Beam – Specimen Interactions Signals Backscattered Electrons Beam electrons scatter, and escape...
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Transcript of Beam – Specimen Interactions Signals Backscattered Electrons Beam electrons scatter, and escape...
![Page 1: Beam – Specimen Interactions Signals Backscattered Electrons Beam electrons scatter, and escape out of specimen primary signal from elastic scattering.](https://reader035.fdocument.pub/reader035/viewer/2022062304/56649cb05503460f94975232/html5/thumbnails/1.jpg)
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
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Backscattered Electrons:
Atomic # dependence
More trajectories intersect surface with higher Z target
Al Au
1μm η = 14.0% 0.2 μm η = 53.5%
Au – same scale as Al
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η = -0.0254 + 0.016Z – 1.86X10-4Z2 + 8.3X10-7Z3
For multi-component material: η = ∑Ciηi
Weak Z contrast
Strong Z contrast
Atomic Number
0 20 40 60 80 1000.0
0.1
0.2
0.3
0.4
0.5
0.6
Bac
ksca
tter
coe
ffic
ient
η
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Si target
00 tilt η=17.5
450 tilt η=30.0
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Backscattered electrons:
Energy distribution
BSE have usually undergone a number of scattering events in target prior to emerging
Al Pb
0 E0 0 E0
Light elements = broad distribution most BSEs E << E0
Heavy elements = distribution skewed toward E0
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Backscattered electrons:
Spatial distribution
Electrons may emerge from an area outside beam incidence area
Al Pb
0 0
Light elements = broad distribution Heavy elements = narrow distribution
2 μm
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Backscattered Electrons
Greater energy loss farther from beam (more inelastic scattering events)
Better BSE resolution obtainable if select only highest energy BSEs
Distance from beam →
# BSE
BSEs within 10% of E0
All BSEs
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Beam – Specimen Interactions
Signals From Inelastic Scattering
• Secondary Electrons
• X-Rays
Continuum
Characteristic
• Auger Electrons
• Cathodoluminescence
Definition: Those electrons emitted with energy less than 50 eV
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
0 1.0
III
II
I
E/E0
dη/d
(E/E
0)In
tens
ity o
f S
E
Depth Z (nm)
0.0 2.5 5.0 7.5
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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)
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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
BSE5 λ
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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 SEtot
distance
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Influence of beam energy
η+δ
E1 E2E0 incident
Shape due mainly to variation in δ
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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
Si target
30kV
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10kV
20nm Au on Si substrate
30kVSE emission volume
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Beam – Specimen Interactions
Signals From Inelastic Scattering
• Secondary Electrons
• X-Rays
Continuum
Characteristic
• Auger Electrons
• Cathodoluminescence
Produced by deceleration of beam electrons in coulomb field of target atoms
→ 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
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X-ray emission from Cu
Cu Kα
Cu Lα
Energy (keV)
0 2 4 6 8 10
1
3
5
7
N x
10-6
pho
tons
/ e- S
ter
theoretical
Actual – due to sample and window absorption + low detector efficiency
Cu Kβ
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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
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Beam – Specimen Interactions
Signals From Inelastic Scattering
• Secondary Electrons
• X-Rays
Continuum
Characteristic
• Auger Electrons
• Cathodoluminescence
INNER SHELL IONIZATION
1) If energy equal or greater than critical excitation potential…
Can eject inner shell electron
2) Atom wants to return to ground stateouter shell electron fills vacancy –
relaxation
Outer shell electron = higher energy state relative to inner shell electron
some energy surplus in the transition → photon emission (X-ray)
Kα
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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 =1.740 keV (7.125Å)E FeKα = 6.404 keV (1.936Å)
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Polar coordinates…
Quantum state of an electron - Quantum numbers
Ψ(r,θ,Φ) = R(r)P(θ)F(Φ)nRadial componentPrincipal quantum number
lColatitudeOrbital quantum number
Ml
AzimuthalMagnetic quantum number
Yields three equations for three spatial variables
Space geometry of the solution of the Schrodinger equation for the hydrogen atom…
Z
X
Y
θΦ
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Rudi WinterAberystwyth University
Quantum state of an electron - Quantum numbersn Principal (shell) 1, 2, 3, …
radial = size K, L, M…
l Orbital – angular momentum
(subshell) 0 to n-1
s (sharp) l = 0
p (principal) l = 1
d (diffuse) l = 2
f (fundamental) l = 3
shape so if n = 2, l = 1: 2pml 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
3 sp
atial
coo
rdin
ates
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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
J Total angular momentum (quantum number j )
l +/- ½ = l + ms
(except l = 0, where J = ½ only)
Rudi WinterAberystwyth University
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The Orbitron:
Mark Winter, Univ. of Sheffield http://winter.group.shef.ac.uk/orbitron
1s 2p
4f
3d
5f
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Quantum Numbers for Electrons in Atomic Electron ShellsX-ray
notationModern 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
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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)
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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)
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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) 2kV beam…
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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) 15kV beam…
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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) 20kV beam…
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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) 50kV beam…
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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 radiationElectron removed from L shellLα electron fills L hole from M shellLβ electron fills L hole from M or N shell
depends on which transition – which L level ionized and which M or N level is the source of the de-excitation electron
Karl Manne Siegbahn
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Energy level representation of Energy level representation of characteristic X-ray emission characteristic X-ray emission processprocess
Kα
L1 (2s) → K (1s) , why not?
Sufficiently energetic beam electron ionizes K shell…
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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
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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.
