Atomic imaging of thin films with surface x-ray diffraction: introducing DCAF

Abstract

A direct method for the retrieval of electron density maps from surface x-ray diffraction data is presented and its performance is evaluated. The method, DCAF (difference map using the constraints of atomicity and film shift), is based on the difference map iteration scheme and uses, apart from the traditional constraints of atomicity, positivity and film thickness, a novel constraint, which we have named the 'film shift', whereby the real space solution is shifted up by an out-of-plane unit cell size of the underlying bulk substrate material if the topmost region of the same thickness contains insignificant electron density. This relaxes the film thickness constraint, which is necessarily loose in order to accommodate structural uncertainties at the film–substrate interface due to intermixing, roughness, and heteroepitaxial strain.<br />DCAF's performance was evaluated by retrieval of the electron density distribution from a real data set, recorded from a five-monolayer film of LaAlO₃ on SrTiO₃, which resulted in an electron density in good agreement with the previously solved structure. Importantly, the stability and reproducibility of the final solution compares favorably with constraint combinations in which the film shift projection is omitted, highlighting the power of this new method. In addition, an example of a full structural solution for a three-monolayer-thick film of La_{1−<em>x</em>}Sr_<em>x</em>MnO₃ on SrTiO₃ is presented, where DCAF electron density retrieval followed by model building and refinement was conducted.<br />It will be shown that DCAF can be successfully applied to thin films for retrieving physically meaningful electron densities, and that it can also serve as a starting point for subsequent structure refinement.