Virtual metrology for process perturbation prediction in lithographic alignment marks using a physics-guided directed attention network

Process perturbations in lithographic alignment marks deform multilayer profiles, break mark symmetry, and introduce alignment position uncertainty. Although alignment position deviation (APD) and wafer quality (WQ) responses contain process-dependent information, retrieving the underlying perturbations remains challenging because the inverse relationship is nonlinear and strongly coupled. We formulate this task as alignment mark virtual metrology, in which process perturbation values are estimated from paired APD/WQ response matrices. To solve this inverse problem, we propose a physics-guided directed attention network (PG-DAN). PG-DAN uses diffraction limit masked attention (DLMA) to inject wavelength, diffraction order, propagation, locality, and identity priors into APD/WQ attention logits, enabling the model to use physically meaningful token relations rather than unconstrained data correlations. A directed decoder further follows multilayer coupling during prediction. Evaluated on a rigorous coupled wave analysis (RCWA) dataset, PG-DAN achieves a mean R² of 0.999875, a mean range-normalized RMSE of 0.34%, and a mean range-normalized MAE of 0.23%, with lower estimation errors than conventional neural inverse models. These results support physics-guided inverse modeling for alignment mark process perturbation estimation.