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
aperture
assembly
objective
sample
Electron Lenses
Principle of electromagnetic focusing
Interaction of electromagnetic field on moving charge (electron)
Vector equation
→
→ →
F = -e(VxB)
Magnitude of F will be
F = -eVBsinθ
where θ is the smaller of two angles
between V and B
Direction of F determined by “right hand rule”
F = Force on electron
V = electron velocity
B = Magnetic field
strength (rotationally
symmetric)
e = charge of electron
Axially symmetric electromagnetic lens
Fe shielding to prevent flux leakage from solenoid
Lens strength:
intensity of field in gaps
proportional to (NxI)
N = # turns of solenoid winding
I = current flowing through windings
Focal Length (f):
Point on Z axis where initially parallel rays cross the axis after
passing through the lens
HIGHER LENS STRENGTH = SHORTER FOCAL LENGTH
B = vector parallel to field
Upper
polepiece
Br = radial component of field (vector
perpendicular to axis)
Bz = axial component of field (vector
High lens
parallel to axis)
strength = short
B varies depending on position in lens
focal length
Results:
Lower
polepiece
Force strongest in the center of the gap
Actual electron paths spiral through lens
Low lens strength =
long focal length
Usually two-stage condenser system
Purpose:
1) Further demagnification of the gun crossover image
2) Control amount of beam entering objective
major effect on beam current at sample
High Lens strength
Small crossover image
Less current entering the objective
Low Lens strength
Large crossover image
More current entering the objective
Electron gun
Condenser
f (high condenser lens strength)
f (low condenser lens strength)
Objective
High condenser strength
Short focal length
Low condenser strength
Sample
Long focal length
Large divergence angle
Small divergence angle
Low current into objective
High current into objective
Objective lens
Purpose: control the size and shape of the final beam spot
Considerations:
Produce small beam diameter
Magnetic field must not hinder detector system from collecting
low eV electrons
Must allow clear path from sample to detectors
Bore must be large
Contain scan coils and Stigmators
Beam-limiting apertures
Aberrations usually increase with focal length – minimize
aberrations
For quantitative analysis
long focal length = long working distance
high takeoff angle and low absorption
For objective
Increase demagnification by increasing lens strength to produce small
spot size
→
Short working distance due to short focal length
→
Short depth of field
Objective lens, therefore,
Controls image focus = beam size
Pinhole lens
Objective lens design
Immersion lens
Snorkel lens
Electron gun
Condenser
High objective
strength
Low objective strength
Short focal length
Small divergence angle
Large divergence angle
Long working distance
Short working distance
Large depth-of-field
Short depth-of-field
Low resolution
long focal length
High resolution
f (high objective lens strength)
Objective
= short working distance
f (low objective lens strength)
= long Working distance
Sample
Effective beam diameter
Current in final beam spot is a
function of:
1) Condenser lens strength
2) Objective aperture size
Objective aperture affects:
1) Current reaching sample
2) Beam size passing through
objective
3) Depth of field
Tradeoff:
Best image resolution with smallest spot size
(smaller aperture)
Direct cutting of current compromises signal
produced as current reduced in final spot
Short
Long working
working distance
distance
Depth of field
Insert smaller
objective aperture
to improve D
Sample surface
D
Plane of focus
Pixel
size
Region of image in
effective focus
Beam current regulation
Feedback to
condensers
Objective aperture
assembly = beam
regulating assembly
Sense current drift on
aperture and adjust
condenser lens strength
to compensate
Production of minimum beam size
Magnification:
S0
Electron
gun
Mc = S0/Si = magnification of condenser
S0 = distance from gun crossover to lens gap
Condenser
Si = distance from gap to where imaged
S1
(related to focal length)
Diameter of beam after passing
through condenser
Objective
di = d0/Mc
Sample
S0 is constant, so
Increase condenser current → decrease in focal length and
increase in demagnification (smaller crossover diameter)
Note that divergence angle also increases so less current
enters objective
For objective:
Increase demagnification to produce small beam diameter, results in:
- short working distance
- short depth of field
Final beam size:
df = d0 / (McMobj)
Current in final beam is a function of:
- condenser lens strength
- objective aperture size
Minimum beam size (and highest resolution) achieved by increasing lens
strength – sacrifice current (and signal / noise)
Quality of final beam at the sample will be affected by:
- lens aberrations
- vacuum quality
- sample effects
Lens aberrations
Spherical
Chromatic
Diffraction
Astigmatism
Coma
Electrons moving in trajectories
further from optic axis are focused
more strongly than those near the
axis
Causes image enlargement (disk = ds)
Diameter of ds = ½ Cs α3
Cs = spherical aberration coefficient
α = angle of outer ray through lens
Cs minimized in short focal length lenses
(e.g., immersion)
For pinhole lenses, can decrease
spherical aberration by decreasing α
using aperture
Lens aberrations
Spherical
Chromatic
Diffraction
Astigmatism
Coma
If energies of electrons passing
through the lens differ, they will
follow different ray paths
Always some spread in initial
electron energies as leave
cathode
W ~ 2 eV
LaB6 ~ 1 eV
FE ~ 0.2 to 0.5 eV
Minimize by decrease in α
Diameter of dc = CCα (ΔE / E0)
Cc = chromatic aberration coefficient
α = convergence angle
Directly related to focal length
Much less significant at high E0
Lens aberrations
Spherical
Chromatic
Diffraction
Astigmatism
Coma
Wave nature of electrons
Diameter of dd = 0.61 λ / α
λelectrons = 1.24 / (E0)1/2
Larger divergence angle (α) = smaller
contribution of dd
Spherical aberration disk ds and aperture diffraction disk dd vs.
