Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission ellipsometry at 45° angle of incidence

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Abstract
Measurements of the polarization states (represented by complex numbers χr and χt, respectively) of light reflected and transmitted by an unsupported or embedded thin film, for totally polarized light (with nonzero p and s components) incident at 45°, permit simple, direct, and explicit determination of the film’s complex refractive index N1independently of film thickness or input polarization. If α = χr/χt, we find that α = rs + rs−1, where rs is Fresnel’s complex reflection coefficient of the ambient–film interface for the s polarization at 45° incidence. From α, rs is determined, and from rs we get N1 = N0(1 + rs2)1/2/(1 + rs), where N0 is the refractive index of the transparent medium surrounding the film. Knowledge of the incident polarization χi allows the film thickness to be determined, also explicitly, by using either of the ratios χi/χr or χi/χt.