Scanning Electron Microscopy (SEM)
Short description
Beam parameters
influence on image
e- gun components
filaments
lenses
Beam-sample interaction
electron scattering
Image formation
Scanning Electron Microscope (SEM)
Field of view:
V-shaped Filament
5x 5 mm2 – 500 x 500 nm2
Resolution: down to 1 nm
Extractor
Beam accelerator
Electron
Column
Scan quadrupole
Deflecting Plates
Image Display
Primary
e- Beam
e- Detector
Backscattered
Electrons
Sample
How to sweep an electron beam
First coil deviate beam from optical axis
Optical axis
Second coil brings beam back
at optical axis on the pivot point
Image formation point by point
collecting signal at each raster point
L
S
L = raster length on sample
W = working distance
S = raster length on screen
L = 10 m, S = 10 cm
Magnification = S/L
10x 102 m
M
 10000X
10x 106 m
M depends on working distance
Effect of beam parameters on image
V0 = beam voltage
ip = beam current
p = beam convergence angle
dp = beam diameter at sample
Effect of beam parameters on image
High resolution mode
Noise on signal
Resolution
ip = beam current
dp = beam diameter
Good compromise
ip = 1 pA, dp = 15 nm
ip = 320 pA, dp = 130 nm
High current mode
Resolution too low
ip = 5 pA, dp = 20 nm
Effect of beam parameters on image
Depth of focus
If p is small, dp changes little with depth, so features
at different heights can be in focus
p = 15 mrad
p = 1 mrad
Effect of beam parameters on image
Electron energy
V0 < 5 kV, beam interaction limited to region close to surface, info on surface details
V0 15 - 30 kV, beam penetrates into sample, info on interior of sample
V0 = beam voltage
Electron column
e- are produced and accelerated
Beam is reduced to increase resolution
Beam is focused on sample
Filament
Wehnelt: focuses e- inside the gun
Controls intensity of emitted e-
Grid connected to filament
with variable resistor
e- exit filament following + lines
The equipontential line shape
has focussing effect and
determines 0 and d0
e- are accelerated to anode and the hole allows
a fraction of this e- to reach the lenses
Filament
Equipotential lines
Filament head
The equipontential line shape
has focussing effect and
determines 0 and d0
Electron beam
Electron column
Filament types
Tungsten hairpin
(most common)
Lanthanum
hexaboride (LaB6)
0.120 mm Tungsten wire
Operating principle: thermionic electron emission
LaB6 crystal 0.20 mm
Filament types
thermionic electron emission
Jc  AcT 2e

Ew
KBT
Ac = 120 A/cm2K2
Ew = work function
To reduce filament evaporation  operate the electron gun
at the lowest possible temperature
Materials of low work function are desired.
Tungsten hairpin
Lanthanum hexaboride (LaB6)
Ew = 4.5 eV
Jc = 3.4
A/cm2
at 2700 K
Lifetime 50-150 hours
Energy width  0.7 eV
Operating pressure
10-5
mbar
Ew = 2.5 eV
Jc = 40 A/cm2 at 1800 °K
Lifetime 200-1000 hours
Energy width  0.3 eV
Operating pressure 10-6 mbar
Filament types
Operating principle:
thermionic electron emission +
Tunnelling
W-Zr crystal 0.20 mm
I = 1 104 A/cm2 at 1800 °C
Lifetime > 1000 hours
Energy width  0.1 eV
Small source dimension (few nm)
Operating pressure 10-9 mbar
Thermal Field
Emission
E gun brightness
Beam current changes throughout the column
Brightness is conserved throughout the column
 d p2 



