Variable wavelength, variable angle ellipsometry including a sensitivities correlation test

Abstract

Combining simultaneously both variable wavelength and variable angle of incidence to assess solutions of the optical parameters of a system, a procedure is developed which provides more information on the optical parameters than methods where either the wavelength or the angle of incidence is held constant. This results in a reduction in the interdependence of the optical parameters, and provides for more acceptable solutions. For a film on a substrate structure, if one knows the substrate optical parameters, the thickness and optical properties of the film can be characterized at each wavelength without the need for (a) a dispersion equation, (b) an independent measurement of the thickness or (c) any special requirements on the substrate optical properties. For a nearly transparent film on an absorbing substrate, all four parameters of the three-medium model (the substrate and film refractive indices, substrate extinction coefficient and film thickness) can be determined. If in addition one uses a dispersion relation for the refractive index in a very weakly absorbing film, the optical properties of an absorbing substrate and the film can be determined unambiguously. As a second major feature of this paper we show that the sensitivity correlation matrix, as well as the traditional parameter correlation matrix, should be calculated if one is to determine the independence of ellipsometric parameter solutions. An SiO 2 film on silicon is used for illustration, but of course the analysis is recommended for more complicated materials systems.