Il Microscopio Elettronico in Trasmissione: principi di

Il Microscopio Elettronico in
Trasmissione: principi di
f
funzionamento
Scuola CIGS preparazione campioni TEM
18-19 Maggio 2009
Stefano Frabboni
Dipartimento
Di
ti
t di Fi
Fisica
i
Università di Modena e Reggio E.
e CNR-INFM-S3
Physics Department
University of Modena and Reggio Emilia
Physics Department
University of Modena and Reggio Emilia
1
Electron
Fundamental constants
De Broglie wavelength
λnon rel =
λ rel
h
=
p
1.22
E (eV )
h
h
= =
p ⎡
⎛
eE
⎢2m0 eE ⎜⎜1 +
2
⎝ 2 m0 c
⎣⎢
⎞⎤
⎟⎥
⎟⎥
⎠⎦
‐1.602 x10‐19C
9.109 x10‐31kg
511 keV
34 J s
6.626 x10‐34
4.14 x10‐15eV s
2.998 x108m/s
e
m0
m0 c 2
h
nm
1/ 2
c
E
(kV)
λnon rel
λ rel
(pm)
(pm)
γ
m/m0
v
(108m/s)
100
3.86
3.70
1.196
1.644
200
2.73
2.51
1.391
2.086
300
2.23
1.97
1.587
2.330
Physics Department
University of Modena and Reggio Emilia
8 anni fa
oggi: 0.07nm!!
Physics Department
University of Modena and Reggio Emilia
2
Analisi strutturali e composizionali con
AEM/HREM
Riconoscimento di una struttura nota
• Composizione chimica (EDX and EELS))
• Dimensioni e simmetria cella unitaria da
confrontare con data-base di strutture note
((D&I))
• Funzione radiale negli amorfi (D, EXELFS)
Determinazione del tipo di stato
condensato (Diffrazioni & Immagini)
• amorfo
• policristallo
• monocristallo
Caratterizzazione di modifiche a strutture
note analisi difetti cristallografici
• Campi di deformazione ⇒ strain ( D& I )
• Misure di disordine statico ((D))
• Studio difetti cristallografici (D,I)
(HREM+Image Simulation)
• Mappe elementali (EDXS, EELS)
Determinazione di una nuova struttura
• Composizione chimica (EDX, EELS))
• Dimensioni e simmetria cella unitaria
(D& I)
• Posizioni atomiche nella cella unitaria
(D& I)
• Studio del legame chimico
(D & ELNES)
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Outline (1)
• Un po’ di ottica:
– lente sottile,
– teoria di Abbe
– aberrazioni
– Risoluzione: point-spread-function e funzione di trasferimento:
• TEM
– elementi elettro-ottici del TEM
•
Sorgenti, lenti magnetiche, spettrometro-filtro energetico (Gatan Imaging Filter)
General Reference
D.B.Williams and C. Barry Carter
“Transmission Electron Microscopy” Plenum Press 1996
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3
Outline (2)
•TEM-interazione elettrone campione
•Interazione elastica:
•modo diffrazione :
•a fascio parallelo (SAD) e a fascio convergente (CBED)
•CBED
CBED filtrato
filt t in
i energia
i (EFCBED)
•modo immagine.
•Contrasto di diffrazione o di ampiezza
•Contrasto di fase o alta risoluzione
•risoluzione spaziale e danno da radiazione:criterio di Rose.
• Interazione anelastica:
•spettri di perdita di energia (EELS)
•immagini e diffrazioni spettroscopiche (EFTEM)
•Microanalisi a raggi X (EDX)
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Lente sottile
Legge di Gauss
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4
Lente sottile
Legge di Gauss
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Convergent thin lens: the focal plane
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5
Teoria di ABBE
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MainAberrations
Aperture (diffraction)aberration
Spherical aberration
Chromatic aberration
ρ A = 0.61
λ
βA
ρ s = C sβ 3
ρ c = C c (ΔE / E)β
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6
Sperical aberration correction
ρ s = C sβ 3
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Cromatic aberration
n(λ) leads to different
focal length for different
wavelength
ρ c = C c (ΔE / E)β
Correction:
Acromatic doublet
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7
Il limite !!
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Teoria di ABBE
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8
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9
Thermoionic emission
LaB6
Figura 4 - Caratteristica del cannone elettronico
from Williams, Carter “Transmission electron microscopy”
Physics Department
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Axial Brightness of the electron source
Ω=2π(1-cosθ)
B = J/Ω [Amp/m2sterad]
Ιt pprovides the current densityy in the solid angle
g
2
that, for small aperture angles is πθ , so that:
Β= J/π θ2 =4 i/ π2 dg2 θ2
Reduced Brightness: Br = B/V conserved along the electron column
This means that current density and the apertures cannot be changed
independently but are related by the gun brightness
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from Williams, Carter “Transmission electron microscopy”
Schottky Emission
1/x
x
The lowering of the potential barrier is ΔΦ ~ 0.4eV
for V ~ 106V/cm
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Physics Department
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11
L.Reimer “Transmission Electron Microscopy”
Springer (1989)
Physics Department
University of Modena and Reggio Emilia
Magnetic deflection (focusing)
F=qvxB
v⊥B⇒
r=
mv
v
=
qB ωc
Hp ::
v // B ⇒ no deflection
r
v
^
B
ρ=
z
Helical trajectories :
Lz =
^
; B = −Bz z
v z = v cos θ
θ
O
^
v = vr r+ v z z
m vx m v
=
sen θ
qB
qB
Lz = vzT= vz2π/ωc
2π mvv
2π mvv ⎛ 1 2
⎞
⎛ 1 2
⎞
cos θ =
⎜1 − θ + ....⎟ = L 0 ⎜1 − θ + .... ⎟
qB
qB ⎝ 2
⎠
⎝ 2
⎠
Δz =
L0 2
L
θ ⇒ ρ = Δ z tan θ ≈ 0 θ 3 ≈ CSθ 3
2
2
Spherical
aberration
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12
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Round Magnetic lens
η=e/m
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Resolution
ρ = [ρ 2A + ρs2 + ρ c2 ]1/ 2
For an electro-optical system
limited by the spherical aberration
⎛ λ
⎝ Cs
β optp = 0.77⎜⎜
⎞
⎟⎟
⎠
1/ 4
~6mrad at 200 keV, Cs=0.5mm
ρ min = 0.91(C s λ3 )
1/ 4
~ 1 nm
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0.1nm resolution?