X-Ray lines and electron transitions
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Originally Ionized shell
Filled from…
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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…
Energy of Kα X-Ray
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From these principles, Bohr realized he could calculate the energy corresponding to an orbit:
m = mass of electrone = charge of electronħ = h / 2π
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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
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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…
Electron bound to + nucleus
And binding energy…
n identifies a stationary state
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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…
For large nFrom expression of binding energy, and orbital frequency of electron, and solving for R in terms of physical constants…
m = mass of electron
e = charge
ε= permittivity constant
From Coulomb’s Law
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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…
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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
An approximate expression for the energy of the Kα X-Ray (Bohr’s early quantum theory)
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Moseley’s Law
X-Ray energy is related to Z…
empirical relationship E = A(Z-C)2
(A and C are constants)
Bohr theory prediction for Kα … E = (10.2)(Z-1)2
Kβ
Kα
Niels Bohr
Henry Moseley
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Produce overall X-ray spectrumCharacteristic peaks superimposed on a continuum background
X-rays can be detected and displayeddiscriminated either by energy (E) or wavelength (λ)
Energy Dispersive Spectrometry (EDS)
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Background
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Complex spectrum from monazite (Ce, La, Nd, Th) PO4
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For heavy elements
Complex spectra → peak overlaps
Note low pk / bkg for Th
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Wavelength Dispersive Spectrometry (WDS)
Si in garnet (pyrope)
TAP monochromator
SiKα
CaKα (2nd order)
SiKβ
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For heavy elements
Complex spectra → peak overlaps
Note low pk / bkg for Th
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Monazite (LIF monochromator) in wavelength region of NdL
EDS spectrum
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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 L M
Si 1.55
Ca 4.03
Fe 7.10
Sn 29.1 4.46
Pt 13.9 3.3
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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
3 g/cm3 10 g/cm320 keV
X-Ray spatial resolution
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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
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5%
10%
25%
50%
75%
Labradorite [.3-.5 (NaAlSi3O8) – .7-.5 (CaAl2Si2O8), Z = 11]
15 kV
Electron energy100% 1%
Energy contours
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Labradorite [.3-.5 (NaAlSi3O8) – .7-.5 (CaAl2Si2O8), Z = 11]
5%
10%
25%
50%
75%
100%
15 kV
10 kV
5 kV1 m
5%
10%
25%
50%
1 kV(~ Na K ionization energy)
(~ Ca K ionization energy)
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Three main conclusions:
For same material: line generation volumeM largeL mediumK 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
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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 keVwill be trace element so ~ double the overvoltage to get reasonable count rates
= 8 keV (minimum beam energy)
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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 % of beam voltage
5 49.68
10 24.84
15 16.56
20 12.42
25 9.936
30 8.28
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Monte Carlo simulation Electron paths Energy contours
5 keV (2.484 keV ionization potential for Pb M-V level is ~50% of the beam energy)
50%~ 40nm
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Monte Carlo simulation Electron paths Energy contours
15 keV (2.484 keV ionization potential for Pb M-V level is ~17% of the beam energy)
17% ~480nm
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Remember, voltage limited to minimum of 8 kV (2x ionization energy of UM-IV)
Spatial resolution limit is then ~120 nm
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Analytical spatial resolution:DAR = (Dbeam
2 + Dscattering2)1/2
Based on depth containing 99.5% of total emitted intensity
Dbeam = beam diameterDscattering = scattering dimension, either depth or radial distribution defined by x-ray emission volumes
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Based on radius containing 99.5% of intensity
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D Beam (nm)
300
D Beam (nm)
800
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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)
Very small perturbation on background of emitted electrons - Very low yield
Low energy - emitted from surface ~ 0.1nm depth (surface analysis technique)
e- (KLILIII)
K2
X-ray X-ray emissionemission
Auger Auger processprocess
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Auger spectroscopy
Sample upper 20Å or so and evaluate kinetic energy of emitted electrons.
Materials Evaluation and Engineering, Inc. http://mee-inc.com/
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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)
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Conduction band Almost Empty
Valence band Almost Full
Eg bandgap
Cathodoluminescence
Initial state1. 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
Emitted photon energy = full band gap energy
ν = E(gap) / h
Emitted photon energy = impurity donor level
ν = E(gap-d) / h
donor level
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Sandstone, secondary electron imageSandstone, secondary electron image
100 m 100 m
Panchromatic CL image. Bright = K-fsp, dark = quartz.Panchromatic CL image. Bright = K-fsp, dark = quartz.
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40x60 micron 560nm 40x60 micron 560nm CL image of diatomsCL image of diatoms
16x12 micron 560nm 16x12 micron 560nm CL image of diatomsCL image of diatoms
Butcher et al. (2003) Photoluminescence and Cathodoluminescence Studies of Diatoms – Nature’s Own Nano-Porous Silica Structures
2.0-1.95 eV. Non-bridging hole centers
2.15eV. Self-trapped excitons related to Si nanoclusters?
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CL countsCL countsIn:Ga ratioIn:Ga ratio Peak CL wavelengthPeak CL wavelength
0.130.13
0.110.11
4000040000
40004000
428nm428nm
418nm418nm
Edwards et al. (2003) Simultaneous composition mapping and hyperspectral cathodoluminescence imaging of InGaN epilayers
Integration of WDS and cathodoluminescence mapping. InGaN epilayers.
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Cathodoluminescence spectrum
Shifts energies and / or intensities due to impurities or crystal dislocations and other defects
Spectrum from GaAlAs
bulk
thin
Thin with lattice defects