Gradient-Based Source Mask Optimization for Extreme Ultraviolet Lithography

Abstract

Extreme ultraviolet (EUV) lithography is the most promising technology for the next generation very-large scale integrated circuit fabrication. EUV lithography invariably introduces distortions in the projected lithographic mask patterns and thus inverse lithography tools are needed to compensate for these. This paper develops two kinds of model-based source and mask optimization (SMO) frameworks, referred to as the parametric SMO and the pixelated SMO, both to provide primary strategies for improving the image fidelity of EUV lithography. In the parametric SMO, the source pattern is defined by a few geometrical parameters. Meanwhile, in the pixelated SMO, the light source is represented by a grid pattern. These two SMO frameworks are established using a nonlinear imaging model that coarsely approximates the optical proximity effect, flare and photoresist effects in an analytic closed-form. In addition, a retargeting method is used to approximately compensate for the mask shadowing effects based on a calibrated shadowing model. Another contribution of this paper is to develop a hybrid cooperative optimization algorithm based on conjugate gradient and compare it to the simultaneous SMO algorithm. It is shown that the hybrid SMO algorithm can achieve superior convergence characteristics and computational efficiency over the simultaneous SMO algorithm.