λ 200 keV = 0.0025nm
d = 0.1nm
⎛ λ
βopt = 0.77⎜⎜
⎝ Cs
C s = 0.5 mm
θ~
1/ 4
⎞
⎟
⎟
⎠
λ
d
~ 25mrad
d ~ 4 β opt
βopt = 6.5 mrad
ρ min = 0.91(C s λ3 )
1/ 4
~ 1 nm
Cs compensation
TEOREMA DI SCHERZER!!
Defocused Many Beam Interference (Coherent) image at Scherzer (res:0.2nm)
Many Beam Interference image with Sextupole Cs correctors (res:0.07nm)
Electron holography (res:0.1nm)
Lensless Imaging (Electron Phtychography) (res:0.07nm)
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Diffraction
Image mode
from Williams, Carter
“Transmission electron
microscopy”
10 nm
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Detector: CCD camera
Linear Dyn range
104 counts
Number of pixels
Pixel size
210x210-211x211
25x25micron2
PSF h(i,j)
(f
(from
MTF)
2-5 pixels
DQE
[SNRout/SNRin]2
~0.8
(100-1000)e/pix
Gain (g)=(<I>)/<Ne>:
2
I raw (i, j ) = g ⋅ h(i, j ) ⊗ I 0 (i, j ) + B (i, j )
I (i, j ) =
I raw (i, j ) − I dark (i, j )
I gain (i, j ) − I darkref (i, j )
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15
From : R.F. Egerton, “Electron Energy Loss spectroscopy in the electron microscope”
The spectrometer
•Cromatic image in the x,z plane
•Acromatic image in the y,z plane
r=
mv
eB
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University of Modena and Reggio Emilia
GIF 200
Q1, Q2: focus of the spectrum on the slit plane
Q3, Q4: Preject the image screeen on the CCD 15x
S1‐S5: Sextupole lenses correct for second order aberrations and geometric distortion
Q5, Q6: project the slit plane on the CCD from Williams, Carter
“Transmission electron
microscopy”
Physics Department
University of Modena and Reggio Emilia
16
L.Reimer “Transmission Electron Microscopy”
Springer (1989)
8 anni fa
oggi: 0.07nm!!
Physics Department
University of Modena and Reggio Emilia
Tecniche di Analisi del TEM
Scuola CIGS preparazione campioni TEM
18-19 Maggio 2009
Stefano Frabboni
Dipartimento
Di
ti
t di Fi
Fisica
i
Università di Modena e Reggio E.
e CNR-INFM-S3
Physics Department
University of Modena and Reggio Emilia
17
Analisi strutturali e composizionali con
AEM/HREM
Riconoscimento di una struttura nota
• Composizione chimica (EDX and EELS))
• Dimensioni e simmetria cella unitaria da
confrontare con data-base di strutture note
((D&I))
• Funzione radiale negli amorfi (D, EXELFS)
Determinazione del tipo di stato
condensato (Diffrazioni & Immagini)
• amorfo
• policristallo
• monocristallo
Caratterizzazione di modifiche a strutture
note analisi difetti cristallografici
• Campi di deformazione ⇒ strain ( D& I )
• Misure di disordine statico ((D))
• Studio difetti cristallografici (D,I)
(HREM+Image Simulation)
• Mappe elementali (EDXS, EELS)
Determinazione di una nuova struttura
• Composizione chimica (EDX, EELS))
• Dimensioni e simmetria cella unitaria
(D& I)
• Posizioni atomiche nella cella unitaria
(D& I)
• Studio del legame chimico
(D & ELNES)
Physics Department
University of Modena and Reggio Emilia
Outline (2)
•TEM-interazione elettrone campione
•Interazione elastica:
•modo diffrazione :
•a fascio parallelo (SAD) e a fascio convergente (CBED)
•CBED
CBED filtrato
filt t in
i energia
i (EFCBED)
•modo immagine.
•Contrasto di diffrazione o di ampiezza
•Contrasto di fase o alta risoluzione
•risoluzione spaziale e danno da radiazione criterio di
Rose.
