Introduction to Spectroscopic Ellipsometry

Michelle Sestak, Ph.D. Applications Scientist HORIBA Scientific, Edison NJ April 10, 2013

 Light and polarization  Jones and Stokes vectors  Jones and Mueller matrices  Optical properties  Theory of ellipsometry  Methods of SE data collection  Instrumentation, with focus on a PME  Data analysis  Conclusions

 Thin Film Applications

 Non-destructive Optical Technique

 Based on Polarization Change

 Indirect, Model-based Approach

 Measure Thickness/Optical Constants & More!

Direction of z propagation y   Magnetic field B(z,t)   E(z,t)  E0x cos( t  kz  x )xˆ  E0 y cos( t  kz   y )yˆ  hc Energy(eV )  h  

 1240eV nm E(eV)  h  (nm)

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

Wave 1, Ex

Wave 2, Ey

 Waves in phase  Arbitrary amplitudes

 Waves 90º out of phase  Equal amplitudes

Most general description of polarization state  Arbitrary phase  Arbitrary amplitudes

E E y E0x rs |rp|

x-y rp-rs  E0y  |rs|

Ex Erp

 r E0x p tan    E0 y rs    x  y  rp  rs

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

 Based on Intensity  Based on amplitude and

2 phase shift of E field; I  E polarization!

I0 Ir Ein Eout

Transmission = I / Io rp j t    tane Reflection = Ir / Io rs

➫ Phase (∆) information much 35.000 more sensitive to ultra-thin films 30.000 25.000 ¶ (ß) 20.000

1nm 15.000 10.000 2 nm 1 2 3 4 5 6 Native SiO2 on c-Si Photon Energy (eV)

0.650 170.000 0.600 160.000 150.000 0.550 140.000 R 0.500 £ (ß) 130.000 0.450 120.000 0.400 110.000 0.350 100.000

1 2 3 4 5 6 1 2 3 4 5 6 Photon Energy (eV) Photon Energy (eV) Simulation @ 70° AOI

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

 Jones Vectors and Jones Matrices  Completely (pure) polarized light  Isotropic sample  Stokes Vectors and Mueller Matrices  Any polarization state  Isotropic or Anisotropic sample

© 20072012 HORIBA,HORIBA, Ltd. Ltd. All Allrights rights reserved. reserved. Jones Vectors   Describe pure polarization states of light   E(z,t)  E0x cos( t  kz  x )xˆ  E0 y cos( t  kz   y ) yˆ

 i x ~ 1  Ex e  J   i  2 2  y  Ey e Ex  Ey  

 Linear with x-axis as line of  Linear polarization oriented at vibration: 45º: 1 1 1     0 2 1

 Linear with y-axis as line of  Right (+) and Left Circular (-): vibration: 1  1  0     2 i 1  

 Elliptical:  Unpolarized: DNE

tan ei       1 



E0x  tan    x  y E0 y

 Polarizer and Analyzer:  Isotropic Sample:

tanei 0 r 0  1 0     p     0 1  0 r  0 0    s 

 Photoelastic Modulator:  Rotation Between Coordinates: 1 0   cos sin        i (t)    0 e   sin cos 

~ ~ E   Ei  r p ~ p   ~   Er s   Ei s   

~ ~ ~ ~ ~r E r   r p 0  E i    r p  p i  ~ p    ~ p    tan e  0 ~r    ~r  ~r  E r s   s   E i s   s  s

For isotropic reflecting surface: rps= rsp= 0

 Track changes in polarization

Light source Detector Polarizer Modulator

Analyzer

Sample

1 0 1 0   tanei 0 1 0 1 E(t)   R(A)R(M ) R(M ) R(P)       i        0 0 0 e   0 1 0 0 0

Analyzer ModulatorSample Polarizer Initial Pol. State

I0 1 cos 2 cos 2A  cos 2(P  M )cos 2M (cos2A  cos 2 )  cos 2(P  M )sin 2Asin 2M sin 2 cos  1 

I s  sin 2(P  M )sin 2Asin 2 sin   sin 2 sin 

I c  sin 2(P  M )sin 2M (cos 2  cos 2A)  sin 2Acos 2M sin 2 cos   sin 2 cos  

 Stokes Vectors

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

 S   I  I   0   x y    S1   I x  I y  S       S I o  I o  2   45 45       S3   Irc  Ilc 

