Isotropic treatment of EMF effects in advanced photomasks

Abstract

Classical methods for modeling electromagnetic scattering from the topography of lithographic reticles must place a high premium on fast computation, and toward that end they apply pre-stored perturbations (e.g. the so-called boundary layers) to feature edges in order to approximate the impact of finite-thickness mask films. Though approximate, these methods involve E&M calculations with vector fields, and so employ edge-field corrections that are different for edges oriented parallel or perpendicular to the vector field. As a result these methods entail a requirement for two separate aerial image simulations using orthogonal source polarizations in order to represent unpolarized illumination. This imposes a minimum 2× runtime penalty relative to baseline thin-mask (TMA) simulations, since the known method for combining the effect of both polarizations into one single set of imaging TCCs applies only to thin-mask calculations. More severe performance penalties are common in so-called sparse imaging methodologies when topographic effects are included, since the separated treatment of feature edges and the internal area of the features can increase the number of memory lookups required. In this paper an isotropic field perturbation approach is evaluated, in which an isotropic edge field correction, common to all edge orientations, mimics the effect of the true parallel and perpendicular edge field perturbations when the mask is illuminated with unpolarized light, as well as in certain cases of polarized illumination. The isofield is not an ad hoc empirical correction but rather an accurate approximation in the limit of modest departures from scalar TMA. More specifically, we show that the isofield model accounts for vector imaging effects with full accuracy in the TMA terms, and in an approximate way in the electromagnetic edge-field terms that becomes accurate when the polarization dependence of the TMA terms is small. We will show with comparison to more rigorous electromagnetic models and simulations, as well as against wafer measurements that the accuracy loss relative to classic polarized EMF correction approach is within a small percentage on mask blanks where the electromagnetic edge field perturbation terms are small relative to the TMA term. Methodology to extend these models into the subwavelength diffraction regime will be discussed. © 2009 SPIE.