Rigorous vectorial modeling for polarized illumination and projection pupil in OPC

Abstract

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 and the effectiveness of optical proximity correction (OPC). However, current OPC/RET modeling software can only model the light source polarization of simple types, such as TE, TM, X, Y, or sector polarization with relatively simple configuration. Realistic polarized light used in scanners is more complex than the aforementioned simple ones. As a result, simulation accuracy and quality of the OPC result will be compromised by the simplification of the light source polarization modeling in the traditional approach. With ever shrinking CD error budget in the manufacturing of IC's at advanced technology nodes, more accurate and comprehensive illumination source modeling for lithography simulations and OPC/RET is needed. On the other hand, for polarized illumination to be fully effective, ideally all the components in the optical lithography system should not alter the polarization state of light during its propagation from illuminator to wafer surface. In current OPC modeling tools, it is typically assumed that the amplitude and polarization state of the light do not change as it passes through the projection lens pupil, i.e. the polarization aberration of projection lens pupil is ignored. 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 will cause CD errors un-tolerable at the 45nm device generation and beyond. We developed an OPC-deployable modeling approach to model arbitrarily polarized light source and arbitrarily polarized projection lens pupil. Based on polarization state vector descriptions of a general illumination source, this modeling approach unifies optical simulations of unpolarized, partially polarized, and completely polarized illuminations. The polarization aberration imposed by the projection lens pupil is modeled via Jones matrix format, and it is applicable to arbitrary polarization aberrations imposed by any components in the lithography system that can be characterized in Jones matrix format. Numerical experiments were performed to study CD impact from illumination polarization and projection lens pupil polarization aberrations, and up to several nanometers impact on optical proximity effect (OPE) was observed, which is not negligible given the extremely stringent CD error budget at 45nm node and beyond. Based on an experimentally measured Jones matrix pupil which intrinsically provides a much better approximation to the physical scanner projection pupil, we propose a more physics-centric methodology to evaluate the optical model accuracy of OPC simulator.