Mask3D-compatible full-vectorial Hopkins imaging for lithographic modeling

As the critical dimension continues to shrink, the mask three-dimensional topography (Mask3D) effects must be taken into account for accurate vectorial modeling of lithographic imaging. In applications such as full-chip simulations as well as mask optimizations, the method of Abbe imaging is unviable due to its high computational cost. In contrast, the conventional formulation of Hopkins imaging is computationally efficient but lacks the generality to incorporate Mask3D effects, which depend on the illumination angle of incidence. Therefore, it is of great importance to develop a Mask3D-compatible Hopkins formulation of optical imaging. This paper presents a full-vectorial Hopkins imaging model that seamlessly integrates Mask3D effects by thoroughly considering the propagation of the vectorial electromagnetic field in the optical lithography system. A multi-dimensional vectorial transmission cross coefficient (TCC) is constructed to accurately respond to the polarization components of the mask transfer matrix in Mask3D models. The vectorial TCC decomposition architecture is developed based on the Lanczos algorithm, which significantly accelerates the generation of optical kernels and aerial images. The proposed model is compatible with off-axis illumination configurations, ensuring the accurate capture of incident-angle-dependent Mask3D behaviors. Simulation results demonstrate that the proposed model achieves full compatibility with common Mask3D models, delivering high imaging efficiency for the full-chip optical proximity correction.