IEC TR 63258-2021 Nanotechnologies – A guideline for ellipsometry application to evaluate the thickness of nanoscale films.
6 Data analysis / interpretation of results
6.1 General Ellipsometry measures changes in light polarization to evaluate the material properties, such as film thickness and dielectric constants. In spectroscopic ellipsometry, the measured spectra are analysed by using the model fitting. Generally, in the case of nanomaterials, there is typically a surface oxide, roughness, and intermixing at the heterointerface of the sample.
The common procedure to deduce material properties from ellipsometry measurements is shown in Figure 2. Evaluations of nanomaterial characteristics by using the ellipsometry measurements are shown in Annex B. In the case of ellipsometry measurements, the intensities or polarization state ratios (complex relative amplitude attenuation) are measured and the ellipsometric angles, that is ellipsometric transfer quantities Ψ and , are calculated. No direct access exists to the parameters in which we are usually interested, such as the dielectric functions (ε), refractive indices (N), compositions and film thicknesses (d). In general, for any planar structure on the substrate, Ψ and Δ could be calculated if thicknesses and refractive indices are known.
On the other hand, for the inverse case, even if Ψ and Δ are known, d and N could not be directly calculated. In order to obtain d and N for each layer, modelling is required. The modelling approach is based on the assumption that the measured Ψ(λ) and Δ(λ) change at each wavelength according to dispersion law. Determination of material properties could be done by describing the fundamental response of a material to an applied electromagnetic field. Each material has unique energy dependence of dielectric function ε. In the visible-near UV range, dielectric response is determined almost entirely by the electronic properties of a material.
A mathematical description of the dielectric properties of a material, as well as its optical properties, as a function of energy (wavelength) is provided by dispersion law (formulae) and can be divided into four categories:
1 ) empirical formulas;
2) classical dispersion models (harmonic oscillator treatment);
3) models based on quantum mechanical calculations;
4) point-by-point calculations.
The flow of spectroscopic ellipsometric data analysis procedure is shown in Figure 2.
6.2 Setting analysis model
Ellipsometric modelling can be divided into four major steps:
1 ) sample structure definition;
2) sample simulation;
3) choice of variables and fitting;
4) a check of model reliability.
In most general cases, to build a sample model one has to define the following unknowns:
a) substrate dielectric function;
b) each layer’s thickness;
c) each layer’s dielectric function and/or composition;
d) overlayer thickness;
e) overlayer dielectric function and/or composition.
Remember that complex dielectric functions and complex optical constants are related by
Equation (1 ) as follows:
ε(λ) = N(λ) 2 (1 )
Using the constructed optical model, calculated data points (Ψ(λ) and Δ(λ)) are obtained.IEC TR 63258 pdf download.