S0 and S1 S2 S3

I S 2  S 2  S 2 S 2  S 2  S 2 P  tp  1 2 3  1 2 3 Itp  Iun S0 I

2 2 2  Totally polarized: S1  S2  S3 1; P 1

2 2 2 2  Partially polarized: S0  S1  S2  S3 ; P 1

2 2 2  Unpolarized: S1  S2  S3  0; P  0

 Linear with x-axis as 1  Linear oriented at 45º:   1 line of vibration: 1   0 0     1 0       0

 Linear with y-axis as  1   Right (+) and Left (-)  1    Circular:   line of vibration: 1  0   0   0           0  1

© 20072012 HORIBA,HORIBA, Ltd. Ltd. All Allrights rights reserved. reserved. Stokes Vector Examples (cont’d)  Elliptical (General):  1      P cos2   Psin2 cos        Psin 2 sin   Unpolarized: 1   0 0     0

 S   M M M M  S   0   11 12 13 14  0   S1   M 21 M 22 M 23 M 24  S1    S   M M M M  S   2   31 32 33 34  2   S   M M M M  S   3 OUT  41 42 43 44  3 IN

 M M M M   1  N 0 0   11 12 13 14     M 21 M 22 M 23 M 24   N 1 0 0  M    M M M M   0 0 C S   31 32 33 34       0 0  S C   M 41 M 42 M 43 M 44   

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

 Complex refractive index (Ñ) ~ N  n  ik Incident ray

θ1 θ1 Index n1  n = refractive index Velocity c c Index n Phase velocity   2 Velocity n θ2 n Refracted ray

 k = extinction coefficient  Loss of wave energy to the material k  4

 Describe reflection at each interface  Depend on angle and polarization direction (p or s)

  i ni    Er nt cosi  ni cos t nt rp       t Ei nt cos i  ni cost   p E  ts  E  n cos  n cos r   r   i i t t s  E  n cos  n cos  i s i i t t

     nt cos i  ni cos t  i   ni r n cos  n cos tan ei  p   t i i t  n  n cos  n cos  t rs i i t t    t  ni cos i  nt cost  Ets

n sin  n sin Use Snell’s Law and invert: i i t t 1/2   i 2   2 1tan e   nt  ni sin i 1 tan i    1 tan ei     

 Total reflection coefficient

rtot  r012  -2i  t01r12t10e 2 r012 -4i  t01r12 r10t10e

θ0 r t r t t r r r t 01 01 12 10 01 12 10 12 10  ... ~ n0  Infinite series solutions d r  r e 2jβ n~ 01 12 1 R p,s  θ1 2jβ Film 1 r01r12e

n~ 2 t01t12 t01r12r10t12 t01r12r10r12r10t12 Film phase thickness Substrate  d  β  2π n1cos1 t012  λ 

 Ellipsometry provides information about:

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

UVISEL SMART-SE

UVISEL 2 AUTO-SE

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

 Mapping

2-D Wafer Plot

2-D Point Values

3-D Wafer Map

 In-line

 Remove absorption at low wavelengths due to O2

 Reflectometry/Transmission  Temperature controlled

Liquid Cell  Electrochemical Cell

Sealed Cell

 Textured Samples

SEM picture of textured c-Si

 Non-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

© 20072012 HORIBA,HORIBA, Ltd. Ltd. All Allrights rights reserved. reserved. Instrumentation P: Polarizer A: Analyzer Rotating Analyzer C: Compensator S: Sample M: Modulator P S A LC: Liquid Crystal Rotating Compensator

P C S A Detector

Phase Modulation

Light Source P S M A Liquid Crystal Phase Modulation P LC S LC A

Fixed Photoelastic Analyzer Modulator Fixed Polarizer (50KHz)

HORIBA UVISEL 2

Detector Optical Fiber

Xe lamp Sample Shutter Monochromator Data Acquisition and Computer (DeltaPsi2)

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

E Ex x n0 modulator n1

d E i y e Ey Piezo electric transducer (50 kHz) d  Signal detected at 50 kHz !!! Elliptically polarized light

 Strained SiO2 bar; birefringence  Modulation at 50 kHz!

