Multi-objective and multi-solution source mask optimization using NSGA-II for more direct process window enhancement

Abstract

Source and mask optimization (SMO) technology is increasingly relied upon for resolution enhancement of photolithography as critical dimension (CD) shrinks. In advanced CD technology nodes, little process variation can impose a huge impact on the fidelity of lithography. However, traditional source and mask optimization (SMO) methods only evaluate the imaging quality in the focal plane, neglecting the process window (PW) that reflects the robustness of the lithography process. PW includes depth of focus (DOF) and exposure latitude (EL), which are computationally intensive and unfriendly to gradient-based SMO algorithms. In this study, we propose what we believe to be a novel process window enhancement SMO method based on the Nondominated Sorting Genetic Algorithm II (NSGA-II), which is a multi-objective optimization algorithm that can provide multiple solutions. By employing the variational lithography model (VLIM), a fast focus-variation aerial image model, our method, NSGA-SMO, can directly optimize the PW performance and improve the robustness of SMO results while maintaining the in-focus image quality. Referring to the simulations of two typical patterns, NSGA-SMO showcases an improvement of more than 20% in terms of DOF and EL compared to conventional multi-objective SMO, and even four times superior to single-objective SMO for complicated patterns.