Ellipsometer

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Ellipsometer

• B93901007 ???

2
Problem Overview

• We have a thin layer of oxide on a Si substrate
  and we want to find its thickness by using an
  ellipsometer. How?

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Overview on Procedure 1/4
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Overview on Procedure 2/4

• Light beam given by a light source passes through
  a combination of tunable polarizer and
  compensator.
• The light then enters the thin layer, the exiting
  beam on the other side should be a combination of
  reflected beam by the air-oxide surface and the
  oxide-substrate surface

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Overview on Procedure 3/4

• The light beam then passes an analyzer made to
  block any linearly-polarized beam.
• The Detector detects the beam
• We tune the polarizer to make the detected beam
  having minimum light intensity (i.e. The exiting
  light linearly-polarized and blocked by the
  analyzer)

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Overview on Procedure 4/4

• The Ellipsometer uses a fitting technique to find
  the complex refractive index and the thickness of
  the oxide

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Discussion 1/10

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Discussion 2/10

• The total reflection coefficient

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Discussion 3/10

• The measurement of the Ellipsometer
• First of all, lets see how the Ellipsometer
  detect this
• We can get a relationship in matrix form

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Discussion 4/10

• Tunable Polarizer matrix be at
  state S
• Tunable Compensator matrix be at
  state S
• Tunable Analyzer Matrix be which
  acts to block a certain direction of
  linear-polarized light

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Discussion 5/10

• Then if we tune the Polarizer and compensator to
  State such that the detected beam is with
  minimal energy (i.e. 0, when the reflected
  electric fields are linearly polarized)
• So we are able to solve this and get and
  , and so is

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Discussion 6/10

• We know that
• So, basically, we want to solve the equation
• for a set of parameters being the solution
• but apparently, not unique.

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Discussion 7/10

• So we must change certain parameters to get more
  equations so that well come up with a unique
  solution
• Since the materials are not-changeable, the only
  choices are the incident angle , and the type
  of light beam (changing )
• Changing the incident angle seems to be better

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Discussion 8/10

• And since each equation runs down to two
  equations actually (real and imaginary part), so
  we need 4 different measurements??
• Lets say, changing the incident angle 4 times,
  which come up with 8 equations and 7 unknowns,
  which seems an unique solution solvable

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Discussion 9/10

• Although we have the equations needed in hand,
  but with so many unknowns and the equations are
  terribly non-linear. So its hard to solve
  directly.
• What Ellipsometer do next is a Fitting
  technique
• Given an initial set of parameters, the
  algorithm takes this set into the equation. Then
  by observing the errors, it tries another more
  possible set of parameters
• By doing this fitting over and over again, the
  Ellipsometer would stop once it thinks the error
  is small enough. The solution set is estimated!

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Discussion 10/10

• Note that Ellipsometer itself do the fitting on
  
• and , where and
• Such that