Mueller matrix polarimetry for immersion lithography tools with a polarization monitoring system at the wafer plane

It will be required for more accurate lithography simulation of complicated mask patterns then ever, under hyper-NA (numerical aperture) projection lens and aggressive small-aperture polarized-light illumination, to construct two systems of polarimetry; one is polarimetry for illumination, and the other is Mueller matrix polarimetry for projection lenses. The former polarimetry already reported by the authors is necessary for us to appreciate how the true polarization state of illumination is. The polarimeter mask described in the paper determines illumination polarization states by Stokes parameters. The latter polarimetry is the main subject of this paper. A Mueller matrix is a translation matrix of the input Stokes parameters to the output Stokes parameters. With the full elements of the Mueller matrix of a projection lens, the Stokes parameters of a light at the wafer plane can be easily predicted from the Stokes parameters of any illumination conditions. This paper proposed a new method of Mueller matrix polarimetry and a monitor mask used for 193-nm immersion lithography tools with a polarization monitor at the wafer plane.