Spectroscopic Ellipsometry: What it is, what it will do, and what it won’t do by Harland G. Tompkins • Introduction • Fundamentals • Anatomy of an ellipsometric spectrum • Analysis of an ellipsometric spectrum • What you can do, and what you can’t do 1-1 H. Tompkins Ellipsometry Introduction Perspective • Spectroscopic Ellipsometry is an optical technique used for analysis and metrology • A light beam is reflected off of the sample of interest • The light beam is then analyzed to see what the sample did to the light beam • We then draw conclusions about the sample • thickness • optical constants • microstructure • Model based •allmeasurement techniques are model based 1-2 H. Tompkins Ellipsometry Fundamentals Polarized Light • The Name • “Ellipsometry” comes from “elliptically polarized light” • better name would be “polarimetry” + • Linearly Polarized = • combining two light beams in phase, gives linearly polarized light 1-3 H. Tompkins Ellipsometry Fundamentals Polarized Light (continued) • Elliptically Polarized • combining two light beams + out of phase, gives elliptically polarized light • Two ways = • pass through a retarder • reflect off a surface • absorbing material • substrate with film 1-4 H. Tompkins Ellipsometry Fundamentals Laws of Reflection and Refraction • Reflection φ = φ i r • Refraction (Snell’s law) • for dielectric, i.e. k = 0 n sin φ = n sin φ 1 1 2 2 • in general Ñ sin φ = Ñ sin φ 1 1 2 2 • sine function is complex • corresponding complex cosine function 2 φ + 2 φ = sin 2 cos 2 1 1-5 H. Tompkins Ellipsometry Fundamentals Reflections (orientation) • Electric Field Vector • Plane-of-Incidence • incoming Ep • normal • outgoing Plane of Incidence Es • s-waves and p-waves • “senkrecht” and “parallel” 1-6 H. Tompkins Ellipsometry Fundamentals Equations of Fresnel • Fresnel reflection coefficients, r p r s • complex numbers 12 12 • ratio of Amplitude of outgoing to incoming • different for p-waves and s-waves φ − φ p Ñ cos Ñ cos φ − φ = 2 1 1 2 s Ñ 1 cos 1 Ñ 2 cos 2 r12 r = Ñ cos φ + Ñ cos φ 12 φ + φ 2 1 1 2 Ñ 1 cos 1 Ñ 2 cos 2 • Reflectance ℜ • ratio of Intensity • square of Amplitude • for a single interface 2 ℜ p = p 2 ℜs = s r12 r12 1-7 H. Tompkins Ellipsometry Fundamentals Brewster Angle (for dielectrics) • r s always negative and non-zero • r p passes through zero •ℜ p goes to zero • The Brewster Angle • sometimes called the principal angle, polarizing angle • Reflected light is s-polarized • ramifications n φ = 2 • tan B n1 φ = φ • cos 2 sin B 1-8 H. Tompkins Ellipsometry Fundamentals “Brewster” Angle, for metals • if k is non-zero, r s and r p are complex • cannot plot r s and r p vs angle of incidence • However, we can still plot the Reflectance •ℜ p has a minimum, although not zero • Actually called the “principal angle” 1-9 H. Tompkins Ellipsometry Fundamentals Reflections with Films φ • Ellipsometry, 1 • Amplitude, phase of outgoing vs Ñ1 incoming φ Ñ 2 d • Reflectometry 2 • Intensity of outgoing vs incoming Ñ3 φ • Total Reflection Coefficient 3 • corresponds to Fresnel Coefficients • complex number rp + r p exp(−j2β) r s + rs exp(−j2β) Rp = 12 23 Rs = 12 23 + p p − β + s s − β 1 r12 r23 exp( j2 ) 1 r12r23 exp( j2 ) d • β is phase change from top to β = 2π Ñ cosφ bottom of film λ 2 2 1-10 H. Tompkins Ellipsometry Fundamentals Ellipsometry and Reflectometry definitions 2 2 • Reflectance ℜp = Rp ℜs = Rs • Delta, the phase difference induced by the reflection •if δ is the phase difference before, and δ the phase difference after the 1 ∆ δ δ 2 reflection then = 1 - 2 • ranges from zero to 360º (or -180 to +180º ) • Psi, the ratio of the amplitude diminutions Rp • ranges from zero to 90º tan Ψ= R s • The Fundamental Equation of Ellipsometry p ∆ j∆ Rp ρ = R ρ = Ψ j tan Ψ = s tan e e s R R 1-11 H. Tompkins Ellipsometry Fundamentals More Perspective • Ellipsometers measure ∆ and Ψ (sometimes only cos ∆ ) • Properties of the probing beam • Quantities such as thickness and index of refraction are calculated quantities, based on a model. • Properties of the sample • Values of ∆ and Ψ are always correct • Whether thickness and index are correct depend on the model • Both precision and accuracy for ∆ and Ψ • Precision for thickness • Accuracy, ??? 