunor Thin specimen Similar to the absorption spectra of the electromagnetic radiation.

16 Responce Inelastic scattering 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. Why?

17 Responce Inelastic scattering Measurement of bandgap. Spatial resolution!

18 Interaction with sample Inelastic scattering Energy transferred to matter Oscillations/vibrations of Molecules ( cm -1 ) and lattice ( cm -1 ) (phonon) Energy losses ~ 0.1 ev (Lattice vibrations are more temperature dependent than molecule vibrations) Ref. Ch Quantified energy states Free electron gas density (plasmon) Energy: E p =(h/2π)ω ~10-30 ev Plasmon frequency: ω=((ne 2 /ε o m)) 1/2 n: free electron density, ε o : dielectric constant 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).)

19 Interaction with sample Inelastic scattering Electron Ionization of inner shells x-ray 3d 6 3d 4 3p 4 3s 2 3p 2 2p 4 2p 2 2s 2 1s 2 K L M K L M Secondary electron EELS 1st. responce Photo electron X-ray photo electron spectroscopy and X-ray absorption spectroscopy

20 X-ray absorption and photo electron spectroscopy More on XPS later in the semester! When the energy of the photons increases, the absorption coefficient μ(ω) decreases. Can also probe occupied and unoccupied valence states Singe wavelength X-ray Commonly: Al Kα Synchrotron radiation

21 X-ray energy filtering The absorption edge of nickel metal at Å lies between the Kα (λ = Å) and Kβ (λ = 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

22 Responce Relaxsation Auger electron The probability to emit an Auger electron or X-ray K L M Characteristic x-ray Siegbahn notation Ex.: Kα 1 Intensity: α>β>γ> and 1>2>3 Fluorescence: electromagnetic radiation generate new electromagnetic radiation

23 Fluorecent yield The relative effectiveness of X-ray generation

24 Example: Detection of continuous and characteristic x-rays Characteristic X-ray energies. E K >E L >E M? The cut-off energy for continous x-rays. Continous X-ray energies

25 Example: Detection of continuous and characteristic x-rays Characteristic X-ray energies. E K >E L >E M Two peaks Limited resolution of the detection method (EDS)

26 Overlapping peaks Improved resolution with wavelength dispersive spectroscopy

27 Stimuli Interaction with sample A very short summary: Elastic Inelastic E 1 = E 2 E 1 > E 2 Excitations: phonon, plasmon, ionization Zero, single, multiple scatteing events Kinematic condition Dynamic conditions