Multi-Objective Defocus Robust Source and Mask Optimization Using Sensitive Penalty

• Main Authors: Pengzhi Wei, Yanqiu Li, Tie Li, Naiyuan Sheng, Enze Li, Yiyu Sun
• Format: Article
• Language: English
• Published: MDPI AG 2019-05-01
• Series: Applied Sciences
• Subjects: computational lithography; source and mask optimization (SMO); defocus robustness; process window enhancement; multi-objective optimization
• Online Access: https://www.mdpi.com/2076-3417/9/10/2151

The continuous decrease in the size of lithographic technology nodes has led to the development of source and mask optimization (SMO) and also to the control of defocus becoming stringent in the actual lithography process. Due to multi-factor impact, defocusing is always changeable and uncertain in the real exposure process. But conventional SMO assumes the lithography system is ideal, which only compensates the optical proximity effect (OPE) in the best focus plane. Therefore, to solve the inverse lithography problem with more uniformity of pattern in different defocus variations, we proposed a defocus robust SMO (DRSMO) approach that is driven by a defocus sensitivity penalty function for the first time. This multi-objective optimization samples a wide range of defocus disturbances and it can be proceeded by the mini-batch gradient descent (MBGD) algorithm effectively. The simulation results showed that a more robust defocus source and mask can be designed through DRSMO optimization. The defocus sensitivity factor <i>s_&#946;</i> maximally decreased 63.5% compared to conventional SMO, and due to the low error sensitivity and the depth of defocus (DOF), the process window (PW) was further enlarged effectively. Compared to conventional SMO, the exposure latitude (EL) maximally increased from 4.5% to 10.5% and DOF maximally increased 54.5% (EL = 5%), which proved the validity of the DRSMO method in improving the focusing performance.