1-12 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples 180 150 film-free • Thin oxides on Silicon 10 Å 25 Å 120 60 Å 100 Å 90 50 ( ° ) ∆ 60 40 film-free 10 Å 25 Å 30 60 Å 30 100 Å 0 ( ° ) 200 400 600 800 1000 20 Ψ Wavelength (nm) 10 0 200 400 600 800 1000 Wavelength (nm) Si Optical Constants 7.0 6.0 6.0 5.0 n Ext. Coeff. ' k SiO2 Optical Constants 1.58 0.10 ' 5.0 4.0 n 1.56 n 4.0 3.0 0.08 Ext. Coeff. ' k ' 1.54 n Index ' Index 3.0 2.0 0.06 k ' 2.0 1.0 1.52 0.04 1.50 1.0 0.0 ' Index k 200 400 600 800 1000 ' 0.02 Wavelength (nm) 1.48 1.46 0.00 200 400 600 800 1000 Wavelength (nm) 1-13 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples • Thicker oxide on Silicon 90 360 2200 Å 2500 Å 60 240 2200 Å 2500 Å 30 120 180 in degrees in degrees ∆ Ψ 150 0 0 200 400 600 800 1000 200 400 600 120800 1000 2200 Å 2500 Å Wavelength (nm) Wavelength (nm)∆ 90 60 30 200 400 600 800 1000 Si Optical Constants 7.0 6.0 Wavelength (nm) 6.0 5.0 n Ext. Coeff. ' k ' 5.0 4.0 n 4.0 3.0 SiO2 Optical Constants 1.58 0.10 Index ' Index 3.0 2.0 k ' 1.56 n 0.08 Ext. Coeff. ' 2.0 1.0 k ' 1.54 1.0 0.0 n 0.06 200 400 600 800 1000 1.52 Wavelength (nm) 0.04 1.50 Index ' Index k ' 1.48 0.02 1.46 0.00 200 400 600 800 1000 Wavelength (nm) 1-14 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples • Polysilicon on oxide on silicon 3 srough 25 Å 2 polysilicon 3000 Å 1 sio2 1000 Å 0 si 1 mm 180 90 120 60 ∆ 60 30 in degrees Ψ 0 200 400 600 800 1000 0 200 400 600 800 1000 Wavelength (nm) Wavelength (nm) polysilicon OC's 6.0 5.0 5.0 4.0 Ext. Coeff. ' ' n 4.0 3.0 3.0 2.0 Index ' Index n k 2.0 k 1.0 ' 1.0 0.0 200 400 600 800 1000 Wavelength (nm) 1-15 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples 1 cr 300 Å • Thin chromium on silicon 0 si 1 mm 180 60 film-free 50 Å 120 40 100 Å 200 Å film-free 300 Å 50 Å Ψ 60 100 Å 20 in degrees 200 Å ∆ 300 Å 0 0 300 400 500 600 700 800 300 400 500 600 700 800 Wavelength (nm) Wavelength (nm) Chromium OC's 5.0 4.5 4.2 4.0 Ext. Coeff. ' 3.9 ' n 3.0 n 3.6 • caveats k 2.0 3.3 Index ' Index 3.0 k 1.0 ' 2.7 0.0 2.4 300 400 500 600 700 800 Wavelength (nm) 1-16 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Determining Film properties from SE spectra • Except for substrates, we cannot do a direct calculation What Ellipsometry Measures: What we are interested in: Film Thickness Refractive Index Psi (Ψ) Surface Roughness ∆ Interfacial Regions Delta ( ) Composition Crystallinity Anisotropy Desired information must be extracted Through a model-based analysis using Uniformity equations to describe interaction of light and materials 1-17 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum How we analyze data: 1-18 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Building the model • Optical Constants • Tabulated list • when OC’s are very well known • single-crystal 1 cauchy 0 Å 0 si 1 mm • thermal oxide of Si, LPCVD nitride • Dispersion Equation • Cauchy equation • dielectrics, primarily • empirical • not K-K consistent λ = + Bn + Cn n( ) An λ2 λ4 1-19 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Building the model • Optical Constants 2 polysilicon 0 Å • Dispersion Equation 1 sio2 1000 Å • Oscillator equation 0 si 1 mm 6.0 5.0 5.0 ' 4.0 k ' 4.0 n 3.0 3.0 2.0 Index ' Index 2.0 1.0 Ext. Coeff. ' 1.0 0.0 0.0 0 300 600 900 1200 1500 1800 0 300 600 900 1200 1500 1800 Wavelength (nm) Wavelength (nm) 5.0 4.0 4.0 30 20 3.0 3.0 ' 25 ' n 2.0 k ' 15 2.0 ' 1.0 20 1.0 10 0.0 2 0 300 600 900 1200 1500 1800 15 0.0 ε 0 300 600 900 1200 1500 1800 1 5 Wavelength (nm) Wavelength (nm) ε 10 0 5 -5 0 -10 0 2 4 6 8 10 0 2 4 6 8 10 Photon Energy (eV) Photon Energy (eV) 1-20 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Building the model • Optical Constants 3 srough 0 Å •Mixture 2 polysilicon 2000 Å 1 sio2 1000 Å • EMA, effective medium 0 si 1 mm approximation • Graded Layers • Anisotropic Layers • Superlattice 1-21 H.