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Electron scatteringLecture 8
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Electrons, photons, neutrons
Electrons interact very strongly with matter Electrons: small, negatively charged particles, directly scatter off of
atom (either nucleus or electron cloud)
X-rays: electromagnetic waves, field exchange with electron cloud Neutrons: heavy, uncharged particles, scatter by direct interaction
with nucleus
Radiation Elastic MeanFree Path () AbsorptionLength () Minimum ProbeSize ()Neutrons 108 109 107X-rays 104 106 103Electrons 102 103 1
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Role of scattering in TEMElectron scattering isthe underlying physicsof TEM
Diffraction: elastic
scattering
Imaging: elastic &
inelastic scattering
Spectroscopy: inelastic
scattering
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Scattering terminologyForward scattering - thin samples
Elastic forward scattering is usually low angle (1-10),
coherent Elastic scatter is less coherent at angles > 10
Inelastic scatter is not coherent
Most is very low angle (< 1) At high angles, inelastic scatter is very sensitive to atomic
weight
Backscattering - thick samplesSingle scattering, vs. plural scattering vs.multiple scattering (>20 events) General want to be in the single to (low #) plural
scattering range
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Elastic scatteringparticle approach onlyarticle approach only
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Elastic scatteringsingle electron / isolated atom
Interaction betweenelectron & atom isCoulombic
Incident electron &
electron cloud
Incident electron &
nucleus
Well want to understand:Interaction cross section
Mean free path
Differential cross section
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Elastic scatteringsingle electron / isolated atom
Interaction cross section expresses the probability of agiven scattering event. Generally: = r2Elastic scattering radius has the form:
relectron = eV
; rnucleus = ZeVZ = atomic weight
e = charge of the electron
V = potential of the electron
= anglemplications:V Z
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Elastic scatteringthrough specimen thickness
Consider instead specimen of N atoms / unit thickness.Total cross section for scattering from specimen:
QT = NT =
NoTA N = # atoms / unit volume
r = density
A = atomic weightScattering probability for a sample of thickness t:QTt= N
oTtA
t mass-thicknessCan re-arrange to give another useful concept:Mean free path: mfp or
mfp = 1
Q= A
NoT
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Elastic scatteringScreened relativistic Rutherford cross sectionCan take into account relativistic effects, screening ofthe nucleus by the electron cloud (see W&C, pp. 39&40).
Scattering Angle, (degrees)
log10(>0)
Scattering Angle, (degrees)
log10(>0)
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Elastic scatteringScreened relativistic Rutherford cross sectionCan be plotted as anequivalent mean freepath vs. incidentenergyThis gives you a goodsense on allowablesample thickness!
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Inelastic scattering
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Inelastic scatteringBremsstrahlung X-ray emissionBraking radiationElectron is decelerated byCoulomb (charge) field ofthe nucleus,electromagnetic radiation(photon) is emittedCan have any energy lessthan the incident energyResults in a continuousbackground signal in anintensity vs. energyspectrum Angulardistribution of
Bremsstrahlung
scatter
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Inelastic scatteringCharacteristic X-raysInteraction w/ inner shellelectronsIf energy sufficient, innershell electron ejected
Atom is ionized
Atom can return to itslowest energy (ground)stateElectron from outer shell tofill the hole in the innershellEnergy required ischaracteristic of theatom
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Inelastic scatteringCharacteristic X-rays - nomenclatureFigure 10.3 Reimer
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Inelastic scatteringCharacteristic X-raysX-rays, as EM radiation canbe considered as eitherwaves or photons
E = h =hc
Energy related towavelength:Each transition has aspecific energy associatedwith it (EK, EL, EM)
EK,EL,EM < Ec
Thus each ionization eventsets of a cascade oftransitions
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Inelastic scatteringCharacteristic X-rays
Fluorescence yield:Strong atomic # dependence: One C K X-ray generated per 1000 ionization events
One Ge K X-ray generated per 2 ionization events Difference associated with relative chance of Auger electron
production
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Inelastic scatteringCharacteristic X-raysX-rays, as EM radiation canbe considered as eitherwaves or photons
E = h =hc
Energy related towavelength:Each transition has aspecific energy associatedwith it (EK, EL, EM)
EK,EL,EM < EcThus each ionization eventsets of a cascade oftransitions
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Inelastic scatteringCharacteristic X-rays
Fluorescence yield:Strong atomic # dependence: One C K X-ray generated per 1000 ionization events
One Ge K X-ray generated per 2 ionization events Difference associated with relative chance of Auger electron
production
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Inelastic scatteringSecondary electron emissionIncident electrons impart energy to electronsin the crystal Slow secondary electrons
Electrons from the conduction or valence band
Require little energy: yields slow, unenergetic (
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Inelastic scatteringcomparison
Comparison of relative cross sections
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Beam damageHigh voltage, high current density electron beamcan do considerable damage to a materialTwo types:
Radiolysis: Inelastic scattering ionization which
breaks bonds Knock-on damage: direct displacement of atoms
Increasing voltage: less radiolysis, more knock-on
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Beam damageKnock-on thresholds
These figures / tables are useful as a rule of thumb Some useful known #s:
Al 170kV, Si 190kV, Carbon Nanotubes < 85 kV top surface, 140 kVelsewhere.
If important to you, you may have to determine this yourself! Argh Sputtering is just displacement damage from the surface
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Beam damagespecimen heatingGenerally, not a worry inmetals, semiconductorsDefinitely so in ceramics,polymersReduce the cross section
Thinner samples Higher voltage
Myths about specimenheating Anecdotal evidence from old
HVEMs said this wassignificant
Due to aperture heating, notsample heating