Page 1
H. Tompkins1-1 Ellipsometry
Spectroscopic Ellipsometry:
• Introduction• Fundamentals• Anatomy of an ellipsometric spectrum• Analysis of an ellipsometric spectrum• What you can do, and what you can’t do
What it is, what it will do, and what it won’t do
by
Harland G. Tompkins
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H. Tompkins1-2 Ellipsometry
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• all measurement techniques are model based
Introduction
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H. Tompkins1-3 Ellipsometry
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
+
=
Fundamentals
Page 4
H. Tompkins1-4 Ellipsometry
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
+
=
Fundamentals
Page 5
H. Tompkins1-5 Ellipsometry
Laws of Reflection and Refraction
• Reflection
• Refraction (Snell’s law)• for dielectric, i.e. k = 0
• in general
• sine function is complex• corresponding complex cosine function
φi = φr
Ñ1 sin φ1 = Ñ 2 sin φ2
n1 sin φ1 = n2 sin φ2
sin 2 φ2 + cos 2 φ2 = 1
Fundamentals
Page 6
H. Tompkins1-6 Ellipsometry
Reflections (orientation)
• Electric Field Vector
• Plane-of-Incidence• incoming• normal• outgoing
• s-waves and p-waves• “senkrecht” and “parallel”
Ep
Es
Plane of Incidence
Fundamentals
Page 7
H. Tompkins1-7 Ellipsometry
Equations of Fresnel
• Fresnel reflection coefficients, • complex numbers
• ratio of Amplitude of outgoing to incoming• different for p-waves and s-waves
• Reflectance• ratio of Intensity• square of Amplitude• for a single interface
r12
p =Ñ 2 cos φ1 − Ñ1 cos φ2
Ñ 2 cos φ1 + Ñ1 cos φ2 r12
s =Ñ 1 cos φ1 − Ñ 2 cos φ2
Ñ1 cos φ1 + Ñ 2 cos φ2
pr12sr12
2
12ss r=ℜ2
12pp r=ℜ
ℜ
Fundamentals
Page 8
H. Tompkins1-8 Ellipsometry
Brewster Angle (for dielectrics)
• r s always negative and non-zero• r p passes through zero• goes to zero• The Brewster Angle
• sometimes called the principal angle, polarizing angle
• Reflected light is s-polarized • ramifications
•
•
pℜ
tan φB =
n2
n1
cos φ2 = sin φB
Fundamentals
Page 9
H. Tompkins1-9 Ellipsometry
“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• has a minimum,
although not zero• Actually called the
“principal angle”
pℜ
Fundamentals
Page 10
H. Tompkins1-10 Ellipsometry
Reflections with Films
• Ellipsometry,• Amplitude, phase of outgoing vs
incoming
• Reflectometry• Intensity of outgoing vs incoming
• Total Reflection Coefficient• corresponds to Fresnel
Coefficients• complex number
• β is phase change from top to bottom of film
d
φ1
φ3
φ2Ñ2
Ñ3
Ñ1
Rp =r12
p + r23p exp(−j2β)
1 + r12p r23
p exp(−j2β)Rs =
r12s + r23
s exp(−j2β)1+ r12
s r23s exp(−j2β)
β = 2π dλ
Ñ2 cosφ2
Fundamentals
Page 11
H. Tompkins1-11 Ellipsometry
Ellipsometry and Reflectometry definitions
• Reflectance
• Delta, the phase difference induced by the reflection• if δ1 is the phase difference before, and δ2 the phase difference after the
reflection then ∆∆∆∆ = δδδδ1 - δδδδ2• ranges from zero to 360º (or -180 to +180º )
• Psi, the ratio of the amplitude diminutions• ranges from zero to 90º
• The Fundamental Equation of Ellipsometry
ℜ p = Rp 2ℜ s = Rs 2
tan Ψ =
Rp
R s
ρ = tan Ψe j∆ tan Ψ ej∆ =
Rp
R ss
p
RR=ρ
Fundamentals
Page 12
H. Tompkins1-12 Ellipsometry
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, ???
