chapter 11 electron energy loss...
TRANSCRIPT
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EELS principle
Textbook: R.F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, 2nd edition
(Chap. 37, 38, 39, 40)
Chapter 9 The introduction of EELS
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Particle picture of scattering
elasticinner-shell inelastic outer-shell inelastic
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TEM beam-specimen interactions and signals
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What is EELS- Electron Energy Loss Spectroscopy
EEL spectrum is collected series energy loss electrons which generated with the inelastic scattering collision with specimen
Energy after inelastic scattering
incident electron energy
Specimen absorption energy
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Atomic-scale view of electron energy loss in TEM
Energy and Momentum Conservation of
scattering process
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energy-band diagram
valence or conduction
band
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Core ionization edges and the core level diagram
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NTHU
Electron Bean E0
E0E0-ΔEP
TEM ColumnEnergy loss
E0-ΔEPE0
SpectrumEnergy-Filter
Image
Energy slit
Plasmon oscillation
Incident electron
Energy-loss electron
Free electron gas
Positive ion cores
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Ray Tracing for a 90 degree magnetic Sector Spectrometer
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EELS instrumentation spectrum/Imaging
• Below the TEM: • Serial EELS (e.g. Gatan 607) • Parallel EELS (e.g. Gatan 666) • Gatan Enfina • Gatan Imaging Filter • In-column: • Prism-mirror (Leo) • Omega Filter (Leo, JEOL)
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A magnetic prism bends, disperses and focuses an electron beam
e v B = F =mv2/R
R = (m/e)(v/B)
R
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Gatan Image Filter (GIF)
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Leo-922 energy-filtering TEM
omega filter
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Omega-filter in-column spectrometer (Four magnetic prisms)
energy-selecting slit
90-120o
After objective lens
optical axis
Diffraction pattern
Diffraction pattern D2 is conjugated with D1
real or virtual image of specimen
real or virtual image of specimen
Before projector lens
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Low loss region Core loss regionZero loss
The EELS looks like
dielectric constant
band gap
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NTHU
EELS spectral information
Bandgap Interband transition (Valence->Conduction)
Dielectric Function
Band gap
Thickness
Interband transition
(valence-> conduction band)
Core loss: electronic structure unoccupied-DOS atomic environment
dσ/dEdΩ=4γ2/aoq4Σi,j|<f|q.r|i>|δ(E+Ef-Ei)~M2ρ(r)
Plasma loss
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Jellium Model
18
The resonant motion of electron gas would be self-sustaining if there were no damping from the atomic lattice.
The displacement x of a “quasi-free” electron (effective mass m) due to a local electric field E must satisfy the equation of motion.
€
m˙ ̇ x + mΓ˙ x = −eEfor a oscillatory field
The displacement has a solution given by
€
x = (eE /m)(ω 2 + iΓω)−1€
E = E exp(−iωt)
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The displacement x give rise to a polarization P
€
P = −enx = εoχE
χis the electronic susceptibility and n is the number of electrons per unit volume
The relative permittivity or dielectric function ε(ω)=1+χ is then given by
€
ε(ω) = ε1 + iε2 =1−ω p2
ω 2 + Γ2+
iΓω p2
ω(γ 2 + Γ2)is the plasmon frequency (the frequency ε1 passes through 0)
€
ω p
€
ω p = (ne2 /(εom))1/ 2
€
Im[ −1ε(ω)
] =ε2
ε12 + ε2
2 =ωΓω p
2
(ω 2 −ω p2 )2 + (ωΓ)2
The energy loss function is defined as
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For RuO2 a=b=0.449 nm, c=0.31 nm (one unit cell has 2Ru and 4O)
Ru : [Kr]4d75s =8 O : [He]2s22p4=6
# of free electrons = 40=2x(8+2x6)
è
While m=9.10956x10-31 kg
e=1.60219x10-19 C
ε0=107/4πc2=8.842x10-12
1 eV=1.60219x10-19 J
Drude Model for Volume Plasmon
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Plasmon loss from RuO2 nanowires
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Correlating electron energy levels with EELS edges
Unoccupied state
2p1/2—>3d2/32p3/2—>3d5/3
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Energy-loss spectrum (log-intensity) of YBCO
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Band Structure of Si
EF
Valence Band
Conduction Band
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Also applicable to studies of: * electronic band structure and chemical bonding * atom-specific near-neighbor distributions (RDF)
