Beam – Specimen Interactions
Signals
Backscattered Electrons
Beam electrons scatter, and escape out of specimen
primary signal from elastic scattering
Example: Cu target
70% absorbed
30% backscattered
Backscattered Electron Coefficient
η = # BSE / # incident electrons
Backscattered Electrons:
Atomic # dependence
More trajectories intersect surface with higher Z target
Al
1μm
η = 14.0%
Au – same scale as Al
0.2 μm
Au
η = 53.5%
0.6
Weak Z contrast
Backscatter coefficient η
0.5
0.4
0.3
0.2
Strong Z contrast
0.1
0.0
0
20
40
60
80
Atomic Number
η = -0.0254 + 0.016Z – 1.86X10-4Z2 + 8.3X10-7Z3
For multi-component material: η
= ∑Ciηi
100
Si target
00 tilt
η=17.5
450 tilt
η=30.0
Backscattered electrons:
Energy distribution
BSE have usually undergone a number of scattering events in target prior to
emerging
Al
0
Pb
E0
Light elements = broad distribution
most BSEs E << E0
0
E0
Heavy elements = distribution skewed
toward E0
Backscattered electrons:
Spatial distribution
Electrons may emerge from an area outside beam incidence area
Al
Pb
0
0
2 μm
Light elements =
broad distribution
Heavy elements = narrow distribution
Backscattered Electrons
Greater energy loss farther from beam (more inelastic scattering events)
Better BSE resolution obtainable if select only highest energy BSEs
BSEs within 10% of E0
# BSE
All BSEs
Distance from beam →
Beam – Specimen Interactions
Signals From Inelastic Scattering
• X-Rays
Definition: Those electrons
emitted
with energy less than
Continuum
50 eV
Characteristic
dη/d(E/E0)
• Secondary Electrons
III
I
II
0
• Auger Electrons
1.0
E/E0
Produced by interaction of beam
and weakly-bound conduction band
electrons.
E transfer = a few eV
Peak emitted ~ 3-4 eV
Very shallow sampling depth
Intensity of SE
• Cathodoluminescence
0.0
2.5
5.0
Depth Z (nm)
7.5
Secondary electron coefficient
δ = # SE / # incident beam electrons
Dependent on atomic number
if λ = mean free path
maximum emission depth ~ 5λ
For metals:
λ ~ 1nm
abundant conduction band electrons
lots of inelastic scattering of SE
Insulators:
λ ~ 10 nm
Information depth for SE ~ 1/100 of BSE
About 1% of primary beam electron range (Kanaya-Okayama range)
Secondary electrons generated by primary beam
electrons entering (I), or backscattering (II)
Can define two SE
coefficients: δI and δII
SE generation generally more efficient via BSE (δII / δI= 3 to 4)
Greater path length in region defined by escape depth, plus increased
scattering cross sections due to larger energy distribution (extending
to lower energies) in BSEs…
primary
5λ
BSE
Secondary electron density (#SE / unit area) defines apparent resolution
Generate SEI within λ / 2 of beam (~0.5nm for metals)
Primary beam ~ unscattered in 5λ region
Diameter of SEI escape = diameter of beam + 2X λ / 2
SEII occur over entire BSE escape area
1 μm or more – but peak sharply in center
SEI
SEII
distance
SEtot
Influence of beam energy
η+δ
E1
E0 incident
Shape due mainly to variation in δ
E2
Some considerations for resolution…
With metal coating, secondary electrons detected primarily
from coating
In some cases, can improve resolution using higher beam
energy (remember – higher kV = higher brightness and
smaller beam spot size
10kV
30kV
Si target
20nm Au on Si substrate
10kV
SE emission volume
30kV
Beam – Specimen Interactions
Signals From Inelastic Scattering
• Secondary Electrons
