Today’s quote:
ψ
“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 particle
…The 4f wave functions (Mark
Winter…the orbitron)
|ψ
2
|
… the probability density
…The 4f electron density
Ψ
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 ≥ ħ (E = energy, t = time)
ΔpΔx ≥ ħ (p = momentum, x = distance, or position)
Uncertainty of electron
energies
ΔE = pΔp/m, ≈ (ΔP)2/m
E electron energy
Vo the potential
barrier
(or position)
X
Electron Optics
Two essential components:
Electron
gun
Cathode
1) Electron source (gun)
Anode
2) Focusing system (lenses)
Alignment
coils
Add scanning apparatus for imaging
Lenses
condensers
Objective
aperture
assembly
objective
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
Filament
heating current
Current and Voltage
Carl Zeiss EVO50
Cameca SX50
Beam voltage
(Read)
Gun emission
current
Beam current
At sample
(HV set)
Beam current
Control
(condensers)
Filament
heating current
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
Metal
Vacuum
E
The work function is the solidstate electronic analog of the
ionization potential (binding
energy) – the amount of
energy required to liberate an
electron from a particular
energy level…
Ew
E
Ef
x
2-5 Volts in metals
Interface
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
Metal
Vacuum
E
Ew
E
Ef
x
Ew = Work function
Ew = E – Ef
Heat electrons to overcome work function
Interface
Self – biased electron gun
Wehnelt cylinder
Filament heating supply
surrounds filament and has small
opening at base
Filament
(Cathode)
Bias
Resistor
Wehnelt
Cylinder
Vbias=ieRbias
0
+
+
Equipotentials
d0
Anode
α0
Beam current ib
High
voltage
supply
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
Filament heating supply
voltage
Filament
Major effect:
Field topology
Bias
Resistor
Vbias=ieRbias
Wehnelt
Cylinder
Change in constant field lines near cathode
Field topology also affected by
0
+
filament-Wehnelt distance
Equipotentials
-
High
voltage
+ supply
d0
Anode
α0
Beam current ib
Low bias
negative field gradient weak
Focusing action weak
Emitted e- see only + field from
anode = high emission current
Produces large crossover size
Poor brightness
High bias
negative field gradient strong
Focusing action strong
Emitted e- see only - field from
Wehnelt = return to filament
Emission current → 0
Cathode tip
Down 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
Emission Current (mA)
200
Emission current
200
Brightness
Optimum bias
voltage
200
-300
-400
Bias Voltage (V)
-500
Saturation
Filament
heating current
Carl Zeiss EVO50
Cameca SX50
Gun emission
current
Filament
heating current
Saturation
Want a well regulated beam current
Emission Current (mA)
200
Operating
filament current
100
50
0
2.0
Filament Current (A)
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
4.0
Saturation
Emission Current (mA)
200
Operating
filament current
100
50
0
2.0
Filament Current (A)
4.0
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
LaB6 – CeB6 cathodes
From Richardson equation:
Jc = AcT2exp(-Ew/kT)
in A/cm2
Ac = material dependant constant
T = emission temperature
k = Botzmann’s constant
So current density (and brightness) increase by
lowering work function (Ew)
At ~ 2700K, each 0.1eV reduction in Ew
→ increase in Jc by 1.5X
REE hexaborides have much lower Ew
compared to W
Principle:
Crystal made by
electric arc
melting of REEB6
powder stick in
inert atmosphere
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)
Graphite
blocks
Mo-Re
supports
Can equal W current density at 1500K
Jc then nearly 100A/cm2 at 2000K
5000 psi
Mini Vogel Mount
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
Field Emission (Fowler-Nordheim Tunneling)
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
Etched carbide
tip (AP Tech)
Field Emission Tip
V1
First
Anode
Second
Anode
V0
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
Tunneling:
Electrons near the Fermi level…
Uncertainty in momentum corresponds to
the barrier height(φ, work function):
(2mφ)1/2
Ralph Fowler
If the uncertainty in position
∆x ≈ ħ/2(2mφ)1/2
is approximately the barrier width
x = φ/Fe (Fe = applied field)
then electrons will have a high probability
of existing on either side
Lothar Nordheim
Werner
Heisenberg
Ralph
Fowler
Tunneling:
If ∆x is on the order of the barrier
width, there will be a finite
probability of finding an electron on
either side
Cathode
Vacuum
Thermionic
Ew
Ew(SE)
Field
emission
Ef for
ZrO2/W
Ef for W
0
1
2
nm
3
4
5
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:
Disadvantages:
Long lifetime
Easily poisoned
Very high resolution
Requires very high vacuum (better
than 10-10 torr)
High depth of field
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.
Now down to
0.15ev with
monochromator
Schottky
Cold Field
LaB6
Tungsten
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
<1
4-6
<1
<1
>1yr.
>1yr.
>1yr.
102-103 hrs
Source Size (nm)
Short-term beam
Current stability (%RMS)
Typical service life
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:
gun tip
extractor
on-axis aperture
off-axis aperture
C0 lens
(Segmented
electrode gun
lens)
36
C0 on
>20 nA
C0 on
beam off-axis
UC gun optics design
tip
axial beam
off-axial
beam
extractor
C0 lens
2nd gun
aperture
deflector
37
slit
– 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
Magellan XHR SEM: three beam modes available
extractor,
2 apertures
SchottkyFEG
segmented
gun lens
aperture
and slit
deflector
Standard
High current
Monochromated (UC)