aperture angle
Lens aberrations
Spherical
Chromatic
Diffraction
Astigmatism
Coma
Magnetic lenses have imperfect symmetry
Enlarges beam diameter and
changes shape
Use stigmators in objective lens
supplies weak correcting field
typically use octupole arrangement
Lens aberrations
Spherical
Chromatic
Diffraction
Astigmatism
Coma
Different focal lengths of electron paths
with different incidence angles
Generally eliminated by proper lens
alignment
Aberrations most significant in objective
Final probe size = quadrature sum of disk diameters…
dp = (dg2 + ds2 + dd2 + dc2)1/2
dg = gaussian probe size
Importance:
At 30 kV, tungsten filament
imax = 1.64 x 10-12 A
diameter dd = 1.4 nm
ds = 2.5 nm
chromatic aberration especially significant for W sources
where ΔE ~ 2-3 eV
Increase effective diameter
1) 30 kV
dp 5nm → 6.5nm
2) 15 kV
→ 9.5 nm
lower energy spread will make a big difference…
Elstar electron column
Schottky - UC,
hot swap gun
Key design elements:
• Large travel/tilt stage compatible
• “DualBeam” SEM-FIB
• Minimum lens aberrations
• Automated aperture selection
• Default small beam current
• Small gun apertures
• High current for analytics >20 nA
• Thermal & environmental stability
• Constant power lenses
• Double magnetic shielding
• Electrostatic scanning
Double magnetic
shielding
Fast beam
blanker
CP
Electrostatic scanning
2- mode objective lens
with with
field -field-free
free and and
coils
immersion capability
New TLD design
CP
vCD
Beam at HV
Beam at landing V
Beam deceleration
I1
I2
CP
Sample
Bias
Magellan XHR SEM: three beam modes available
extractor,
2 apertures
SchottkyFEG
segmented
gun lens
aperture
and slit
deflector
Standard
High current
Monochromated (UC)
Performance improvement with monochromator
25-75% edge resolution [nm]
4.5
total, UC off Beam voltage 1 kV
chromatic and
total, UC on The
spherical aberration
contributions dominate at
Cc, UC off
high aperture angles…
Cc, UC on
diffraction
Cs
4
3.5
3
2.5
2
Spherical
1.5
Diffraction effects
dominate everything
at low aperture
angles…
1
Chromatic
More current
(better S/N)
Improved resolution
0.5
0
0
10
20
alpha [mrad]
30
UC allows larger α therefore
lower diffraction (dd)
40
Magellan: Resolution improvement UC off and on
UC off
•
•
1 kV, no beam deceleration
256 nm HFW in both cases
UC on
Beam deceleration: enhancing resolution and contrast
Beam
What is beam deceleration?
New optics mode enabling high resolution imaging
and high surface sensitivity at very low kV
BD specifications:
• Landing energy range: 30 keV down to 50 eV
• The deceleration (Bias) can be continuously
adjusted by the user
Benefits:
• Enhances the resolution
• Provides additional contrast options
• Greatest benefit at 2kV and below
2-mode final lens
TLD
HV
vCD
Landing V
Sample
Bias
If Bias=0 (no BD):
Landing V = HV
Extending low kV resolution via UC and BD
50
V
25-75% edge resolution [nm]
3.5
3
BD on, UC on
BD off, UC on
BD off, UC off
2.5
2
1.5
1
0.5
0
10
100
1000
10000
Landing voltage [Volt]
100000
50 V with 1 kV beam deceleration
850 nm HFW
Practical considerations:
Must optimize:
 Instrument alignment (gun, lenses, apertures)
 Minimum vibration
 Minimum stray fields
 Specimen contamination
 Clean apertures
Then go for minimum spot size if resolution is the goal
However, ultimate resolution depends on the detected signal, a function of:
Minimum spot size AND
Emission volume of signal… beam-specimen interactions
Electron gun
Condenser
Objective
Sample