Compact modeling of stochastics and application in OPC

To maintain good critical dimension control, optical proximity correction (OPC) has relied on fast compact models to capture the underlying lithography process in advanced nodes. Compact models have always been deterministic in the sense that they predict the average dimensions or contours on wafer. With the introduction of extreme ultraviolet (EUV) lithography, this approach breaks down due to large variabilities in EUV lithography processes. Recently, empirical correlations were found between this variability and imaging metrics, allowing the development of compact models. Such stochastic models have been used successfully to predict hotspots. In this paper an attempt is made to apply such stochastic models during OPC to reduce the number of stochastic failures. Different OPC strategies are applied on an advanced random logic and SRAM design, focusing on a via layer with a calibrated stochastic model. Through simulations, we show that the failure rate can be reduced by using a stochastic model during OPC, at the expense of edge placement error. However, when reducing the stochastic band width to match the process variation band width, no meaningful differences were observed between process-window OPC and stochastic OPC due to uniformity of pattern dimensions in sample layout.