transmission electron microscopy skills:electron scattering lecture 8

8/8/2019 Transmission Electron Microscopy Skills:Electron scattering Lecture 8

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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

transmission electron microscopy skills:electron scattering lecture 8

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