Inversion of ellipsometry data using constrained spline analysis.

Abstract

Ellipsometry is a highly sensitive and powerful optical technique of thin film characterization. However, the indirect and nonlinear character of the ellipsometric equations requires numerical extraction of interesting information, such as thicknesses and optical constants of unknown layers. A method is described to perform the inversion of ellipsometric spectra for the simultaneous determination of thickness and optical constants without requiring particular assumptions about the shape of a model dielectric function like in the traditional method of data fitting. The method is based on a Kramers-Kronig consistent description of the imaginary part of the dielectric function using a set of points joined by pieces of third-degree polynomials. Particular connection relations constrain the shape of the constructed curve to a physically meaningful curve avoiding oscillations of natural cubic splines. The connection ordinates conditioning the shape of the dielectric function can be used, together with unknown thickness or roughness, as fitting parameters with no restriction on the material nature. Typical examples are presented concerning metal and semiconductors.