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Optical spectroscopy in materials science 12.
EllipsometryEmission spectroscopy
Kamarás KatalinMTA Wigner [email protected] part by Hajnalka Tóháti, Wigner RCP
Spectroscopy and the structure of matter 12. 1
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Spectroscopy and the structure of matter 12.
EllipsometryFried MiklósLohner Tivadar MTA EK MFAPetrik Péter
Snell’s law:(Snellius – Descartes-törvény:Snellius - Gesetz: )
bbaa nn ϕϕ sinsin =
From the boundary conditions of Maxwell’s equations:the tangential components of E and H are continous at the interface
nEEkcH
c
c
==
=
=×
ω
ω
ω
HEk
HEkmaking use of
2
SOPRA →Semilab
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Spectroscopy and the structure of matter 12.3
Fresnel’s equations
tpbiprpa
tpbrpipa
tsbbisrsaa
tsisrs
EEEEnEEn
EnEEnEEE
ϕϕ
ϕϕ
cos)(cos)(
cos)(cos
=+
=−−=−
=+
Fresnel coefficients:
ip
rpp E
Er =
is
rss E
Er =ip
tpp E
Et =
is
tss E
Et =
rpipp err θ= rsi
ss err θ=
2* rrrR ==
),,,(,,, babaspsp nnfttrr ϕϕ=
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Spectroscopy and the structure of matter 12.4
Measured quantitiesIncident light: linear polarization Reflected light: elliptical polarization
ΔΨ== i
s
p err
tanρ
Ellipsometric angles:s
p
rr
=Ψtan rsrp θθ −=Δ
Spectroscopic ellipsometry: )(),( ωω ΔΨ
Source
Sample
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Ellipsometric angles
Spectroscopy and the structure of matter 12.5
Forrás: Tamáska István, 2009
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Spectroscopy and the structure of matter 12.6
Measurement: rotating analyzer setup
Polarizer: fixed angle (P)Analyzer rotating: A(t)
APP
PAPPPP
AI 2sinsincos2sin)Re(2cos
sincossincos
1)(222222
222
det ++
+−
+=ρ
ρρρ
iii APAPAI 2sin),(2cos),(1~)(det ρβρα ++
Ptan11tan
αα
−+=Ψ 21
cosα
β−
=Δ
Kompenzátor
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Spectroscopy and the structure of matter 12.7
Evaluation: Isotropic, infinite two-phase model
)tansin)1()1((sin)( 222
2222
aaaarb nsamplen ϕϕρρϕε
+−+==
If na = 1:
aaar ϕϕρρρρϕε 22
22
2222 tansin
)'(21)"(4)1(sin'
++−−+=
aar ϕϕρρ
ρρε 2222
2
tansin)'(21)1("4"
++−−=
00sintan"0" <Δ<−<ΔΨ=> πρε r
convention! (measured quantity: cos Δ)
ρ = + "
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Spectroscopy and the structure of matter 12.8
Accuracy of measurement
Brewster angle: rp=0tan φa(B) = nb/na
2,0 π=Δ=Ψ
cos Δ is the measured quantity – optimal range is where it is the most sensitive to Δhowever, sensitivity to angle of incidence is also large there sensitivity of Ψ to angle is small around minimum
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Spectroscopy and the structure of matter 12.9
Dependence on angle of incidence
YBa2Cu3O7 20 KR.M.A. Azzam, N.M. Bashara: Ellipsometry and Polarized Light.North-Holland, Amsterdam, 1977
K.Kamarás, D.van der Marel, C.C.Homes, T.Timusk:Physica C 235, 1085 (1994)
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Spectroscopy and the structure of matter 12.10
Advantages - disadvantages
Advantages:• direct determination of complex dielectric function (with appropriate model)• no reference needed• scattered light, small surface discontinuities cause small errors• non-destructive• remote sensing possible (visible range)
Disadvantages: • large angle of incidence – large light spot, large sample area required• evaluation complicated• many parameters of the sample have to be known beforehand.