• Interazione anelastica:
•spettri di perdita di energia (EELS)
•immagini e diffrazioni spettroscopiche (EFTEM)
•Microanalisi a raggi X (EDX)
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18
CTEM
HREM
SAED
CBED
Electron-specimen interactions
Backscatterd
Electrons
Incident
Electron
Beam
(200 kV)
Auger
Electrons
Visible
light
Characteristic
X-ray
EELS
EFTEM
Secondary
Electrons
thickness~ 100nm
EDXS
Bremsstrahlung
X-ray
Elastically
Scattered
Electrons
Direct beam
Inelastically
Scattered
Electrons
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PERCHE’ ASSOTTIGLIARE IL CAMPIONE?
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University of Modena and Reggio Emilia
19
Effetto dello spessore del
campione
sulla distribuzione energetica
del fascio trasmesso
t~200nm
t~40nm
t~400nm
t>1000nm
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University of Modena and Reggio Emilia
(Transmitted) Electron-specimen interactions
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University of Modena and Reggio Emilia
20
Small angle Elastic Scattering: (e-,atomic V(r))
Wentzel potential
First approx
few%
accuracy
V (r ) =
eZ
4πε 0 r
exp[− r / R ];
R = a H Z −1 / 3 ; a H = 0.0529nm : Bohr radius
Atomic scattering factor:
∞
2 m e e 2 (Z − f X ( q ) )
2πme
f e (q) =
V (r ) exp(− 2πiq ⋅ r )dr =
2
∫
h2
q2
h −∞
n
f e (q) = ∑ A j exp(− B j q 2 ), A j , B j fitting parameters (Peng et al.1996)
j =1
f X (q ) = ∫ ρ (r ) exp[−2πiq ⋅ r ]dr = ∫ ρ (r ) exp(−2πiq ⋅ r )
K0
K0
Ks
2θ
f(q)
(Å)
q
q=
ρ(r)= electronic
charge density
silicon
2 sin ϑ
λ
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-1
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q/2 (Å )
Elastic scattering from assembly of atoms:diffraction
f(q)
(Å)
f (q) =
2 m e e 2 (Z − f X ( q ) )
h2
s2
Scattered
crystal
Intensity
I(θ)
q/2=sin( θ)/λ (Å-1)
poly
Scattered
Intensity
amorphous
I(θ)
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21
Single elastic scattering approximation
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Working example :
Atomic scattering vs. diffraction
from R. Neder and T. Proffen (http://www.kri.physik.uni-muenchen.de/crystal/teaching/)
Physics Department
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Reciprocal Lattice
from R. Neder and T. Proffen (http://www.kri.physik.uni-muenchen.de/crystal/teaching/)
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Original structure: direct lattice
The structure chosen for this set of examples is an
artificial structure in the space group Pnnn. The lattice
constants have been chosen as 7.5, 10 and 12.5 Å.
Simple projection of the structure along [001]
from R. Neder and T. Proffen (http://www.kri.physik.uni-muenchen.de/crystal/teaching
/)
Physics Department
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Original structure:Fourier transform and reciprocal lattice
from R. Neder
and T. Proffen
(http://www.kri
.physik.uniphysik unimuenchen.de/cr
ystal/teaching/
)
Physics Department
University of Modena and Reggio Emilia
Modification:
Shift atom
Modification: Shift atom
Fourier Transform and Reciprocal lattice
from R. Neder and T. Proffen (http://www.kri.physik.uni-muenchen.de/crystal/teaching
/)
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Modification:
Shift atom
from R. Neder and T. Proffen (http://www.kri.physik.unimuuenchen.de/crystal/teaching/)
1. The intensity of the Bragg reflections is fully determined by the
Fourier transform of the unit cell.
2. The positions of the Bragg reflections remain invariant to changes of
within the unit cell.
3. The intensity of the Bragg reflections are changed if the atoms are
moved to new sites within the unit cell. This sensitivity forms the basis
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for successful structure refinements.
University of Modena and Reggio Emilia
Modification:
Expanding the
lattice
Close inspection
p
of the Fourier
transforms shows that the
corresponding maxima of the red
curve are slightly higher than those
of the blue curve. This increase is
due to the fact that the maxima
have shifted to smaller reciprocal
space vectors. Closer to the
reciprocal space origin the
scattering factors of the atoms are
larger and thus the calculated
intensity increases.
