Polarization Aberrations: A Comparison of Various Representations

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Polarization AberrationsA Comparison of Various
Representations
Greg McIntyre,a,b Jongwook Kyeb, Harry Levinsonb
and Andrew Neureuthera

• a EECS Department, University of California-
  Berkeley, Berkeley, CA 94720
• b Advanced Micro Devices, One AMD Place,
  Sunnyvale, CA 94088-3453

FLCC Seminar 31 October 2005
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Purpose Outline
Purpose
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(No Transcript)
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Why is polarization important in optical
lithography?
Z component of E-field introduced at High NA from
radial pupil component decreases image contrast
?
z
?
x
Low NA
High NA
mask
?
Z-component negligible
?
wafer
Increasing NA
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Polarization and immersion work together for
improved imaging
Immersion lithography can increase depth of focus
Dry
Wet
?l
?a
liquid
resist
resist
NA .95 sin(?a)
NA .95 nl sin(?l)
?a 71.8?
?l 39.3?
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Polarization and immersion work together for
improved imaging
Immersion lithography can also enable hyper-NA
tools (thus smaller features)
Dry
Wet
Minimum feature
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Thus, polarization state is important. But there
are many things that can impact polarization
state as light propagates through optical system.
Mask polarization effects
Illuminator polarization design
Polarization aberrations of projection optics
Source polarization
Wafer / Resist
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Polarization Aberrations
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Traditional scalar aberrations

• Scalar diffraction theory Each pupil location
  characterized by a single number (OPD)

Typically defined in Zernikes
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Polarization aberrations
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Changes in polarization state
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Sample pupil (physical properties)
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Mueller-pupil
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Mueller Matrix - Pupil

• Consider time averaged intensities

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Mueller Matrix - Pupil

• Recast polarization aberration into Mueller pupil

Mueller Pupil
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Mueller Matrix - Pupil
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Mueller Matrix - Pupil
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Jones-pupil
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Jones Matrix - Pupil
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Jones Matrix - Pupil
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Jones Matrix - Pupil
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Pauli-pupil
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Pauli-spin Matrix - Pupil
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Meaning of the Pauli-Pupil
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Usefulness of Pauli-Pupil to Lithography
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The advantage of Pauli-Pupils
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Proposed simulation flow
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Simulation example
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A word of caution
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Constraints of Causality Reciprocity
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Differential Jones Matrix
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Differential Jones Matrix
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Other representations
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E-field test representation
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Intensity test representation
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Covariance Coherency Matrix
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Additional comments on polarization in lithography
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Conclusion

• Polarization is becoming increasingly important
  in lithography
• Compared various representations of polarization
  aberrations proposed Pauli-pupil as language
  to describe them
• Proposed simulation flow and input format
• Multiple representations of same pupil help to
  understand complex and non-intuitive effects of
  polarization aberrations