Polarization aberration modeling via Jones matrix in the context of OPC

The increasingly stringent demand for shrinkage of IC device dimensions has been pushing the development of new resolution enhancement technologies in micro-lithography. High NA and Ultra-High NA (NA>1.0) applications for low k1 imaging strongly demand the adoption of polarized illumination as a resolution enhancement technology since proper illumination polarization configuration can greatly improve the image contrast hence pattern printing fidelity. For polarized illumination to be fully effective, ideally all the components in the optical system should not alter the polarization state during propagation from illuminator to wafer surface. In current OPC modeling tools, it is typically assumed that the amplitude and polarization state of the electric field do not change as it passes through the projection lens pupil. However, in reality, the projection lens pupil of the scanner does change the amplitude and the polarization state to some extent, and ignorance of projection pupil induced polarization state and amplitude changes may cause CD errors which are un-tolerable at the 45nm device generation and beyond. We developed an OPC-deployable modeling approach to model polarization aberration imposed by the projection lens pupil via Jones matrix format. This polarization aberration modeling capability has been integrated into the Synopsys OPC modeling tool, ProGen, and its accuracy and efficiency have been validated by comparing with an industry standard lithography simulator SolidE. Our OPC simulations show that the impact of projection lens pupil polarization aberrations on optical proximity effect (OPE) could be as large as several nanometers, which is not negligible given the extremely stringent CD error budget at 45nm node and beyond. This modeling approach is applicable to arbitrary polarization aberrations imposed by any components in the lithography system that can be characterized in Jones matrix format. Based on an experimentally measured Jones matrix pupil which intrinsically provides a much better approximation to the physical scanner pupil, we propose a more physics-centric methodology to evaluate the optical model accuracy of OPC simulator.