 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˚]

Use Regression Analysis

Measurement Model Fit Results

EXPERIMENTAL DATA EXPERIMENTAL DATA 19 350 19 350 Thickness 18 Layer 2 18 17 300 17 300 16 16 15 15 Optical Constants 250 250 14 Layer 1 14 Delta (°) 13 13 Delta (°) 12 200 12 200 11 11 Roughness… Psi (°) Psi Psi (°) Psi 10 150 10 150 9 Substrate 9 8 8 100 100 7 7 6 6 50 50 5 5 4 4 (n,k) = f(lambda) for the TiO2 layer 1.5 2 2.5 3 3.5 1.5 2 2.5 3 3.5 3.2 E (eV) E (eV) 0.5 3.1 0.45 3 0.4

2.9 0.35 Im(Index) 2.8 0.3

2.7 0.25 Re(Index) 2.6 0.2 0.15 2.5 0.1 2.4 0.05 2.3 0 400 500 600 700 800 lambda (nm)

N: Total number of measurables P: Total number of fit parameters

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

 Real and imaginary terms of optical properties are not independent!     2  2   1  1  P d  0   2   2

  2  1   1 2    P d   0   2   2  2 2 1  n  k

 2  2nk

© 20072012 HORIBA,HORIBA, Ltd. Ltd. All Allrights rights reserved. reserved. Implications of KK Relationship  Refractive index (n):  Always follows slope of k  Always increasing for absorbing materials, except in regions of anomalous dispersion

0.7 3.15 0.65 3.1 0.6 3.05 0.55 3 0.5 2.95 0.45 2.9 0.4 n 2.85 0.35k 2.8 0.3

2.75 0.25 2.7 0.2 2.65 0.15

2.6 0.1

2.55 0.05 0 350 400 450 500 550 600 650 700 750 800 Wavelength (nm)

3 AlGaAs n

2 SiNx

SiO2

1 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 Wavelength (nm)

© 20072012 HORIBA,HORIBA, Ltd. Ltd. All Allrights rights reserved. reserved. Anomalous Dispersion: Absorbing Region  Refractive index (n) increases with increasing λ except where absorption peak occurs

0.7 3.15 0.65 3.1 0.6 3.05 0.55 3 0.5 2.95 0.45 2.9 0.4

n 2.85 0.35k 2.8 0.3 2.75 0.25 2.7 0.2

2.65 0.15

2.6 0.1 2.55 0.05 0 350 400 450 500 550 600 650 700 750 800 Wavelength (nm)

 Goal: 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

At home: entertainment, comfort, security, appliances, energy savings…

Our health: In the car: medical imaging, engine control and portable diagnostics, powertrain, car body and DNA analysis, safety, navigation... implantable devices… On the go: At work: mobile phones, PDAs, printers, PCs, MP3 players, tablets… …

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

Structure

 Si: crystalline, nano, micro, poly, amorphous, textured...  Compound semiconductor: III-V, SiGe, CdTe, CIS, CIGS...  Organics: PCBM, P3HT, PEDOT:PSS... Emitter  Transparent conducting oxides Absorber (TCO): SnO2, ZnO, ITO...

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

 Devices:  TFT-LCD  LED, OLED  Materials:  a-Si, Poly-Si,  SiN, SiO2,  MgO,ITO,SnO2,ZnO  Liquid crystals,…  Antireflection (AR) coating  Polarizing filters

© 20072012 HORIBA,HORIBA, Ltd. Ltd. All Allrights rights reserved. reserved. 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 microspot capabilities can be crucial

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

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

 Materials:

 SiOx, High/Low refractive multilyers  SiN,TiOx, WOx,…

 Objective:  Selective capture of protein  Biosensors  Materials:  Substrate: Gold  Layers: DNA, proteins

 Objective:  Hardness  Antifriction coatings  Decorative coating  Anticorrosion coating  Materials:

 SiOx, TiO2, Al, Al2O3,CrO2, DLC  TiN, …

 Objective:  Microelectronics, Display & solar cells on flexible substrate

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

Low Cost Production Low Power Consumption

 Optical 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

Check our website for future webinars on spectroscopic ellipsometry!

For additional information or questions about ellipsometry, please visit:

www.horiba.com/ellipsometry

Or email:

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