Physical conversion of Stokes parameters which are multiplied by a general Mueller matrix into Jones vectors applicable to the lithographic calculation

Abstract

Completer polarimetry for immersion lithography equipment that comprises Stokes polarimetry of illumination and Mueller matrix polarimetry of projecting optics had been established. It was found that illumination and projecting optics were slightly different from our expectation. These differences might affect optical proximity correction and source mask optimization. However, no lithographer can desterilize parameter sets from the polarimetry for the use of lithography calculation because of their formats, Stokes parameters and Mueller matrix. Conventional lithography simulators require the Jones vector and Jones matrix only. When the illumination was partial polarization or the projecting optics was partially polarizing or partially depolarizing, the Jones calculus cannot support these situations. The Mueller calculus is needed for the case that involves polarizationdepolarization and depolarization-polarization translations. Previous works showed that actual un-polarization of illumination was somewhat polarized in the scan (y) direction and an actual catadioptric projecting optics has a little degrees of polarizance in the slit (x) direction. On the other hand, if you took the aberration effects into the lithography calculation, you had to use the Jones calculus. Therefore, for the lithography calculation with actual polarization data as well as actual aberration data, a special technique is required to handle these data. This paper describes how to physically convert Stokes parameters, which are multiplied by a general Mueller matrix, into Jones vectors. This method permits us to use the actual polarization data to the lithography calculation.