Characterizing Illumination Angular Uniformity with Phase

40 Pages·2005·1.17 MB·English

Polarization Aberrations:
A 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
FLCC
Purpose & Outline
Purpose
: to compare multiple representations and propose a
common ‘language’ to describe polarization aberrations for optical
lithography
Outline
• What is polarization, why is it important
• Polarization aberrations: Various representations
• Physical properties
• Mueller matrix – pupil
• Jones matrix – pupil
• Pauli-spin matrix – pupil
• Others (E vs. E , coherence- & covariance - pupil)
in out
• Preferred representation
• Proposed simulation flow & example
• Causality, reciprocity, differential Jones matrices
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McIntyre, FLCC, 10/31/05
What is polarization?
Polarization is an expression of the orientation of the lines of electric flux
in an electromagnetic field. It can be constant or it can change either
gradually or randomly.
• Pure polarization states
Oscillating Polarization
Propagating EM wave
electron state
e-
Linear Circular Elliptical
E eiφ
y,out
Vector y,out
representation
in x y plane
E eiφ
x,out x,out
• Partially polarized light =
superposition of multiple pure states
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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
<
Low NA High NA x <
y
mask
TM
TE
φ
Z-component E = E sin(φ)
z TM
φ
negligible = E NA
TM
wafer
Increasing NA
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Scanner vendors are beginning to engineer
polarization states in illuminator?
Purpose: To increase exposure latitude (better contrast) by
minimizing TM polarization
Choice of illumination setting depends on features to be printed.
ASML, Bernhard (Immersion symposium 2005)
TE
Polarization orientation
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Polarization and immersion work together
for improved imaging
Immersion lithography can increase depth of focus
Dry
Wet
θ
l
θ
a
liquid
resist
resist
NA = .95 = sin(θ ) NA = .95 = n sin(θ )
a l l
θ = 71.8° θ ~ 39.3°
a l
λ
=
Depth of focus
2n(1- cos(θ))
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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
Last lens
Last lens θ
element l
element
liquid
air
resist
resist
Total internal reflection
NA = n sin(θ ) > 1
l l
prevents imaging
λ
Minimum feature = k
1
NA
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Polarization is needed to take full advantage
of immersion benefits
• Immersion increases DOF and/or decreases minimum feature
• Polarization increases exposure latitude (better contrast)
Dry, unpolarized
Dry, polarized
Wet, unpolarized
Wet, polarized
Wet
Dry
NA=0.95, Dipole 0.9/0.7, 60nm equal L/S (simulation)
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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
Illuminator effects
polarization design
Polarization
aberrations
of projection
Source optics
polarization
Wafer / Resist
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Polarization Aberrations
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