In situ x-ray reflectivity studies of dynamics and morphology during heteroepitaxial complex oxide thin film growth

We present a method, based on refraction effects in continuous, stratified media, for quantitative analysis of specular x-ray reflectivity from interfaces with atomic-scale roughness. Roughness at interfaces has previously been incorporated into this framework via Fourier transform of a continuous height distribution, but this approach breaks down when roughness approaches the atomic scale and manifests discrete character. By modeling the overall roughness at interfaces as a convolution of discrete and continuous height distributions, we have extended the applicability of this reflectivity model to atomic-scale roughness. The parameterization of thickness and roughness enables quantitative analysis of time-resolved in situ reflectivity studies of thin film growth, modeling step-flow, layer-by-layer and three-dimensional growth within a single framework. We present the application of this model to the analysis of anti-Bragg growth oscillations measured in situ during heteroepitaxial growth of La0.7Sr0.3MnO3 on < 001 > SrTiO3 at different temperatures and pressures, and discuss the evolution of surface morphology.