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

Abstract

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

Joint optimization of source, mask, and pupil in optical lithography

“…25,26 Consequently, the mask-induced phase deformation can be partially compensated by a manipulation of the pupil lens. 12 Indeed, the simulation results exhibit that primary spherical aberrations (Zernike term z 9 ) have the highest sensitivity, which means a large impact on linewidth through focus, and 1D lines are also prone to be affected by other spherical aberrations such as secondary spherical (Zernike term z 16 ) since the spherical aberrations have radially dependent and rotationally symmetric form. 26 The wavefront function W (ρ, θ) in this paper is therefore composed of primary and secondary spherical aberrations to further improve the imaging performance, as follows:…”

“…First, unlike SMO, the proposed scheme takes advantage of the fact that pupil phase manipulation can partially compensate for thick mask topography effects. 12 It incorporates some helpful pupil aberration terms into imaging systems of the optimization process, which makes the resulting source and mask robust against specific pupil aberrations, thereby being robust against similar imaging impact caused by mask topography. Second, the whole optimization procedure is performed based on the thin mask model, which makes sure that the speed is faster than that based on rigorous model.…”

Robust source and mask optimization compensating for mask topography effects in computational lithography

“…Previous studies have found that mask topography effects have similar impact on the lithography imaging performance to those caused by wave aberrations [27,28]. Consequently, the mask-induced phase deformation can be partially compensated by a manipulation of the pupil lens [20]. Indeed, the simulation results exhibit that primary spherical aberrations (Zernike term z 9 ) have the highest sensitivity, which means a large impact on linewidth through focus, and 1D lines are also prone to be affected by other spherical aberrations such as secondary spherical (Zernike term z 16 ) since the spherical aberrations have radially dependent and rotationally symmetric form [28].…”

“…This paper focuses on a robust algorithm using inverse synthesis technique to co-optimize the source and the mask, and the major contributions are twofold. First, unlike SMO, the proposed scheme takes advantage of the fact that pupil phase manipulation can partially compensate for thick mask topography effects [20]. It incorporates some helpful pupil aberration terms such as primary and secondary spherical aberrations through statistical model of Zernike polynomials, resulting in the optimal source and mask that are not only robust against specific pupil aberration, but are also robust against similar imaging effects caused by mask topography.…”