4 
A

solid angle  2 
  p2
2
R
 dp  1
  2
2 
  p
ip
4i p
current


 2 2 2
2
area  solid angle  d p 
 dp p

   p2
 4 


dp
R
p
Tungsten hairpin
dp: 30 – 100 m
 = 105 A/sr cm2
Lanthanum hexaboride (LaB6)
dp: 5 – 50 m
 = 106 A/sr cm2
Thermal Field Emission
dp: 5 nm
 = 108 A/sr cm2
Electromagnetic Lenses
Demagnification of beam crossover image (d0)
to get high resolution (small dp)
d0: 5 – 100 m
for filaments
High demag
needed
Beam focussing
coils
d0: 5 nm
for TFE
Low demag
needed
Fringe field
radial
parallel
F  e ( v  B)
Electromagnetic Lenses
Focusing process
e- interacts with Br and Bz separately
-e (vz x Br) produces a force into screen
Fqin giving e- rotational velocity vqin
vqin interacts with Bz
produces a force toward optical axis
Fr = -e (vqin x Bz)
f = focal length
the distance from the point
where an electron first begins to
change direction to the point
where it crosses the axis.
The actual trajectory of the electron will be a spiral
The final image shows this spiraling action as a rotation of the image as the objective lens strength is changed.
Electromagnetic Lenses
Lens coil current and focal length
I = lens coil current
N = number of coils
V0 = accelerating voltage
f 
V0
NI 2
Increasing the strength (current) of the lens reduces the focal distance
Comparison to optical lenses
Demagnification of beam crossover image (d0) = object
Beam crossover
1
f
Magnification M 
q
p

1
p
Demagnification m 
d0 = tungsten diameter = 50 m
Scaling from the figure, the demag factor is 3.4 so d1 = d0/m = 14.7 m
CONDENSER LENSES: the aim is to reduce the beam diameter

p
q
1
q
Objective Lenses
Scope: focus beam on sample
Pinhole
No B outside
Large samples
Long working
distances (40 mm)
High aberrations
Snorkel
B outside lens
Large samples
Separation of secondary
from backscattered eLong working distances
Low aberrations
They should contain:
Scanning coil
Stigmator
Beam limiting aperture
They also provide
further demagnification
Immersion
Sample in B field
Small samples
Short working distances (3 mm)
Highest resolution
Low aberrations
Separation of secondary
from backscattered e-
Effect of aperture size
Aperture size: 50 – 500 m
Decrease 1 for e- entering OL to a
a determines the depth of focus
Determines the beam current
Reduces aberrations
Effect of working distance
m
1
f
Increase in WD  increase in q 
m smaller  larger d  lower resolution but longer depth of focus

p
q
1
p

1
q
Effect of condenser lens strenght
Weak
f 
V0
NI 2
m
p
q
Higher Ibeam
Lower dp
Strong
Decrease q1 and
increase p2
 larger m
Lower Ibeam
Higher dp
Increase in condenser strenght (current)  longer q  larger m and smaller d
Also it brings a beam current reduction, so a compromise between current and resolution is needed
Gaussian probe diameter
The distribution of emission intensity from filament is gaussian with size dG
 
4i p
 dp p
2
ip 
2
2
dG 
dG = FWHM
4i p
 2  p2
 2dG2 p2
4
With no aberrations, keeping dG constant would allow to increase ip by only increasing p
Spherical aberrations
Origin: e- far from optical axis
are deflected more strongly

e- along PA gives rise to gaussian image plane
No aberration
e- along PB cross the optical axis in ds
So at the focal plane there
is a disk and not a point
ds 
Cs 3
2
Spherical aberration disk of least confusion
Cs = Spherical aberration coefficient  f
For immersion and snorkel Cs ~ 3 mm
For pinholes Cs ~ 20-30 mm
So one need to put an aperture
Aperture diffraction
To estimate the contribution to beam
diameter one takes half the diameter
of the diffraction disk
dd 
0.61 
nm

sr

1.24
E
eV
Chromatic aberrations
Origin: initial energy difference of accelerated electrons
Chromatic aberration disk of least confusion
 E 


 E0 
dC  CC  
For tungsten filament E = 3 eV
At 30 KeV E/E0 = 10-4
At 3 KeV E/E0 = 10-3
d p  dG2  ds2  dd2  dC2
Cs = Chromatic aberration coefficient  f
Astigmatism
Origin: machining errors, asymmetry in coils, dirt
Result: formation ow two differecnt
focal points
Effect on image:
Stretching of points into lines
Can be compensated with octupole stigmator
Astigmatism
Beam-sample interaction
Simulation of e- trajectories
Backscattered eSilicon
V0 = 20 KV
TFE,  = 1 108 A/sr cm2
dp = 1 nm
Ib = 60 pA
Main reason of large interaction volume:
Elastic Scattering
Inelastic scattering
Beam-sample interaction
Elastic Scattering
0
Elastic scattering cross section
Q  1.62x 10
20
2
 
