A fast mask three-dimensional model based on multi-directional filtering

Mask three-dimensional (M3D) effects have significant influence on the imaging performance of lithography system at advanced technology nodes. Especially, inverse lithography technique has currently driven the development of pixelated or curvilinear masks with freeform geometric features, which make it harder to accurately calculate the diffraction near-field (DNF) of thick masks. Although precise, the M3D model based on rigorous electromagnetic field simulators are time-consuming. Thus, this paper proposes a fast M3D model for the freeform thick-mask pattern based on multi-directional filtering approach. Given an arbitrary freeform thick-mask pattern, its boundary features oriented in different directions are first extracted by using a set of pre-designed decomposition modules. For different kinds of features, the corresponding directional-filters are pre-trained based on a DNF dataset. Then, the thick-mask DNF can be calculated by applying the multi-directional filtering method on the decomposed mask patches. A set of numerical experiments indicate that the proposed model is much faster than the rigorous simulation method, and more accurate compared with the fast thick-mask model based on fully convolutional network.