Optimal 3D phase-shifting masks in partially coherent illumination

Gradient-based phase-shifting mask (PSM) optimization methods have emerged as an important tool in computational lithography to solve for the inverse lithography problem under the thin-mask assumption, where the mask is considered a thin two-dimensional object. As the critical dimension printed on the wafer shrinks into the subwavelength regime, thick-mask effects become prevalent and thus these effects must be taken into account in PSM optimization methods. Thick-mask effects are particularly aggravated and pronounced in etching profiles with abrupt discontinuities and trench depths. PSM methods derived under the thin-mask assumption have inherent limitations and perform poorly in the subwavelength scenario. This paper focuses on developing three-dimensional PSM optimization methods that can overcome the thick-mask effects in lithography systems with partially coherent illumination. The boundary layer model is exploited to simplify and characterize the thick-mask effects, leading to a gradientbased PSM optimization method. Several illustrative simulations are presented.