Introduction to Spectroscopic Ellipsometry · © 2007 HORIBA, Ltd. All rights reserved.© 2012 HORIBA, Ltd. All rights reserved. Photon Energy (eV) 1 2 3 4 5 6 ¶ (ß) 35.000 30.000

© 2007 HORIBA, Ltd. All rights reserved.

Introduction to Spectroscopic Ellipsometry


Michelle Sestak, Ph.D.

Applications Scientist

HORIBA Scientific, Edison NJ

April 10, 2013

© 2007 HORIBA, Ltd. All rights reserved.© 2012 HORIBA, Ltd. All rights reserved.

Outline Light and polarization Jones and Stokes vectors Jones and Mueller matricesOptical properties Theory of ellipsometryMethods of SE data collection Instrumentation, with focus on a PME Data analysis Conclusions


Ellipsometry Overview Thin Film Applications

Non-destructive Optical Technique

Based on Polarization Change

Indirect, Model-based Approach

Measure Thickness/Optical Constants & More!


Light

hcheVEnergy )(

ykztExkztEtzE yyxx ˆ)cos(ˆ)cos(),( 00

z

y

Electric field E(z,t)

Magnetic field B(z,t)

Direction of propagation

x


Electromagnetic Spectrum

)(1240)(

nmnmeVheVE


Polarization

X

Y

Z

Wave 1, Ex

Wave 2, Ey

Defined by orientation and phase of E-field vector Superposition of two orthogonal waves


Linear PolarizationWaves in phase Arbitrary amplitudes


Circular PolarizationWaves 90º out of phase Equal amplitudes


Elliptical PolarizationMost general description of polarization state Arbitrary phase Arbitrary amplitudes


Ellipse Characterization

rsrpyx

s

p

y

x

rr

EE

0

0tan

Ex

Ey

E0y

E0x

x-y

Erp

Ers

|rs|

rp-rs

|rp|


Ellipsometry and Polarization

Measures changes in polarization state of light Difference in phase shift (∆) Ratio of amplitude change ()


Ellipsometry vs. Reflectometry

I0 Ir

It

Based on Intensity Based on amplitude and phase shift of E field; polarization!

Ein Eout

2EI

Transmission = It / Io

Reflection = Ir / Io

j

s

p etanrr


Photon Energy (eV)654321

¶ (ß)

35.000

30.000

25.000

20.000

15.000

10.000


£ (ß)

170.000160.000150.000140.000130.000120.000110.000100.000


R

0.650

0.600

0.550

0.500

0.450

0.400

0.350

Ellipsometry Vs Reflectivity➫ Phase (∆) information much more sensitive to ultra-thin films

Simulation @ 70° AOI

1 nm

2 nm

Native SiO2 on c-Si


Mathematics of Ellipsometry

An optical element will change the polarization state of light, but how?

Jones Vectors and Jones MatricesCompletely (pure) polarized light Isotropic sample

Stokes Vectors and Mueller Matrices Any polarization state Isotropic or Anisotropic sample


ykztExkztEtzE yyxx ˆ)cos(ˆ)cos(),( 00

Jones Vectors

y

x

iy

ix

yxeEeE

EEJ

22

1~

Describe pure polarization states of light


Linear with y-axis as line of vibration:

Linear with x-axis as line of vibration:

01

Jones Vector Examples

10

Linear polarization oriented at 45º:

Right (+) and Left Circular (-):

11

21

i1

21


Unpolarized: DNE Elliptical:

Jones Vector Examples (cont’d)

1tan ie

yxy

x

EE

0

0tan


Isotropic Sample:

Rotation Between Coordinates:

Polarizer and Analyzer:

Photoelastic Modulator:

