Automating rules-based optical proximity correction via scattered data interpolation

In advanced technology nodes, optical proximity correction (OPC) solutions employ a blend of rules-based and model-based treatments to correct the intended circuit design. Rules-based OPC (RB-OPC) is based on a table or series of tables that prescribe discrete treatments for a feature as a function of its surrounding environment. RB-OPC is typically utilized for applications such as etch-bias compensation, silicon process-bias definition, and OPC model correction. One drawback to defining a rules-based table (RBT) is that the empirical measurements used to populate the table are typically sparse in terms of feature size and pitch, requiring the OPC engineer to fully populate the RBT by other means. Rather than manually interpolating the RBT, scattered-data interpolation techniques could be used to automatically populate the RBT at the desired level of granularity. Scattered data interpolation is commonly used in applications such as meteorology and terrain cartography as it relies on unevenly distributed sparse sample points to characterize the behavior of an entire region. In this study, the proposed technique was applied to correct optical OPC model error on a 28-nm implant level and compared with the baseline process, which uses an empirically calibrated OPC model. XOR analysis confirmed that the desired RB-OPC treatments were applied after optical OPC model correction for one-dimensional features, but two-dimensional features require independent characterization and correction. Experimental results also demonstrated comparable performance between the baseline empirical OPC model and variants of RB-OPC treatment, as all methods resulted in patterns with a global root mean square percentage error between 11% and 12%. The next steps of this study include testing applications in etch bias characterization, as well as testing alternative interpolation methods.