• X-Rays
Continuum
Characteristic
Produced by deceleration of beam
electrons
• Auger
in Electrons
coulomb field of target
atoms
• Cathodoluminescence
→ energy loss
Expressed as emission of X-Ray
photon
Results in continuous spectrum
Most energetic = lowest wavelength
Short λ limit = Duane-Hunt limit
Results in background spectrum
X-ray emission from Cu
7
N x 10-6 photons / e- Ster
Cu Lα
5
Cu Kα
theoretical
3
Actual – due to sample and
window absorption + low detector
efficiency
Cu Kβ
1
0
2
4
6
Energy (keV)
8
10
X-ray continuum
Increase beam energy
Max continuum energy increases (short λ limit decreases)
Intensity at given energy increases
Intensity is a function of Z and photon energy
Kramers’ Law
I (continuum) ~ ipZ (E0 –Ev)/Ev
ip = probe current
Z = atomic #
E0 = beam energy
Ev = continuum photon energy
Background intensity is a determining factor in detection limits
Beam – Specimen Interactions
Signals From Inelastic Scattering
• Secondary Electrons
• X-Rays
Continuum
Characteristic
INNER SHELL IONIZATION
1) If energy equal or greater than critical excitation
potential…
Can eject inner shell electron
• Auger Electrons
Vacuum
2) Atom wants to return to ground state
outer shell electron fills vacancy –
Valence level
relaxation
• Cathodoluminescence
M…
Kα
LIII (2p3/2)
LII (2p1/2)
LI (2s)
K (1s)
Outer shell electron = higher energy state
relative to inner shell electron
some energy surplus in the transition
→ photon emission (X-ray)
The emitted X-ray is characteristic of the target element –
Wavelength (or energy) = the transition energy
Therefore is a manifestation of the electron configuration.
Example:
E SiKα =
E FeKα =
1.740 keV (7.125Å)
6.404 keV (1.936Å)
Quantum state of an electron - Quantum
numbers
Z
Polar coordinates…
θ
Space geometry of the
solution of the
Schrodinger equation for
the hydrogen atom…
Y
Φ
Ψ(r,θ,Φ) = R(r)P(θ)F(Φ)
X
n
l
Radial component
Principal
quantum number
Ml
Colatitude
Orbital
quantum number
Azimuthal
Magnetic
quantum number
Yields three
equations for
three spatial
variables
Quantum state of an electron - Quantum numbers
3 spatial coordinates
n
l
Principal (shell)
1, 2, 3, …
radial = size
K, L, M…
Orbital – angular momentum
(subshell) 0 to n-1
ml
s (sharp)
l=0
p (principal)
l=1
d (diffuse)
l=2
f (fundamental)
l=3
shape
so if n = 2, l = 1:
2p
Orbital – Orientation (Magnetic, energy shift,
or energy level for each subshell)
orientation
l to – l
ex: for l = 2: ml = -2, -1, 0, 1, 2
Rudi Winter
Aberystwyth University
Quantum state of an electron - Quantum numbers
ms
Spin
½,-½
Single electron state of motion… n, l, ml, ms
or: n, l, j, ml
Rudi Winter
Aberystwyth University
J Total angular momentum (quantum number j )
l +/- ½
= l + ms
(except l = 0, where J = ½ only)
The Orbitron:
Mark Winter, Univ. of Sheffield
http://winter.group.shef.ac.uk/orbitron
1s
4f
2p
3d
5f
Quantum Numbers for Electrons in Atomic Electron Shells
X-ray
notation
Modern
notation
n
l
j=l+s
(2j + 1)
K
1s
1
0
1/2
2
LI
2s
2
0
1/2
2
LII
2p1/2
2
1
1/2
2
LIII
2p3/2
2
1
3/2
4
MI
3s
3
0
1/2
2
MII
3p1/2
3
1
1/2
2
MIII
3p3/2
3
1
3/2
4
MIV
3d3/2
3
2
3/2
4
MV
3d5/2
3
2
5/2
6
NI
4s
4
0
1/2
2
NII
4p1/2
4
1
1/2
2
NIII
4p3/2
4
1
3/2
4
NIV
4d3/2
4
2
3/2
4
NV
4d5/2
4
2
5/2
6
NVI
4f5/2
4
3
5/2
6
NVII
4f7/2
4
3
7/2
8
Ionization processes - Critical Excitation Potential
What voltage is necessary to ionize an atom?
