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Ellipsometry has long been a valuable technique for the optical characterization of layered systems and thin films. While simple systems like epitaxial silicon dioxide are easily characterized, complex systems of silicon and carbon junctions have proven difficult to analyze. Traditional model dielectric functions for layered silicon homojunctions, a system with a similar structure to modern transistors, often have correlated parameters during ellipsometric data analysis. Similarly, epitaxial graphene as grown from thermal sublimation of silicon from silicon carbide or through chemical vapor deposition, tend to have model dielectric function parameters that correlate with the optical thickness of the graphene due to its extreme thinness. In the case of highly oriented pyrolytic graphite (HOPG), the exact optical properties of the material are difficult to quantify due to an inability to perform ellipsometry measurements perpendicular to the optical axis.
It is the goal of this work to identify key methods and models appropriate for analyzing ellipsometric data including but not limited to: iso- and aniso-type silicon homojunctions, silicon carbide, epitaxial graphene, and bulk HOPG. Though a variety of models and techniques are used, the common theme of this work is the reduction of model parameters by enforcing physical models during the data fitting process. Iso-type silicon junctions were successfully characterized using terahertz to mid-infrared standard ellipsometry measurements coupled with a physically appropriate model that enforces drift, diffusion, and depletion effects. In contrast, characterization of free charge carriers within epitaxial graphene requires use of magneto-optic generalized ellipsometry and the optical Hall effect, but allows the independent determination of the mobility, effective mass, and free charge carrier density. Characterizing epitaxial graphene and HOPG in the visible to ultra-violet spectral range requires development of a model dielectric function based on the tight binding band structure of graphene, and is verified by ellipsometry data of graphene grown by chemical vapor deposition. This model can be extended for use in analyzing HOPG phenomenologically. Alongside appropriate use of effective medium approximations, the model dielectric function for graphene developed here can be used for non-ideal samples of epitaxial graphene grown on silicon carbide.
Advisers: Mathias Schubert, Tino Hofmann