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.
Wafer leveling data are usually used inside the exposure tool for ensuring good focus, then discarded. This paper describes the implementation of a monitoring and analysis solution to download these data automatically, together with the correction profiles applied by the scanner. The resulting height maps and focus residuals form the basis for monitoring metrics tailored to catching tool and process drifts and excursions in a high-volume manufacturing (HVM) environment.
In this paper, we present four six cases to highlight the potential of the method: wafer edge monitoring, chuck drift monitoring, correlations between focus residuals and overlay errors, and pre-process monitoring by chuck fingerprint removal.
Feedback control of overlay errors to the scanner is a well-established technique in semiconductor manufacturing . Typically, overlay errors are measured, and then modeled by least-squares fitting to an overlay model. Overlay models are typically Cartesian polynomial functions of position within the wafer (Xw, Yw), and of position within the field (Xf, Yf). The coefficients from the data fit can then be fed back to the scanner to reduce overlay errors in future wafer exposures, usually via a historically weighted moving average. In this study, rather than using the standard Cartesian formulation, we examine overlay models using Zernike polynomials to represent the wafer-level terms, and Legendre polynomials to represent the field-level terms. Zernike and Legendre polynomials can be selected to have the same fitting capability as standard polynomials (e.g., second order in X and Y, or third order in X and Y). However, Zernike polynomials have the additional property of being orthogonal over the unit disk, which makes them appropriate for the wafer-level model, and Legendre polynomials are orthogonal over the unit square, which makes them appropriate for the field-level model. We show several benefits of Zernike/Legendre-based models in this investigation in an Advanced Process Control (APC) simulation using highly-sampled fab data. First, the orthogonality property leads to less interaction between the terms, which makes the lot-to-lot variation in the fitted coefficients smaller than when standard polynomials are used. Second, the fitting process itself is less coupled – fitting to a lower-order model, and then fitting the residuals to a higher order model gives very similar results as fitting all of the terms at once. This property makes fitting techniques such as dual pass or cascading  unnecessary, and greatly simplifies the options available for the model recipe. The Zernike/Legendre basis gives overlay performance (mean plus 3 sigma of the residuals) that is the same as standard Cartesian polynomials, but with stability similar to the dual-pass recipe. Finally, we show that these properties are intimately tied to the sample plan on the wafer, and that the model type and sampling must be considered at the same time to demonstrate the benefits of an orthogonal set of functions.