Electron Optics

Two essential components:

1) Electron source (gun)

2) Focusing system (lenses)

Add scanning apparatus for imaging

Electron gun

Cathode

Anode

Alignment coils

Lenses condensers

objective

Objective aperture assembly

sample

Current and Voltage

Voltage = electrical potential (volts)

consider as the speed or energy of electrons

SEMs 1-50 kV (or keV)

Current = number of electrons/unit time (amps)

1 coulomb ~ 6 x1018 electrons

1 amp = 1 coulomb/sec

SEMs typically operate in the picoamp (10-12A) to nanoamp (10-9A) range (final beam current at sample)

so at 1nA ~ 9X109 electrons/sec

Current and Voltage

Cameca SX50Carl Zeiss EVO50

Beam currentAt sample

Gun emission current

Filament heating current

Filament heating current

Beam currentControl (condensers)

Beam voltage

(Read)

(HV set)

Electron Guns

Purpose:Provide source of electrons

Large, stable current in small beam

Located at the top of the column

Topics:

1) Thermionic emission

2) Tungsten cathode

3) LaB6 / CeB6 cathodes

4) Field emission and Schottky sources

Thermionic emission

Work function of metal:

Energy required to elevate an electron from the metal to vacuum

Ef = Fermi level

highest energy state in conduction band in this case

E = Work necessary to remove electron to infinity from lowest state in metal

Ew = Work function

Ew = E – Ef

Heat electrons to overcome work function

Metal Vacuum

Interface

Ew

Ef

E

E

x

Self – biased electron gun

Wehnelt cylinder

surrounds filament and has small opening at base

Biased negatively between 0 and -2500V relative to the cathode

Equipotentials = field lines

Emitted electrons are drawn toward anode by applied potential (usually +15kV in probe)

converge to crossover - attempt to follow the highest potential gradient (perpendicular to field lines)

Forms first lens

Cathode current density (emission current density)

Richardson Law:

Jc = AcT2exp(-Ew/kT)in A/cm2

Ac = material dependant constant

T = emission temperature

k = Botzmann’s constant

For W: T = 2700K Ew = 4.5ev

Jc = 3.4 A/cm2

Improve current density? Use cathode material of lower Ew

Emitted electrons repelled by Wehnelt

Column lenses produce demagnified image of the gun crossover to give the final beam spot at the sample

Biasing of electron gun and saturation

Variable bias resistor in series with negative side of HV power supply and filament

Apply current to heat filament

negative voltage will be applied across Wehnelt cylinder

Change in resistance produces directly related change in negative bias voltage

Major effect: Field topology

Change in constant field lines near cathode

Field topology also affected by

filament-Wehnelt distance

Low bias

negative field gradient weak

Focussing action weak

Emitted e- see only + field from anode = high emission current

Produces large crossover size

Poor brightness

High bias

negative field gradient strong

Focussing action strong

Emitted e- see only - field from Wehnelt = return to filament

Emission current → 0

Cathode tipDown column toward anode

An optimum bias setting exists in conjunction with the filament – Wehnelt distance for maximum brightness

Bias and distance are adjustable parameters on most instruments

-300

200

200

200

-500-400

Em

issi

on C

urre

nt (A

)

Bias Voltage (V)

Emission current

Brightness

Optimum bias voltage

Cameca SX50Carl Zeiss EVO50

Gun emission current

Filament heating current

Filament heating current

Saturation

Saturation

Want a well regulated beam current

Increase if – heat filament to overcome Ew of cathode = emission

Proper bias = ib does not vary as if increased above critical value = saturation plateau

As if increases, bias increases also

negative field increases and limits the rise in ib

0

200

100

50

4.02.0

Em

issi

on C

urre

nt (A

)

Filament Current (A)

Operating filament current

Saturation

0

200

100

50

4.02.0

Em

issi

on C

urre

nt (A

)

Filament Current (A)

Operating filament current

Improvements in beam performance:

Increase current density (more potential signal in smaller beam spot)

Can increase the current density at the gun crossover by increasing brightness

Higher brightness = More current for same sized beam

Smaller beam at same current

Increase brightness by:

Increase voltage (E0)

Increase current density by lowering work function (Ew)

Cathode types:

Tungsten

LaB6 – CeB6

Field Emission

cold

thermal

Schottky

Tungsten cathode

Wire filament ~ 100μm diameter

hairpin – V shaped

operating temperature = 2700K

Jc = 1.75 A/cm2

Ew = 4.5ev

electrons leave from emission area ~ 100x150 μm

Could theoretically increase brightness by increasing temperature

D0 = 100μm

α = 3x10-3 rad

At 2700K and 25kV

Jc = 1.75 A/cm2

β = 6x104 A/(cm2sr) brightness = measure of radiant intensity

Filament life ~ 320/Jc (hrs)

180-200 hrs

Increase temperature to 3000K

Jc = 14.2 A/cm2

β = 4.4x105 A/(cm2sr)

~23 hrs

Brighter sources are attractive, but tungsten:

reliable

stable

relatively inexpensive

Failure due to

W evaporation at high temperature in good vacuum

Sputtering from ion bombardment in poor vacuum

From Richardson equation:

