A deflection distortion correction method for high-speed electron-beam lithography

Electron beam lithography (EBL) systems rely on highly precise and responsive deflection fields to ensure nanoscale pattern fidelity. However, various physical factors—such as nonuniformity in the deflection field, nonlinearity in driver output current, and other internal and external system effects—collectively introduce complex nonlinear distortions. These distortions degrade writing accuracy and increase stitching and overlay errors. Conventional linear or global polynomial correction models are limited in their capacity to accurately capture localized, irregular distortions. To address this limitation, this study presents a distortion correction approach based on 2D tensor product B-spline interpolation. The method involves acquiring secondary electron images from standard grid samples, extracting sub-pixel feature coordinates. A smooth and continuous deformation field is then reconstructed via B-spline fitting. Subsequently, an inverse mapping compensation model is derived to enable real-time correction of the electron beam trajectory. Simulation results and experimental validation confirms the effectiveness of the method. With only an 11 × 11 twisted grid and a 6 × 6 sampling set, fourth-order B-spline correction achieves a root mean square error (RMSE) of 0.132 pixels (≈13.7 nm), outperforming the optimal fifth-order polynomial model. For dense 41 × 41 twisted grids, the third-order B-spline model under a 21 × 21 sampling set yields an RMSE ∼14.9% lower than that of the fifth-order polynomial model. Compared with global polynomial models, the B-spline-based approach offers superior accuracy and enhanced robustness to noise at lower model orders. This method provides a practical solution for hardware-level electron beam deflection control and establishes a foundation for future adaptive correction strategies.