Spectroscopic Ellipsometry:
What it is, what it will do,
and what it won’t do
by
Harland G. Tompkins
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1-1
Introduction
Fundamentals
Anatomy of an ellipsometric spectrum
Analysis of an ellipsometric spectrum
What you can do, and what you can’t do
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
•
1-2
all measurement techniques are model based
H. Tompkins
Ellipsometry
Fundamentals
Polarized Light
• The Name
•
•
“Ellipsometry” comes from
“elliptically polarized light”
better name would be
“polarimetry”
+
• Linearly Polarized
•
1-3
=
combining two light beams
in phase, gives linearly
polarized light
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
φi = φr
• Refraction (Snell’s law)
•
for dielectric, i.e. k = 0
•
in general
n1 sin φ1 = n 2 sin φ 2
Ñ 1 sin φ 1 = Ñ 2 sin φ 2
•
•
sine function is complex
corresponding complex cosine function
sin 2 φ 2 + cos 2 φ 2 = 1
1-5
H. Tompkins
Ellipsometry
Fundamentals
Reflections (orientation)
• Electric Field Vector
• Plane-of-Incidence
•
•
•
incoming
normal
outgoing
Ep
Es
Plane of Incidence
• s-waves and p-waves
•
1-6
“senkrecht” and “parallel”
H. Tompkins
Ellipsometry
Fundamentals
Equations of Fresnel
• Fresnel reflection coefficients,
•
complex numbers
p
12
r
r12s
• ratio of Amplitude of outgoing to incoming
• different for p-waves and s-waves
Ñ 2 cos φ 1 − Ñ 1 cos φ 2
r =
Ñ 2 cos φ 1 + Ñ 1 cos φ 2
p
12
• Reflectance
•
•
•
ℜ
ratio of Intensity
square of Amplitude
for a single interface
p 2
12
ℜ =r
p
1-7
Ñ 1 cos φ 1 − Ñ 2 cos φ 2
r =
Ñ 1 cos φ 1 + Ñ 2 cos φ 2
s
12
s 2
12
ℜ =r
s
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
•
tan φ B = 2
n1
•
1-8
cos φ 2 = sin φB
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
φ1
• Ellipsometry,
•
Amplitude, phase of outgoing vs
incoming
• Reflectometry
•
•
p
p
r12
+ r23
exp(− j2β )
R =
p p
1 + r12 r23 exp(− j2β )
β is phase change from top to
bottom of film
1-10
φ2
d
Ñ3
φ3
corresponds to Fresnel
Coefficients
complex number
p
•
Ñ2
Intensity of outgoing vs incoming
• Total Reflection Coefficient
•
Ñ1
s
s
+
r
r
s
12
23 exp(− j2β )
R =
s s
1+ r12
r23 exp(− j2β )
d
β = 2 π   Ñ2 cos φ 2
λ
H. Tompkins
Ellipsometry
Fundamentals
Ellipsometry and Reflectometry definitions
• Reflectance
ℜ = R
p
p2
s 2
ℜ = R
s
• Delta, the phase difference induced by the reflection
•
if δ1 is the phase difference before, and δ2 the phase difference after the
reflection then
•
∆ = δ1 - δ 2
ranges from zero to 360º (or -180 to +180º )
• Psi, the ratio of the amplitude diminutions
•
tan Ψ =
ranges from zero to 90º
Rp
Rs
• The Fundamental Equation of Ellipsometry
Rp
ρ= s
R
1-11
ρ = tan Ψ e
j∆
tan Ψ e
H. Tompkins
j∆
Rp
= s
R
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
• Thin oxides on Silicon
150
∆(°)
120
50
90
60
film-free
10 Å
25 Å 30
60 Å
100 Å
40
Ψ(°)
film-free
10 Å
25 Å
60 Å
100 Å
30
0
200
400
20
600
800
1000
Wavelength (nm)
10
0
200
400
600
800
1000
Wavelength (nm)
Si Optical Constants
6.0
n
k
5.0
5.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
200
400
600
Wavelength (nm)
800
0.0
1000
SiO2 Optical Constants
1.58
0.10
1.56
n
k
0.08
1.54
0.06
1.52
0.04
1.50
0.02
1.48
1.46
200
400
600
800
Ext. Coeff. ' k'
4.0
Ext. Coeff. ' k'
Index 'n'
6.0
Index 'n'
7.0
0.00
1000
Wavelength (nm)
1-13
H. Tompkins
Ellipsometry
The Anatomy of an Ellipsometric Spectrum
Examples
• Thicker oxide on Silicon
360
2200 Å
2500 Å
60
∆ in degrees
Ψ in degrees
90
30
240
2200 Å
2500 Å
120
180
150
0
200
400
600
800
0
200
1000
400
800
120
2200 Å
2500 Å
1000
Wavelength (nm)
∆
Wavelength (nm)
600
90
60
30
200
Si Optical Constants
