Compact modeling of stochastics and application in OPC

Abstract

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.

Towards efficient and accurate cost functions for EUVL stochastic-aware OPC correction and verification: via failure probability versus image and process variation band metrics

“…It was also observed that, at least for a couple of relatively small test cases, a similar stochastic failure probability improvement can be achieved using PV band metrics corresponding to specially selected values of process variation parameters 5 .…”

“…The fact that the stochastic via failure probability cannot always be accurately predicted from a via NILS value, has been demonstrated experimentally 2 . The accurate EUVL stochastic models have been proposed and successfully verified recently 3,4 -aware OPC using these stochastic models demonstrated improvements of the via stochastic failure probabilities by orders of magnitude 5 .…”

“…Prediction, mitigation and control of EUVL exposure-resist stochastic variability and stochastic failure probabilities have been the subjects attracting significant interest among EUV lithographers in the past decades [1][2][3][4][5] . The attention is presently turning towards stochastic-aware OPC and verification tools capable of efficiently optimizing and verifying billions of features on a single IC layer 5 .…”