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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
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
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=
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
Ellipsometric angles
Spectroscopy and the structure of matter 12.5
Forrás: Tamáska István, 2009
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
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 = + "
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
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)
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.
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
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
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)
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
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
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?
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
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
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
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
Spectroscopy and the structure of matter 12. 21
H
Fe
Emission spectroscopy
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)
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
Spectroscopy and the structure of matter 12. 24
Detectable elements
Spectroscopy and the structure of matter 12. 25
Inductively coupled plasma (ICP)
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
Spectroscopy and the structure of matter 12.27
ICP plasma
Spectroscopy and the structure of matter 12. 28
ICP-AES – Detection limits
Spectroscopy and the structure of matter 12.29
Emission spectra: effect of temperature
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
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)
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
Spectroscopy and the structure of matter 12. 33
Types of luminescence
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
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
Spectroscopy and the structure of matter 12. 36
Molecular spectroscopy
Fluorescence – Typical fluorophores
Typically aromatic molecules
Usually no fluorescence
in condensed state
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
Spectroscopy and the structure of matter 12. 38
Professor Alexander Jablonski
1898 – 1980
Thermal excitation
Delayed Fluorescence
Luminescence – Jablonski diagram
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
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
Spectroscopy and the structure of matter 12. 41
Fluorescence – Stokes shift
Sir George Gabriel Stokes1819 – 1903
Visual observation of Stokes shift
Molecular spectroscopy
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 = =
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
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
45
Fluorescence – Eu-based fluorophores
White llight illumination
UV light (365 nm)
Spectroscopy and the structure of matter 12.
Molecular spectroscopy
46Spectroscopy and the structure of matter 12.
Spectrofluorimeter – Fluorolog 3
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
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