Must overcome the electron binding energy – depends on
Electron quantum state (shell, subshell, and angular momentum)
Atomic # (Z)
Electron binding energies (eV)
Element
K
L-I
L-II
L-III
M-I
M-II
M-III
1s
2s
2p1/2
2p3/2
3s
3p1/2
3p3/2
6 C
284.2*
7 N
409.9*
37.3*
8 0
543.1*
41.6*
11 Na
1070.8+
63.5+
30.65
30.81
12 Mg
1303.0+
88.7
49.78
49.50
13 Al
1559.6
117.8*
72.95
72.55
14 Si
1839
149.7*b
99.82
99.42
15 P
2145.5
189*
136*
135*
16 S
2472
230.9
163.6*
162.5*
26 Fe
7112
844.6+
719.9+
706.8+
91.3+
52.7+
52.7+
29 Cu
8979
1096.7+
952.3+
932.7
122.5+
77.3+
75.1+
57 La
38925
6266
5891
5483
1362*b
1209*b
1128*b
82 Pb
88005
15861
15200
13035
3851
3554
3066
92 U
115606
21757
20948
17166
5548
5182
4303
Electron binding energies (eV)
Element
2kV beam…
K
L-I
L-II
L-III
M-I
M-II
M-III
1s
2s
2p1/2
2p3/2
3s
3p1/2
3p3/2
6 C
284.2*
7 N
409.9*
37.3*
8 0
543.1*
41.6*
11 Na
1070.8+
63.5+
30.65
30.81
12 Mg
1303.0+
88.7
49.78
49.50
13 Al
1559.6
117.8*
72.95
72.55
14 Si
1839
149.7*b
99.82
99.42
15 P
2145.5
189*
136*
135*
16 S
2472
230.9
163.6*
162.5*
26 Fe
7112
844.6+
719.9+
706.8+
91.3+
52.7+
52.7+
29 Cu
8979
1096.7+
952.3+
932.7
122.5+
77.3+
75.1+
57 La
38925
6266
5891
5483
1362*b
1209*b
1128*b
82 Pb
88005
15861
15200
13035
3851
3554
3066
92 U
115606
21757
20948
17166
5548
5182
4303
Electron binding energies (eV)
Element
15kV beam…
K
L-I
L-II
L-III
M-I
M-II
M-III
1s
2s
2p1/2
2p3/2
3s
3p1/2
3p3/2
6 C
284.2*
7 N
409.9*
37.3*
8 0
543.1*
41.6*
11 Na
1070.8+
63.5+
30.65
30.81
12 Mg
1303.0+
88.7
49.78
49.50
13 Al
1559.6
117.8*
72.95
72.55
14 Si
1839
149.7*b
99.82
99.42
15 P
2145.5
189*
136*
135*
16 S
2472
230.9
163.6*
162.5*
26 Fe
7112
844.6+
719.9+
706.8+
91.3+
52.7+
52.7+
29 Cu
8979
1096.7+
952.3+
932.7
122.5+
77.3+
75.1+
57 La
38925
6266
5891
5483
1362*b
1209*b
1128*b
82 Pb
88005
15861
15200
13035
3851
3554
3066
92 U
115606
21757
20948
17166
5548
5182
4303
Electron binding energies (eV)
Element
20kV beam…
K
L-I
L-II
L-III
M-I
M-II
M-III
1s
2s
2p1/2
2p3/2
3s
3p1/2
3p3/2
6 C
284.2*
7 N
409.9*
37.3*
8 0
543.1*
41.6*
11 Na
1070.8+
63.5+
30.65
30.81
12 Mg
1303.0+
88.7
49.78
49.50
13 Al
1559.6
117.8*
72.95
72.55
14 Si
1839
149.7*b
99.82
99.42
15 P
2145.5
189*
136*
135*
16 S
2472
230.9
163.6*
162.5*
26 Fe
7112
844.6+
719.9+
706.8+
91.3+
52.7+
52.7+
29 Cu
8979
1096.7+
952.3+
932.7
122.5+
77.3+
75.1+
57 La
38925
6266
5891
5483
1362*b
1209*b
1128*b
82 Pb
88005
15861
15200
13035
3851
3554
3066
92 U
115606
21757
20948
17166
5548
5182
4303
Electron binding energies (eV)
Element
50kV beam…
K
L-I
L-II
L-III
M-I
M-II
M-III
1s
2s
2p1/2
2p3/2
3s
3p1/2
3p3/2
6 C
284.2*
7 N
409.9*
37.3*
8 0
543.1*
41.6*
11 Na
1070.8+
63.5+
30.65
30.81
12 Mg
1303.0+
88.7
49.78
49.50
13 Al
1559.6
117.8*
72.95
72.55
14 Si
1839
149.7*b
99.82
99.42
15 P
2145.5
189*
136*
135*
16 S
2472
230.9
163.6*
162.5*
26 Fe
7112
844.6+
719.9+
706.8+
91.3+
52.7+
52.7+
29 Cu
8979
1096.7+
952.3+
932.7
122.5+
77.3+
75.1+
57 La
38925
6266
5891
5483
1362*b
1209*b
1128*b
82 Pb
88005
15861
15200
13035
3851
3554
3066
92 U
115606
21757
20948
17166
5548
5182
4303
Kα
ψp1
ψp
ψp2
ψ1s
Kβ
ψp1
ψp
ψp2
ψ1s
Energy (or wavelength) of an X-ray depends on
Which shell ionization took place
Which shell relaxation electron comes from
K radiation
Electron removed from K shell
Kα
electron fills K hole from L shell
Kβ
electron fills K hole from M shell
L radiation
Electron removed from L shell
Lα
electron fills L hole from M shell
Lβ
electron fills L hole from M or N shell
Karl Manne
Siegbahn
