optical spectroscopy in materials science 12. ellipsometry...

Optical spectroscopy in materials science 12.

EllipsometryEmission spectroscopy

Kamarás KatalinMTA Wigner FKkamaras.katalin@wigner.mta.huEmission 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