Gradient-Based Source and Mask Optimization in Optical Lithography

Abstract

Source and mask optimization (SMO) has been proposed recently as an effective solution to extend the lifespan of conventional 193 nm lithography, although the process is computationally intensive. In this study, we propose a highly effective and efficient method for source optimization and improve a previous method for mask optimization. An SMO framework is implemented by integrating them. Based on pixel-based source and mask representation, the gradients of the objective function are utilized to guide optimization. In addition to maintain the image fidelity, extra penalties are added into the objective function to increase the depth of focus (DOF) and regularize the source and mask patterns. In our SMO framework, a specially designed mask optimization procedure is performed to enhance the algorithm robustness. Afterward, the source optimization and mask optimization are performed alternatively. Convergence results can be acquired using only two or three iteration cycles. This method is demonstrated using two mask patterns with critical dimensions of 45 nm, including a periodic array of contact holes and a cross gate design. The results show that our method can provide great improvements in both image quality and DOF. The robustness of our method is also verified using different initial conditions.