depends on which b transition – which L level ionized and which M
or N level is the source of the de-excitation electron
Energy level representation of
characteristic X-ray emission process
Vacuum
Valence level
M…
Kα
LIII (2p3/2)
LII (2p1/2)
LI (2s)
Sufficiently energetic
beam electron ionizes
K shell…
K (1s)
L1 (2s) → K (1s) , why not?
Selection rules for allowed transitions involving photon emission
(conservation of angular momentum)
Change in n (principal) must be ≥ 1
Change in l (subshell) can only be +1 or -1
Change in j (total angular momentum) can only be +1, -1, or 0
The photon, following Bose-Einstein statistics, has an intrinsic angular
momentum (spin) of 1.
So a K-shell vacancy must be filled by an electron from a p-orbital, but
can be 2p (L), 3p (M), or 4p (N)
So can’t fill K from L1 (2s) in transitions involving photon
emission
X-Ray lines and electron transitions
Normal (diagram) level
Energy level (core or valence) described by removal of single
electron from ground state configuration
Diagram lines
Originate from allowed transitions between diagram levels
Non-diagram (Satellite) lines
Generally originate from multiply-ionized states
Two vacancies of one shell (e.g. two K ionizations) → hypersatellite
Other effects from: Auger effect,
Coster-Kronig (subshell) transitions, etc.
Originally
Ionized
shell
Filled
from…
Energy of Kα X-Ray
Bohr’s Three Postulates:
1) There are certain orbits in which the electron is stable and does not
radiate
The energy of an electron in an orbit can be
calculated - that energy is directly proportional to the
distance from the nucleus
Bohr simply forbids electrons from occupying just any orbit around the
nucleus such that they can’t lose energy and spiral in…
2) When an electron falls from an outer orbit to an inner orbit, it loses
energy
…expressed as a quantum of electromagnetic radiation
3) A relationship exists between the mass, velocity and distance from
the nucleus of an electron and Planck’s quantum constant…
From these principles, Bohr realized he could calculate the energy
corresponding to an orbit:
m = mass of electron
e = charge of electron
ħ = h / 2π
If an electron jumps from orbit n=2 to orbit n, the energy loss is:
energy is radiated, and expressing Plank’s relationship in terms of angular
frequency (ω), rather than frequency (ν):
Bohr theoretically has expressed Balmer’s formula and could
calculate the Rydberg constant knowing m, e, c, and ħ
Balmer and Paschen series in terms of frequency (n and m
are integers)…
Multply both sides by Plank’s constant, h …Bohr
assumes this is equal to the energy difference
between two stationary states….
Single set of energy values to account
for E differences…
And binding
energy…
Electron bound to +
nucleus
n identifies a stationary state
Bohr assumes that proton and electron orbit around center of mass to
derive orbital frequency of electron, then, arrives at an expression for
radiation frequency for electron cascading through stationary states…
From expression of binding energy, and orbital
frequency of electron, and solving for R in
terms of physical constants…
For large n
m = mass of electron
e = charge
ε= permittivity
constant
From Coulomb’s Law
Substituting the expression for R into expression for
binding energy, gives binding energies of stationary
states (Z is atomic #)
Now, an electron making K transition moves in field of force –
potential energy function:
Seeing the charge of the
nucleus (Z-1)e, and the
other n=1 electron.
