Compensating the overlay modeling errors in lithography process of wafer stepper

The overlay modeling errors are commonly modeled as the sum of inter-field and intra-field errors in lithography process of wafer stepper. The inter-field errors characterize the global effect while the intra-field errors represent the local effect. To have a better resolution and alignment accuracy, it is important to model the overlay errors and compensate them into tolerances. This paper proposes a weighted least squares (WLS) estimator for two general overlay error models such that more accurate linear term parameters of the overlay error can be obtained. First, the least squares (LS) estimator is applied to obtain the parameters of linear and nonlinear terms. We intend to estimate the parameters of linear term while taking the nonlinear term as our modeling residual errors. Next, we use the WLS estimator to obtain more accurate parameters of linear term and thus reduced the modeling errors by choosing appropriate stepper control parameters. The WLS estimator is applied to a real data set collecting 537 wafers from a wafer fabrication facility. The test results demonstrate that the estimated linear term parameters of the WLS estimator are much more close to the assumed ones than the LS estimator.