04 electron optics - Dipartimento di Fisica

Probe particle Electron
Electron mean free path in a solid
Electron beam sources
Electrons can be easily
produced by thermoionic
emission from a hot
filament, extracted by an
electric field, focussed
and accelerated to the
desired kinetic energy.
Virtual Cathode
Richardson Law
J c  AT 2 exp(  Ew / KT )
T filament temperature
Ew work function
K Boltzmann constant
A costant
Tungsten cathode
•
•
•
•
•
•
Hair pin filament with a curvature of 100m
Working temperature 2700-3000K
Emitted current Jc=1,75 A/cm-2
Vacuum needed 10-3 Pa (10-5 mbar)
Average lifetime 60-100 ore
The work function can be reduced by covering the filament with Thorium
Lanthanum hexaboride cathode (LaB6)
• LaB6 crystal with 1mm2 area cut along (100) or (211)
face corresponding to the minimum work function.
• Working temperature 1700 K-2100 K
• Emitted current 40-100 A/cm-2
• Vacuum needed 10-6 Pa (10-8 mbar)
• Average lifetime undefined
Field Emission Cathode
The single crystal tungsten rod biased at 3000
V at room temperature.
Photoemitting area: few nm2.
Superconducting cathodes: resolutions of few
meV achieved.
The beam is then accelerated to the requested
energy by the second anode (up to 1 MeV for
TEM).
Field Emission Cathode
Current:
• Curvature of the tip 20-200 nm
• Vacuum needed 10-7 Pa (10-9 mbar)
Intensity and Brilliance
Concept of current density :
Jb=4ib/d02
ib= total integrated current at the cathode;
d0= diameter of the beam at the cross–over
It is limited by lens aberrations and by the slits .
Concept of Brilliance (β):
current density per solid angle
(A cm-2 sr -1)
0
0= half angle of the cone of the
trajectories in the cross-over
  4ib /( (d0 0 ) )
Maximum value: β= JceV0/kT
with Jc e T current density and cathode temperature
V0 dpotential difference between cathode and anode plate
2
Comparison of the different cathodes
Emitter
(work function)
Life
(hours)
Source
size
Brilliance at 25KV
(for TEM/SEM use)
W (thermoionic)
(4.5 eV)
60-100
100
1 A cm-2sr-1
LaB
(2.0)
W (field
emission)
300-500
5m
20-50 A cm-2sr-1
300-1000
<10 nm
100-1000 A cm-2sr-1
Commercial Electron
gun for Auger
Experiments
Electron beam lenses
• Lenses for electron beams are based either on electrostatic
or magnetic fields
• In the former case the deflection of the electron rays is only
proportional to the electric charge. They are therefore
optimal for slow electrons (up to 10 keV)
• In the latter case the deflection is caused by Lorentz force
proportional to charge and speed. They are therefore beter
for swift electrons
Le lenti elettromagnetiche danno minori aberrazioni ma i
campi magnetici sono difficili da confinare spazialmente.
A bassa energia servirebbero campi magnetici
estremamente intensi e le lenti magnetiche sono pertanto
inutilizzabili.
Similmente ad alte energie servirebbero campi elettrici
troppo intensi e le lenti elettrostatiche sono inutilizzabili.
Electrostatic
Electron Optics
Deflection of an electron passing
through a region characterized by a
uniform electric field E and a related
potential difference V.
While the vertical component of v is
changed the horizontal one is conserved
sinα v 2 n 2
v
v


sin   ||
sin   ||
sinβ
v
n1
v1
v2
1
1
1
2
2
mv 2  mv 1  eV
2
2
sinα v 2 n 2
V


 1
sinβ v1 n1
V0
Snell law
Effective
U ( x)
v( x )
n( x ) 
 const
refraction index
v1
v1
1 1

f n2

n2
n1
dn
1

r ( x) n2

x2
x1
1 dn
dx
r ( x) dx
r(x) curvature
Electrostatic lenses
Low energy electrons are best focused by electrostatic
lenses. Electron lenses are metallic apertures.
In part (a), the configuration is set to produce convergence;
and in (b), divergence.
Part (c) shows a single, symmetrical lens that is capable of
focusing.
In each case, equipotential lines are drawn.
Electromagnetic Lenses
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•
•
•
cylindric soft iron shiled containing a coil.
current flows through the coil generating a
magnetic field oriented parallel to the lens
axis
The magnetic field bends the trajectories.
Trajectories originating from one point
converge again forming the image
Magnetic lenses for electrons
2
e