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Spectroscopy and the structure of matter 12. 11
Experimental setup
UV-VIS ellipsometer(MPI Stuttgart)
)()(,),( ωεωω ><ΔΨAI
Pseudodielectric function <ε>:approximation calculated with isotropic two-phase modelindependent of angle of incidence!!!!can be used for routine tasks with appropriate calibration
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Spectroscopy and the structure of matter 12. 12
Modern ellipsometer
Woollam M2000DI – (MFA)Rotating compensator spectroscopic ellipsometerrange: 190-1700 nmminimum focus spot 0.15 mm
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Spectroscopy and the structure of matter 12.13
Evaluation: multilayer systems
...),,,,( ccbba dd εεϕρ
www.jawoollam.com
knowing (n-2) parameters,any two unknown quantities can be determined (e.g. thickness)
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Spectroscopy and the structure of matter 12. 14
Fitting procedureswww.jawoollam.com
model
If n(ω) is known, more than twoparameters can be fitted
more angles of incidence – more information
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Sensitivity of ellipsometry
°−=ΔΨ 02.001.0, -> 0.01nm sensitivity on layer thickness
d (nm) Δ Ψ
0 179.257 10.448
0.1 178.957 10.448
0.2 178.657 10.449
0.3 178.356 10.450
0.4 178.056 10.451
0.5 177.756 10.453
1 176.257 10.462
Precise calibration (e.g. angleof incidence) is crucial!
Spectroscopy and the structure of matter 12. 15
Source: Tamáska István, 2009
Technology: process monitoringprocess control
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Spectroscopy and the structure of matter 12.16
Application
• quick determination of dielectric function• thickness measurement, technology control• investigation of distribution in layered systems
(comparison with model calculations)• ideal for semiconductors, multilayers • small sensitivity in case of transparent and strongly absorbing samples
“Kramers-Kronig transformation is arbitrary –ellipsometry gives directly the dielectric function”
What’s wrong with this sentence?
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Spectroscopy and the structure of matter 12.17
Combination of ellipsometry and Kramers-Kronig analysis
K. Kamarás, K.-L.Barth, F.Keilmann, R.Henn, M.Reedyk, C.Thomsen, M.Cardona, J.Kircher, P.L.Richards, J.-L.Stehlé:J. Appl. Phys. 78, 1235 (1995)
0.0
0.5
1.0
300 KR
0
15
30
100 1000
0
15
30
Fig. 1. Kamaras et al.
Frequency (cm-1)
k
n
SrTiO3
0
30
60
100 Kn
30 70 110 1500
30
60
k
0
20
40
200 K
30 70 110 1500
20
40
0
15
30
300 K
30 70 110 1500
15
30
Fig. 2. Kamaras et al. Frequency (cm-1)
scaling of normal-incidence reflectance to ellipsometrylow-frequency extrapolations depend on slope of curve
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Take-home message• Basics of ellipsometry: illumination of sample with linearly polarized light under
finite angle; analyzing polarization state of reflected (elliptically polarized) light
• Measured quantity: ratio of Fresnel coefficients • Ellipsometric angles ψ, Δ depend on sample dielectric function and angle of
incidence • Pseudodielectric function (isotropic, infinite, two-phase model) • Multilayer systems: any 2 parameters can be determined when the others are
known (mostly thickness of known materials) • Modeling, process control, remote sensing
Spectroscopy and the structure of matter 12.
ΔΨ== i
s
p err
tanρ
18
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Összefoglalás• Ellipszometria alapjai: minta megvilágítása lineárisan polarizált fénnyel véges
beesési szöggel ; a visszavert (elliptikusan polarizált) fény analizálása
• Mért mennyiség: Fresnel-együtthatók aránya• A ψ, Δ ellipszometrikus szögek a minta dielektromos függvényétől és a beesési
szögtől függenek• Pszeudodielektromos függvény (izotrop, végtelen, kétfázisú modell) • Többrétegű rendszerek: bármely 2 paraméter meghatározható, ha a többi ismert
(legtöbbször ismert anyagokból álló rétegek vastagsága) • Modellezés, folyamatirányítás, távoli érzékelés
Spectroscopy and the structure of matter 12.
