Mask polarization effects in hyper NA systems

The non-paraxial correction term of high-NA effect was studied for scalar field in optical microlithography. However, the correction term of scalar field should be modified for vector field. Based on a thin mask, the characteristic of vector field can be described with the Symthe-Kirchhoff formula. The non-paraxial correction term of vector field can be derived with the combination of both the law of energy conservation and sine condition on entrance pupil and exit pupil. The correction term of vector field depends on the degree of polarization of incident light. As the result, the correction term of TE wave of vector field is the same characteristic as that of scalar field. However, the correction term of TM wave of vector is different from that of scalar field.