Jones Matrices

0001

)(0

01tie

s

pi

rre0

0100tan

cossinsincos


s

p

si

pi

s

p

sr

pr

rr

EE

rr

EE

~~

~~

~00~

~~

Single Interface: Jones Vectors/Matrices

For isotropic reflecting surface: rps= rsp= 0

sr

pr

EE~~

si

pi

EE~~

i

s

p err

tan~~


Light Propagation: Jones Matrices

01

0001

)(100tan

)(0

01)()(

0001

)( PRe

MRe

MRARtEi

i

Analyzer Modulator PolarizerSample

Track changes in polarization

Sample

Light sourceDetector

Polarizer Modulator

Analyzer

Initial Pol. State


PME Jones Formalism

)(cos)(sin)()( 02 tItIIItEtI cs

1cos2sin2sin2sin)(2cos)2cos2(cos2cos)(2cos2cos2cos10

MAMPAMMPAI

cos2sincos2sin2cos2sin)2cos2(cos2sin)(2sin

sin2sinsin2sin2sin)(2sin

MAAMMPI

AMPI

c

s


Stokes Vectors

lcrc

yx

yx

IIIIIIII

SSSS

Soo 4545

3

2

1

0

Describe partial (& pure) polarization states (unpolarized, partially polarized)

S0 and S1 S2 S3


ISSS

SSSS

III

Puntp

tp23

22

21

0

23

22

21

Stokes Vectors (cont’d)

Totally polarized:

Partially polarized:

Unpolarized:

1;123

22

21 PSSS

1;23

22

21

20 PSSSS

0;023

22

21 PSSS


Linear with y-axis as line of vibration:

Linear with x-axis as line of vibration:

Stokes Vector Examples

0011

001

1

Linear oriented at 45º:

0101

Right (+) and Left (-)Circular:

1001


Stokes Vector Examples (cont’d) Elliptical (General):

Unpolarized:

sin2sincos2sin2cos

1

PP

P

0001


Mueller Matrix

INOUTSSSS

MMMMMMMMMMMMMMMM

SSSS

3

2

1

0

44434241

34333231

24232221

14131211

3

2

1

0

Non-ideal depolarizing samplesRepresents effects of optical components or sample

on Stokes vector


Isotropic Sample

Mueller matrix of a c-Si sample acquired by Auto SE

CSSC

NN

MMMMMMMMMMMMMMMM

M

0000

001001

44434241

34333231

24232221

14131211


Optical Properties

n = refractive index

Phase velocity

k = extinction coefficient

Loss of wave energy to the material

4

k

Complex refractive index (Ñ)

iknN ~

Index n1

Velocity c

Incident ray

Refracted ray

θ1

θ2

θ1

Index n2

Velocity nnc


Complex Fresnel Coefficients

tiit

tiit

pi

rp nn

nnEEr

coscoscoscos

ttii

ttii

si

rs nn

nnEEr

coscoscoscos

Describe reflection at each interface

Depend on angle and polarization direction (p or s)

ni

nt

i

t

Ets


ttii

ttii

tiit

tiit

s

pi

nnnnnnnn

rr

e

coscoscoscoscoscoscoscos

tan

2/122

tan1tan1tan1sin

i

i

iiit eenn

ttii nn sinsin

Determination of Optical Properties

Use Snell’s Law and invert:

nii

tEts

nt


Optical Interference

1cosnλd2πβ 1

Film phase thicknesst01t12 t01r12r10t12 t01r12r10r12r10t12

t01r12r10r12t10r01 t01r12t10

2n~

1n~

0n~θ0

θ1

Substrate

Film

d

...1010

21201

101201

012

4i-

2i-

eetrrt

trt

rrtot

2jβ1201

2jβ1201

sp, err1errR

Total reflection coefficient

Infinite series solutions

t012

r012


Information from SE Ellipsometry provides information about:

Film thickness Optical properties Surface roughness Interfacial mixing Composition Crystallinity Anisotropy Depolarization Uniformity by both depth and area