* Band gap analysis for optoelectronic material * dielectric response, ε(ω,q)
What EELS can do
Typically applied to: * measurement of specimen thickness * analysis of elemental composition
* phase identification via signature in EELS fine structure
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Measurement of specimen thickness
t/λ = ln(It/I0)
λ ~ 100 nm but depends on Z, E0 and β Value obtained from calibration specimen or from tables (for common materials) or from parameterized formula
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EELS fine structure (Egerton and Whelan, 1974)
CB1CB2
plural
π*σ*
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K-edge spectra of diamond and grain from the
Allende meteorite
(Blake et al., Nature 332, 1988, 611)
π*
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Oxidation state of Cr in a bacterium
(Daulton et al, M&M 7, 479, 2001)
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Compare the EELS and EDX technique
• Prior to the 1980, most EDX detector were protected (from the water vapor and hydrocarbon in the microscope column) by a 10µm thickness beryllium window, which strongly absorbs photons of energy less than 1000eV and percludes analysis of elements of atomic number less than 11.
• With development of ultrathin (UTW) or atmospheric-pressure (ATW), elements down to boron can be routinely detected, making EDX competitive with EELS for microanalysis of light elements in a TEM specimen.
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• EELS and x-Ray Signal Generation
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atomic number
X-ray fluorescence yield (log scale) as a function of atomic number
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• The EELS is one step signal, while EDX is a two step signal (low x-ray fluorescence yield for low Z). In general, the yield rate of the EELS is higher than EDX.
• the signal of EELS concentrates in a small angle range of the transmitted beam, but the EDX signal spans around larger angle range.
• (a) These two cause EELS has higher core loss signal• (higher Signal to noise ratio, EELS has less recording
time)
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(b) EDX has better Signal/ background ratio
Background of EELS:arises from the inelastic scattering from the atomic electron whose binding energy less than the edge energy
Background of EDX:arises from bremsstrahlung
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u The beam broaden effect
EDX bulk beam broaden size for SEM system
EDX thin film (TEM) beam broaden size
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(c)x-ray has larger interaction volume than that of electron. The ultimate spatial resolution is higher for EELS than for EDX , but the thin crystal is required for EELS
Broaden by elastic scattering of x-ray limited by
the accept angle
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For example:Specimen thickness :100nm, b is about 10nm
Nano EDX Beam size (d) :0.5 nmThe resolution limit: R=5.25 nm atomic weight
The EDX spatial resolution limitBeam broaden formula: density
The EDX spatial resolution ( R ) equation:
Energy of Indicate electron beam
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• Follow previous slice, the beta angle for EDX is about 0.82 rad=820mrad
• For EELS image mode, the beta angle is about 13.06 mrad
For example: The beam size is about 0.5nm;
specimen thickness is about 100nmThe EDX beam Rmax is 5.256nm
EELS Rmax is about 0.6nm
de-localization of energy loss electron
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• (d) EELS is an absolute, standardless quantitation technique, but quantification error may exist in the case of crystal.
• (e) Structural information is available, but more operator intensive is required.
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(f) Comparison of EELS and XEDS sensitivity (depends on strongly on SNR, but not SBR) (Leapman et al.)EELS is capable of detecting smaller concentrations of elements of low atomic number
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(g) EDX resolution is 50 - 100 eV so
there is peak overlap below 1000eV
EELS resolution is
~ 1 eV so edge overlap can be less
(stainless steel, Zaluzec 1984)
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EELS vs. EDXS
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NTHU
擷取可以定量分析之三維空間EELS訊息I(x,y, ΔE)。
•STEM EFTEM
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What is EFTEM- Energy Filtering Transmission Electron Microscopy
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• A contrast-enhancement technique: – it improves contrast in images and diffraction patterns by
removing inelastically scattered electrons that produce background “fog”.
