B-spline parametrization of the dielectric function applied to spectroscopic ellipsometry on amorphous carbon

The remote plasma deposition of hydrogenated amorphous carbon $(a-C:H)$ thin films is investigated by in situ spectroscopic ellipsometry (SE). The dielectric function of the $a-C:H$ film is in this paper parametrized by means of B-splines. In contrast with the commonly used Tauc–Lorentz oscillator, B-splines are a purely mathematical description of the dielectric function. We will show that the B-spline parametrization, which requires no prior knowledge about the film or its interaction with light, is a fast and simple-to-apply method that accurately determines thickness, surface roughness, and the dielectric constants of hydrogenated amorphous carbon thin films. Analysis of the deposition process provides us with information about the high deposition rate, the nucleation stage, and the homogeneity in depth of the deposited film. Finally, we show that the B-spline parametrization can serve as a stepping stone to physics-based models, such as the Tauc–Lorentz oscillator.