Film

Interface

Substrate

Surface


Methods of SE Data Collection ex-situ Spectroscopic Ellipsometry

UVISEL

UVISEL 2

SMART-SE

AUTO-SE


Methods of SE Data Collection (cont’d)

in-situ Spectroscopic Ellipsometry Nucleation parameters Film growth modes Optical properties w/o oxide Film growth profiles



Mapping

3-D Wafer Map

2-D Point Values

2-D Wafer Plot



In-line


Methods of SE Data Collection (cont’d) Vacuum Ultraviolet (VUV) Spectral Range of 147-850 nm (NIR option to 2100 nm) Remove absorption at low wavelengths due to O2



Reflectometry/Transmission Temperature controlled



Electrochemical CellLiquid Cell

Sealed Cell



Textured Samples

SEM picture of textured c-Si


Ellipsometry AdvantagesNon-destructive, non-invasive, and non-contact

Precise and reproducible

Very sensitive to ultra-thin films <10 nm

Applicable to almost any thin film materials (polymers, semiconductors, dielectrics, metals, alloys, etc.)

Ideal for in-situ applications


InstrumentationLi

ght S

ourc

e Detector

P

P

P

A

A

S

S

S

A

C

M

P AS LC

Rotating Analyzer

Rotating Compensator

Phase Modulation

Liquid Crystal Phase Modulation

P: PolarizerA: AnalyzerC: CompensatorS: SampleM: ModulatorLC: Liquid Crystal

LC


Phase Modulated Ellipsometer

Optical Fiber

Data Acquisition

and Computer

Detector

Monochromator

Xe lamp

Shutter

Sample

Fixed

AnalyzerPhotoelastic

Modulator (50KHz)

Fixed Polarizer

(DeltaPsi2)

HORIBA UVISEL 2


Photoelastic Modulator Principle

Elliptically polarized light

modulator

Linearly polarized light

Piezo electric transducer (50 kHz)

Signal detected at 50 kHz !!!

d

ExEx

Ey ei Ey

n0

n1

d

Strained SiO2 bar; birefringence

Modulation at 50 kHz!

An electrically driven retarder introducing a phase shift varying sinusoidally with time


PME Advantages Fixed elements

Excellent precision on ∆

Very fast acquisition rate (~1 ms/point)

Covers a wide spectral range from 190-2100 nm

High polarization modulation rate of 50 kHz

Ψ and ∆ are measured over their full range; Ψ [0˚, 90˚] and ∆ [0˚, 360˚]


SE Data Analysis

EXPERIMENTAL DATA

E (eV)3.532.521.5

Psi (

°)

19181716151413121110

987654

Delta (°)

350

300

250

200

150

100

50

Substrate

Layer 1

Layer 2

Measurement Model Fit Results

Thickness

Optical Constants

Roughness…

(n,k) = f(lambda) for the TiO2 layer

lambda (nm)800700600500400

Re(

Inde

x)

3.2

3.1

3

2.9

2.8

2.7

2.6

2.5

2.4

2.3

Im(Index)

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

EXPERIMENTAL DATA

E (eV)3.532.521.5

Psi (

°)

19181716151413121110

987654

Delta (°)

350

300

250

200

150

100

50

Use Regression Analysis


Data Fitting

2

2ThExp

N

2 )X-X( 1- P - 2N

1 =

In phase modulated ellipsometry X represents the couple (Is, Ic)

N: Total number of measurablesP: Total number of fit parameters

Goodness of fit:


Kramers-Kronig (KK) Transformation

0 222

121

dP

0 221

212

dP

Real and imaginary terms of optical properties are not independent!