And from the equation above for binding
energy, the transition energy is…
An approximate expression for the energy of
the Kα X-Ray (Bohr’s early quantum theory)
Or about (10.2 eV)(Z-1)2
So:
O = 0.5 keV
Si = 1.7 keV
Ca = 3.7 keV
Fe = 6.4 keV
Moseley’s Law
Niels Bohr
X-Ray energy is related to Z…
empirical relationship
E = A(Z-C)2
(A and C are constants)
Bohr theory prediction for Kα
…
Kα
Kβ
Henry Moseley
E = (10.2)(Z-1)2
Produce overall X-ray spectrum
Characteristic peaks superimposed on a continuum background
X-rays can be detected and displayed
discriminated either by energy (E) or wavelength (λ)
Energy Dispersive Spectrometry (EDS)
Background
Complex spectrum from monazite (Ce, La, Nd, Th) PO4
For heavy elements
Complex spectra → peak overlaps
Note low pk / bkg for Th
Wavelength Dispersive Spectrometry (WDS)
SiKα
Si in garnet (pyrope)
TAP monochromator
CaKα (2nd order)
SiKβ
For heavy elements
Complex spectra → peak overlaps
Note low pk / bkg for Th
Monazite (LIF monochromator) in wavelength region of NdL
EDS spectrum
Depth of production of X-Rays
X-Rays generated over much of the interaction volume
Characteristic X-Rays produced in electron range where electron energy
exceeds critical excitation potential
Z dependent
Recall ionization energies (keV)…
K
Si
1.55
Ca
4.03
Fe
7.10
Sn
29.1
Pt
L
M
4.46
13.9
3.3
X-Ray region will be dependant on both Z and
density (ρ)
Φ(ρZ)
High density = limited depth of production
Deeper production for low energy ionizations
X-Ray spatial resolution
3 g/cm3
20 keV
10 g/cm3
Run PHIROZ95, Casino, Win X-Ray
Compare effects of
different beam energies
different materials
Different lines generated in different regions of interaction volume
Depends on electron energy distribution so function of:
Initial voltage
Material properties (Z, ρ)
Critical excitation potentials for ionization events of interest
75%
50%
25%
10%
5%
Energy contours
Electron energy
100%
Labradorite [.3-.5 (NaAlSi3O8) – .7-.5 (CaAl2Si2O8), Z = 11]
15 kV
1%
10 kV
50%
1 mm
5 kV
25%
(~ Ca K ionization energy)
10%
5%
5%
1 kV
(~ Na K ionization energy)
10%
25%
50%
75%
100%
Labradorite [.3-.5 (NaAlSi3O8) – .7-.5 (CaAl2Si2O8), Z = 11]
15 kV
Three main conclusions:
For same material:
line
M
L
K
generation volume
large
medium
small
K line of heavy element is excited from smaller region than K line
of light element
K line of an element is excited from smaller volumes in denser, or
higher average Z materials
Putting it together…
Pb, Th, and U in monazite
Ionization energy for PbM-V level (to generate PbMα) = 2.484 keV
Ionization energy for ThM-V level = 3.332 keV
Ionization energy for UM-IV level (to generate UMβ) = 3.728 keV
will be trace element so ~ double the overvoltage to get
reasonable count rates
= 8 keV (minimum beam energy)
2.484 keV ionization potential…
This is the lowest required energy of the three elements (Pb, Th, U)
and will, therefore, limit the analytical resolution
beam voltage
5
10
15
20
25
30
% of beam voltage
49.68
24.84
16.56
12.42
9.936
8.28
5 keV
(2.484 keV ionization potential for Pb M-V level
is ~50% of the beam energy)
Monte Carlo simulation
Electron paths
Energy contours
50%~
40nm
15 keV (2.484 keV ionization potential for Pb M-V level
is ~17% of the beam energy)
Monte Carlo simulation
Electron paths
Energy contours
17%
~480nm
2,500
Analysis resolution in monazite
Depth of PbM-V ionization (nm)
2,000
1,500
1,000
500
0
0
5
10
15
20
