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

Electron LensesPrinciple of electromagnetic focusing

Interaction of electromagnetic field on moving charge (electron)

Vector equation

Magnitude of F will be

F = -eVBsinθwhere 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

→ → →F = -e(VxB)

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

Br = radial component of field (vector perpendicular to axis)

Bz = axial component of field (vector parallel to axis)

B varies depending on position in lens

Results:

Force strongest in the center of the gap

Actual electron paths spiral through lens

Low lens strength = long focal length

High lens strength = short focal length

f

f

Upper polepiece

Lower polepiece

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

Sample

Objective

Condenser

Electron gun

f (low condenser lens strength)

f (high condenser lens strength)

Low condenser strengthLong focal length

Small divergence angle

High current into objective

High condenser strengthShort focal length

Large divergence angle

Low 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

Objective lens design

Pinhole lens

Snorkel lensImmersion lens

Depth of field

Depth of field

Sample

Objective

Condenser

Electron gun

f (high objective lens strength)

= short working distance

f (low objective lens strength)

= long Working distance

Effective beam diameter

High objective strengthShort focal length

Large divergence angle

Short working distance

Short depth-of-field

High resolution

Low objective strengthlong focal length

Small divergence angle

Long working distance

Large depth-of-field

Low resolution

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

Depth of field

Plane of focusD

Region of image in effective focus

Long working distance

Sample surface

Short working distance Insert smaller objective aperture to improve D

Pixel size

Objective aperture assembly = beam regulating assembly

Sense current drift on aperture and adjust condenser lens strength to compensate

Beam current regulation

Feedback to condensers

Production of minimum beam size

Magnification:

Mc = S0/Si = magnification of condenser

S0 = distance from gun crossover to lens gap

Si = distance from gap to where imaged

(related to focal length)

Diameter of beam after passing

through condenser

di = d0/Mc

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

Sample

Objective

Condenser

Electron gun

S0

S1

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

Diameter of dc = CCα (ΔE / E0)

Cc = chromatic aberration coefficient

α = convergence angle

Directly related to focal length

Much less significant at high E0

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

Lens aberrations

Spherical

Chromatic

Diffraction

Astigmatism

Coma

Diameter of dd = 0.61 λ / α

λelectrons = 1.24 / (E0)1/2

Larger divergence angle (α) = smaller contribution of dd

Wave nature of electrons

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

ComaDifferent 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 + ds

2 + dd2 + dc

2)1/2

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…

dg = gaussian probe size

Sample

CP

CP

Schottky - UC, hot swap gun

Double magnetic shielding

Electrostatic scanning

Fast beam

Bias

2 - mode objective lens with field - free and immersion capability

Sample

CP

CP

Schottky - UC, hot swap gun

Double magnetic shielding

Electrostatic scanning

blanker

Bias Beam deceleration

2 - mode objective lens coils with field-free and immersion capability

Beam at HV Beam at landing V

vCD

New TLD design

Elstar electron column

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

CPI1I2

CPI1I2

CPI1I2

Magellan XHR SEM: three beam modes available

Schottky-FEGextractor,2 apertures

segmentedgun lens

aperture and slit

deflector

Standard High current Monochromated (UC)

Performance improvement with monochromator

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 10 20 30 40alpha [mrad]

25-7

5% e

dge

reso

lutio

n [n

m]

total, UC offtotal, UC onCc, UC offCc, UC ondiffractionCs

Beam voltage 1 kV

Improved resolution

More current (better S/N)

Chromatic

Spherical

UC allows larger α therefore lower diffraction (dd)

Diffraction effects dominate everything at low aperture angles…

The chromatic and spherical aberration contributions dominate at high aperture angles…

Magellan: Resolution improvement UC off and on

• 1 kV, no beam deceleration• 256 nm HFW in both cases

UC off UC on

Beam deceleration: enhancing resolution and contrast

If Bias=0 (no BD):Landing V = HV

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 userBenefits:

• Enhances the resolution • Provides additional contrast options• Greatest benefit at 2kV and below

Bias

HVLanding V

Beam

vCD

Sample

TLD

2-mode final lens

Extending low kV resolution via UC and BD

0

0.5

1

1.5

2

2.5

3

3.5

10 100 1000 10000 100000

Landing voltage [Volt]

25-7

5% e

dge

reso

lutio

n [n

m] BD on, UC on

BD off, UC onBD off, UC off

50 V with 1 kV beam deceleration

850 nm HFW

50 V

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

SEM variables and secondary electron imaging – essential tradeoffs

Res. DOF S/N charge Res. DOF S/N charge Res. DOF S/N charge Res. DOF S/N charge

Higher Voltage (kV) Higher Current Longer WD Larger Obj. Aperture

decrease

increase

Arrows illustrate result (increase or decrease) on increasing kV, current, working distance, or objective aperture diameter

Metal coatC-coat

Res. = resolutionDOF = Depth-of-FieldS/N = Signal/noiseCharge = propensity for charging

Complex