Effective medium approximations for modeling optical reflectance from gratings with rough edges

Line edge roughness (LER) has been identified as a potential source of uncertainty in optical scatterometry measurements. Characterizing the effect of LER on optical scatterometry signals is required to assess the uncertainty of the measurement. However, rigorous approaches to modeling the structures that are needed to simulate LER can be computationally expensive. In this work, we compare the effect of LER on scatterometry signals computed using an effective medium approximation (EMA) to those computed with realizations of rough interfaces. We find that for correlation lengths much less than the wavelength but greater than the rms roughness, an anisotropic EMA provides a satisfactory approximation in the cases studied.