Index 'n'
4.0
4.0
3.0
3.0
2.0
2.0
1.0
400
600
Wavelength (nm)
800
1000
0.0
1000
SiO2 Optical Constants
1.58
0.10
1.56
n
k
0.08
1.54
0.06
1.52
0.04
1.50
0.02
1.48
1.46
200
400
600
800
Ext. Coeff. ' k'
5.0
1.0
200
800
5.0
Ext. Coeff. ' k'
n
k
600
Wavelength (nm)
6.0
6.0
Index 'n'
7.0
400
0.00
1000
Wavelength (nm)
1-14
H. Tompkins
Ellipsometry
The Anatomy of an Ellipsometric Spectrum
Examples
• Polysilicon on oxide on silicon
3
2
1
0
srough
polysilicon
sio2
si
25 Å
3000 Å
1000 Å
1 mm
180
90
∆
Ψ in degrees
120
60
60
30
0
200
0
200
400
600
800
400
600
800
1000
Wavelength (nm)
1000
Wavelength (nm)
5.0
5.0
4.0
4.0
3.0
3.0
2.0
n
k
2.0
1.0
200
400
600
800
1.0
Ext. Coeff. ' k'
Index 'n'
polysilicon OC's
6.0
0.0
1000
Wavelength (nm)
1-15
H. Tompkins
Ellipsometry
The Anatomy of an Ellipsometric Spectrum
Examples
1 cr
0 si
• Thin chromium on silicon
300 Å
1 mm
180
60
Ψ
40
∆ in degrees
film-free
50 Å
100 Å
200 Å
300 Å
20
0
300
400
500
600
700
120
film-free
50 Å
100 Å
200 Å
300 Å
60
0
300
800
400
500
600
700
800
Wavelength (nm)
Wavelength (nm)
Chromium OC's
5.0
4.5
4.2
Index 'n'
• caveats
3.9
3.0
n
k
3.6
3.3
2.0
3.0
1.0
0.0
300
Ext. Coeff. ' k'
4.0
2.7
400
500
600
700
2.4
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:
Psi (Ψ)
Delta (∆)
Desired information must be extracted
Through a model-based analysis using
equations to describe interaction of
light and materials
1-17
Film Thickness
Refractive Index
Surface Roughness
Interfacial Regions
Composition
Crystallinity
Anisotropy
Uniformity
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
1 cauchy
0 si
• single-crystal
0Å
1 mm
• thermal oxide of Si, LPCVD nitride
•
Dispersion Equation
• Cauchy equation
•
dielectrics, primarily
•
empirical
•
not K-K consistent
n(λ ) = An +
1-19
Bn
2 +
λ
Cn
λ4
H. Tompkins
Ellipsometry
Analysis of an Ellipsometric Spectrum
Building the model
• Optical Constants
•
2 polysilicon
1 sio2
0 si
Dispersion Equation
• Oscillator equation
6.0
5.0
Ext. Coeff. ' k'
Index 'n'
5.0
4.0
3.0
2.0
1.0
0.0
0
300
600
900
1200
1500
4.0
3.0
2.0
1.0
0.0
0
1800
300
600
Wavelength (nm)
900
1200
1500
1800
Wavelength (nm)
5.0
4.0
30
4.0
20
3.0
15
25
2.0
0.0
0
300
5
600
900
1200
1500
1800
ε2
1.0
10
'k'
'n'
3.0
ε1
0Å
1000 Å
1 mm
2.0
20
1.0
15
0.0
0
300
600
Wavelength (nm)
900
1200
1500
1800
Wavelength (nm)
10
0
5
-5
-10
0
0
0
2
4
6
Photon Energy (eV)
1-20
8
10
2
4
6
8
10
Photon Energy (eV)
H. Tompkins
Ellipsometry
Analysis of an Ellipsometric Spectrum
Building the model
• Optical Constants
•
Mixture
• EMA, effective medium
approximation
1-21
•
Graded Layers
•
Anisotropic Layers
•
Superlattice
3
2
1
0
srough
polysilicon
sio2
si
H. Tompkins
0Å
2000 Å
1000 Å
1 mm
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
• “done” is a relative term
•
1-23
does it make sense
A wise old sage once said:
“You can have it all, you just
can’t have it all at once.”
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
•
1-24
polymer on glass
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
•
•
1-25
classic experiment of Archer
how far can you be off?
H. Tompkins
Ellipsometry
What you can do, and what you can’t do
Optical Constants of Very Thin Films
making it better
• DUV or VUV
•
•
directions
shorter wavelengths
extinction coefficient often
nonzero
• IR
•
1-26
absorption bands are different for
different materials
H. Tompkins
Ellipsometry
What you can do, and what you can’t do
Optical Constants of Very Thin Films
φ1
Ñ1
Ñ2
Fundamental Limitation
• Our ability to make films with:
•
•
1-27
φ2
Ñ3
d
φ3
plane parallel interfaces
uniformity
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