Z  
   tan 0 
2
E  
-2


events
electron atom/cm2 


Elastic mean free path =
distance between scattering events

A
(cm)
N0Q
Q (Si )
0 5
1keV
 1.66x 10
15
events
electron atom/cm2 
(Si )1keV5  1.2 nm
0
events
electron atom/cm2 
nm
 5
18
Q (Si )30
keV  1.84x 10
0
 5
3
(Si )30
keV  1.08x 10
0
Z = atomic number;
E = e- energy (keV);
A = atomic number
N0 = Avogadro’s number;
 = atomic density
Silicon
 = 2.33 g/cm3
Z = 14
A = 28
N0 = 6.022 1023
Inelastic Scattering
Beam-sample interaction
Inelastic scattering energy loss rate
dE
Z  1.166Ei 
4
 2e N0
ln

ds
AEi  J

Z = atomic number
A= atomic number
N0 = Avogadro’s number
 = atomic density
Ei = e- energy in any point inside sample
J = average energy loss per event
J  9.76Z  58.5Z 0.19 x 103
The path of a 20 KeV e- is of the
order of microns, so the interaction volume
is about few microns cube
Eb = 20 KeV
Beam-sample interaction
Interaction volume
Energy
transferred
to sample
Simulation
20 KeV beam incident on PMMA
with different time periods
Influence of beam parameters on beam-sample interaction
Beam energy
10 KeV
20 KeV
Fe
30 KeV
Elastic scattering
cross section
Q 
1
E2
dE
1

ds
E
Longer 
Lower loss rate

A
(cm)
N0Q
Inelastic scattering
energy loss rate
Influence of beam parameters on beam-sample interaction
Incidence angle
Smaller and asymmetric interaction volume
45°
Fe
60°
surface
Scattering of e- out of the sample
Reduced depth
Same lateral dimensions
Influence of sample on beam-sample interaction
Atomic number
C (Z=6)
C, k shell
V0 = 20 keV
Fe (Z=26)
Fe, k shell
Elastic scattering
cross section
10% to 50% of the beam electrons are backscattered
They retain 60% to 80% of the initial energy of the beam
Reduced linear dimensions of interaction volume
Q Z2
dE
Z
ds
Inelastic scattering
energy loss rate
Influence of sample on beam-sample interaction
Atomic number
Ag (Z=47)
Ag, k shell
V0 = 20 keV
U (Z=92)
U, k shell
More spherical shape of interaction volume
Signal from interaction volume (what do we see?)
Backscattered electrons
Secondary electrons
Backscattered e-
BSE dependence
Backscattered electron coefficient

BSE
i
 BSE
i
iB
Monotonic increase
Relationship between
 and a sample property (Z)
This gives atomic number contrast
60°
If different atomic species are present in the sample
  Ci i
i
Ci = weight concentration
BSE dependence
Incidence angle
( )  n cos
n = intensity at normal
Line length: relative intensity of BSE
Strong influence on BSE detector position
60°
BSE dependence
Energy distribution
Lateral spatial distribution
The energy of each BSE depends on the
trajectory inside sample, hence different
energy losses
Region I: E up to 50 %
Becomes peaked with increasing Z
Region good for
high resolution
Gives rise to loss in lateral
resolution
At low Z the external region increases
BSE dependence
Sampling depth
Percent of 
Fraction of maximum
e- penetration
(microns)
RKO defines a circle on the surface (center in the beam) spanning the interaction volume
Sampling depth is typically 100 -300 nm
for beam energies above 10 keV
Signal from interaction volume (what do we see?)
Energy distribution of electrons emitted by a solid
Secondary electrons
Energy: 5 – 50 eV
Probability of e- escape from solid
p e

 = e- mean free path
z

Secondary electrons
Origin: electron elastic and inelastic scattering
SURFACE
SENSITIVE
SE1 = secondary due directly to incident beam
Beam resolution
SE2 = secondary generated by backscattered electrons
Carbon: SE2 /SE1 = 0.18
Low backscattering cross section
Gold: SE2 /SE1 = 1.5
High backscattering cross section
Aluminum: SE2 /SE1 = 0.48
Copper: SE2 /SE1 = 0.9
BSE resolution
SE Intensity angular distribution: cos
Image formation
Backscattered e-
Volume sensitive
Sampling depth
~ 100 -300 nm
Secondary e-
Surface sensitive
p e

