Radiative properties of silicon wafers with microroughness and thin-film coatings
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The bidirectional reflectance distribution function (BRDF) that describes the scattered energy distribution is the most fundamental radiative property to calculate other properties. Although recent progress in surface metrology allows topography measurement in an atomic level, most studies still assume statistical distributions of roughness because of difficulty in roughness modeling. If the BRDF of rough silicon wafers is modeled with assumptions, predicted radiative properties may be inaccurate because non-Gaussian and anisotropic roughness of some wafers cannot be approximated with known statistics. Therefore, this thesis focuses on development of BRDF modeling that accounts for anisotropic roughness to accurately predict radiative properties of rough silicon surfaces with thin-film coatings. Monte Carlo ray-tracing methods are developed to consider multiple scattering and the change of polarization states and to satisfy physical laws such as the reciprocity principle. Silicon surface topographic data measured with an atomic force microscope are incorporated into the ray-tracing algorithms to model anisotropic roughness statistics. For validation, BRDF and emittance predictions are compared with measurements using an optical scatterometer and an integrating sphere. Good agreement between prediction and measurement demonstrates that the incorporation of topography measurement into BRDF modeling is essential for accurate property prediction. Roughness effects on the BRDF are so strong that BRDFs also reveal anisotropic features regardless of the presence of coating. Anisotropic roughness increases multiple scattering although first-order scattering is dominant, and thus enhances emittance noticeably. Silicon dioxide coating changes the magnitude of BRDF and emittance and reduces the anisotropic roughness effect on emittance enhancement. The research in this thesis advances the method to predict radiative properties by incorporating anisotropic rough statistics into BRDF modeling.