FLCC Polarization Aberrations: A Comparison of Various Representations FLCC Seminar 31 October 2005 Greg McIntyre , a,b Jongwook Kye b , Harry Levinson b and Andrew Neureuther a Department, University of California- Berkeley, Berkeley, CA Advanced Micro Devices, One AMD Place, Sunnyvale, CA 94088-34
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FLCC Polarization Aberrations: A Comparison of Various Representations FLCC Seminar 31 October 2005 Greg McIntyre, a,b Jongwook Kye b, Harry Levinson b.
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FLCC
Polarization Aberrations:A Comparison of Various
Representations
FLCC Seminar31 October 2005
Greg McIntyre,a,b Jongwook Kyeb, Harry Levinsonb and Andrew Neureuthera
a EECS Department, University of California- Berkeley, Berkeley, CA 94720b Advanced Micro Devices, One AMD Place, Sunnyvale, CA 94088-3453
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FLCCMcIntyre, FLCC, 10/31/05
Purpose
• What is polarization, why is it important• Polarization aberrations: Various representations
: to compare multiple representations and propose a common ‘language’ to describe polarization aberrations for optical lithography
Purpose & Outline
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FLCCMcIntyre, FLCC, 10/31/05
What is polarization?
Vector representation in x y plane
Ex,out ei
Ey,out ei y,out
x,out
• Pure polarization states
e-
• Partially polarized light = superposition of multiple pure states
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.
Linear Circular Elliptical
Oscillating electron
Propagating EM wave Polarization state
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FLCCMcIntyre, FLCC, 10/31/05
Why is polarization important in optical lithography?
xz
y
Low NA
High NA
Z component of E-field introduced at High NA from radial pupil component decreases image contrast
Z-component negligible
TMTE
mask
wafer
Increasing NA
= ETM NAEz = ETM sin()
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FLCCMcIntyre, FLCC, 10/31/05
Scanner vendors are beginning to engineer polarization states in illuminator?
Choice of illumination setting depends on features to be printed.
ASML, Bernhard (Immersion symposium 2005)
Polarization orientationTE
Purpose: To increase exposure latitude (better contrast) by minimizing TM polarization
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FLCCMcIntyre, FLCC, 10/31/05
Polarization and immersion work together for improved imaging
Immersion lithography can increase depth of focus
a
NA = .95 = sin(a)
a = 71.8NA = .95 = nl sin(l)
l ~ 39.3
l
liquid
resistresist
WetDry
))cos(-2n(1
Depth of focus
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FLCCMcIntyre, FLCC, 10/31/05
Immersion lithography can also enable hyper-NA tools (thus smaller features)
Minimum feature NA
1k
Total internal reflection prevents imaging
NA = nl sin(l) > 1
l
liquid
resistresist
Last lens element
Last lens element
air
Polarization and immersion work together for improved imaging
Thus, polarization state is important. But there are many things that can impact polarization state as light propagates through optical system.
Illuminator polarization design
Source polarization
Mask polarization effects
Polarization aberrations of projection optics
Wafer / Resist
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FLCCMcIntyre, FLCC, 10/31/05
Polarization Aberrations
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FLCCMcIntyre, FLCC, 10/31/05
Traditional scalar aberrationsScalar diffraction theory: Each pupil location characterized by a Scalar diffraction theory: Each pupil location characterized by a
single number (OPD)single number (OPD)
Typically defined in Zernike’sTypically defined in Zernike’s
ddeeaEayxE ikyxikDiffWafer
),('sin'cos),,(),','(
2
0
1
0
1
),(),( ,1 0
, mnn
n
mmn ZA
defocus astigmatism coma
Optical Path Difference
Ein eiin Eout eiout
a: illumination frequency
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FLCCMcIntyre, FLCC, 10/31/05
Polarization aberrations
Subtle polarization-dependent wavefront distortions cause intricate (and often non-intuitive) coupling between complex electric field components
Ex,in ei x,in Ex,out ei
Ey,in ei y,in Ey,out ei y,out
x,out
Each pupil location no longer characterized by a single number
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FLCCMcIntyre, FLCC, 10/31/05
Changes in polarization stateDiattenuation: Retardance:
Degrees of Freedom:• Magnitude• Eigenpolarization orientation
•Eigenpolarization ellipticity
•Eigenpolarization ellipticity
Degrees of Freedom:• Magnitude• Eigenpolarization orientation