Abstract
The Monte-Carlo method is adopted to define the roughness of the mask structure. A random surface height variation described by power spectral density for the rough surfaces of an extreme ultraviolet (EUV) mask is redefined in order to calculate the field in the image plane. A general explicit formula of the scattering, which is analogous to Feynman's approach, is derived, and it is adapted to the EUV mask structure to evaluate the effect of the surface roughness of the side wall of the mask topography on the image formation. The multiple random scattering problems are dealt with the different pattern types, which are an isolated pattern and a dense pattern, in order to compare field variations in phase and amplitude with the ideal flat surface.