Today’s quote: “Physical concepts are free creations of the human mind, and are not, however it...
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Transcript of Today’s quote: “Physical concepts are free creations of the human mind, and are not, however it...
Today’s quote:
“Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility of the meaning of such a comparison.”
A. Einstein, 1938 (from Gary Zukav The Dancing Wu Li Masters)
ψ
The wave function describes the state of motion of a particleψ
…The 4f wave functions (Mark Winter…the orbitron)
… the probability density|ψ |2
…The 4f electron density
Electron transmission across a potential barrier
Δ(A)Δ(B) ≥ (| ψ|[A,B]|ψ |)/2 A and B are observables, or measurable properties (energy, position, momentum, spin, etc.)ΔEΔt ≥ (E = energy, t = time)ħΔpΔx ≥ (p = momentum, x = distance, or ħposition)
ΨE electron energy
X
Vo the potential barrier
Uncertainty of electron energies ΔE = pΔp/m, ≈ (ΔP)2/m
(or position)
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
The work function is the solid-state electronic analog of the ionization potential (binding energy) – the amount of energy required to liberate an electron from a particular energy level…
Metal Vacuum
Interface
Ew
Ef
E
E
x
2-5 Volts in metals
Thermionic emission
Work function of metal:
Energy required to elevate an electron from the metal to vacuum
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 cathodeField topology also affected by filament-Wehnelt distance
Low biasnegative field gradient weak
Focusing action weak
Emitted e- see only + field from anode = high emission current
Produces large crossover size
Poor brightness
High biasnegative field gradient strong
Focusing 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:Principle:
Cathode = tungsten rod, very Cathode = tungsten rod, very sharp point (<100nm)sharp point (<100nm)
Apply 3-5kV potential relative to Apply 3-5kV potential relative to first anode (very strong field at first anode (very strong field at tip, >10tip, >1077 V/cm) V/cm)
Electrons can escape cathode Electrons can escape cathode without application of thermal without application of thermal energyenergy
Very high vacuum (10Very high vacuum (10-10-10 torr or torr or better)better)
Use second anode for Use second anode for accelerating electronsaccelerating 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
Electrons near the Fermi level…Uncertainty in momentum corresponds to the barrier height(φ, work function):
(2mφ)1/2
If the uncertainty in position ∆x ≈ ħ/2(2mφ)1/2
is approximately the barrier widthx = φ/Fe (Fe = applied field)
then electrons will have a high probability of existing on either side
Electrons near the Fermi level…Uncertainty in momentum corresponds to the barrier height(φ, work function):
(2mφ)1/2
If the uncertainty in position ∆x ≈ ħ/2(2mφ)1/2
is approximately the barrier widthx = φ/Fe (Fe = applied field)
then electrons will have a high probability of existing on either side
Tunneling:
Ralph Fowler
Lothar Nordheim
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
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
36
Monochromator gun concept• Extend two mode approach to make a monochromator:
1) use an off-axis extractor aperture and2) a strong C0-lens setting to create dispersion:
C0 on>20 nA
C0 onbeam off-axis
gun tipextractor
C0 lens(Segmented electrode gun lens)
off-axis apertureon-axis aperture
37
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)