Towards Utilizing Multimodal Optimization to Search for Strontium Titanate Surface Structures*

Understanding crystalline surface-property relationships is crucial for the advancement and production of new technologies. Diffraction based characterization, such as X-Ray Reflectivity (XRR), probes electron distribution at surfaces, but data inversion is difficult.  Computational methods such as Density Functional Theory (DFT) are used to minimize energy, but may not accurately reflect realistic experimental conditions. Our developing software FOXPy computes XRR signals from DFT and permits local optimization to determine low energy surface structures. We further enhance the structure search by joining FOXPy to the Fully Automated from Nanoscale to Atomic Structure from Theory and Experiments (FANTASTX) software to perform global optimization.  FANTASTX utilizes machine learning algorithms to minimize an objective function which quantifies the fitness of a structural model using both DFT energy and experimental XRR measurements.  We aim to discover a structure that is a global minimum of our objective function, thus providing optimal agreement with both experiment and theory. As an example, we investigate the surface of Strontium Titanate (STO), improving our understanding of how epitaxial growth occurs on this common substrate.