Source optimization incorporating margin image average with conjugate gradient method

Abstract

Source optimization (SO) becomes increasingly important to resolution enhancement in sub-32 nm lithography nodes because the dense pattern configurations significantly limit the capability of mask correction. A key step in SO is the image formation by Abbe's method, which is a linear operation of integrating all source points' images incoherently to form aerial images. However, the aerial images are usually converted to resist images through the nonlinear sigmoid function. Such operation loses the merit of linearity in optimization and leads to slow convergence and time-consuming calculation. In this paper we propose a threshold-based linear resist model to replace the sigmoid model in SO. The effectiveness of our proposed model can be clearly seen from mathematical analysis. We also compare results based on linear and sigmoid models. Highly similar optimal sources are obtained, but the linear model has a significant advantage over the sigmoid in terms of convergence rate and simulation time. Furthermore, the process variations characterized by exposure-defocus (E-D) windows are still in similar trends for optimal sources based on two different resist models.