Fundamentals
Page 13
H. Tompkins1-13 Ellipsometry
Examples
• Thin oxides on Silicon
The Anatomy of an Ellipsometric Spectrum
Si Optical Constants
Wavelength (nm)200 400 600 800 1000
Inde
x 'n
'
Ext. C
oeff. 'k'
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
nk SiO2 Optical Constants
Wavelength (nm)200 400 600 800 1000
Inde
x 'n
'
Ext. C
oeff. 'k'
1.46
1.48
1.50
1.52
1.54
1.56
1.58
0.00
0.02
0.04
0.06
0.08
0.10
nk
Wavelength (nm)200 400 600 800 1000
Ψ (
° )
0
10
20
30
40
50
film-free10 Å25 Å60 Å100 Å
Wavelength (nm)200 400 600 800 1000
∆ (
° )
0
30
60
90
120
150
180
film-free10 Å25 Å60 Å100 Å
Page 14
H. Tompkins1-14 Ellipsometry
Examples
• Thicker oxide on Silicon
The Anatomy of an Ellipsometric Spectrum
Wavelength (nm)200 400 600 800 1000
Ψ in
deg
rees
0
30
60
90
2200 Å2500 Å
Wavelength (nm)200 400 600 800 1000
∆ in
deg
rees
0
120
240
360
2200 Å2500 Å
Wavelength (nm)200 400 600 800 1000
∆
30
60
90
120
150
180
2200 Å2500 Å
Si Optical Constants
Wavelength (nm)200 400 600 800 1000
Inde
x 'n
'
Ext. C
oeff. 'k'
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
nk
SiO2 Optical Constants
Wavelength (nm)200 400 600 800 1000
Inde
x 'n
'
Ext. C
oeff. 'k'
1.46
1.48
1.50
1.52
1.54
1.56
1.58
0.00
0.02
0.04
0.06
0.08
0.10
nk
Page 15
H. Tompkins1-15 Ellipsometry
Examples• Polysilicon on oxide on silicon
The Anatomy of an Ellipsometric Spectrum
Wavelength (nm)200 400 600 800 1000
Ψ in
deg
rees
0
30
60
90
Wavelength (nm)200 400 600 800 1000
∆
0
60
120
180
polysilicon OC's
Wavelength (nm)200 400 600 800 1000
Inde
x 'n
'
Ext. Coeff. 'k'
1.0
2.0
3.0
4.0
5.0
6.0
0.0
1.0
2.0
3.0
4.0
5.0
nk
0 si 1 mm1 sio2 1000 Å2 polysilicon 3000 Å3 srough 25 Å
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H. Tompkins1-16 Ellipsometry
Examples
• Thin chromium on silicon
• caveats
The Anatomy of an Ellipsometric Spectrum
Wavelength (nm)300 400 500 600 700 800
∆ in
deg
rees
0
60
120
180
film-free50 Å100 Å200 Å300 Å
Wavelength (nm)300 400 500 600 700 800
Ψ
0
20
40
60
film-free50 Å100 Å200 Å300 Å
0 si 1 mm1 cr 300 Å
Chromium OC's
Wavelength (nm)300 400 500 600 700 800
Inde
x 'n
'
Ext. Coeff. 'k'
0.0
1.0
2.0
3.0
4.0
5.0
2.4
2.7
3.0
3.3
3.6
3.9
4.2
4.5
nk
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H. Tompkins1-17 Ellipsometry
Determining Film properties from SE spectra• Except for substrates, we cannot do a direct calculation
What Ellipsometry Measures: What we are interested in:
Analysis of an Ellipsometric Spectrum
Psi (Ψ)Delta (∆)
Film ThicknessRefractive Index
Surface Roughness Interfacial Regions
CompositionCrystallinityAnisotropyUniformityDesired information must be extracted
Through a model-based analysis using equations to describe interaction of
light and materials
Page 18
H. Tompkins1-18 Ellipsometry
How we analyze data:Analysis of an Ellipsometric Spectrum
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H. Tompkins1-19 Ellipsometry
Building the model• Optical Constants
• Tabulated list• when OC’s are very well known• single-crystal• thermal oxide of Si, LPCVD nitride
• Dispersion Equation• Cauchy equation
• dielectrics, primarily• empirical• not K-K consistent
Analysis of an Ellipsometric Spectrum
42)( λλλ nnn
CBAn ++=
0 si 1 mm1 cauchy 0 Å
Page 20
H. Tompkins1-20 Ellipsometry
Building the model• Optical Constants
• Dispersion Equation• Oscillator equation
Analysis of an Ellipsometric Spectrum
Wavelength (nm)0 300 600 900 1200 1500 1800
Inde
x 'n
'
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Wavelength (nm)0 300 600 900 1200 1500 1800
Ext.
Coe
ff. 'k
'
0.0
1.0
2.0
3.0
4.0
5.0
Photon Energy (eV)0 2 4 6 8 10
ε2
0
5
10
15
20
25
30
Photon Energy (eV)0 2 4 6 8 10
ε 1
-10
-5
0
5
10
15
20
0 si 1 mm1 sio2 1000 Å2 polysilicon 0 Å
Wavelength (nm)0 300 600 900 1200 1500 1800
'n'
0.0
1.0
2.0
3.0
4.0
5.0
Wavelength (nm)0 300 600 900 1200 1500 1800
'k'
0.0
1.0
2.0
3.0
4.0
Page 21
H. Tompkins1-21 Ellipsometry
Building the model• Optical Constants
• Mixture• EMA, effective medium
approximation
• Graded Layers• Anisotropic Layers• Superlattice
Analysis of an Ellipsometric Spectrum
0 si 1 mm1 sio2 1000 Å2 polysilicon 2000 Å3 srough 0 Å
Page 22
H. Tompkins1-22 Ellipsometry
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
Analysis of an Ellipsometric Spectrum
A wise old sage once said:
“The best way to solve a problem is to have solved one just like it yesterday.”
Page 23
H. Tompkins1-23 Ellipsometry
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
• “done” is a relative term• does it make sense
Analysis of an Ellipsometric Spectrum
A wise old sage once said:
“You can have it all, you just can’t have it all at once.”
Page 24
H. Tompkins1-24 Ellipsometry
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
What you can do, and what you can’t do
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H. Tompkins1-25 Ellipsometry
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?
What you can do, and what you can’t do
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H. Tompkins1-26 Ellipsometry
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
What you can do, and what you can’t do
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H. Tompkins1-27 Ellipsometry
Optical Constants of Very Thin Films
Fundamental Limitation• Our ability to make films with:
• plane parallel interfaces• uniformity
What you can do, and what you can’t do
d
φ1
φ3
φ2Ñ2
Ñ3
Ñ1
Page 28
H. Tompkins1-28 Ellipsometry
Acknowledgements
• Bell Laboratories, prior to the divestiture (< 1982)
• Motorola• J. A. Woollam Co., Inc.
• James Hilfiker
• Stefan Zollner