transmission electron microscopy skills:basic properties of electrons and electron sources lecture 2

8/8/2019 Transmission Electron Microscopy Skills:Basic Properties of Electrons and Electron sources Lecture 2

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Basic Properties of Electronsasic Properties of ElectronsandndElectron sourceslectron sourcesLecture 2ecture 2


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Basic properties of electronsasic properties of electronsa reminderreminder


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Basic properties of electronsasic properties of electronswaveave-particle dualityarticle duality

Waveave - particle duality of electrons is a manifestedarticle duality of electrons is a manifestedroutinely in the electron microscope.outinely in the electron microscope.Letets think about this:think about this:

Electron accelerated at 100kV:lectron accelerated at 100kV: Electron currentlectron current 1.0.0 A 100122 electrons / seclectrons / sec Implication: each electron separated bymplication: each electron separated by 1.6 mm.6 mmThis implies that there is only one electron that ishis implies that there is only one electron that is

interacting with the specimen at any given time.nteracting with the specimen at any given time.

v 0.5c 1.6 108 m/s


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Despite this both particle & wave phenomena areespite this both particle & wave phenomena areobserved:bserved: Electron diffractionlectron diffraction - wave phenomenonave phenomenon Electron interferencelectron interference - interference between different wavesnterference between different waves Photoelectric effecthotoelectric effect - particle phenomenonarticle phenomenon

Key pointey point Get used to the idea that you consider the electron aset used to the idea that you consider the electron as bothothroutinely when using the TEMoutinely when using the TEM

Diffractioniffraction - think wavehink wave Scatteringcattering - think particlehink particle



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A wave is a periodic disturbance in both space and time:wave is a periodic disturbance in both space and time:

Consider two waves with slightly different frequencies:

1 = sin kx+t[ ]2 = sin k+k( )x+ +( )t[ ]

Superimpose these two waves, use a bit of trigonometry:1 +2 = = 2cos

2

t+k2

x

sin k+

k2

x +

2

t

Modulatedamplitude Sine wave

= sin

2x

+t

= sin kx+t

( )with k =

2


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An analogue to this isn analogue to this is beatseats in music.n music.Letets look at this dynamically a bit:look at this dynamically a bit:http://galileo.phys.virginia.edu/classes/109N/more_stuff/Appletsttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.htmlsines/GroupVelocity.html

From Hummel
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.htmlhttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.htmlhttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.htmlhttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.htmlhttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.html


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A wave is a periodic disturbance in both space and time:wave is a periodic disturbance in both space and time:

Consider two waves with slightly different frequencies:

1 = sin kx+t[ ]2 = sin k+k( )x+ +( )t[ ]

Superimpose these two waves, use a bit of trigonometry:1 +2 = = 2cos

2

t+k2

x

sin k+

k2

x +

2

t

Modulatedamplitude Sine wave

= sin

2x

+t

= sin kx+t

( )with k =

2


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Two cases are illustrative:wo cases are illustrative:

0 ; k 0

Infinitely long wave packetmonochromatic wave plane wave

Phase velocity (velocity of the wave):v= x

t=+k+k

='t'

From Reimer


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Consider instead that you have many waves superimposed (i.e.onsider instead that you have many waves superimposed (i.e.1,2, ... ... ) which fill frequencies betweenhich fill frequencies between andnd , wherewhere isslarge:arge: Reduces to one wave packeteduces to one wave packet This wave packet can be considered ashis wave packet can be considered as the electron as particlehe electron as particle

vg =

x

t=

k

Group velocity (velocity of the particle):From Reimer


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Basic properties of electronsasic properties of electronsDe Brogliee Broglie Eqnqn.:: =h p

Key point: the higher the voltage, the smaller the wavelength

eV=m

ov2

2ll energy is kinetic, i.e.:p=mov= 2moeV( )

1 2Momentum is:=

h

(2moeV)1 2

Substituting:

Relativisticcorrectionneeded =

h

2moeV 1+eV

2moc2

1

2


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Basic properties of electronsasic properties of electronsAcceleratingcceleratingVoltage (kV)oltage (kV) Nonon-relativisticelativisticwavelength (avelength () Relativisticelativisticwavelength (avelength () Massass(x mm o)

Velocityelocity(x 10108 m/s/s ) Velocityelocity(x cc)10000 0.0386.0386 0.0370.0370 1.196.196 1.644.644 0.54.5420000 0.0273.0273 0.0251.0251 1.391.391 2.086.086 0.69.6930000 0.0223.0223 0.0197.0197 1.587.587 2.330.330 0.78.7840000 0.0193.0193 0.0164.0164 1.783.783 2.484.484 0.83.83

1000000 0.0122.0122 0.0087.0087 2.957.957 2.823.823 0.94.94


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Electron wavelength & resolutionlectron wavelength & resolutionResolution (Rayleigh criterion):esolution (Rayleigh criterion):

