Source optimization for image fidelity and throughput

Abstract

In this study we first review existing source optimization methods. Lack of rigorous formulations motivates discussion of the optimization objectives and constraints. We stress the importance of using weighted and so-called Sobolev norms. Second, we state the main optimization problem as a set of the optimization objectives in a form of functional norm integrals to maximize image fidelity and source smoothness. We reduce this to a non-negative least square (NNLS) problem, which is solved by standard numerical methods. Third, we analyze solutions for important practical cases: alternating phase shifting applied to regular and semiregular pattern of contact holes, two types of SRAM cells with design rules from 130 to 250 nm, and a complex semidense contact layer pattern. Finally, we show how constraint optimization can be used to smooth strong off-axis quadrupole illuminations to achieve better image fidelity for some selected layout patterns.