z

Image formation
Many different signals can be extracted from beam-sample interaction
So the information depends on the signal acquired, is not only topography
Image formation
The beam is scanned along a single vector (line) and the same scan generator
is used to drive the horizontal scan on a screen
Signals to be recorded
For each point the detector collects a current
and the intensity is plotted
or the intensity is associated with
a grey scale at a single point
A one to one correspondence is established between
a single beam location and a single point of the display
Magnification M = LCRT/Lsample
But the best way is to calibrate the instrument
Image formation
Digital image: array (x,y,Signal)
Signal: output of ADC
Pixel = picture element
Resolution =
2n
8 bits = 28 = 256 gray levels
16 bits = 216 = 65536 gray levels
Pixel is the size of the area on the sample from which information is collected
Considering the matrix defining the: Pixel edge dimension
DPE
LSAMPLE

NPE
Actually is a circle
Length of the scan on sample
number of steps along the scan line
The image is focused when
the signal come only from a
the location where the beam
is addressed
At high magnification there
will be overlap between two pixel
Image formation
For a given experiment (sample type) and experimental conditions (beam size, energy)
the limiting magnification should obtained by calculating the area generating
signal taking into account beam-sample interactions and compare to pixel size
2
deff  dB2  d BSE
beam
Area producing BSe-
V0 = 10 keV, dB = 50 nm
on Al, dBSE = 1.3 m
 deff = 1.3 m
on Au dBSE = 0.13 m  deff = 0.14 m
10x 10 cm display
There is overlapping
of pixel signal intensity
Different operation settings
for low and high magnification
Depth of field
Depth of field D = distance along the lens axis (z) in the object plane
in which an image can be focused without a loss of clarity.
To calculate D, we need to know where from the focal plane the beam is broadened
Broadening means adjacent pixel overlapping
The vertical distance required to broaden a beam r0 to a radius r (causing defocusing) is
tan  
r
D /2
For small angles
tan  
r
D /2

D
2r

Depth of field
D
2r
r 
D
How much is r?

0 .1
M
On a CRT defocusing is visible when two pixels are overlapped 
r = 1 pixel (on screen 0.1 mm)
But 1 pixel size referred to sample depends on magnification
mm
0.2
M
To increase D, we can either reduce M or reduce beam divergence
Beam divergence is defined by the beam defining aperture
mm
 