 B
t
m
AC  v||t 
t independent of 
2mv cos 
eB
A magnetic lens for electrons.
Part (a) schematically shows the
trajectory of an electron
entering a "long" solenoid. The
electron follows a helical path
around the magnetic field lines
with a period t.
Part (b) shows an iron-shielded
solenoid and representative
magnetic field lines.
Magnetic lenses are better for
high energy electrons for which
electrostatic lenses would
require too high electric fields.
Aberrations are also smaller.
with cos 1 for small angles
aberrations
spheric aberration
Electrons moving along
trajectories at different
distance from the axis are
focussed at different
distances from the lens.
Electron lenses are subject to the same
aberrations as optical lenses.
For paraxial trajectories, i.e. parallel to the lens
axis but at different distance :
Chromatic aberration
Electrons with different velocities
(i.e. different wavelengths) are
focussed at different distances
from the lens.
Coma and
astigmatism
The axial symmetry of the lens is
lost for non paraxial rays.
The spherical aberrantion gives
rise to a comet like image
Vertical and horizzontal objects
will be imaged at different focal
points
TEM: Correction of astigmatism
Lens aberrations and lens
imperfections induce asymmetries
in the lens fields leading to a
distorted image. Such distortions
can be compensated with correction
coils which correct the magnetic
field of the lenses
Electron Detectors and Multiplyers
• Fluorescent screen
- A dye is electronically excited and decays emitting visible
photons which are then observed by inspection or recorded by a
photocamera (at least 10-9 A needed on a spot for a visible
signal)
• Faraday Cup
- Incoming electrons are collected by an anode (10-11 A needed)
and transformed into current pulses which are eventually
transformed into a tension pulse, amplified and transmitted to
the electron counting electronics
• Resistive anode
The current arriving on a resistive rectangular plate is recorded
at its corners. The four measured current values allow to
determine the position at which the beam hits the resistive
plate.
• Single electron multiplyers : Dynode multipliers
Channeltrons
Channelplates
Electron Multiplyiers
Dynode-based Electron Multiplier
Dynodes are insulating glass shells. The electron current is
multiplied at each collision.
Gains as high as 1010÷1011 can be achieved with electron
multipliers working at a few kV
Channeltron
• Channeltrons are continuous dynodes
allowing for gains up to 108.
• It consists of an empty, usually horn
shaped, glass tube polarized to several kV.
• The outgoing current is collected by a
Faraday Cup at the exit of the device.
• The output current for single incoming
electrons entering into the device is in the
pA range.
• The signal is then converted to tension, by
recording the potential difference across a
resistor, and preamplified electronically.
Channelplate
• Channeltrons may be organized into channel
plates for position sensitive detectors.
• Gain limit 107. The current is then collected
on a resistive anode with four contacts.
• Main limit: anisotropic signals may induce
anisotropic heating and cause thermal shock
and rupture of the device.
Electron Energy Analyzers
Retarding field
analyzer (RFA)
A grid at negative
potential V prevents
electrons with kinetic
energy lower than a
given threshold to reach
the detector
(fluorescent screen)
Advantage: high angle acceptance, position sensitive
Application: Low energy electron diffraction (LEED) and Auger
electron spectroscopy (AES)
Electron Energy Analyzers
Cylindrical Mirror Analyser (CMA)
Single or double pass system.
The device is based on a strong chromatic aberration
Large angle acceptance
High sensitivity (currents up to 100 X lower than for RFA)
Application: Auger Electron Spectroscopy
Hemispherical
Analyzer
Advantage:
3Dim focussing.
Angle resolution 3°
Application:
Angle resolved
photoemission
Low energy electron bemas and high resolution
Cylindrical Deflectors (CDA) as Monochromators and Analyzers:
the ribbon shaped beam
Ideal, not terminated device, first order focus at 127,3°
Main advantage: the current is
distributed over a rectangular slit:
lower space charge
→ higher throughput
Application: High Resolution Electron
Energy Loss Spectroscopy
Application: High Resolution Electron Energy Loss
Spectrometer (HREELS)
La trasmissione di monocromatori e analizzatori di elettroni è limitata,
come per qualsiasi altro dispositivo ottico elettronico dalle aberrazioni.
Questi dispositivi possono essere ottimizzati mediante simulazioni delle
traiettorie degli elettroni che li attaversano.
Attualmente sono disponibili commercialmente spettrometri HREEL
basati su CDA con risoluzione limite di 0.5 meV nel fascio diretto
(sviluppati da H.Ibach, commercializzati da SPECS e LK Technologies).
I dispositivi SDA utilizzati in fotoemissione possono giungere anch’essi a
risoluzioni di pochi meV. Quelli migliori sono a doppio passo ed hanno
traiettorie di passo dell’ordine del metro (Scientia). Dispositivi meno
pretenzioni vengono prodotti da Omicron e Specs. Sono a singolo passo
e raggiungono risoluzioni sui 50 meV, normalmente sufficienti per
analizzare elettroni fotoemissi da stati di core (XPS).
HREELS per misure magnetiche: deflessione a 90°
La deflessione a 90° permette di conservare una
eventuale polarizzazione in spin degli elettroni
Comparison CDA/SDA
• First order focus at 127.3°; second order focus at 180°.
• For the CDA 127 device the focal plane position angle is displaced
to lower angles by the distortions induced by the equipotential
entrance and exit plates and to higher angles by space charge
(Borsch effect). The actual position of the focus is moreover
controlled by the bias at the upper and lower plates, closing the
device in the vertical plane. Most modern devices are toroid shaped
to achieve some vertical focusing.
• The second order focus of the SDA allows the use of channel plates
to record simultaneously different energies. This characteristic is,
however, lost at high currents because of the shift of the position of
the focus induced by space charge. Main use of SDA is as analyzer
in photoemission.
• For CDA the beam is ribbon shaped since entrance and exit slits
have a rectangular shape. The energy resolution is then determined
by s/r where s is the width of the slit and r the radius of the central
electron trajectory, while the feed current depends also on the slit
height, h. Typically s0.3 mm and h3 mm.
• In SDAs the use of rectangular slits is more problematic since
focussing occurs in two directions. CDAs are therefore superior as
electron beam monochromators. The price to pay are rectangular
rather than cylindrical electron lenses which have larger aberrations.