Understanding the impact of rigorous mask effects in the presence of empirical process models used in optical proximity correction (OPC)

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Some practical aspects of integrating a mask modeling solution into the Optical Proximity Correction (OPC) framework are discussed. Specifically, investigations were performed to understand to what degree empirical process models used in OPC can compensate for mask effects when a Kirchhoff mask model is used. It is shown that both Constant Threshold Resist (CTR) models as well as more complex variable threshold process models can both compensate for mask effects at a single plane of focus. However, when looking through process window, neither process model can predict the focal behavior of Electro-Magnetic Field (EMF) simulators. The impact of mask effects will therefore need to be modeled in OPC, since process models cannot fully compensate for their effects. Heuristic approaches to modeling mask effects, like a constant biasing of feature edges, are then investigated and compared to more complex mask modeling solutions like Domain Decomposition Methods (DDM). It is shown that these heuristic approaches can be effective at single planes of focus to partially mitigate mask effects, however, do not provide complete solutions to predict and compensate for mask effects. DDM stands in stark contrast to heuristic methods, correctly predicting the through focus behavior of EMF simulations for the tested pitches and CDs. The impact of optical diameter (periodic boundary conditions) is also investigated to understand how the introduction of mask periodicity effects from optical diameter degrades the benefits derived from mask modeling. It is shown that as much as a 33% reduction in CD predictability is observed from an optical model with a 1um optical diameter compared to a 2.56um optical diameter. Finally, both a Kirchhoff mask model and a DDM mask model are compared to see which mask model more accurately explains experimental CD measurement data from a 65nm process. The DDM model generally reduces the edge placement error (EPE) on the calibrated focal data by 0.3-1.0nm.