Jc = AcT2exp(-Ew/kT) in A/cm2

Ac = material dependant constantT = emission temperaturek = Botzmann’s constant

So current density (and brightness) increase by lowering work function (Ew)

LaB6 – CeB6 cathodes

At ~ 2700K, each 0.1eV reduction in Ew → increase in Jc by 1.5X

REE hexaborides have much lower Ew compared to W

Principle:

Use LaB6 or CeB6 single crystal

La atoms are mobile in B lattice when heated

- Evaporate during thermionic emission

-La (or Ce) replenished at tip by diffusion

-Low work function relative to W ~2.4eV (~ 4.5eV for W)

Can equal W current density at 1500K

Jc then nearly 100A/cm2 at 2000K

Mini Vogel Mount

Mo-Re supports

Graphite blocks

5000 psi

Crystal made by electric arc melting of REEB6 powder stick in inert atmosphere

2 results:

1) Low evaporation rate at low temperature → long lifetime

2) From Langmuir relation:

β = 11,600JcE0/(πT)

two sources of same current density and E0

one at 1500K, one at 3000K

low T source = twice as bright

Advantages:

Long lifetime

Small d0 = high resolution

Disadvantages of REE hexaboride cathodes

Very chemically reactive when hot (forms compounds with all elements except C – poisons cathode

Requires exceptionally good vacuum (10-7 torr or better)

Expensive

Ew depends on crystal orientation

As crystallites evaporate, emission can change

Best orientation = Ew less than 2.0eV

Better processing has improved performance

lowest Ew

better stability

Mechanical failure eventually…

LaB6 vs. CeB6

CeB6 has generally lower evaporation rate and is less sensitive to C contamination

Principle:

Cathode = tungsten rod, very sharp point (<100nm)

Apply 3-5kV potential relative to first anode (very strong field at tip, >107 V/cm)

Electrons can escape cathode without application of thermal energy

Very high vacuum (10-10 torr or better)

Use second anode for accelerating electrons

Field Emission (Fowler-Nordheim Tunneling)

First Anode

SecondAnode

Field Emission Tip V1 V0

Etched carbide tip (AP Tech)

Werner Heisenberg and the uncertainty principle(1927, age 25)

The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. --Heisenberg, uncertainty paper, 1927

Tunneling:

Quantum effect by which electrons can “pass” through the potential barrier to overcome the work function

The applied field deforms the potential barrier, and unexcited electrons “leak” through the barrier

∆p • ∆x ≈ ħ/2

Heisenberg uncertainty implies an uncertainty

in position ∆x

WernerHeisenberg

RalphFowler

Tunneling:

If ∆x is on the order of the barrier width, there will be a finite probability of finding an electron on either side

Thermionic

Field emission

Ef for ZrO2/W

Ef for W

Cathode Vacuum

0 1 2 3 4 5

nm

Ew Ew(SE)

Field emission = very high current density

~105 A/cm2 (recall ~3 A/cm2 for W thermionic cathodes)

Very small emission region (~ 10nm)

So brightness = 100s of times greater than thermionic emission at the same voltage

Advantages:

Long lifetime

Very high resolution

High depth of field

Disadvantages:

Easily poisoned

Requires very high vacuum (better than 10-10 torr)

Current instabilities prevent practical application to microanalysis

Expensive

Limited current output

Schottky emitters:

Thin layer of ZrOx further lowers work function. Using both high tip potential and thermal activation (2073K) to enhance emission

Suppressor cap eliminates unwanted emission away from the tip

Results in larger and more stable current compared to cold field emission

Resolution approaches that of cold field emission.

Schottky Cold Field LaB6 Tungsten

Source Size (nm) 15 3 104 >104

Energy Spread (ev) 0.3-1.0 0.2-0.3 1.0 1.0-3.0

Brightness (A/cm2SR) 5x108 109 107 106

Short-term beam Current stability (%RMS)

<1 4-6 <1 <1

Typical service life >1yr. >1yr. >1yr. 102-103 hrs

Now down to 0.15ev with monochromator

30

Monochromator gun concept

• Extend two mode approach to make a monochromator:

1) use an off-axis extractor aperture and

2) a strong C0-lens setting to create dispersion:

C0 on>20 nA

C0 onbeam off-axis

gun tip

extractor

C0 lens(Segmented electrode gun lens)

off-axis apertureon-axis aperture

31

UC gun optics design

– UC = “UniColore”: monochromator gun– 2 extractor apertures:

• 1 for on-axial beam: normal beam• 1 for off-axial beam: UC beam

– C0-lens focuses off-axial beam:• select beam energies with aperture• dispersion is in 1 direction: use slit• ΔE ≈ 0.15 eV

– Extra deflector below slit:• steers off-axis beam onto optical axis

– Geometry fits into Elstar gun module

extractor

C0 lens

2nd gun

deflector

off-axial

axial beam

tip

beam

aperture slit

Magellan XHR SEM: three beam modes available

Schottky-FEGextractor,2 apertures

segmentedgun lens

aperture and slit

deflector

Standard High current Monochromated (UC)