Ellipsometric Analysis of Thin Films

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Ellipsometric Analysis of Thin Films

• Alexander Couzis
• ChE 5535

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Principles of Ellipsometry
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Linear Polarization vs. Elliptical Polarization
If E2mp m0, 1, 2, 3 ---gt waves are in phase
This wave has a fixed amplitude ie it is linearly
polarized
If E(2m1)p m0, 1, 2, 3 ---gt waves are out
of phase
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Circular Polarization
Scalar amplitude, but direction varies with time.
Amplitude is not restricted to a single plane as
before, but instead rotates so that the axis of
rotation is opposite to the direction of motion
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Elliptically Polarized Light
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Ellipsometer
An ellipsometer measures the changes in the
polarization state of light when it is reflected
from a sample. If the sample undergoes a change,
for example a thin film on the surface changes
its thickness, then its reflection properties
will also change. Measuring these changes in the
reflection properties can allow us to deduce the
actual change in the film's thickness.
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Null Ellipsometry

• Ellipsometry is a sensitive optical technique for
  determining properties of surfaces and thin
  films.
• If linearly polarized light of a known
  orientation is reflected at oblique incidence
  from a surface then the reflected light is
  elliptically polarized. The shape and orientation
  of the ellipse depend on the angle of incidence,
  the direction of the polarization of the incident
  light, and the reflection properties of the
  surface. We can measure the polarization of the
  reflected light with a quarter-wave plate
  followed by an analyzer the orientations of the
  quarter-wave plate and the analyzer are varied
  until no light passes though the analyzer. From
  these orientations and the direction of
  polarization of the incident light we can
  calculate the relative phase change, ?, and the
  relative amplitude change, ?, introduced by
  reflection from the surface.

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Polarization of Light
To simplify reflection and transmission
calculations, the incident electric field is
broken into two plane polarized components. The
plane of incidence is denoted by the "wheel" in
the pictures below. The normal to the surface and
all propagation vectors (ki,kr,kt) lie in this
plane.
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Ellipsometry

• The ellipsometry is an optical technique devoted
  to the analysis of surfaces. It is based on the
  measurement of the variation of the polarization
  state of the light after reflection on a plane
  surface. The technique of ellipsometry has been
  discovered one hundred years ago but it is only
  fifteen years ago, thanks to the development of
  electronic and computers that the technique
  expand largely in numerous fields.
• The strong advantages of ellipsometry are its non
  destructive character, its high sensitivity due
  to the measurement of the phase of the reflected
  light, its large measurement range (from
  fractions of monolayers to micrometers ), and the
  possibilities to control in real time complex
  processes.

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Ellispometry
After reflection on a sample surface, a linearly
polarized light beam is generally elliptically
polarized. The reflected light has phase changes
that are different for electric field components
polarized parallel (p) and perpendicular (s) to
the plane of incidence. Ellipsometry measures
this state of polarization or more precisely the
complex ratio r written as where ? and ? are
the amplitude ratio and phase shift,
respectively, of the p and s components and are
the ellipsometric parameters (often given as
tan?, cos?) measured as described in the Signal
treatment and calibration section. The
reflectance coefficients are directly related to
the optical constants of the surface by assuming
the ambient is air (Fresnel relations ) where n
is the complex refractive index n N -iK of the
surface.
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Ellipsometry

• The angle of refraction may be obtained using
  Snell-Descartes's Law
• Thus if the sample is an ideal bulk, the real and
  imaginary parts of the complex refractive index
  may be calculated from the measured tan ? and cos
  ? parameters with the knowledge of the incidence
  angle. The optical index and thickness of a
  transparent layer on known substrate can also be
  deduced in the same way. This kind of analysis is
  characteristic of a single wavelength
  ellipsometric measurement.

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MEASUREMENT TECHNIQUES

• Different measurement techniques of the
  polarization after reflection exist. They all use
  the same optical components a source, a
  polarizer, an analyzer and a detector. At these
  basic elements different other components like
  modulators or compensators can be added.

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Extinction method
The method uses the extinction of the signal to
make an angular measurement. The optical setup is
constituted by a monochromatic source (laser or
lamp spectrograph ), a polarizer, a compensator
(a quarter wavelength plate for example), an
analyzer and a photomultiplier tube. The
polarization is linear after the polarizer. It is
elliptical after the compensator which is
orientated to obtain a linear polarization after
reflection on the sample. The analyzer is then
orientated to extinguish the beam. The
orientation of the polarizer P, of the
compensator C and of the analyzer A allow to
obtain the ellipsometric parameters of the sample
from
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Extinction method
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Theory of the Rotating Polarizer Technique
The field amplitude is splitted into the S and P
components perpendicular and parallel to the
plane of incidence respectively. The effect of
each element is represented by a complex matrix
On the Detector the field amplitude is
Finally the intensity, I, seen by the detector
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Extraction of Physical Parameters
Ellipsometry is not a direct deductive method
except in one simple case the case of a bulk
material. It is generally necessary to build a
priori multilayer models to extract physical
informations after numerical adjustement. Case
of a substrate In the ideal case of a substrate
without native oxide and surface roughness the
ellipsometric parameters depend only on the angle
of incidence and on the indices of the substrate.
The following expression can be obtained
nijki is the refractive index of the
substrate F0 is the angle of incidence, n0 is the
refractive index of the medium
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Multilayer System

• Field Continuity
• Propagation across one layer

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Multilayer System
We define the field amplitude E and E- of the
wave propagating in the positive and in the
negative direction respectively. At the depth z,
the field is represented by the vector The
field continuity at the interface between the
layer i and the layer i1 is represented by

• E(zi-) is the value of the electric field in the
  layer i at the interface with the layer i1.
• E(zi) is the value of the electric field in the
  layer i1 at the interface with the layer i.
• ri,i1 and ti,i1 and the reflection and
  transmission coefficients at the interface
  between layer i and i1.

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Multilayer System
Propagation across one layer is represented by a
transfert matrix Li following where

The angle phi is
deduced from the Snell-Descartes relation. At the
surface the expression of the field amplitudes is
finally expressed by an iterative formula At
the interface between substrat and layer N, we
assume that E1 and E-0. Finally the reflection
coefficients are obtained making the amplitude
ratio of the incident and reflected waves.
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Polymer Adsorption Isotherms(Takahashi A. and
Kawagushi M., Advances in Polymer Science, 1982,
46, 1.)
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Polymer Adsorption Kinetics
Time dependent studies have mainly been reported
using ellipsometry for the measurement of the
amount adsorbed and the thickness of the layer.
They state that the equilibrium thickness was
reached within several hours while the
equilibrium adsorbance was attained only after
one day.
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Grafting KineticsMacromolecules 1999, 32,
4532-4538
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Adsorption of Surfactants at the Air-Liquid
InterfaceLangmuir 1999, 15, 1400-1409
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Multilayer Growth and Wetting ofC2Cl2F4
Physisorbed on GraphiteLangmuir 1998, 14,
4904-4907
Vapor Pressure Below Saturation
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