RAP
DW
Depth of field
 
Optical
RAP
DW
SEM
Detector
Everhart-Thornley
Secondary + BSE
Grid Positive: BSE+SE
Grid negative: only BSE
The bias attracts most of SE
solid angle acceptance: 0.05 sr
Geometric efficiency: 0.8 %
Topographic contrast
Intensity of SE and BSE depends on
beam/sample incidence angle ()
and on detector/sample angle ()
BSE coefficient increase with 
BSE emission distribution ~ cos 
SE emission distribution ~ sec 
Detector position and electron energy window are important
Topographic contrast
Negative bias cage to exclude secondary e- Detector is on one side of sample  anysotropic view
- Small solid angle of acceptance  small signal
- High tilt angle
Dierctional view
High contrast due to orientation of
sample surfaces
Analogy to eye view
Topographic contrast
Contributions:
Direct BSE+SE
SE distribution intensity I ~ sec 
Positive bias cage to accept secondary e-
Variation in SE signal between two surfaces with different 
dI = sec  tan  d
So the contrast is given by dI/I = tan  d
The SE are collected from most emitting surfaces since
the positive bias allows SE to reach the detector
Analogy to eye view
High resolution imaging
High resolution signal if selected in energy
SE1 : e- directly generated by beam
BSE1 : low energy loss (<2%) e- from beam
SE2 : e- generated by BSE into sample
BSE2 : higher energy loss e- from beam
High resolution signal
generated by BSE1, SE1
Separation of signal is necessary to obtain high resolution
Silicon
V0 = 30 KV
TFE,  = 1 108 A/sr cm2
dp = 1 nm
Ib = 60 pA
SE1 - BSE1 width = about 2 nm
Beam penetration depth = 9.5 m
Emission area = 9.5 m
FWHM = 2 nm
Low mag
Scan width at 10000 X = 10x10 m2
image 1024x1024, pixel width 10 nm
Scanning at low M means field of view
larger than SE2 emission area
So there is large overlap between pixel
And the changes are due only to SE2 variations
High mag
Scan width at 100000 X = 1x1 m2
image 1024x1024, pixel width 1 nm
Scanning at high M means field of view
smaller than SE2 emission area
So as the beam is scanned, no changes in
SE2 but changes are due to SE1
SE2 gives large random noise
Carbon nanotubes
SEM in FOOD
Schematic representation of gaseous SED
the role of imaging gas in VP-SEM
SEM in FOOD
‘‘bloomed’’ chocolate.
50 μm
Blades of cocoa butter present on the surface
Image taken with sample at 5 °C
using nitrous oxide at ~ 100 Pa (0.8 torr)
as imaging gas
20 μm
SEM in FOOD
VP-SEM image of commercially produced mayonnaise.
Image taken with sample at 5.0 °C
using water vapor at around 670 Pa (5.0 torr) as imaging gas.
Light continuous phase is water
mid grey discrete phase is oil.
Darkest grey areas are air bubbles
Disadvantages of conventional SEM techniques
insulating specimens
impossibility of examining hydrated samples without altering their state (drying or freezing)
Sample preparation treatments introduce artifacts
No studies of dynamic processes for such samples
V-shaped Filament
Scanning Auger
Microscopy (SAM)
Extractor
Deflecting Plates
Primary
e- Beam
Electron Energy Analyzer
e- Detector
Backscattered
Electrons
Chemical Map
Sample
Auger Spectrum
Auger Spectroscopy
Ekin
Evac
EF
VB
M2,3 3p
M1 3s
e-
e-
L2,3 2p
L1 2s
K 1s
Ground State
XYZ Auger Process
One-Particle Scheme
Energy Conservation
EK(XYZ) = KE of Auger electron
EB(X) = BE of X level
EB(Y) = BE of Y level
EB(Z) = BE of Z level
One-Hole
Initial State
De-Excitation
Auger Process
EK(XYZ)= EB(X)-EB(Y)-EB(Z)-
Two-Hole
Final State
Usually additional terms must be included
accounting for the two-hole final state
correlation interaction and the relaxation effects
EK(XYZ)= EB(X)-EB(Y)-EB(Z)-F+R-
F Two-Hole Final State Correlation Energy
R Two-Hole Relaxation Energy
Eb One electron binding energy
Evac
VB
M2,3
M1
L2,3
L1
K
Ekin
EF
Auger Process
Nomenclature
KL1M2
L1L2M1
Auger Process
Coster-Kronig Process
(the initial hole is filled by an electron
of the same shell)
Core-Core-Core Transition
Core-Core-Valence Transition
Core-Valence-Valence Transition
CCC
CCV
CVV
L1L2M1
KL1M2
Ekin
Ekin
Evac
VB
Evac
EF
VB
M2,3
M2,3
M1
M1
L2,3
L2,3
L1
L1
K
K
EF
Competitive processes
Auger
Electron
X-Ray
Fluorescence
EF
3d M4,5
3p M2,3
3s M1
2p L3
2p L2
2s L1
Relative Probabilities of Relaxation
by Auger Emission and
by X-Ray Fluorescence Emission
Photon
1s K
For lines originating from shell L and M the Auger yield remains much
higher than X-ray emission
Principal Auger Lines while
Spanning the Periodic Table of the
Elements
CHEMICAL SENSITIVITY
Electron distribution spectrum
Pulse Counting Mode
Derivative Mode
Since Auger emission lines are often very broad and weak, their
detectability is enhanced by differentiating of the spectrum
Chemical environment sensitivity
Gas
Solid
Auger Electron Spectroscopy
Quantitative Analysis
In analogy to what developed for XPS,
one can determine the atomic concentration (Ci)
of the atomic species present
in the near-surface region of a solid sample
Ci Atomic Concentration of the i-th species
si Orbital Sensitivity Factor of the i-th species
Ii Spectral Intensity Related to the i-th species
Ii
si
Ci 
Ii
s
i
i
Au N6,7VV
Si L2,3VV
Auger Spectra as Measured
at Selected Points of the
Self-organized Agglomerated
Au/Si(111) Interface
Island
Flat region
Si L2,3VV Auger Line Shape as
Measured at Selected Points
of the Self-organized
Agglomerated Au/Si(111)
Interface
Island
Flat region