The term “spectroscopic ellipsometry” refers to ellipsometric measurements that are carried out at various wavelengths of the incident beam. With spectroscopic ellipsometry, an experiment provides not just one set of Δ & Ψ but it gives a large set of these ellipsometric angles as a function of photon energy. This allows for the characterization of complex multilayer systems even when several physical parameters are unknown, and for the measurement of a material’s dielectric function in a thin film layer. Due to its great versatility, spectroscopic ellipsometry is an established technique in modern thin film analytical labs, and in quality control for industrial fabrication.
Thick layers, complex materials and multilayer systems usually cannot be characterized by using single wavelength ellipsometry. The more unknown parameters are included in an optical model, the more independent sets of Δ & Ψ are needed to perform reliable numerical fitting of the wanted parameters. Spectroscopic ellipsometry yields enough information from the sample to make modelling feasible even when several physical parameters of the sample have to be determined. Common spectroscopic ellipsometers apply broadband light sources that cover the visible range (VIS) and parts of both the ultraviolet (UV) and the near infrared (NIR) range of the electromagnetic spectrum.
In many cases, the optical constants of the materials included in a complex sample are known as a function of photon energy and can be loaded into an optical model from a database. Spectroscopic ellipsometry then gives access to structural parameters of complex samples.
Typical fields of applications are:
• multilayer stacks with more than one unknown layer thickness
• a single thick film layer (up to 1 µm layer thickness) where Δ & Ψ are ambiguous in the case of single wavelength ellipsometry
• characterization of volume fractions or compositions of binary material layers via effective medium theories (e.g. Bruggemann effective medium approximation (EMA), Lorentz-Lorenz model, Maxwell-Garnett model):
• surface roughness
• material-void volume fraction, e.g. in a layer of nanoparticles
• alloy compositions
Furthermore and in contrast to single wavelength ellipsometry, spectroscopic ellipsometry simultaneously gives access to both the optical constants and layer thickness of a thin film layer.
This achieved by applying so called dielectric function models (e.g. Tauc-Lorentz model, Cauchy model, or Drude model) that assume a functional relationship between the material’s complex (electric) permittivity ε and the vacuum wavelength λ (or equivalent photon energy) of the probing light. Each function model has a certain small number of free parameters whose values are obtained from numerical optimization of the optical model that is chosen for the sample. The relationship N=√ε then yields the complex refractive index N that is defined as N=n+ik with the refractive index n and the extinction coefficient k.
As Spectroscopic ellipsometry gives access to a thin film layer’s dielectric function ε(λ), it may also be used to obtain physical parameters that can be deduced from the material’s dielectric function that was obtained via dielectric function modeling. Typical examples in the UV, VIS, and NIR range are:
• characterization of electronic band gap in the UV and VIS range (Tauc-Lorentz model)
• free carrier absorption in the NIR (Drude model)
More about imaging-ellipsometry.
Principles of Ellipsometry