Numerical analysis of x-ray reflectivity data from organic thin films at interfaces

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Abstract
An efficient numerical analysis procedure of x-ray reflectivity data from ultrathin organic films at interfaces is presented. It allows virtually exact modeling of reflectivity data in the entire q-vector range including the critical angle and below with minimum fit parameters and calculation effort. The electron density profile is interpreted as a linear superposition of the air/film interface, the internal film structure, and the film/substrate interface. The reflectivities at the interfaces are calculated from the accurate Fresnel reflectivities. The internal film structure is parameterized in a Fourier series and its reflectivity contribution is calculated from refraction-corrected, approximated (linearized) Fresnel reflectivities. Additionally, a new way of weighing measurement errors is introduced. It allows the selective optimization of the fit in those data sections which are considered especially significant. Finally, we show further how to determine the degree of correlation (interdependencies) between the fit parameters and how to obtain absolute errors (the significance) of all fit parameters.