Comparative study of the transmission ellipsometric function contours and the Smith chart
Berzett, Wade A.
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Transmission ellipsometry is governed by the transmission ellipsometric function (TEF) of a film-substrate system. The function can be analyzed through a series of constant-thickness contours and constant-angle-of-incidence contours in the complex plane. It has been observed that these TEF contours for a zero film-substrate system bear strong resemblances to the families of curves that make up the Smith chart for transmission lines. In this thesis we present a comparative study of the TEF and the Smith chart, specifically through the distinct similarities of their respective families of curves. It is shown that both TEF and Smith chart have similar contours in both the positive and negative imaginary half planes. The Smith chart’s contours originate from a complex plane with linear boundaries. It is bisected into symmetric positive and negative imaginary half planes of equal areas that are conjugate of each other. When transformed to the Smith chart, it is normalized and the conjugate relationship remains intact. All contours in the positive imaginary half plane of the Smith chart are symmetric to all of the contours in the negative half plane of the Smith chart. TEF contours originate from a non-complex reduced thickness plane. This plane has a non-linear upper boundary. It is bisected into two equal areas but non-symmetric, half planes. When transformed to the complex τ plane, the likeness of the constant-angle-of-incidence contours and constant-thickness contours to the Smith chart contours become a function of the material indices. As the film-substrate systems material indices are increased, the range of the non-linear boundary of the ф – dr plane is reduced and the TEF contours more closely resemble the Smith chart.