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13 March 2012Source optimization incorporating margin image average with
conjugate gradient method
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.