Reducing systematic LCDU of dense contact hole arrays on wafer via source optimization

Background: Contact hole variability is an important problem in the application of extreme ultraviolet lithography for memory applications. One method to reduce it is source optimization. An important source of on-wafer variability is the variability on mask. This can transfer in very different ways for different illumination pupils. Aim: Understand root cause of pupil-dependency of mask variability transfer to wafer. Predict which source can best reduce it. Approach: Look at the background diffraction intensity (BGI) caused by mask variability to explain aerial image LCDU. We make predictions of wafer LCDU based on how BGI transfers for different pupils and compare it to experimental data. Results: BGI has a spectrum that is given by the shape of the contact hole and is mostly concentrated at small spatial frequencies. For large sigma pupils much less BGI is transferred through the lens than for small sigma pupils. On wafer LCDU is well predicted by BGI divided by NILS. Conclusions: Large sigma pupils transfer much less BGI than small sigma pupils, so they reduce LCDU on wafer. For relaxed pitches, small sigma pupils can increase NILS by capturing additional diffraction orders of the periodic pattern. This can outweigh the larger BGI transferred and lead to smaller systematic LCDU for small sigma pupils. For high-NA, the central obscuration reduces BGI for small sigma pupils but large sigma pupils are still preferred. Tachyon SO can find the right pupils to minimize systematic LCDU by adding a large supercell clip with mask LCDU into the optimization.