Modeling polarization for Hyper-NA lithography tools and masks

Abstract

We present a comprehensive modeling study of polarization effects for the whole optical chain including exposure tool and mask, with strong emphasis on the impact of the Jones Matrix of the projection lens. First we start with the basic of polarization and then the polarization effect of each components of the optical chain will be discussed. Components investigated are source polarization, rigorous EMF effect, mask blank birefringence, pellicle effect and projection lens. We also focus on comparing the relative merits of different types of representation of Jones matrix of the projection lens and outlined ways to decompose the Jones Matrix. Methodologies such as Pauli matrix, PQM, Jones-Zernike expansion and IPS-Zernike expansion are among the ones investigated. The polarization impact on lithography and OPC on realistic 45nm and 32nm node process levels is discussed. Issues in OPC modeling with Jones Matrix is highlighted. Concerns regarding the standardization of the implementation of Jones Matrix in the lithography community are considered and a standard has been proposed and received wide acceptance. Last we discuss the challenge of using polarization and some novel ideas to deal with polarization in hyper NA era. Throughout the paper the resist component is not included so as to isolate the effect of resist from that of the other components.