Parratt-based and model-independent X-ray reflectivity fitting procedure for nanoscale thin film characterization

A general-purpose fitting procedure is presented for X-ray reflectivity data. The Parratt formula was used to fit the low-angle region of the reflectivity data and the resulting electron density profile (continuous base EDP or cbEDP) was then divided into a series of electron density slabs of width 1 angstroms (discrete base EDP or dbEDP), which is then easily incorporated into the Distorted Wave Born Approximation (DWBA). An additional series of density slabs of resolution-limited width are overlapped to the dbEDP, and the density value of the each additional slab is allowed to vary to further fit the data model-independently using DWBA. Because this procedure combines the Parratt formula and the model-independent DWBA fitting, each fitting method can always be employed depending on the type of thin film. Moreover, it provides a way to overcome the difficulties when both fitting methods do not work well for certain types of thin films. Simulations show that this procedure is suitable for nanoscale thin film characterization.