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Courtesy of R. Balboni , CNR IMM Bo
Physics Department
University of Modena and Reggio Emilia
Crystalline sample: The structure factor Fg
V(r): crystal potential
B(r): atomic/molecular base: potential veriation in the unit cell
L(r): Bravais lattice
V (r) = B(r ) ⊗ L(r ) where
+∞
L(r) = ∑ u ,v ,wδ (r − n1a + n2 b + n31c), B(r ) = ∑ j B j (r − rj )
−∞
a b,
a,
b c =lattice parameters
The Fourier trasform of V(r):
A(q ) = FT[V(r)]= FT[B(r)] • FT[L(r)] = FT[B(r)] • L-1(g)
q: reciprocal space vector, L-1(g) : reciprocal lattice, g: reciprocal lattice vector
+∞
L−1 (g) = ∑ h,k ,l δ (q − g )
−∞
A(q ) = FT[ B(r )] • L-1 (g) =
F
g
Ω0
=
1
Ω0
∑f
j
con
g = ha * + kb * + lc*
1
1
Fg
F (q) • L-1 (g) =
F (q) =
Ω0
Ω0
Ω0
g
[
(g) exp − 2πig • r j
]
j
Ω 0 = volume of the unit cell
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TEM sample
V(r ) = [B(r ) ⊗ L(r)] ⋅ S(r )
A(q ) = (FT[B(r )] • L-1 (g)) ⊗ FT[S(r)]
A(s) ∝
F
sin(πts)
, s = deviation Bragg condition, t = thickness
Ω 0 πs
g
Fg2 ⎛ sin(πts) ⎞ 2
I g (s, t ) = 2 2 ⎜
⎟
k Ω 0 ⎝ πs ⎠
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Diffraction
Image mode
10 nm
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27
CTEM and Selected Area Electron Diffraction
(SAED)
10 nm
2d hkl sin(θB ) = λ
transmitted
beam
D hkl
L
2
⎡
⎤
λL
3⎛ D ⎞
=
⎢1 + ⎜ hkl ⎟ + .....⎥
D hkl ⎢⎣ 8 ⎝ L ⎠
⎥⎦
2 sin(θB ) ≈ 2 tan(θB ) ≈ 2θB ≈
d hkl
Δd hkl
≈ 0.001 − 0.01
d hkl
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I hkl = js
2π 2 m 2 e 2
h
4
2
KNVcp hkl Vg λ2 d hkl
js densità di corrente, K: numero di cristalli con N celle unitarie Ve volume di una cella con N celle unitarie, V
volume di una cella
unitaria, phkl: molteplicità del piano hkl, Vg: fattore di struttura, λ lunghezza d’onda, dhkl
spaziatura dei piani.
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Multiple beam effetcs:
Conventional diffraction vs.
Convergent Beam Diffraction
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MgO/Fe/MgO
Cross section (image mode)
10nm
10nm
Misura dello spessore dei film
MgO (001)
Fe (001)
MgO (001)
Qualità delle interfaccia
Au
MgO
ΔtFe~ 9nm
ΔtMgO~ 12nm
50nm
Film Fe
Film MgO
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MgO/Fe/MgO Cross section (diffrazione)
MgO
Fe
MgO
Film superficiale di MgO: scarsa qualità cristallina,
presenza di MgO policristallino
Film Fe: presenza di due grani
(001), (101)
Substrato MgO: ottima qualità cristallina, MgO
perfettamente orientato secondo l’asse di zona (001)
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SiC/GaN heterostructures: polarity
determination
g=(0002)
GaN
[0001]
convergent
beam
SiC
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Many Beams interaction
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Polarity in Compound Semiconductors
EXPERIMENT
N
N
Ga
Ga
[0001]
SIMULATION
[0001]
[0001]
SIMULATION
[0001]
[0001]
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CBED patterns → analysis of high angle
diffracted beams
g3
2θ
g2
Ewald sphere
construction
HOLZ LINES
g1
g2
g1
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Symmetry and strain in Si/Si1-xGex/Si
heterostructures
30 nm
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32
CBED STRAIN
MEASUREMENTS
electron
probe
High Order Laue
Zones (HOLZ) lines
their p
position is very
y
sensitive to lattice
parameter variations
(strain) as:
Δθ
θ
=−
Δa ΔE 0
=
a
2E0
unstrained
silicon
strained silicon
(isotropic )10-3
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AUTOMATIC PROCEDURE
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33
Energy Filtered Diffraction, zero‐loss
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Energy Filtered CBED
Experimental
pattern
(Room temperature)
Experimental pattern
(energy filtered,
EW=5 eV, Room
temperature)
Simulation
(EMS software by P.
Stadelmann
(1987))
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Zero loss filtering: dependence of HOLZ line pattern on
energy window (EW) amplitude
EELS
spectrum
pixels
eV
pixels
eV
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35
Quantitative Diffraction and bonding
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MODO IMMAGINE
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36
The atom as a weak phase object
V (r ) =
eZ
4πε 0 r
exp[− r / R ];
R = a H Z −1 / 3 ; a H = 0.0529nm : Bohr radius
Lichte, Rep. Prog. Phys. 71 (2008) 016102
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Courtesy of A. Parisini, CNR IMM Bo
Physics Department
University of Modena and Reggio Emilia
37
Courtesy of A. Parisini, CNR IMM Bo
PB: Come trasformare l’informazione contenuta nella fase
Dell’onda trasmessa in Intensità osservabile?
•Filtraggio spaziale
•Piatto di fase
Courtesy of A. Parisini, CNR IMM Bo
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Filtraggio spaziale
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38
C
T
E
M
10 nm
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University of Modena and Reggio Emilia
Low resolution (~1nm)
imaging
Introduction to Electron
Microscopy and Microanalysis
Vick Guo 1985
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39
Amplitude contrast
Si
Ni
C
10 nm
hole
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Amplitude contrast: BF, DF
Fascio
incidente
Campione
Lente
Obiettivo
Diaframma
obiettivo
1° Immagine
Bright Field
Dark Field: Tilted
Mode
Introduction to Electron
Microscopy and Microanalysis
Vick Guo 1985
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40
Resolution
ρ = [ρ 2A + ρs2 + ρ c2 ]1/ 2
For an electro-optical system
limited by the spherical aberration
⎛ λ
⎝ Cs
β optp = 0.77⎜⎜
⎞
⎟⎟
⎠
1/ 4
~6mrad at 200 keV, Cs=0.5mm
ρ min = 0.91(C s λ3 )
1/ 4
~ 1 nm
Physics Department
University of Modena and Reggio Emilia
0.1nm resolution?
