The successful combination of electromagnetic scattering simulations and optical measurements allows for thequantification of deep-subwavelength features, including thicknesses via ellipsometry and parameterized geometriesvia scatterometry. Although feature size reduction has slowed in recent years, nanoelectronics still yieldsever-smaller structures, thus optical measurement capabilities are ever-challenged. The critical problem is thatthe optical properties of materials often become thickness dependent at sub-5 nm, greatly complicating accuratefitting. These optical properties can be characterized empirically using ellipsometry and used with other priorinformation to reduce uncertainties via hybrid metrology, but atomistic modeling offers a unique perspective onthe macroscopic optical response from features with dimensions only a few atoms in width. To illustrate thepotential of such modeling, we have performed a series of density-functional theory (DFT) calculations for anultrathin film, Si with hydrogen-terminated Si(111) surfaces. Kohn-Sham wavefunctions determined in DFT areinstrumental in solving for the dielectric tensor of these configurations, as the in-plane and out-of-plane componentscan differ greatly with respect to incident wavelength and Si thickness. Techniques for DFT and dielectrictensor determination are reviewed, highlighting both their limitations and potential for improving optics-basedmetrology. The thickness- and wavelength-dependence of the resulting tensor components are parameterizedusing Tauc-Lorentz and Lorentz oscillators. Using an illustration from goniometric reectometry, the quantitativeeffects upon dimensional metrology of employing the full thickness-dependent dielectric tensor are comparedagainst simpler approximations of these optical properties. Reductions in parametric uncertainty in the thicknessand optical constants are evaluated with a prior knowledge of the ultrathin film's thickness with uncertainties.
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