Evaluation of various compact mask and imaging models for the efficient simulation of mask topography effects in immersion lithography

In this work, correction techniques in the spatial and frequency domains are applied to improve the accuracy of less rigorous but more efficient mask models. This allows to reproduce the electromagnetic field (EMF) effects predicted by the rigorous model preserving the simplicity of the Kirchhoff model. In the frequency domain, two approaches are considered. First, a Jones pupil function is introduced in the projector pupil plane to describe amplitude, phase and polarization effects which are introduced by the mask. Second, a correction process performed directly on the scalar spectrum is used to tune the diffraction orders that get into the pupil of the optical projection system. Since a vector imaging description is needed to include the polarization phenomena, the spectra of the different polarization components are constructed from the scalar spectrum using correspondingly calibrated filters. In the spatial domain the well-known boundary layer model is considered.1 The bright features of the thin mask are surrounded with a semi-transparent region with a certain width, transmission and phase. Alternatively, the bright mask features of the Kirchhoff model are modified by adding delta functions to the edges of the absorber. All correction functions for spatial and frequency are obtained by a calibration with a rigorous model. The validity of these filtering techniques for different feature sizes and pitches is investigated.