λ 200 keV = 0.0025nm
d = 0.1nm
⎛ λ
βopt = 0.77⎜⎜
⎝ Cs
C s = 0.5 mm
βopt = 6.5 mrad
1/ 4
⎞
⎟
⎟
⎠
θ~
λ
d
~ 25mrad
d ~ 4 β opt
Cs compensation
Defocused Many Beam Interference (Coherent) image at Scherzer (res:0.2nm)
Many Beam Interference image with Sextupole Cs correctors (res:0.07nm)
Electron holography (res:0.1nm)
Lensless Imaging (Electron Phtychography) (res:0.07nm)
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41
Phase object and Zernike phase plate
Physics Department
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Zernike phase plate
g( x ) = e iΦ ( x ) ≈ 1 + iΦ ( x ) a meno di termini quadratici
2
1 + iΦ ( x ) = 1 + Φ 2 ( x ) ≈ 1 a meno di termini quadratici
Ma se riesco a moltiplicare per i o la parte diffratta dall' oggetto Φ ( x ),
o quella trasmessa si ha :
2
1 − Φ ( x ) = 1 − 2Φ ( x ) + Φ 2 ( x ) ≈ 1 − 2Φ ( x ) a meno di termini quadratici
In the back focal plane of the objective lens :
Fourier Transform
g(u ) = F(g ( x )) = δ (u ) + iF(Φ ( x ))
g ⊗ (u ) = δ (u ) + iiF(Φ ( x )) = (δ (u ) − F(Φ ( x ) )
F −1 (g ⊗ (u )) = 1 − Φ ( x )
2
I = 1 − Φ ( x )) = (1 - 2Φ ( x ) + Φ 2 ( x )) ≈ 1 − 2Φ ( x )
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Aberrations and phase shifts
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43
Physics Department
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Courtesy of A. Parisini, CNR IMM Bo
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Formazione
dell’immagine in contrasto di
fase: Teoria di Abbe
f ( x, y ) = exp[−iσV p ( x, y )]
≈ 1 − iσV p ( x, y )
H
R
E
M
• e − iχ ( u , v ) • A ( u , v )
I( x, y) = 1 − 2σVpab ( x, y)
Physics Department
University of Modena and Reggio Emilia
Example of phase transfer function
sinχ
λ3
1
⎛1⎞ 1
χ ⎜ ⎟ = πC s 4 + πΔfλ 2
d
d
⎝d ⎠ 2
Optimum defocus (Scherzer defocus )Δf :
1
Δ f = − 1 . 2 (λ C s
)1 / 2
~ 43 nm
for optimum resolution
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Image simulation as a function of defocus, d, and thickness,t
Silicon, [110] direction, Cs=0.5mm λ=0.0025nm
White atoms
Black atoms
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High
Resolution
Experimental image [110]Si/amorphous Silicon interface
Electron
Microscopy
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46
Immagini HREM direttamente interpretabili
(debole oggetto di fase)
Au grain boundary [010]
orientation
InAsSb- InAs interface
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Il campione: Criterio di risoluzione di Rose
ρ2 =
e(S/N)2
fDC2
Radiation Damage
D : dose
e : carica elettrone
S/N : rapporto segnale rumore ≈ 5
f : efficienzadi raccolta≈ 1
C : contrasto (5%)
risoluzione ρ = 0.1nm
D = 16 C/cm2
risoluzione ρ = 0.5nm
D = 0.16 C/cm2
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Electron-specimen interactions
(inelastic-transmitted:EELS)
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Electron Energy Loss
Spectroscopy
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Energy Resolution
Energy resolution is limited by the
probe-energy distribution and
spectrometer resolution
Measure as width of the zero-loss peak
Probe energy resolution (depends
on gun current)
» W: 2-3 eV
» LaB6: >1 eV
» Warm FEG: 0.55-0.9 eV
» Cold W FEG: 0.25-0.5 eV
» Monochromated FEG:
– 0.01 eV demonstrated
– 0.1-0.3 eV typical use
– Approximately Gaussian
zero-loss peak
Physics Department
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EELS in TEM/STEM
•
Analyze energies of electrons transmitted through
the specimen
•
Advantages:
–
–
–
–
–
–
•
Spatial resolution in fixed beamTEM ~ d, the
electron beam size
Detectability ~ 10x better than EDS
Any solid
Qualitative analysis of any element of Z > 1
Quantitative analysis by inner-shell ionization
edges of elements
Rich signal includes chemical information, etc.
Difficulties:
–
–
–
Need very thin specimen: t < 40 nm
Intensity weak for energy losses ΔE > 300 eV
L- and M- edges not very obvious for some
elements
from Williams and Carter, Transmission
Electron Microscopy, Springer, 1996
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Three Spectral Regions
•
Zero-loss peak
– FWHM:energy resolution
– Very intense
•
Low-loss region
– 0-50 eV loss
– Plasmon losses
– Inter/intra band transition
•
Inner-shell ionizations
– 30 eV loss and higher
– Microanalysis
– Very low intensity
from Williams and Carter, Transmission
Electron Microscopy, Springer, 1996
from Williams and Carter, TransmissionPhysics
ElectronDepartment
Microscopy, Springer, 1996
University of Modena and Reggio Emilia
The Two EELS Modes
• Image Mode (image on the viewing screen)
– Spatial Selection
• Position analysis area on optic axis, lift screen
• Area selected is effective aperture size demagnified back to the specimen plane
• Spatial resolution poor (10-30 nm)
• Diffraction Mode (diffraction on the viewing screen)
– Spatial Selection
• Select area with focused beam
• Area selected is function of beam size and beam spreading
–
–
< 1 nm in FEG STEM at 0.5 nA
~ 10 nm in W electron gun at 0.5 nA
• Best for high spatial resolution microanalysis
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How to optimize your EELS
experiments by adjusting the
collection angle of your
spectrometer
Definition of α and β in a (S)TEM.
