Compensating Modeling Overlay Errors Using the Weighted Least-Squares Estimation

The lithography performed on a stepper is a key process of integrated circuit manufacturing. To have a better resolution and alignment accuracy in lithography, it is important to model the overlay errors and compensate them into tolerances. The systematic overlay errors are commonly modeled as the sum of inter-field and intra-field errors. The inter-field errors describe the global effect, while the intra-field errors indicate the local effect. In this paper, two overlay error models are introduced, and a weighted least-squares (WLS) estimator is developed to derive the more accurate linear term parameters of the overlay errors. The least-squares (LS) estimator is applied to the Arnold ten-parameter model for estimating the parameters of linear and nonlinear terms. We intend to estimate the parameters of a linear term, while taking the nonlinear term as our modeling residual errors. Then, we use the WLS estimator to derive the more accurate linear term parameters in the Perloff eight-parameter model. Finally, the WLS estimator is applied to real data collected from 453 wafers provided by a wafer fabrication facility in Taiwan. Test results demonstrate that the linear term parameters estimated by the WLS estimator are much more accurate than those obtained by the LS estimator.