Introduction to Spectroscopic Ellipsometry

Outline 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

Ellipsometry Overview Thin Film Applications Non-destructive Optical Technique Based on Polarization Change Indirect, Model-based Approach Measure Thickness/Optical Constants & More!

Light x Electric field E(z,t) z Direction of propagation y Magnetic field B(z,t) E( z, t) Ex cos( t kz x) xˆ E y cos( t kz y) yˆ Energy( ev ) h hc

Electromagnetic Spectrum E( ev) h 4eV nm ( nm)

Polarization Defined by orientation and phase of E-field vector Superposition of two orthogonal waves X Wave, E x Y Wave, E y Z

Linear Polarization Waves in phase Arbitrary amplitudes

Circular Polarization Waves 9º out of phase Equal amplitudes

Elliptical Polarization Most general description of polarization state Arbitrary phase Arbitrary amplitudes

Ellipse Characterization E y x - y E x E y E rs rp - rs r p r s E x E rp tan E E x y r r p s x y rp rs

Ellipsometry and Polarization Measures changes in polarization state of light Difference in phase shift ( ) Ratio of amplitude change ()

Ellipsometry vs. Reflectometry Based on Intensity I E Based on amplitude and phase shift of E field; polarization! I I r E in E out I t Transmission = I t / Io Reflection = I r / Io r r p s tane j

Ellipsometry Vs Reflectivity Phase ( ) information much more sensitive to ultra-thin films 35. 3. 5. (ß). nm nm Native SiO on c-si 5.. 3 4 Photon Energy (ev) 5 6.65.6.55 R.5.45.4.35 7. 6. 5. 4. (ß) 3.... 3 4 Photon Energy (ev) 5 6 Simulation @ 7 AOI 3 4 Photon Energy (ev) 5 6

Mathematics of Ellipsometry 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

7 HORIBA, Ltd. All rights reserved. HORIBA, Ltd. All rights reserved. y kz t E x kz t E t z E y y x x ˆ ) cos( ˆ ) cos( ), ( Jones Vectors y x i y i x y x e E e E E E J ~ Describe pure polarization states of light

Jones Vector Examples Linear with x-axis as line of vibration: Linear with y-axis as line of vibration: Linear polarization oriented at 45º: Right (+) and Left Circular (-): i

Jones Vector Examples (cont d) Elliptical: Unpolarized: DNE tan e i tan E E x y x y

7 HORIBA, Ltd. All rights reserved. HORIBA, Ltd. All rights reserved. Isotropic Sample: Rotation Between Coordinates: Polarizer and Analyzer: Photoelastic Modulator: Jones Matrices ) ( t i e s p i r r e tan cos sin sin cos

7 HORIBA, Ltd. All rights reserved. HORIBA, Ltd. All rights reserved. s p s i p i s p s r p r r r E E r r E E ~ ~ ~ ~ ~ ~ ~ ~ Single Interface: Jones Vectors/Matrices For isotropic reflecting surface: r ps = r sp = s r p r E E ~ ~ s i p i E E ~ ~ i s p e r r tan ~ ~

7 HORIBA, Ltd. All rights reserved. HORIBA, Ltd. All rights reserved. Light Propagation: Jones Matrices ) ( tan ) ( ) ( ) ( ) ( P R e M R e M R A R t E i i Analyzer Modulator Polarizer Sample Track changes in polarization Sample Light source Detector Polarizer Modulator Analyzer Initial Pol. State

PME Jones Formalism I( t) E( t) I I I s sin ( t) I c cos ( t ) I cos cos A cos ( P cos ( P M )sin Asin M sin cos M )cos M (cos A cos ) I s sin ( P M )sin Asin sin sin sin I c sin ( P M ) sin cos sin M (cos cos A) sin Acos M sin cos

7 HORIBA, Ltd. All rights reserved. HORIBA, Ltd. All rights reserved. Stokes Vectors lc rc y x y x I I I I I I I I S S S S S o o 45 45 3 Describe partial (& pure) polarization states (unpolarized, partially polarized) S and S S S 3

