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.
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.
A new simulation method with Chebyshev expansion is proposed to calculate three-dimensional resist profiles in a short
time using Fast Cosine Transform (FCT) algorithm. This method can be applied to the solution of the full 3D model for
OPC and LCC, and it is valid to evaluate the cross-sectional resist shape under the condition where the influence of
reflection wave from the underlayer is significant. We show the results of evaluation with regard to accuracy and
precision, expanding three-dimensional profiles using Chebyshev expansion. In addition, we report the comparison with