Improvement of model kernel representation in process simulation by taking pattern correlation into account

In the modern photolithography simulation, the computation demand on resolution enhancement techniques (RETs) and optical proximity corrections (OPCs) is proportional to the simulation runtime of the model, which is dependant on the number of the kernels retained with the constrain of the model accuracy. Thus, it is essential to retain as few kernels as possible in the model calibration. Traditionally, the kernels are retained based upon their contribution to the aerial image, which is solely determined by the magnitudes of the eigenvalues. This method works well for arbitrary photolithography masks. However, real masks are never arbitrary and random. Instead, they have regular shapes and arrangements as governed by design rules, indicating the contributions from the retained kernels are statistically correlated to each other. By taking such correlations into account, the system representation can be improved to contain fewer kernels for a constant model accuracy. In this paper, the mathematical derivation of the pattern correlation concept is discussed and the concept is applied to a contact layer illuminated by a Quasar optical system with λ = 193 nm and NA = 0.8. Significant improvement of model kernel representation is observed, four improved kernels vs 15 original kernels, and the new methodology is justified by comparing the difference of the aerial image intensities between the full kernel representation and the retained kernels representation at sampling points.