Efficient scattering simulations for equivalent extreme ultraviolet mask multilayer structures by modified transmission line theory and finite-difference time-domain method

Abstract

The modified transmission line theory is used to calculate equivalent refractive indices of the extreme ultraviolet (EUV) mask multilayer (ML) over wavelengths from 13.35 to 13.65 nm for finite-difference time-domain (FDTD) simulation. Generally speaking, a fine mesh requiring huge memory and computation time are necessary to get accurate results in an FDTD simulation. However, it is hard to get accurate results for ML simulation due to the thin thickness of each layer. By means of an equivalent refractive index, the ML can be treated as one layer with the bulk effective material. Using FDTD simulations, we study the reflectivities of 40 Mo/Si ML and bulk material cases. The ML structure and bulk material with periodic excessive surface roughness as well as patterned with periodic contact holes are also studied by using two- and three-dimensional FDTD simulations. The simulation cases for a single wavelength and for a full-bandwidth EUV light source with a 6 ML system are studied. The results from each simulation show that the root mean square error between ML simulations and the bulk material simulations are confined within 3.3%, and all cases indicate that the FDTD computation time of bulk material is about half as compared with a 40-ML simulation.