7 HORIBA, Ltd. All rights reserved. HORIBA, Ltd. All rights reserved. I S S S S S S S I I I P un tp tp 3 3 Stokes Vectors (cont d) Totally polarized: Partially polarized: Unpolarized: ; 3 P S S S ; 3 P S S S S ; 3 P S S S

7 HORIBA, Ltd. All rights reserved. HORIBA, Ltd. All rights reserved. Linear with y-axis as line of vibration: Linear with x-axis as line of vibration: Stokes Vector Examples Linear oriented at 45º: Right (+) and Left (-) Circular:

Mueller Matrix Non-ideal depolarizing samples Represents effects of optical components or sample on Stokes vector S S S S 3 OUT M M M M 3 4 M M M M 3 4 M M M M 3 3 33 43 M M M M 4 4 34 44 S S S S 3 IN

Isotropic Sample M M M M M 3 4 M M M M 3 4 M M M M 3 3 33 43 M M M M 4 4 34 44 N N C S S C Mueller matrix of a c-si sample acquired by Auto SE

Optical Properties Complex refractive index (Ñ) ~ N n ik Incident ray n = refractive index Phase velocity c n Index n Velocity n θ θ θ Index n Velocity c Refracted ray k = extinction coefficient Loss of wave energy to the material k 4

Complex Fresnel Coefficients Describe reflection at each interface Depend on angle and polarization direction (p or s) i r p E E r i p n n t t cosi cos i n n i i cost cos t n i n t t E ts r s E E r i s n n i i cosi cos i n n t t cost cos t

Determination of Optical Properties n i n t i t E ts tan e i r r p s n n n n t t i i cosi n cosi n cosi n cos n i i i t t cost cost cost cos t Use Snell s Law and invert: n i sin i n t sin t n t n i sini tan tan e i tan e i i /

Optical Interference Total reflection coefficient r tot r t r t e -i n ~ ~ n Film θ θ r r t r t t r r r t d t... r r t e -4i Infinite series solutions jβ r re R p,s jβ r r e n ~ Substrate t t t r r t t r r r r t t Film phase thickness d π n λ β cos

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 Surface Film Interface Substrate

Methods of SE Data Collection ex-situ Spectroscopic Ellipsometry UVISEL SMART-SE UVISEL 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

Methods of SE Data Collection (cont d) Mapping -D Wafer Plot -D Point Values 3-D Wafer Map

Methods of SE Data Collection (cont d) In-line

Methods of SE Data Collection (cont d) Vacuum Ultraviolet (VUV) Spectral Range of 47-85 nm (NIR option to nm) Remove absorption at low wavelengths due to O

Methods of SE Data Collection (cont d) Reflectometry/Transmission Temperature controlled

Methods of SE Data Collection (cont d) Liquid Cell Electrochemical Cell Sealed Cell

Methods of SE Data Collection (cont d) Textured Samples SEM picture of textured c-si

Ellipsometry Advantages Non-destructive, non-invasive, and non-contact Precise and reproducible Very sensitive to ultra-thin films < nm Applicable to almost any thin film materials (polymers, semiconductors, dielectrics, metals, alloys, etc.) Ideal for in-situ applications

P: Polarizer A: Analyzer C: Compensator S: Sample M: Modulator LC: Liquid Crystal Instrumentation Rotating Analyzer P S Rotating Compensator A Light Source P C Phase Modulation P S S M A A Detector Liquid Crystal Phase Modulation P LC S LC A

Phase Modulated Ellipsometer Fixed Analyzer Photoelastic Modulator (5KHz) Fixed Polarizer HORIBA UVISEL Detector Monochromator Sample Data Acquisition and Computer (DeltaPsi) Optical Fiber Shutter Xe lamp

Photoelastic Modulator Principle An electrically driven retarder introducing a phase shift varying sinusoidally with time Linearly polarized light E x n E x modulator n Piezo electric transducer (5 khz) d E y d e i E y Signal detected at 5 khz!!! Elliptically polarized light Strained SiO bar; birefringence Modulation at 5 khz!

