Modeling clear phase-mask materials for sub-50 nm X-ray application

Summary form only given. This paper presents a powerful modeling approach to the X-ray exposure operating space of a silicon nitride clear phase-shifter mask to produce sub-50 nm features. Although silicon nitride was examined, the approach can be used to model many other materials including Si, metals, and oxides, including complex shapes. Because this type of mask relies on both diffraction and phase shifting, the four factors, absorber thickness, absorber wall slope, gap, and CD were identified as critical to the resulting intensity profile. By first developing a central composite experimental design, we then used a wavefront modeling toolset to calculate intensity and linewidth responses for each of the response surface cells. Excellent second-order models were fit to the data for each of the responses.