Optimization of alignment in semiconductor lithography equipment

Recent enhanced integration of semiconductors permits less and less overlay error at exposure. Accordingly, higher-order alignment adjustment, which considers not only linear but also nonlinear error components, has been recently carried out. However, conventional higher-order alignment adjustment methods are based on least squares, and thus are only approximation approaches toward the goal of maximizing die yields. In particular, outliers taking place at exposure or alignment measurement strongly affect alignment adjustment and decrease die yields. From such a background, this paper models a problem finding optimal higher-order alignment adjustment under the purpose of maximizing die yields as an integer programming problem. Furthermore, we evaluate the proposed method based on integer programming and conventional least-squares approaches using numerical simulation. The experimental results demonstrate that the proposed method produces a solution that is excellent compared to the conventional approaches, irrespective of existence of outliers.