Availability study of CFD-based Mask3D simulation method for next generation lithography technologies

In progress of lithography technologies, the importance of Mask3D analysis has been emphasized because the influence of mask topography effects is not avoidable to be increased explosively. An electromagnetic filed simulation method, such as FDTD, RCWA and FEM, is applied to analyze those complicated phenomena. We have investigated Constrained Interpolation Profile (CIP) method, which is one of the Method of Characteristics (MoC), for Mask3D analysis in optical lithography. CIP method can reproduce the phase of propagating waves with less numerical error by using high order polynomial function. The restrictions of grid distance are relaxed with spatial grid. Therefore this method reduces the number of grid points in complex structure. In this paper, we study the feasibility of CIP scheme applying a non-uniform and spatial-interpolated grid to practical mask patterns. The number of grid points might be increased in complex layout and topological structure since these structures require a dense grid to remain the fidelity of each design. We propose a spatial interpolation method based on CIP method same as time-domain interpolation to reduce the number of grid points to be computed. The simulation results of two meshing methods with spatial interpolation are shown.