Improved modeling performance with an adapted vectorial formulation of the Hopkins imaging equation

Abstract

The Hopkins imaging theory for partially coherent light is adapted to include vector EM field interference inside a resist film stack. The negligible on-axis component of the EM field before the entrance pupil is ignored and this form is suitable for modeling IC lithographic projection printing. A new module, called TCCcalc, that is part of the Mentor Graphics’ Calibre Workbench modeling suite includes the vector image model inside resist can faithfully capture all physical effects that take place. Reduced contrast of the TM polarization, induced spherical aberration and standing wave creation are identified through examples to be the most important effects at high NA imaging. Application of the new vector image model to experimental data leads to a 20% reduction in the error between simulation and experiment for NA up to 0.75.