Introduction to Ellipsometer
1. Data Analysis and Data Aquisition

Data acquisition

Ellipsometry measures the complex reflectance ratio, ρ , of a system, which may be parametrized by Ψ and Δ. The polarization state of the light incident upon the sample may be decomposed into an s and a p component (the s component is oscillating perpendicular to the plane of incidence and parallel to the sample surface, and the p component is oscillating parallel to the plane of incidence). The amplitudes of the s and p components, after reflection and normalized to their initial value, are denoted by rs and rp, respectively. Ellipsometry measures the complex reflectance ratio, ρ (a complex quantity), which is the ratio of rp over rs:

Thus, tan(Ψ) is the amplitude ratio upon reflection, and Δ is the phase shift (difference). (Note that the right hand side of the equation is simply another way to represent a complex number.) Since ellipsometry is measuring the ratio (or difference) of two values (rather than the absolute value of either), it is very robust, accurate, and reproducible. For instance, it is relatively insensitive to scatter and fluctuations, and requires no standard sample or reference beam.

Data analysis

Ellipsometry is an indirect method, i.e. in general the measured Ψ and Δ cannot be converted directly into the optical constants of the sample. Normally, a model analysis must be performed. Direct inversion of Ψ and Δ is only possible in very simple cases of isotropic, homogeneous and infinitely thick films. In all other cases a layer model must be established, which considers the optical constants (refractive index or dielectric function tensor) and thickness parameters of all individual layers of the sample including the correct layer sequence. Using an iterative procedure (least-squares minimization) unknown optical constants and/or thickness parameters are varied, and Ψ and Δ values are calculated using the Fresnel equations. The calculated Ψ and Δ values, which match the experimental data best, provide the optical constants and thickness parameters of the sample.

Light and polarization