Soo - even at 100 kV, we haveven at 100 kV, we have = 0.040.04More than sufficiently small to image atomsore than sufficiently small to image atoms(diameterdiameter 0.3.3)Lens imperfections (largely sphericalens imperfections (largely sphericalaberration, chromatic aberration) limitberration, chromatic aberration) limitresolutionesolution

= 0.61sin

0.61


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Angles & Distancesngles & Distances Some things worth rememberingome things worth remembering We deal often with very small angles:e deal often with very small angles:

1 = 17.517.5 milliradiansilliradians (mradrad) 155 mradrad

We use very high magnifications: At 1000 X, 1 cm = 10 m

At 10,000X, 1 cm = 1 mAt 50,000X, 1 cm = 200 nmAt 100,000X, 1 cm = 100 nm

At 500,000X, 1 cm = 20 nm = 200

I just memorize these two


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Electron sourceslectron sources


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Electron sourceslectron sourcesWhat are source characteristics?hat are source characteristics?

Brightness, Temporal (rightness, Temporal (E) coherency and Spatial) coherency and Spatialcoherency / source sizeoherency / source sizeSource types?ource types?

Thermionichermionic, Schottkychottky field emission, Cold fieldield emission, Cold fieldemissionmissionHow do electron guns work?ow do electron guns work? Thermionichermionic, Field emission (both types)Field emission (both types)How / why do you measure gun propertiesow / why do you measure gun properties Beam current, convergence angle, beam diameter,eam current, convergence angle, beam diameter,

energy spread, spatial coherencynergy spread, spatial coherency


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Source characteristicsource characteristicsBrightnessrightnessDefinition:efinition:

Brightness:rightness: Current densityCurrent densityper unit solid angleper unit solid angle

Current density is: #Current density is: #electrons per unit area perelectrons per unit area perunit timeunit time

Some properties:ome properties: Beam diameter: dBeam diameter: doo Cathode emission current:Cathode emission current: iiee

SemiSemi--angle of divergenceangle of divergencefrom source:from source: oo


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Brightness:rightness:

This is a key parameter:his is a key parameter: impacts exposure timesmpacts exposure times analytical worknalytical work

100133Cold fieldold fieldemissionmission

5100100Schottkychottky1009Thermionichermionic

Brightness (A/mrightness (A/m2srr)

=ie

doo( )

2

Note: text has an error inNote: text has an error in defdefnn of solid angleof solid angle

Source characteristicsource characteristicsBrightnessrightness


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Source characteristicsource characteristicsTemporal coherency & energy spreademporal coherency & energy spreadTemporal coherency refers to the energy spreademporal coherency refers to the energy spreadof the sourcef the source

Analogue to light optics isAnalogue to light optics is colorcolor Coherence length:Coherence length:

c =

vhETypicalypical E

TungstenTungsten thermionicthermionic: 3: 3 eVeV

LaBLaB66 thermionicthermionic: 1: 1 eVeV

SchottkySchottkyfield emission:field emission: 0.80.8 eVeV

Cold field emission: 0.3Cold field emission: 0.3 eVeV Note this is on top of 200 to 300Note this is on top of 200 to 300 keVkeV

Important with respect to EEL spectroscopymportant with respect to EEL spectroscopy


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Source characteristicsource characteristicsSpatial coherency & source sizepatial coherency & source sizeSpatial coherency is associated with the physicalpatial coherency is associated with the physical pointointof originf origin of the electronsf the electronsRelated to theelated to the effective source sizeffective source size (ddc)::

dc FEG!? Not necessarilyhe answer is clear => FEG!? Not necessarily Expensive (+ $700k), fExpensive (+ $700k), fringes in HREM images,ringes in HREM images, less intense whenless intense whenbeam is spreadbeam is spread

To improve spatial coherency:o improve spatial coherency:dc (FEG);FEG); ( kV);V); ( aperture)perture)


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Source characteristicsource characteristicsStabilitytabilityStability is important:tability is important:

HREM imagingHREM imaging

MicroanalysisMicroanalysis

Typical stabilities in modernypical stabilities in modern TEMEMs are:re:RippleRipple: 1: 1 ppmppm RMS (latest are 0.1RMS (latest are 0.1 ppmppm RMS)RMS)DriftDrift: 2: 2 ppmppm over 10 minute periodsover 10 minute periods

Thermionichermionic > Schottkychottky FEG > Cold FEGEG > Cold FEG


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Emission physicsmission physics


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Emission physicsmission physicsthermionichermionic emissionmissionRecall:ecall: work functionork function Energy required toEnergy required to

remove an electronremove an electronfrom a materialfrom a material

Schottkychottky effectffect IncludesIncludes image fieldimage field

Thermionichermionic emissionmission Energy supplied by heatEnergy supplied by heat

alonealone


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Emission physicsmission physicsthermionichermionic emissionmissionRichardson Law:ichardson Law:

jc = ATc2 exp

kT

Exponential dependenceExponential dependencemeans 10% change inmeans 10% change in ,,

