Image simulation of projection systems in photolithography

The well-established Abbe formulation is one of today's most common approaches for the accurate image simulation of partial coherent projection systems used in semiconductor lithography. The development and application of lithographic imaging systems close to the theoretical resolution limits and the desire for the simulation of larger mask areas with high accuracy require several extensions of the classical Abbe approach. This paper presents the basics of the Abbe approach including the so-called Hopkins assumption. For the accurate simulation of today's lithography systems important physical effects like strong off-axis illumination, small feature sizes, ultra-high NAs, a polarization dependent behavior, imaging demagnification, aberrations, apodizations, and Jones pupils have to be described and taken into account. The resulting extensions of the Abbe approach are presented. The accuracy, flexibility, and computational performance of the new approach are demonstrated by application examples.