α is called the convergence semi-angle and is determined by the microscope’s
settings, especially the condenser lens and aperture. The α angles
corresponding to the different configuration of your TEM should be provided by
the TEM manufacturer or measured using a known diffraction pattern (cf. Fig.3.)
β is called the collection semi-angle and is determined by the objective aperture,
the spectrometer entrance aperture, the camera length and the mechanical
specification of the instrument. (This article will explain in detail how to measure
β for different configurations).
Physics Department
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Measure of the collection semi-angle β
Diffraction (or STEM-EELS) mode
β=(Radius of the spectrometer aperture) / (Camera
length × Geometric factor)
The “diffraction pattern” method. (only possible with GIFs)
Using the desired camera length (or choosing the “EELS” option of your
microscope), observe a diffraction pattern of a known structure on your
GIF camera. Looking at the shadow of the entrance aperture, the
collection angle
angle, β,
β can be determined using the known diffraction
pattern as a reference to calibrate your image. Even α can be obtained
by measuring the size of the diffraction spot as shown on Fig.3.
Aperture GIF e angolo di accettanza 2β ( totale) a 8mm di C.L., 200keV
Misurata da una SAD di Si 110 inserendo le aperture.
0 6 mm ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 5.5 mrad
0.6 mm 5 5 mrad
2mm‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 16‐18 mrad
3mm‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 24 mrad (estrapolazione)
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How does the collection angle
affect my experiments?
In EELS, the spectrometer measures the number of electrons that have lost a specific amount of energy. The excitation
of atoms in the sample will result in characteristic edges in the measured spectrum. The intensity of those edges is
directly proportional to the number of atoms present and the scattering cross section of the studied element. The cross
section is a function type of edge and depends strongly on the scattering angle.
It’s critical to have a collection angle large
enough to collect an important fraction of
the desired scattered signal. Moreover,
because the cross section’s angular
dependence varies significantly between
elements, β can have a strong influence on
the quantification calculation.
An easy way to know how large the collection angle, β ,
should be for your experiment is to evaluate the
characteristic angle for a particular energy-loss event,
θE=Eedge/2E
/ 0, where
h Eedge is the
h transition edge
d energy andd
E0 is the energy of the incident electron beam. With a β ~ 3
θE, it’s usually possible to collect about half of the signal,
which should be appropriate for most of applications.
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Low‐Loss Region: Plasmons
•
Collective oscillations of weakly bound
electrons (conduction, valence band)
– Most prominent in free-electron metals
– But also present in semiconducting
materials
•
Analysis:
– Energy loss sensitive to changes in freeelectron density
– Microanalysis of Al and Mg alloys
•
Thickness measurements
– Plasmon mean-free-path, λp ~100 nm
– Multiple peaks for thick specimens
from Egerton
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52
Plasmons: applications
from Egerton
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University of Modena and Reggio Emilia
Thickness Measurements
• Log ratio method
⎛I ⎞
= ln⎜ T ⎟
λ
⎝ Io ⎠
t
λ is total mean free path for all
scattering
– IT is area under entire spectrum
– Io is area under zero-loss
– Subtract background
g
first for
best accuracy
Rough estimate of λ:
λ ∼ 0.8Εο nm
so for 100-keV electons
λ is 80-120
80 120 nm various
materials
Very thin specimens:
t = λp(Ip/Io)
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Inner‐Shell Ionization Losses
•
Inner-shell electron ejected by beam
electron
– We measure energy loss in beam
electron after event
•
Ionization event occurs before emission
of either x-ray or Auger electron emitted
– Get EELS signal regardless
•
Can observe “edges” for all inner-shell
electrons
– K
K-shell
shell electron (1s)
– L-shell electron (2s or L1) (2p or L2 , L3)
from Spence, in High Resolution Electron Microscopy, Buseck et al. (eds.),Oxford, 1987
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54
Edge Energy ‐ Edge Shape
• K-edge
– Ideal triangular “saw tooth”
sitting on background
• Intensity decreases beyond edge
– Less chance of ionization
above Ec since cross section
decreases with increasing E
c
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
Physics Department
University of Modena and Reggio Emilia
L‐Series Edges and White Lines
White lines
• Each element has
characteristic edge
g energy
gy
• Sharp white lines are
present when d-band
unfilled
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Edge Fine Structure
•
ELNES - electron loss near edge
structure
– Sensitive to chemical bonding
effects
– To ~ 50 eV beyond edge
•
EXELFS - extended energy-loss
fine structure
– Analogous to EXAFS
– Sensitive to atomic nearest
neighbors
– Located beyond 50 eV for several
hundred eV
from Williams and Carter, TransmissionPhysics
ElectronDepartment
Microscopy, Springer, 1996
University of Modena and Reggio Emilia
from Garvie, Craven, and Brydson, American Mineralogist, 79, (1984) 411-425
Carbon ELNES
Carbon K-edges of
minerals containing the
carbonate anion
compared with three
forms of pure carbon
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Tetrahedral vs. Octahedral
Si L2,3
Al L2,3
Crysoberyl
Rhodizite
Calculation for Al
octahedrally
coordinated to O
from Garvie, Craven, and Brydson (1984)
from Brydson (1989)
Physics Department
University of Modena and Reggio Emilia
Fe L2,3 Edge in Minerals
• Chemical shift
• Shape change
Almandine
Hedenbergite
Hercynite
Fe “orthoclase”
Brownmillerite
Andradite
Van Aken and Liebscher, Phys Chem Minerals 29 (2002) 188-200
Physics Department
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Oxidation State
• L3/L2 ratiosa
– Fe – FeO FeO
– Fe3O4
– γ‐Fe2O3
– α‐Fe2O3
3.8±0.3
46
4.6
5.2
5.8
6.5
(depends on peak stripping method)
• Chemical shiftb
– Fe Fe –> FeO 1.4±0.2 FeO 1.4±0.2
eV
from Colliex et al. (1991)
a.
