Calculations of Phase Shift and Reflectivity for Phase Shifting Masks Employing Multi-Layer Films

Abstract

Calculations of phase shift and reflectivity of multi-layer phase shifting masks have been carried by a method of matrix calculus for light propagating in slabs of isotropic media. The results show that a phase noise of several degrees exists as a result of variation in material parameters due to multiple interference phenomenon in the films. The magnitude of this phase noise tends to grow for increasing refractive index of the phase shift layer. It is shown that both the phase noise and the reflectivity can be minimized with proper choice of materials. Best materials for phase shift layer should have a refractive index of 1.5 such as SiO2 or 2.0, and good etch stop layer should have low refractive index and a thickness chosen to minimize reflectivity.