nkkn

22

221


Implications of KK RelationshipRefractive index (n): Always follows slope of k Always increasing for absorbing materials,

except in regions of anomalous dispersion

Wavelength (nm)800750700650600550500450400350

n

3.15

3.1

3.05

3

2.95

2.9

2.85

2.8

2.75

2.7

2.65

2.6

2.55

k

0.7

0.65

0.6

0.55

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0


Normal Dispersion: Dielectric

SiO2

SiNx

AlGaAs

Refractive index (n) decreases with increasing λ

Wavelength (nm)800780760740720700680660640620600580560540520500480460440420400

n

4

3

2

1


Anomalous Dispersion: Absorbing RegionRefractive index (n) increases with increasing λ

except where absorption peak occurs

Wavelength (nm)800750700650600550500450400350

n

3.15

3.1

3.05

3

2.95

2.9

2.85

2.8

2.75

2.7

2.65

2.6

2.55

k

0.7

0.65

0.6

0.55

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0


Quality of ResultsGoal: find simplest, realistic model

Minimize

Are results physical?Negative k? K-K consistent? Follow anomalous or normal dispersion?

Other indicators Error bars (90% confidence limits)Correlation matrix


Applications-Thin FilmsAt home: entertainment, comfort, security, appliances, energy savings…

In the car: engine control and powertrain, car body and safety, navigation...

On the go: mobile phones, PDAs, MP3 players, tablets…

Our planet: energy-saving solutions, solar power, greener cars…

Our health: medical imaging, portable diagnostics, DNA analysis, implantable devices…

At work: printers, PCs, …


Thin Films in Photovoltaics

Si: crystalline, nano, micro, poly, amorphous, textured...

Compound semiconductor: III-V, SiGe, CdTe, CIS, CIGS...

Organics: PCBM, P3HT, PEDOT:PSS...

Transparent conducting oxides (TCO): SnO2, ZnO, ITO...

AR coating: SiNx, TiOx… Metal contacts: Al, Ca, Mg…

Absorber

Emitter

Structure


Thin Films in Displays

Devices: TFT-LCD LED, OLED

Materials: a-Si, Poly-Si, SiN, SiO2, MgO,ITO,SnO2,ZnO Liquid crystals,… Antireflection (AR) coating Polarizing filters


Thin Films in Optoelectronics Devices:

High sensitivity NIR & IR detectors Laser Diodes (LED) High speed electronics

Materials: III-V compounds II-VI compounds Ternary alloys Quternary alloys Multiquantum well

GaN, SiO2 ,TiO2..

Vision and microspotcapabilities can be crucial


Thin Films in Microelectronics Materials:

a-Si, Poly-Si, SiN, SiO2, High , Low materials Materials for 90 nm lithography ( DUV ) New materials : Graphene,

Nanomaterials


Thin Films in Optical Coatings

Applications: Antireflection coating Filtering coatings Antiscratch coating Decorative coatings Electrochromic coatings

Materials: SiOx, High/Low refractive multilyers

SiN,TiOx, WOx,…


Thin films in Biochemistry

Objective:Selective capture of proteinBiosensors

Materials:Substrate: Gold

Layers: DNA, proteins


Thin Films in Metallurgy Objective:

Hardness Antifriction coatings Decorative coating Anticorrosion coating

Materials: SiOx, TiO2, Al, Al2O3,CrO2, DLC

TiN, …


Emerging Applications & Materials

Objective:Microelectronics, Display

& solar cells on flexible substrate

Materials :Substrate: PET Layers: Polymers, a-Si…

Low Cost Production

Low Power Consumption


SummaryOptical technique for studying thin film thickness

and optical properties Ellipsometry vs. Reflectometry

Jones/Stoke vectors and Jones/Mueller matrices used for light propagation

Model based approach

Many data collection methods

Wide field of applications


Thank you!

Check our website for future webinars on spectroscopic ellipsometry!


Questions?

For additional information or questions about ellipsometry, please visit:

www.horiba.com/ellipsometry

Or email:

[email protected]

Documents

Introduction to Spectroscopic Ellipsometry · © 2007 HORIBA, Ltd. All rights reserved.© 2012 HORIBA, Ltd. All rights reserved. Photon Energy (eV) 1 2 3 4 5 6 ¶ (ß) 35.000 30.000