b.
Colliex et al., Phys. Rev. B 44 (1991) 11,402-11,411
Leapman et al. Phys. Rev. B 26 (1982) 614-635
Physics Department
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EELS Quantification
• Single scattering in a very thin specimen assumed
• For each element assume:
PK = the
th probability
b bilit for
f ionization
i i ti
σK = the ionization cross section
N = number of atoms per unit area
IK = PK IT
⎛ t ⎞
PK = Nσ K exp⎜ ⎟
⎝ λK ⎠
IK ≈ Nσ K IT (very thin specimen, t ≈ 0)
I
N = K for a single element when IT is known
σ K IT
Not collecting all the electrons so we must use IK (β,Δ) and σ K (β,Δ)
where σ K (β,Δ) = partial ionization cross - section
See Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, Springer,
1996
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Department
University of Modena and Reggio Emilia
58
From :EELS
Charles Lyman
Lehigh University
Bethlehem, PA
EELS Quantification Procedure
Collect spectrum with
known collection angle
β from a very thin
specimen region
NA =
IA (β,Δ )
I A (β,Δ ) σ KB (β,Δ )
N
or A = KB
σ A (β,Δ
Δ )IT
N B IK (β,Δ
Δ ) σ KA (β,Δ
Δ)
Calculate (Ib = A E-r over δ =
20-50 eV) and remove
background under edge
Extracted
edge intensity
Integrate edge intensity
for a certain energy
window Δ
IA (β,Δ )
Determine sensitivitiy
factor called the “partial
ionization cross
section”
Low-loss
intensity ~
IT
IB (β,Δ )
Fitted
background
Courtesy J. Hunt
Physics Department
University of Modena and Reggio Emilia
Microanalysis Example
From :
EELS
Charles Lyman
Lehigh University
Bethlehem, PA
Courtesy J. Hunt
Physics Department
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Specimen Thicknesss Requirement
• Microanalysis requires a very thin
specimen
– Estimate by:
y
I
p
Io
≤
1
10
– Estimate thickness using:
t ≈ λp(Ip/Io) for very
thin only
– Assuming λp ~ 100 nm:
t ~ 10 nm for
microanalysis
from Williams and Carter, Transmission Electron Microscopy, Springer,
1996 Department
Physics
University of Modena and Reggio Emilia
If Plural Scattering Occurs…
Deconvolute to get this
For quantitation of
the ionization edge
we need a true
single scattering
distribution
Plural scattering
removed by a
deconvolution
procedure
from Williams and Carter, Transmission
Electron Microscopy, Springer, 1996
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Spatial Resolution
•
EELS not affected by beam spreading
like XEDS
– Only electrons within 2β are collected
•
Diffraction mode
•
TEM mode
– Beam size governs spatial resolution
– Selection apertures govern spatial
resolution
Lens aberrations will limit both
•
Delocalization
– Ionization by a “nearby” fast electron
EELS ionization loss spectra have been
obtained from single columns of atoms
Physics
Department
from Williams and Carter, Transmission Electron
Microscopy,
Springer, 1996
University of Modena and Reggio Emilia
Spatial resolution of EELS:
delocalization
from Egerton
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Atomic Resolution EELS Analysis
(S. Pennycook Group, ORNL)
Atomic-resolution Z-contrast STEM
image of CaTiO3 doped with La
La M4,5 edges
La M4,5 edges only observed in spectrum
collected directly from bright spot in image:
single-atom resolution
M. Varela et al, Phys. Rev. Lett. 92 (2004) 095502
Physics Department
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Summary
What Can We Get from EELS?
• Microanalysis by ionization-loss edges
– Light
Li ht element
l
t analysis
l i complements
l
t XES
• Specimen thickness measurements
– Complements XES when absorption correction needed
• Bonding information from near-edge fine structure (ELNES)
– Fingerprints of edge shape
• Reveal metal oxides, sulfides, carbides, nitrides, etc.
