Etch proximity correction for curvilinear layout: curve sampling with ML etch bias model

Conventional etch bias models used in etch proximity correction (EPC) are developed for rectilinear layouts, where bias is evaluated at discrete edge centers and applied in the direction perpendicular to the edge. These methods cannot be applied to curvilinear layouts, in which etch bias varies continuously along smooth curves and the correction direction is not well-defined. We propose a curve sampling method that adaptively places sampling points along curvilinear edges, with dense sampling at high-curvature regions where etch bias changes rapidly and sparse sampling elsewhere. An MLP model is trained to predict etch bias at each sampling point using local geometric features and neighborhood information. EPC is then performed by iteratively correcting the layout based on the predicted bias. Experimental results demonstrate that the proposed MLP model achieves 1.59nm RMSE, a 49% improvement over model-based methods. When EPC is performed based on the proposed sampling method and the corrected layouts are evaluated through etching simulation, the resulting vertex placement error (VPE) distribution exhibits a 14.7% reduction in 3σ and a 30.2% reduction in maximum VPE compared to EPC with uniform sampling.