Accelerating voltage (keV)
25
30
35
800
Analysis resolution in monazite
700
Remember, voltage limited to minimum
of 8 kV (2x ionization energy of UM-IV)
Depth of PbM-V ionization (nm)
600
500
Spatial resolution limit is then ~120 nm
400
300
200
100
0
0
2
4
6
8
10
Accelerating voltage (keV)
12
14
Analytical spatial resolution:
DAR = (Dbeam2 + Dscattering2)1/2
Dbeam = beam diameter
Dscattering = scattering dimension, either
depth or radial distribution defined by xray emission volumes
Based on depth containing 99.5% of total emitted intensity
Based on radius containing 99.5% of intensity
2000
φ(ρZ) Analytical
Resolution
PbMα in Monazite
AR Pb Mα (nm)
1500
D Beam
(nm)
1000
800
600
500
400
300
50
10
0
0
AR Pb Mα (nm)
2000
10
E0 keV
20
30
20
30
Radial Analytical
Resolution
PbMα in Monazite
1500
D Beam
(nm)
1000
800
600
500
400
300
50
10
0
0
10
E0 keV
500
Beam
diameter
400 nm
AR Pb Mα (nm)
400
300 nm
300
200 nm
200
Analytical Resolution
PbMα in Monazite
100 nm
Radial
φ(ρZ)
50 nm
10 nm
100
4
5
6
7
8
E0 keV
9
10
11
Other signals from inelastic scattering
Auger process
Core level ionization
De-excitation via internal conversion and emission of another electron rather than X-Ray
→
doubly ionized state
Can result in satellite X-ray emission (Characteristic of electron configuration)
e- (KLILIII)
Vacuum
X-ray
emission
Ka2
Vacuum
Auger
process
Valence level
Valence level
M…
M…
LIII (2p3/2)
LII (2p1/2)
LI (2s)
LIII (2p3/2)
LII (2p1/2)
LI (2s)
K (1s)
K (1s)
Very small perturbation on background of emitted electrons - Very low yield
Low energy - emitted from surface ~ 0.1nm depth (surface analysis technique)
Auger spectroscopy
Sample upper 20Å or so and evaluate kinetic energy of
emitted electrons.
Materials Evaluation and Engineering, Inc.
http://mee-inc.com/
Cathodoluminescence
Some insulators and semiconductors emit photons in the visible
and UV when exposed to the electron beam
~ empty conduction band
~ full valence band
The band gap has characteristic energy
1) Promote electron to conduction band
Electron – hole pair
2) Recombination
3) Excess energy = band gap energy
Expressed as photon (visible)
Cathodoluminescence
Emitted photon energy =
full band gap energy
Emitted photon energy =
impurity donor level
ν = E(gap) / h
ν = E(gap-d) / h
Conduction band
Almost Empty
Eg
bandgap
donor level
Valence band
Almost Full
Initial state
1. Inelastic scattering imparts
energy to specimen. Electron
promoted to conduction band.
2. Recombination of electron-hole
pair results in photon emission
Electron promoted from
impurity donor level
100 mm
Sandstone, secondary electron image
100 mm
Panchromatic CL image. Bright = K-fsp, dark = quartz.
40x60 micron 560nm
CL image of diatoms
2.0-1.95 eV. Non-bridging
hole centers
2.15eV. Self-trapped
excitons related to Si
nanoclusters?
16x12 micron 560nm
CL image of diatoms
Butcher et al. (2003) Photoluminescence and
Cathodoluminescence Studies of Diatoms – Nature’s Own NanoPorous Silica Structures
Integration of WDS and
cathodoluminescence
mapping. InGaN
epilayers.
In:Ga ratio
0.13
40000
428nm
0.11
4000
418nm
CL counts
Peak CL wavelength
Edwards et al. (2003) Simultaneous composition mapping and hyperspectral
cathodoluminescence imaging of InGaN epilayers
Cathodoluminescence spectrum
Shifts energies and / or intensities due to impurities or
crystal dislocations and other defects
thin
bulk
Thin with lattice
defects
Spectrum from GaAlAs