ΔΨ== i
s
p err
tanρ
19
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Spectroscopy and the structure of matter 12. 20
Atomic emission spectroscopy (AES)
o Flame test
o Flame emission photometry
o Atomic absorption spectrophotometry
o Inductively coupled plasma
Molecular spectroscopy
o IR emission spectroscopy
o Luminescence
Emission spectroscopy
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Spectroscopy and the structure of matter 12. 21
H
Fe
Emission spectroscopy
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Spectroscopy and the structure of matter 12.22
Atomic emission spectroscopy - Flame testWalt Wolland, Bellevue Community Collegehttp://www.800mainstreet.com/s/s.html
Ba Ca K Li Na Rb
Quantitative methods: flame photometry, atomic absorption spectroscopy (AAS)
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Spectroscopy and the structure of matter 12. 23
Flame Emission Photometry (FEP) Atomic Absorption Spectroscopy (AAS)
• Excitation: thermal energy of the flame
• Flame: - most frequent: acetylene and air
- vaporization → homogeneous atomic cloud
- excitation, but not ionization, of atoms
• Vaporizer → sample solution
• Temperature: 2000 – 3000 ̊ C
• Requirement: constant composition, temperature and structure of the flame
Atomic emission spectroscopy
http://www.cee.vt.edu/ewr/environmental/teach/smprimer/aa/aa.htmlhttp://www.resonancepub.com/atomicspec.htm
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Spectroscopy and the structure of matter 12. 24
Detectable elements
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Spectroscopy and the structure of matter 12. 25
Inductively coupled plasma (ICP)
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Spectroscopy and the structure of matter 12. 26
ICP Kitchen area
Ar gas excited at radio frequency
Temperature up to 8000 ̊ C
Low concentration
Plasma torch: 3 concentric quartz
tubes, streaming Ar
Outside→ cooling
Central→ plasma
Inside→ carrier gas for sample
Plasma state: electric excitation→
high temperature fireball
Observation in the upper part of the fireball: low concentration, more lines
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Spectroscopy and the structure of matter 12.27
ICP plasma
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Spectroscopy and the structure of matter 12. 28
ICP-AES – Detection limits
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Spectroscopy and the structure of matter 12.29
Emission spectra: effect of temperature
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Spectroscopy and the structure of matter 12. 30
Infrared emission spectroscopy
Temperature: 100 – 200 o C
Keresztury Gábor, Mink János, Kristóf JánosMTA Kémiai Kutatóközpont, Veszprémi Egyetem
Strong emission“BLACKBODY”
INTERFEROMETER
The model of layer structure
TITANIUM plate
WHITE
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Spectroscopy and the structure of matter 12.31
Self-absorption
G. Keresztury, J. Mink, J. Kristóf: Anal. Chem. 67, 3782 (1995)
tb – transmittance of the bulk
ts – transmittance of the surface
E - emittance
The spectral shape depends on:• effective thickness of the layers (d1, d2)• thickness of emitting, absorbing layers (de, da)
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Spectroscopy and the structure of matter 12. 32
Light emission by excited molecules
Fluorescence of different sized CdSe quantum dots
Joseph R. Lakowicz – Principles of fluorescence spectroscopy, 3rd edition
Molecular spectroscopy – Luminescence
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Spectroscopy and the structure of matter 12. 33
Types of luminescence
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Spectroscopy and the structure of matter 12. 34
Chemiluminescence/bioluminescence
Chemiluminescence – is the emission of light as the result of a chemical reactionBioluminescence – one type of chemiluminescence;the light is produced and emitted by a living organism
e.g. firefly, deep-sea fish, jellyfish, squids, bacteria, planktons, mushrooms
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Spectroscopy and the structure of matter 12.35
Luminescence
Fluorescence Phosphorescence
Emission: From excited singlet state From excited triplet state Transition: Allowed „Forbidden” Emission rate: Fast: 108 s-1 Slow: 103 – 100 s-1
Average lifetime: 1 – 10 ns ms – s
Example:
0 sec 1 sec 640 sec
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Spectroscopy and the structure of matter 12. 36
Molecular spectroscopy
Fluorescence – Typical fluorophores
Typically aromatic molecules
Usually no fluorescence
in condensed state
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Spectroscopy and the structure of matter 12. 37
Fluorescence – the beginning
Sir John Fredrich William Herschel1792 – 1871
Fluorescence of quinine is the most widely used example up to now
Molecular spectroscopy
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Spectroscopy and the structure of matter 12. 38
Professor Alexander Jablonski
1898 – 1980
Thermal excitation
Delayed Fluorescence
Luminescence – Jablonski diagram
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Spectroscopy and the structure of matter 12.
