Rigorous electromagnetic field simulation of the impact of photomask line-edge and line-width roughness on lithographic processes

Abstract

The impact of edge profile roughness of the absorber lines on an optical photomask has been studied by means of rigorous electro-magnetic field (EMF) simulation for the mask diffraction spectrum and subsequent imaging. Roughness has been modeled using two different approaches, a sinusoidal description and an algorithm known from literature-based on Fourier transformation. The latter can arbitrarily create rough profiles and surfaces based on the three morphological parameters standard deviation σ, roughness exponent α, and correlation length ξ. In this study, the standard deviation has been kept fixed while varying the remaining two morphological parameters, still showing impact on the lithographic process. A software interface for use of the generated profiles with the Waveguide EMF solver of the Dr.LiTHO lithography simulation suite has been implemented. It was shown by means of image analysis and study of the resulting process windows that mask roughness is partially transferred to the aerial image. Isolated and dense features behave differently, leading inter alia to an iso-dense bias different to that of ideal lines. Due to the roughness, process windows now depend on the position along the line. Determing process windows at multiple positions for statistical analysis implies a reduction of the effective process window. Correlation length ξ has shown to be an important parameter and, thus, morphology should not be ignored in the modeling of rough lines. Tapered sidewalls can add to the shift of the process windows in the same order of magnitude.