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Shrinking technology nodes and smaller process margins require improved photolithography overlay
control. Generally, overlay measurement results are modeled with Cartesian polynomial functions for both intra-field
and inter-field models and the model coefficients are sent to an advanced process control (APC)
system operating in an XY Cartesian basis. Dampened overlay corrections, typically via
exponentially or linearly weighted moving average in time, are then retrieved from the APC system
to apply on the scanner in XY Cartesian form for subsequent lot exposure. The goal of the above
method is to process lots with corrections that target the least possible overlay misregistration
in steady state as well as in change point situations. In this study, we model overlay errors on
product using Zernike polynomials with same fitting capability as the process of reference (POR) to
represent the wafer-level terms, and use the standard Cartesian polynomials to represent the
field-level terms. APC calculations for wafer-level correction are performed in Zernike basis while
field-level calculations use standard XY Cartesian basis. Finally, weighted wafer-level correction
terms are converted to XY Cartesian space in order to be applied on the scanner, along with
field-level corrections, for future wafer exposures. Since Zernike polynomials have the property of
being orthogonal in the unit disk we are able to reduce the amount of collinearity between terms
and improve overlay stability. Our real time Zernike modeling and feedback evaluation was performed
on a 20-lot dataset in a high volume manufacturing (HVM) environment. The measured on-product
results were compared to POR and showed a 7% reduction in overlay variation including a 22% terms
variation. This led to an on-product raw overlay Mean + 3Sigma X&Y improvement of
5% and resulted in 0.1% yield improvement.
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