Luminescence in molecules
Franck-Condon principleR: configuration coordinateabsorption (vertical)
relaxation
emission (vertical)
relaxationIntersystem crossing: singlet– tripletInternal conversion: into vibrationally excited state of higher singlet Fluorescence: singlet - singletPhosphorescence: singlet – triplet (delayed)
http://www.shsu.edu/~chemistry/chemiluminescence/JABLONSKI.html
http://en.wikipedia.org/wiki/Franck-Condon_principle
Jablonski diagram
39
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Spectroscopy and the structure of matter 12. 40
Franck-Condon principle
Mirror imageFluorescence basics
During an electronic transition a change from onevibrational energy level to another will be morelikely to happen if the two vibrationalwavefunctions overlap more significantly
Electronic excitation does not greatly alter the nuclear geometry
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Spectroscopy and the structure of matter 12. 41
Fluorescence – Stokes shift
Sir George Gabriel Stokes1819 – 1903
Visual observation of Stokes shift
Molecular spectroscopy
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Spectroscopy and the structure of matter 12. 42
Fluorescence – Lifetime (τ) and quantum yield (Q)
- These are the two most important characteristics
where Γ – emission rate of fluorophores
knr – number of non-radiative transitions to ground state S0
if there is Stokes shift, Q < 1
1nrk
τ =Γ +Lifetime: average time between excitation and emission
if knr = 0, intrinsic lifetime
Molecular spectroscopy
quantum yield = Q = =
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Spectroscopy and the structure of matter 12. 43
Fluorescence – Quenching
Reasons:
collision with other molecules
(quenchers)
formation of non-fluorescent complexes
resonance energy transfer (RET)
Quenching – intensity of fluorescence decreases
Molecular spectroscopy
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Spectroscopy and the structure of matter 12. 44
Fluorescence – Resonance energy transfer
emission spectrum of donor overlaps with absorption spectrum of acceptor no intermediate photon dipole-dipole interaction between donor and acceptor
By Alex M Mooney - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23197114
Molecular spectroscopy
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Fluorescence – Eu-based fluorophores
White llight illumination
UV light (365 nm)
Spectroscopy and the structure of matter 12.
Molecular spectroscopy
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46Spectroscopy and the structure of matter 12.
Spectrofluorimeter – Fluorolog 3
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Take-home message• Atomic emission spectroscopy: flame test, flame emission photometry, atomic
absorption spectroscopy, inductive coupled plasma• Infrared emission spectroscopy: vibrational levels, self-absorption• Molecular spectroscopy: types of luminescence• Jablonski diagram: absorption, fluorescence, phosphorescence, internal conversion,
intersystem crossing• Quantum yield and lifetime• Resonance energy transfer
Spectroscopy and the structure of matter 12. 47
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Összefoglalás• Atomi emissziós spektroszkópia: lángfestés, lángfotometria, atomabszorpciós
spektroszkópia• Infravörös emissziós spektroszkópia: rezgési szintek, önabszorpció• Molekulaspektroszkópia: lumineszcencia típusok• Jablonski-diagram: abszorpció, fluoreszcencia, foszforeszcencia, belső
konverzió, intersystem crossing• Kvantumhatásfok és élettartam• Rezonáns energiatranszfer
Spectroscopy and the structure of matter 12. 48