– Chemical shifts
• L3/L2 ratio can reveal a change in oxidation state
– Use known standards for comparison, e.g., Fe, FeO, Fe2O3, Fe304
• ……Interatomic distances from extended energy-loss fine structure
(EXELFS)
– Information similar to EXAFS, but from nano-sized region rather than the
bulk
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EFTEM
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Aberrazioni e risoluzione
Aberrazione sferica
ρ s = C sβ 3
Aberrazione di apertura
ρ A = 0.61
λ
βA
1/ 2
Aberrazione cromatica
⎡⎛ ΔV ⎞ 2 ⎛ ΔI ⎞ 2 ⎤
ρc = C c ⎢⎜
⎟ + 4⎜ ⎟ ⎥ β A
⎝ I ⎠ ⎥⎦
⎢⎣⎝ V ⎠
ρ = [ρ 2A + ρs2 + ρ c2 ]1/ 2
Per un sistema ottico limitato dalla aberrazione
sferica:
1/ 4
⎛ λ ⎞
βopt = 0.77⎜⎜ ⎟⎟
⎝ Cs ⎠
(
ρmin = 0.91 Cs λ3
)
1/ 4
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Useful Analogy: BF TEM
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Energy Filtered Images
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Energy-Filtered TEM (EFTEM)
Element Maps - Not Spectrum Images
Elemental Maps of a SiC/Si3N4 ceramic
Short Acquisition Time (3 maps, 250K pixels) = 50s
Carbon
RGB composite
Oxygen
Nitrogen
Courtesyy John Hunt,, Gatan
Physics Department
University of Modena and Reggio Emilia
EFTEM detection limits
•
Typically 2-5% local atomic concentration of most elements
–
–
•
1% is attainable for many elements in ideal samples
10% for difficult specimens that are thick or of rapidly varying thickness
Sensitivity limited by:
–
–
–
–
–
Diffraction contrast
Small number of background windows
Signal-to-noise
Thickness
Artifacts
•
If you can see the edge in the spectrum, you can probably map it
•
EFTEM spectrum image can map lower concentrations than the 3-window
method ( FEG and STEM!!!)
–
Better background fits because there are more fitting channels
Courtesy John Hunt, Gatan
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65
EFTEM Elemental Mapping
• Three-Window Method
– Subtract edge background
using two pre
pre-edge
edge images
(dotted line)
Courtesy John Hunt, Gatan
Physics Department
University of Modena and Reggio Emilia
EFTEM Elemental Mapping: Example 1
Aluminum
Titanium
6 layer metallization test structure
3 images each around:
O K edge:
Ti L23 edge:
Al K edge:
@ 532 eV
@ 455 eV
@ 1560 eV
1 µm
Oxygen
Superimpose three color layers
to form RGB composite
O
Ti
Al
Courtesy John Hunt, Gatan
Physics Department
University of Modena and Reggio Emilia
66
EFTEM Elemental Mapping: Example 2
BF image
N
Ti
O
Al
Si
Unfiltered bright-field TEM image of semiconductor device structure and
elemental maps from ionization-edge signals of N-K, Ti-L, O-K, Al-K, and
Si-K.
Color composite of all 5 elemental maps
displayed on the left,showing the device
construction.
Courtesy John Hunt, Gatan
Physics Department
University of Modena and Reggio Emilia
Spatial resolution of EFTEM: aberrations and delocalization
d = Cc *β *ΔE/E
Cc = chromatic aberration constant
β = the acceptance angle of the objective
aperture
ΔE = range of energies contributing to the
image
Blurr will be especially
p
y large
g for thick, high-Z
g
specimens.
Reduce blurr by:
Using a small energy window (ΔE)
Select energy loss ΔE by changing the gun
voltage (vary kV)
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MgO/Fe/MgO
Cross section (image mode)
10nm
Misura dello spessore dei film
10nm
Qualità delle interfaccia
MgO (001)
Fe (001)
MgO (001)
Au
MgO
ΔtFe~ 9nm
50nm
ΔtMgO
g ~ 12nm
Film F
Fil
Fe
Film MgO
Physics Department
University of Modena and Reggio Emilia
MgO/Fe/MgO MAPPE EELS
mappa Fe
Ok
FeL3
FeL2
mappa O
40 eV
view
O
( K edge, 532 eV)
view
Fe
( L edge, 708 eV)
Intensity (a.u.))
40 eV
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
O
Fe
60
70
80
90
100
110
Depth (nm)
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68
Thick sections
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Thick sections
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70
EDXS
•MMF 0.1%
•Typical Energy resolution150 eV
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71
From Zaluzec
http://www.amc.anl.gov/Docs/ANL/AAEM/AAEMHome
Page.html
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Physics Department
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Physics Department
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Physics Department
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Check the crystallographyc orientation of your sample!!!
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Physics Department
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Strategy for Analysis of Unknown Phases
• Start with light microscopy, SEM, powder x-ray diffraction (XRD), the
library
– Straightforward interpretation (usually helps TEM analysis)
– Less expensive
– Far more time may be needed to prepare a suitable thin specimen
• Use at least two analysis methods
– EDS and CBED (powerful when used together)
•
•
•
•
Determine the elements present (EDS)
Determine the phases present (CBED)
All electron transparent specimens
Keep the ICDD PDF handy to identify d-values
– EELS and HREM (structure images)
• Determine the elements present (EELS)
• Obtain d-values of the phases (HREM)
• Only very thin specimens
BUT : carefully prepare your TEM sample
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Thank you very much for attention!
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78