Analysis of nanometer-sized aligned conical pores using small-angle x-ray scattering

Small-angle x-ray scattering (SAXS) was used to quantitatively study the morphology of aligned, monodisperse conical etched ion tracks in thin films of amorphous $\mathrm{SiO}{}_{2}$ with aspect ratios of around $6:1$ and in polycarbonate foils with aspect ratios of around $1000:1$. This paper presents the measurement procedure and methods developed for the analysis of the scattering images and shows results obtained for the two material systems. To enable accurate parameter extraction from the data collected from conical scattering objects, a model fitting the two-dimensional (2D) detector images was developed. The analysis involved fitting images from a sequence of measurements with different sample tilts to minimize errors, which may have been introduced due to the experimental setup. The model was validated by the exploitation of the geometric relationship between the sample tilt angle and the cone opening angle, to an angle observed in the features of the SAXS images. We also demonstrate that a fitting procedure for 1D data extracted from the scattering images using a hard cylinder model can also be used to extract the cone size. The application of these techniques enables us to reconstruct the cone morphologies with unprecedented precision.