Propagation effects of partial coherence in optical lithography

Abstract

A method based on optimal expansions is described for making an order of magnitude speed up in the analysis of partial coherence effects of scattering in optical lithography, inspection, and alignment. This method expands the incident mutual intensity from the illumination into coherent nonuniform plane waves whose effects can be added incoherently. For three-dimensional structures, the CPU time is reduced by an order of magnitude over the uniform plane wave approach of Abbe. For two-dimensional structures, the number of simulations with the decomposition technique has been found to be about three times smaller than with Abbe’s approach. The method has been incorporated into TEMPEST and shown to give accurate results and reduced CPU time in applications of imaging an attenuated phase shift mask, patterning of gates over an active area well in silicon, and inspection of a trench in silicon dioxide, where the CPU time savings are most significant due to large NA’s and high σ’s. Results for an embedded phase shift mask show the need to generalize Hopkin’s method to include effects of the dependence of the diffraction efficiencies on the angle of incidence. The inclusion of partial coherence in regions of topography scattering show beneficial imaging effects in that reflective notching is reduced as σ is increased.