Quantification of two-dimensional structures generalized for OPC model verification

Model based optical proximity correction (OPC) today has become a necessity in advanced lithography for 65nm and 45nm design rules in order to achieve production-worthy pattern fidelity. The typical practice is to use a limited set of test structures to calibrate and determine the OPC model parameters. The guide for the selection of test structures for OPC model calibration has been mainly relied on experience and physical intuition. To date, there is no known quantification methodology to ensure that the calibrated model from a limited set of test structures can reliably "cover" a full-chip OPC application without any ambiguity under a known set of design rule constraints. Doubts from this ambiguity demand an extra design for manufacturing (DFM) verification step in addition to the already lengthy OPC application process. This is since semiconductor manufacturing requires that the post-OPC mask data contains no errors, or at least no catastrophic errors induced by OPC treatment, e.g., bridging or short. However, such DFM verification tools are again based on a perilous assumption that either one can use the same or yet another "calibrated" model from a limited set of test structures to check the OPC treated full-chip data for all possible trouble spots. In reality, a "calibrated" model may never be able to apply adequately to those of random two-dimensional (2-D) pattern structures on a full-chip that are lithographically unrelated to the limited set of test structures used for the model calibration. To ensure a more comprehensive coverage of the OPC model, we need a methodology that can quantify generalized 2-D test structures suitable for model calibration. In this paper, we propose a method to quantify generalized, 2-D patterns by representing them in "imaging signal space". The method that translates geometrical design rules into the boundary in "imaging signal space" is elaborated. We propose several critical quantities to characterize OPC model on a quantitative foundation to assess model from a statistical point of view.