<title>Mathematical and CAD framework for proximity correction</title>

Fast lithography simulation and its use in optical proximity correction (OPC) is the topic of this paper. We summarize a model-based OPC system which uses simulation in a feedback loop to generate corrections to the mask. At the heart of our OPC system are tools for fast simulation of the optical and process physics of lithography. For image simulation, we apply a sum of coherent systems approximation to Hopkins partial coherence model and then use lookup tables for high speed sparse image simulation over arbitrary mask geometry. Image intensity simulation at a single point is achieved with O(M_e) computation where M_e is the number of polygon edges in a region surrounding the point. This allows more than 10,000 aerial image points per second and mask image perturbation speeds of 51,000 points per second on an HP700 workstation. A simplified physically based, empirically parameterized resist model is then used to determine edge placements, given the image intensity samples. Together, these systems make up a 'process-tuned' simulation model which can be used for OPC. The accuracy of the overall model is shown by comparing to empirical measurement data. By integrating the fast simulation tools with our OPC system, we can correct a 48 X 27 micrometers ² area in 6 iterations at 96 sec/iteration.