Study of recent CFD-based scheme for analyzing 3D mask effects

Abstract

Mask-induced aberration, which causes the deterioration of pattern fidelity owing to the phase difference between the diffraction orders in sub-wavelength lithography conditions, is an intricate problem. To evaluate the extent of the effect computationally, a rigorous electromagnetic field solver is applied. Reduction in the computation time of full-3D calculation is desirable in order to calculate practical patterns of mask layout in short period of time. We propose a new approach based on the Constrained Interpolation Profile (CIP) scheme with Method of Characteristics (MoC) to achieve the reduction of computation time. The CIP scheme is characterized by high accuracy to maintain the phase of each propagating wave using spatial derivatives. Constrained interpolation with derivatives is efficient for reducing the number of cells in the spatial domain because the requirement for keeping the phase accuracy of wavefront is relaxed. Non-uniform meshing also reduces the amount of computation time. The CIP scheme connects the mask topography simulation using non-uniform mesh to the traditional imaging algorithm smoothly. In this paper, we discuss the accuracy of CIP-based Mask3D simulation and the applicability to lithography issues.