Parameter fitting in grazing incidence x-ray reflectometry

Abstract

A method for parameter identification in grazing incidence x-ray reflectometry is presented. It is based on a nonlinear least-squares approach with on-line low-pass filtering and fits the measured reflectivity curve as a function of the incidence angle to a simulation model. The filter is applied in the (angular) frequency domain; it introduces, even for strong filtering, no bias and renders the result independent of the angular stepsize of the data. Automatic restarting helps to determine the global solution. The commonly used roughness model is generalized to non-normal distributions in order to assess data with large scattering vectors. The method is demonstrated for data from single and double film samples. Thickness and roughness can be determined with an accuracy of about 0.2 nm. However, only in special cases it is possible to determine accurately materials constants such as compositional fractions or densities. Absorption cannot be neglected, but the corresponding parameters are difficult to determine separately.