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

Abstract

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.

Analytical modeling and three-dimensional finite element simulation of line edge roughness in scatterometry

“…stitching errors) may be larger than the wavelength and roughness induced scatter as described by the formalism presented here is observable. For small structures and small spatial wavelength perturbations, however, no other diffraction orders than the zeroth order exist and other descriptions like the effective layer model [15,16] must be used to account for roughness.…”

Effect of surface roughness on optical heating of metals

“…Systematic investigation of reflection and scattering [32] have been performed for sinusoidal-shaped surface morphologies [24], other well-defined geometries [11,15,16,17,23,33] and sub-surface defects [21,34]. Simplified models exist also for special cases, where the optical wavelength is much smaller (or much larger) than the in-plane periodicity of a surface pattern [35].…”

“…(22) for the actual temperature of the reference material and inserting these results into Eq. (23). Both, the actual temperature as well as the temperature difference between sample and reference are shown.…”

“…Recent years have seen a tremendous progress in the understanding of the optical properties of surfaces with nanoscopic up to microscopic roughness [15]- [17], surfaces decorated with or embedding small particles [12], [18]- [22], or regular, non-planar surfaces, including defects [11,23,24]. Nevertheless, a full, rigorous description of the scattering from an arbitrary metallic surface is still rather challenging.…”

Structural and optical properties of cobalt slanted nanopillars conformally coated with few-layer graphene

“…10,12,[24][25][26] The effective dielectric function tensor described by the AB-EMA is composed of three major components e eff,a , e eff,b , and e eff,c along the major axes a, b, and c of an orthorhombic system. e eff,j with j ¼ a, b, and c given in implicit form by 12,27 X m n¼1 f n e n À e eff ;j e eff ;j þ L j e n À e eff ;j ð Þ ¼ 0 :…”