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 φ = φ n 1 sin 1 n 2 sin 2

• in general φ = φ Ñ 1 sin 1 Ñ 2 sin 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 • cos φ = φ 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 j Ψ = ρ = tan Ψ e tan e s R s 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 ' Coeff. Ext. k SiO2 Optical Constants 1.58 0.10 ' 5.0 4.0 n 1.56 n 4.0 3.0 0.08 ' Coeff. Ext. 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 ' Coeff. Ext. 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 ' Coeff. Ext. 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. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Building the model • Seed Values • Thickness • process engineer’s guess • analyst's guess • trial-and-error • till it looks good • Cauchy coefficients

•An between ~ 1.4 and 2.2 • higher for poly or a_Si • Oscillators • tough • “GenOsc” formalism A wise old sage once said: “The best way to solve a problem is to have solved one just like it yesterday.”

1-22 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum The regression process • Don’t turn all the variables loose to begin with • e.g. for a Cauchy • thickness first

• then An and thickness

• then include Bn • add in extinction coefficient • For a stack • don’t try to determine thicknesses and OC’s simultaneously • creative deposition A wise old sage once said: • “done” is a relative term “You can have it all, you just • does it make sense can’t have it all at once.”

1-23 H. Tompkins Ellipsometry What you can do, and what you can’t do Requirements

• plane parallel interfaces • roughness • film must be uniform • graded layers • anisotropic layers •multilayers • need to know something about OC’s • coherence • patterned wafers • non-uniform thickness • macroscopic roughness • helps if the film-of-interest is on top • optical contrast • polymer on glass

1-24 H. Tompkins Ellipsometry What you can do, and what you can’t do Optical Constants of Very Thin Films

• consider a single wavelength (632.8 nm) at 70° • oxynitride on silicon • Delta/Psi trajectories

• below 100Å, very difficult to determine index, n • distinguishing one material from another • determining thicknesses in a stack • e.g., ONO • however, if you’re willing to assume n, can determine thickness of very thin film • classic experiment of Archer • how far can you be off? 1-25 H. Tompkins Ellipsometry What you can do, and what you can’t do Optical Constants of Very Thin Films

making it better directions • DUV or VUV • shorter wavelengths • extinction coefficient often nonzero •IR • absorption bands are different for different materials

1-26 H. Tompkins Ellipsometry What you can do, and what you can’t do Optical Constants of Very Thin Films

φ1

Ñ1

φ2 Ñ2 d

Ñ3 Fundamental Limitation φ3 • Our ability to make films with: • plane parallel interfaces • uniformity

1-27 H. Tompkins Ellipsometry Acknowledgements

• Bell Laboratories, prior to the divestiture (< 1982) • Motorola • J. A. Woollam Co., Inc. • James Hilfiker • Stefan Zollner

1-28 H. Tompkins Ellipsometry