<title>Some image modeling issues for I-line, 5X phase-shifting masks</title>

Abstract

The current image-theoretical basis for phase shifting masks (PSMs) relies on the scalar and Kirchhoff approximations, which neglect vector wave and edge diffraction effects around the mask. In this paper we use EMFlex finite element modeling to quantify vector diffraction effects, and show a method for modeling broadband illumination using the code's transient (optical pulse) capability and the Fourier transform in time. Simulations indicate that: the Kirchhoff approximation applied to etched quartz PSMs can lead to unacceptable errors due to a dark boundary layer on the quartz sidewall; diffraction produces relatively strong vector wave fields near feature edges but their contribution to the lithographic image is negligible; and the paraxial partial coherence approximation is generally valid for 4x or 5x projection systems. We discuss examples illustrating needs for better PSM metrology and phase measurements.