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We present a framework to analyze the performance of optical imaging in a hyper numerical aperture (NA)
immersion lithography scanner. We investigate the method to quantify imaging performance by computing upperand
lower-bounds on the threshold normalized image log-slope (NILS) and the depth of focus (DOF) in conjunction
with the traditional image quality metrics such as the mask error enhancement factor (MEEF) and the linearity for
various different pitches and line to space (LS) duty cycles. The effects of the interaction between the light
illumination and the feature size are extensively characterized based on the aerial image (AI) behavior in particular
for the extreme dipole illumination that is one of the commonly used off-axis illuminations for sub-100nm logic and
memory devices, providing resolution near the physical limit of an optical single patterning step. The proposed
aerial imaging-based DOF bounds are compared to the results obtained from an experimentally calibrated resist
model, and we observed good agreement. In general, the extreme dipole illumination is only optimal for a single
particular pitch, therefore understanding the through-pitch imaging performance bound, which depends on the
illumination shape, pattern size, and process conditions, is critically important. We find that overall imaging
performance varies depending upon the number of diffracted beams passing through the scanner optics. An even
number of beams provides very different trends compared to the results from an odd-number of beams. This
significant non-linear behavior occurs in certain pitch regions corresponding to 3 beam interference imaging. In this
region the imaging performance and the pattern printability become extremely sensitive to the LS duty cycle. In
addition, there is a notable tradeoff between the DOF and the NILS that is observed in the problematic 3-beam
region and this tradeoff eventually affects the achievable process window (PW). Given the practical real world
constraints such as the design rules and target design restrictions, computing upper- and lower-bounds of the
through-pitch DOF and NILS will be especially useful for both lithographers and metrology target designers in
understanding this complex behavior, as well as helping in the design of optimal targets used for applications
including alignment, overlay control, and process control in high volume semiconductor manufacturing.
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