Application of a B-spline model dielectric function to infrared spectroscopic ellipsometry data analysis

Abstract

The flexibility of the Kramers–Kronig-consistent basis spline (B-spline) function provides advantages over traditional physics-based oscillator functions for analyzing infrared spectroscopic ellipsometry data. Oscillator functions require that the user identify the spectral location of every absorption, choose the correct oscillator line shape, and choose the correct number of oscillators (which can be difficult for organic films that have many overlapping absorption peaks). The user must also choose starting parameters sufficiently close to the final values so that the regression fit converges. Weak absorptions can be difficult to identify when they overlap with strong absorption features, or they can be obscured when there are large interference oscillations in the spectroscopic ellipsometry data. The B-spline function’s flexibility allows the user to model the infrared, dielectric-function line shape for any material, and it requires far less user input and judgment to obtain the dielectric function of a material. The user must simply define the spacing of control nodes, which can usually be obtained from a reference dielectric function or by a preliminary fit to a spectral region where the material is transparent. A “wavelength-range-expansion” fit can then be used to obtain the dielectric function for the remaining spectral range.