• A mapping technique: – it creates elemental maps by forming images with inelastically
scattered electrons. • An analytical technique: – it records and quantifies electron energy-loss spectra to provide
precise chemical analysis of TEM samples.
The features of EFTEM
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The standard EFTEM elemental mapping images
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Diameter: (8 inches)
如何在具有圖案結構上之試⽚片決定介電材質之介電常數。︒
Copper
Dielectric layer
Si Substrate
Copper Dual-Damascene Structure
Cross-sectional TEM image
•銅製程與低介電常數材料已是半導體元件發展趨勢 0.13µm 乃⾄至於 90nm 的製程技術
A
B
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NTHU
傳統之介電常數量測
Al electrode
Dielectric layer( td ,ε )
Si substrate
VDC
~ A
利⽤用的MOS Capacitor結構來量測其C-V 曲線得到電容值反推得到介電層之介電常數值
( ε0 : 真空介電常數 )
因此對於有結構圖案之試⽚片無法使⽤用此⽅方法量測介電層之介電常數值。
€
VDC =tdCd
ε0
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x
y
ΔE
71 im
ages
ABD
Si3N4
SiO2
Si
Extract image- spectrum from a 2.822 nm2 area
71 data channels
Cou
nts
Electron Energy Loss (eV)
影像能譜(ESI)之擷取Dielectric Function Imaging
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NTHU
A
B
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Dielectric Function image
0eV 9eVElectron energy Loss (eV)
X
Y-10
226eV
18 nm3eV
Black Diamond
SiO2
Si3N4
Siε1
-10
0eV 9eV
X
Y
506.5eV
18 nm 2eV 4eV
Black Diamond
SiO2
Si3N4
Si
ε2
Lo, Chen, L. Chang and Kai et al., Journal of electron Microscopy (2000)
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介電常數分佈影像圖(dielectric constant map)
Materials �ε������� ���ε���SiO2 3.8 4.20±0.31Si3N4 3.6 3.72±0.30
Black Diamond TM 2.5~2.8 2.69±0.27
2.3
4.6
Dielectric constant
B l a c k Diamond
Si3N4
SiO2
Si 50 nm
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Band gap energy Imaging
• Bruley and Brown ( parabolic band )
J1(E) : a = 0.5 a=1.5 ( direct band gap ) ( in-direct band gap )
agEEEMEJ )()()∝( 21 −=ρ
M: transition Matrix from Valence band to conduction band ρ(E): Density of state of condution band
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NTHU
AlN/GaN Quantum Well
AB
GaNAlN
AlN
GaN
AlNGaN
Al-L edge
EELS spectra
TEM image
AlN
AlNGaN
ΔE
Series ESI images
EDX
EELS
GaN/AlN multi-layers were grown on Si substrate by MBE
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NTHU
GaNGaNAlN AlNAlN
AlN GaNAlN
Band Gap Map
Tsai, Kai,Chen,L. Chang, Journal of Electron Microscopy (2003)
The map of band energy of AlN/GaN layers is obtained using electron spectroscopy imaging (ESI) technique. The average band-gap energy of AlN and GaN is determined to be about 5.62 ± 0.35 eV and 3.47 ± 0.36 eV, respectively.
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NTHU
Chemical Bonding sp2/sp3 Map
Yan, Kai, Chen,L. Chang, JEM (2002)
5 nmNiP
EELS element Mapsp2/sp3 Map
€
fsp 2 =[ area(π *)area(π * +σ *)
]specimen
[ area(π *)area(π * +σ *)
]reference
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NTHU
α-Fe2O3
Fe
Cu0003 -12-13
-12-10
SiSubstrate(100)
Cu
Fe
α-Fe2O3
Structure of the specimen
Znoe axis(10-10)
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NTHU
Y
Energy axis From646eV~742eV
X
5 nmspecimen
Y
Image to Spectrum
Fe
α-Fe2O3
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NTHU
CuFe
α-Fe2O3
Cu
Fe
α-Fe2O3
Valence State Mapping