Pixelated source and mask optimization for immersion lithography

Immersion lithography systems with hyper-numerical aperture (hyper-NA) (NA > 1) have become indispensable in nanolithography for technology nodes of 45 nm and beyond. Source and mask optimization (SMO) has emerged as a key technique used to further improve the imaging performance of immersion lithography. Recently, a set of pixelated gradient-based SMO approaches were proposed under the scalar imaging models, which are inaccurate for hyper-NA settings. This paper focuses on developing pixelated gradient-based SMO algorithms based on a vector imaging model that is accurate for current immersion lithography. To achieve this goal, an integrative and analytic vector imaging model is first used to formulate the simultaneous SMO (SISMO) and sequential SMO (SESMO) frameworks. A gradient-based algorithm is then exploited to jointly optimize the source and mask. Subsequently, this paper studies and compares the performance of individual source optimization (SO), individual mask optimization (MO), SISMO, and SESMO. Finally, a hybrid SMO (HSMO) approach is proposed to take full advantage of SO, SISMO, and MO, consequently achieving superior performance.