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A comparative study is made of four methods for treating the graded nature of the Si–SiO2 interface in the analysis of ellipsometry data: (1) the stratified-media model, in which the total number of layers is large (>10); (2) the three-boundary approximation, in which the interface is treated as a single, homogeneous layer; (3) the two-boundary approximation, in which the effects of the interface are incorporated into an effective oxide-layer thickness; and (4) the integral-equation method, approximated to first order, of Plieth and Naegele [ Surf. Sci. 64, 484 ( 1977)]. The Si–SiO2 transition layer is assumed to have optical functions that vary monotonically between those of Si and SiO2 in six different ways. In each of the six cases, the ellipsometry parameters ψ and Δ are computed for the air–SiO2-interface bulk-Si system by using the four methods stated above. The results illustrate the sensitivity of ellipsometry to the interface layer and reveal that the interface layer must be properly taken into account for accurate analysis. It is concluded that the three-boundary approximation is not necessarily more accurate than a judiciously applied two-boundary model and that the first-order approximation of Plieth and Naegele introduces sizable errors at short wavelengths for the Si–SiO2 interface.
© 1982 Optical Society of America
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