Computational Lithography

Chapter 9

Source and Mask Optimization

In Chapters 5–8, a set of computationally efficient pixel-based OPC and PSM optimization algorithms based on gradient-based searches have been introduced for inverse lithography. These optimization methods, as well as other traditional RETs, fix the source during the optimization and limit the degrees of freedom that can be optimized in the mask patterns. OPC design, for instance, is usually limited by the competing requirements of lithography optimization and has to strike a balance between image contrast and pattern length when printing dense patterns [92]. To overcome these limitations, a set of simultaneous source and mask optimization (SMO) methods have been developed recently, where the synergy is exploited in the joint optimization of the source and mask patterns. The optimized source and mask patterns of SMO algorithms fall well outside the realm of known design forms and lead to solutions closer to global minimums.

Several source and mask optimization algorithms have been proposed in the literature. Burkhardt et al. introduced an algorithm to analytically predict the pupil pattern for an arbitrary periodic mask feature, where the optimized illumination depends only on stepper parameters and mask geometry [10]. Gau et al. proposed an algorithm to optimize the source for features at many pitches [24]. Recently, Rosenbluth et al. introduced the idea of simultaneous optimization of the source and mask [73]. Progler et al. presented an ...