T yields factor of 8T yields factor of 8increase in emissionincrease in emission

Function of T, surfaceFunction of T, surface

condition &condition &crystallographycrystallography

Materialaterial (eVV) Tm (K)K)Css 1.9.9 30101Cuu 4.45.45 1358358Coo 4.4.4 1768768W 4.5.5 3695695

LaBaB6 2.7.7 2800800CeBeB6 2.5.5 highigh Lifetime: WLifetime: W 200 hr;200 hr;

LaB6LaB6 1000 hr ; CeB1000 hr ; CeB66 1500 hr1500 hr

SputteringSputtering


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Emission physicsmission physicsField emissionield emissionAdditional electric fielddditional electric fieldlowers barrierowers barrier

V = eE x(If field is sufficientlyf field is sufficientlystrong, electrons cantrong, electrons cantunnel outunnel outSchottkychottky FEGEG

Temp & fieldTemp & field ZrOZrO/W @1800k)/W @1800k)Cold FEGold FEG Field onlyField onlyUHV necessaryHV necessary


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Emission physicsmission physicsFor field emission use instead Fowleror field emission use instead Fowler - Nordhiemordhiem Eqnqn:

jc =

k1E2

expk

2

3 2

E

Energy distribution for allcases (thermionic,Schottky, cold FEG) isMaxwell-Boltzmann


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Electron sourceslectron sourcesWhat are source characteristics?hat are source characteristics?

Brightness, Temporal (rightness, Temporal (E) coherency and Spatial) coherency and Spatialcoherency / source sizeoherency / source sizeSource types?ource types?

Thermionichermionic, Schottkychottky field emission, Cold fieldield emission, Cold fieldemissionmissionHow do electron guns work?ow do electron guns work?

Thermionichermionic, Field emission (both types)Field emission (both types)

How / why do you measure gun propertiesow / why do you measure gun properties Beam current, convergence angle, beam diameter,eam current, convergence angle, beam diameter,

energy spread, spatial coherencynergy spread, spatial coherency


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Emission physicsmission physicssummaryummary

Conventional TEMonventional TEM - LaBaB6 / CeBCeB6Schottkychottky FEGEG - Conventional analyticalonventional analyticalCold FEBold FEB - Very high end analyticalery high end analytical

(A/mA/m2sr)r) E(eVV) d Vacuumacuum(PaPa)W 1009 1.5.5 - 3 200 - 500 m 100-3LaBaB6 51009 1 - 2 100 - 200 m 100-4SchottkychottkyFEGEG 5 100100 0.7.7 15 nm5 nm 100-6Cold FEGold FEG 100133 0.3.3 2.5 nm.5 nm 100-8


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Probe comparisonrobe comparisonRadiationadiation Source Brightnessource Brightness(particles/cmparticles/cm2srr eVV) Elastic Meanlastic MeanFree Path (ree Path () AbsorptionbsorptionLength (ength () MinimuminimumProbe Size (robe Size ()

Neutronseutrons 100144100266100299

1008 1009 1007X-raysays 1004 1006 1003Electronslectrons 1002 1003 1

Cold FEG is the brightest continuous radiation sourceold FEG is the brightest continuous radiation sourceknown in the universe.nown in the universe.Because of high spatial & temporal coherency can beecause of high spatial & temporal coherency can befocused to the smallest probe available (0.78ocused to the smallest probe available (0.78!))Lots of energy, lots of potential for specimen damageots of energy, lots of potential for specimen damage


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Electron Gunslectron GunsHow do they work?ow do they work?


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Electron gunslectron gunsthermionichermionicFilament heated to giveilament heated to givethermionichermionic emissionmission

Directly (W) or indirectlyirectly (W) or indirectly(LaBLaB6)Filament at negativeilament at negativepotential to groundotential to groundWehneltehnelt produces a smallroduces a smallnegative biasegative bias

Brings electrons torings electrons tocrossoverrossover

http://www.matter.org.uk/tem/electron_gun/electron_gun_simulation.htm
http://www.matter.org.uk/tem/electron_gun/electron_gun_simulation.htmhttp://www.matter.org.uk/tem/electron_gun/electron_gun_simulation.htm


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Electron gunslectron gunsthermionichermionicTungsten LaB6


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Electron gunslectron gunsthermionichermionic

Perfect saturation / bias aids filament lifetimeerfect saturation / bias aids filament lifetimeAlso yields smallest source size, best coherency, bestlso yields smallest source size, best coherency, bestimagesmages


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Electron gunslectron gunsfield emissionield emissionFirst anode (Virst anode (V1) isisextraction voltagextraction voltageSecond anode (Vecond anode (V2) acts asacts asan electrostatic lensn electrostatic lensAs ans an opertatorpertator, you slowlyyou slowlyincrease Vncrease V1

Thathats pretty much it.pretty much it. Automated in latestutomated in latestmachinesachines

Different extractionifferent extractionvoltages for differentoltages for differentoperation modesperation modes


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Electron gunslectron gunssummaryummary

transmission electron microscopy skills:basic properties of electrons and electron sources lecture 2

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