Fixed elements PME Advantages Excellent precision on Very fast acquisition rate (~ ms/point) Covers a wide spectral range from 9- nm High polarization modulation rate of 5 khz Ψ and are measured over their full range; Ψ [, 9 ] and [, 36 ]

SE Data Analysis Use Regression Analysis Measurement Model Fit Results Psi ( ) 9 8 7 6 5 4 3 9 8 7 6 5 4.5 EXPERIMENTAL DATA.5 3 E (ev) 35 3 5 5 5 3.5 Delta ( ) Layer Layer Substrate Psi ( ) 9 8 7 6 5 4 3 9 8 7 6 5 4.5 EXPERIMENTAL DATA.5 3 E (ev) 35 3 5 5 5 3.5 Delta ( ) Thickness Optical Constants Roughness (n,k) = f(lambda) for the TiO layer 3..5 3..45 3.4.9.35 Re(Index).8.7.6.5.4.3 4 5 6 lambda (nm) 7.3.5..5..5 8 Im(Index)

Goodness of fit: Data Fitting (X - ) X = Th Exp N - P - N N: Total number of measurables P: Total number of fit parameters In phase modulated ellipsometry X represents the couple (Is, Ic)

Implications of KK Relationship Refractive index (n): Always follows slope of k Always increasing for absorbing materials, except in regions of anomalous dispersion 3.5 3. 3.5 3.95.9.7.65.6.55.5.45.4 n.85.35k.8.3.75.5.7..65.5.6..55.5 35 4 45 5 55 6 Wavelength (nm) 65 7 75 8

Normal Dispersion: Dielectric Refractive index (n) decreases with increasing λ 4 n 3 AlGaAs SiN x SiO 4 4 44 46 48 5 5 54 56 58 6 6 64 Wavelength (nm) 66 68 7 7 74 76 78 8

Anomalous Dispersion: Absorbing Region Refractive index (n) increases with increasing λ except where absorption peak occurs 3.5 3. 3.5 3.95.9 n.85.8.75.7.65.6.55.7.65.6.55.5.45.4.35k.3.5..5..5 35 4 45 5 55 6 Wavelength (nm) 65 7 75 8

Quality of Results Goal: find simplest, realistic model Minimize Are results physical? Negative k? K-K consistent? Follow anomalous or normal dispersion? Other indicators Error bars (9% confidence limits) Correlation matrix

Applications-Thin Films At home: entertainment, comfort, security, appliances, energy savings Our health: medical imaging, portable diagnostics, DNA analysis, implantable devices At work: printers, PCs, 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

Thin Films in Photovoltaics Structure Si: crystalline, nano, micro, poly, amorphous, textured... Compound semiconductor: III-V, SiGe, CdTe, CIS, CIGS... Organics: PCBM, P3HT, PEDOT:PSS... Transparent conducting oxides (TCO): SnO, ZnO, ITO... AR coating: SiN x, TiO x Metal contacts: Al, Ca, Mg Emitter Absorber

Thin Films in Displays Devices: TFT-LCD LED, OLED Materials: a-si, Poly-Si, SiN, SiO, MgO,ITO,SnO,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, SiO,TiO.. Vision and microspot capabilities can be crucial

Thin Films in Microelectronics Materials: a-si, Poly-Si, SiN, SiO, High, Low materials Materials for 9 nm lithography ( DUV ) New materials : Graphene, Nanomaterials

Thin Films in Optical Coatings Applications: Antireflection coating Filtering coatings Antiscratch coating Decorative coatings Electrochromic coatings Materials: SiO x, High/Low refractive multilyers SiN,TiOx, WOx,

Thin films in Biochemistry Objective: Selective capture of protein Biosensors Materials: Substrate: Gold Layers: DNA, proteins

Thin Films in Metallurgy Objective: Hardness Antifriction coatings Decorative coating Anticorrosion coating Materials: SiO x, TiO, Al, Al O 3,CrO, 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

Summary 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

Questions? For additional information or questions about ellipsometry, please visit: www.horiba.com/ellipsometry Or email: ellipsometry.us@horiba.com