Two-dimensional optimized trapezoid self-convolution window for enhancing Moiré-based lithography alignment

Abstract

Classical windows are widely used in image processing to suppress spectral leakage. However, their limited effectiveness constrains their application in high-precision measurement tasks, such as lithography alignment based on Moiré fringe phase analysis. To address this limitation, this paper introduces an innovative two-dimensional optimized trapezoid self-convolution window (2D-OTSCW). This novel class of windows is generated through multiple time convolutions of an optimized trapezoid window, designed to achieve a narrow main lobe width of 6.89π/N and an optimal peak sidelobe level of − 31.6 dB by tuning the upper-to-lower base ratio (γ = 16 %). Theoretical analyses confirm that increasing the convolution order enhances the sidelobe suppression capability of 2D-OTSCWs, thereby mitigating spectral leakage. Additionally, the performance of the 2D-OTSCWs is evaluated against two extreme self-convolution windows (SCWs) (i.e., triangular and rectangular SCWs). Simulation and experimental results demonstrate the superior performance of 2D-OTSCWs over classical windows, which significantly enhances the phase extraction accuracy. This improvement enables alignment precision at an impressive sub-2-nm (1.86 nm) level, meeting the stringent requirements of next-generation lithography. This study not only introduces a robust window function design strategy for spectral analysis but also establishes a foundation for advancing high-precision alignment in lithography and related fields.